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Old 13th October 2014, 08:55 AM   #161
calebprime
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For some time, I'd heard that Gunther Schuller always used the same tone row, and that some other musicians in the Schuller world had even used it for improv -- people like Ran Blake and students.

But I never heard what the actual series was, until I dug up this interview:

http://dothemath.typepad.com/dtm/int...chuller-2.html

Gunther is rather coy about revealing the series, as you might expect.

There's some interesting stuff here about Ornette Coleman, as well.

The moral lesson (or the takeaway, as people say) here is that concentration on one thing over a long period of time can be of benefit to an artist.

The other point is that this series isn't particularly magical or special in itself.

Full excerpt of relevant part of interview:

EI:* Right. Now, I’ve heard something to the effect that you actually write almost all your pieces off the same row; is that true?

GS:* Well, I have lately.

When I started, and all of us of my generation starting to write twelve-tone music, having studied all the music of Schoenberg, Berg and Webern and all that, we found that every time they wrote a new piece they created a new row.* And I’m a high-school dropout, I never went to college or music school or anything, and so I had no education in these matters at all, but as I began to sort of look into this I could not find anywhere where it says you must not use a row a second time.* It just had become a habit, because those three guys did it and so it was understood.* And we all did that—Leon Kirchner did that, Don Martino, I did.
And one time in 1976, I wrote my first violin concerto, with a row which not only I loved almost as a theme or as a motivic element, but also because I found that it was so rich in feeding me, that I said to myself, “Goddamn it, why do I have to throw this away?” And I just decided I’m gonna use it again.* And I said to myself, “Gunther, don’t be stupid now; if the next piece comes out exactly”—I had no idea what would happen—“if the next piece comes out more or less the same, forget it, that’s not the point.”* Well, not only did it not come out the same, it was so totally different, even based on the same row.* So since 1976, I have now used this same row in every piece for the last—well, for all those years, and it must be something like 30 or 40 compositions.

EI:* Now, what is the row?

GS:* You want to know it?

EI:* Yeah, I want the magic row!

GS:* Oh, by the way, before I forget to mention it, it has now gotten into the jazz world through Ran Blake.

EI:* I heard that as well.

GS:* And I’ve heard a lot of ensemble improvisations using the row.* And not in the absolute strict way of Schoenbergian orthodoxy, but nonetheless, and they all know it. Well, it is… [A phone ring is intruding over the preceding exchange, and a third party now says “should we stop for a second?” and then there’s a doorbell breaking in causing a breakdown in the interview…]

GS:* Who’s that.... oh my god...

EI:* It’s because you’re about to say what the row is. The universe is like, “Don’t tell him the row! Don’t tell Ethan Iverson the row!”

GS:* I can play it on the piano...

EI:* Well, can you just tell me the pitches?

GS:* Yeah, sure.* Of course comes in twelve transpositions, as they all do, and there’s the prime form, the retrograde form, the inversion and the retrograde inversion. And when you have all that, bundled, it’s 48 row possibilities. So, if I sing one prime version, or say, it’d be C#—half a step up, D—a fourth up, to G—B-flat, minor third. Now, let’s say I’ll go down, a diminished fifth to E—half step up to F—then A, major third—then a major second to B natural—and then come G#, F#, E-flat, C. Now, I don’t know how much of that you remember, but you will see that there are huge tonal elements in it.

EI:* Exactly.* In fact, one of the pieces of yours I really admire is the Third String Quartet, which has a large G-minor quotation that’s based on a Beethoven fragment...

GS:* ...that worked in because the second, third and fourth notes in this row, in that transposition, happen to be a G-minor chord, third inversion.* And so there are these tonal components, but then also the usual dissonant elements, minor 2nds and major 7ths—but the final five notes really fascinate me, because [sings] “dee-dee-dee-dee-dee,” guess what that is?* I mean, that’s one of the most famous jazz chords.* You put a D natural underneath that, and you’ve got a D raised-9th chord.

EI:* Absolutely.

GS:* Or 11th or a 13th. And I just sort of stumbled on that.* I mean, I know I was not intellectually out to make that kind of a row, but it turns out once I looked at many of the rows that I had used before, some 70, 80 of them, they all were heading in this direction, of combining tonal elements with atonal.* And what’s interesting in those first notes—the C#, D, G, B-flat—if I invert that now, and let’s say start with the same C# or D-flat, it goes D-flat, C, G, E, and now I’ve got a C major triad in there.* Now it’s a major triad; the triad in the other one is a minor triad.* And now, if you then, as I do and have for years and years, work in different segmentations of the row—tetrachords, trichords, pentachords, heptachords, seven notes together, or whatever, or dyads, that’s just two notes—that is the loosening-up that Schoenberg himself developed back in 1928, when he went basically into this hexachordal division, using the first six notes of a row for the melody and the other six notes for the accompaniment, and then he broke that further apart into... and Webern took it down to trichords.* So that’s been around a long time.* So when I do that, and I use it even more freely, I can have any kind of usage of those twelve pitches.* My whole intent is—and this is only the one primary one of the whole thing in the beginning, in the first place, namely to preserve the total chromaticism of any given moment in the music.* It could ultimately be a chord which would have twelve notes in it—that’s the simplest.

And by the way, the reason the continuity of the pitches as first ordained by Schoenberg, you "have to use every pitch before you can use it again," which meant that there was an absolute sequence to those pitches, well, that’s a little bit unreal, because if I put together a six-part chord, you cannot tell me what the sixth sequence of those is, and same with a twelve-tone chord, so there sort of the sequencing goes out.

*
(Now, I know a lot of serial music is done that way, and including the real hardcore serialism where you derive numbers from these, that’s a whole separate thing.)

Anyway, so by my loosening up the usage of these components of this row, and by my also having the choice to use two versions of the row simultaneously, or four, you open up a whole universe of possibilities that are certainly not restricting, which is always the main argument by people who don’t understand twelve-tone, who hate it, they say it’s too restrictive and mathematical and all of that, but it actually feeds you, it helps you to—I see note combinations in this row, which I’ve now used for 33 years, that I didn’t see ten years ago. And I’ve looked at this damn thing so much... I don’t even need it, I also could improvise with it.

But when I realized that some of the inversions of the row are almost the same as the prime, except that two notes are in a different position, that’s like cousins, you know.* And that’s nice, and if I want cousins, well, I’ll use them!* But if I want enemies then I’ve got all kinds of other possibilities, where nothing seems to relate into anything tonal or preordained.* And so when you then also have in orchestral pieces or instrumental pieces the possibility of using three notes of a row, whatever they might be, in let’s say the first violins, and then you can use three other notes of the row in the violas, and in the first violins you can switch to another form of the row—this again opens up a vast new territory, it’s just mindboggling.* I mean, one cannot even in describing it oversee it, overview it.* And what it achieves is this inherent, almost guarantee—a guarantee of the inherent purity of the twelve-tone concept.* Because it doesn’t break the basic rules of twelve-tone.

EI:* The language remains authentic.

GS:* That’s right.* And insofar as you really learn how to use it—I’m now so fluent in it, I mean I almost don’t even have to think anymore, it’s an amazing experience, it’s like an improvisation—then it preserves its own integrity, cause you’re never going out of it . And again I want to emphasize, I don’t like the word “atonal”; I don’t like the word “twelve-tone.” They are both negative terms, certainly “atonal,” because it means “anti-.”* And Schoenberg often said, “I wish people wouldn’t use this.”* But what this is about for me is to preserve the most possible chromaticism, total chromaticism, highest chromaticism.* Let’s forget about atonality: chromaticism, that what it’s about, and that’s a good word and legitimate and right, because, let’s face it, the acoustic harmonic series already presents us with a chromatic template.* And it goes beyond that into microtones and so on.* So there it all is.* And this is just a full representation of those possibilities.* And then you can go even further—and these are all choices that composers have a right to make—you can go very subtly into something that sounds more tonal or you can become aggressively dissonantal and chromatic, and every possible variation of that.*



Quote:
Gunther Schuller: So, if I sing one prime version, or say, it’d be C#—half a step up, D—a fourth up, to G—B-flat, minor third. Now, let’s say I’ll go down, a diminished fifth to E—half step up to F—then A, major third—then a major second to B natural—and then come G#, F#, E-flat, C.
C#, D, G, Bb, E, F, A, B, G#, F#, Eb, C

or standard matrix:

C#..D.. G.. Bb..E.. F.. A.. B.. G#..F#..Eb..C
C.. C#..F#..A.. Eb..E.. G#..Bb..G.. F.. D.. B
G.. G#..C#..E.. Bb..B.. Eb..F.. D.. C.. A.. F#
E.. F.. Bb..C#..G.. G#..C.. D.. B.. A.. F#..Eb
Bb..B.. E.. G.. C#..D.. F#..G#..F.. Eb..C.. A
A.. Bb..Eb..F#..C.. C#..F.. G.. E.. D.. B.. G#
F.. F#..B.. D.. G#..A.. C#..Eb..C.. Bb..G.. E
Eb..E.. A.. C.. F#..G.. B.. C#..Bb..G#..F.. D
F#..G.. C.. Eb..A.. Bb..D.. E.. C#..B.. G#..F
G#..A.. D.. F.. B.. C.. E.. F#..Eb..C#..Bb..G
B.. C.. F.. G#..D.. Eb..G.. A.. F#..E.. C#..Bb
D.. Eb..G#..B.. F.. F#..Bb..C.. A.. G.. E.. C#

intervals of series: 1,5,3,6,1,4,2,9,10,9,9,1

prime form of 6-note sets: 0,1,3,4,6,9

Basic tonal analysis: The pitches make a G minor 9 chord, with the C# and E used as chromatic upward approach-notes, overlapping with a D octotonic scale segment -- F,A,B,G#,F#,Eb,C.

So it works as a tonic/dominant combination.

Quote:
Gunther Schuller: But when I realized that some of the inversions of the row are almost the same as the prime, except that two notes are in a different position, that’s like cousins, you know.* And that’s nice, and if I want cousins, well, I’ll use them!
Well, a computer search shows that the closest cousins he could be talking about aren't all that close. They are these two retrograde inversions, rotated:


ri/9/5.D..F#..G..C#..E..A..Bb..B..Ab..F..Eb..C..
p/0/0:.C#.D...G..Bb..E..F..A...B..Ab..F#.Eb..C..

ri/3/7:C#..G..Bb..Eb..E..F..D..B..A..F#..Ab..C..
p/0/0:.C#..D..G...Bb..E..F..A..B..Ab.F#..Eb..C..

(Pardon the hasty attempt at formatting. I don't feel like learning about tables, right now. )

Here's a pairing with a rotated 5m transformation of the row that produces only major or minor thirds, as well as reinforcing the G minor to D7 #9 Schuller is talking about:

5x/ri/8/6:F..Bb..E...G..Ab..C#..F#..Eb..C...D...B..A..
p/0/0:....C#.D...G...Bb.E...F...A...B...Ab..F#..Eb.C..

I've looked at a few other aspects of the series, but there isn't anything that striking.

Curiosity satisfied.

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Last edited by calebprime; 13th October 2014 at 09:05 AM.
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Old 14th October 2014, 05:10 AM   #162
calebprime
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More on "cousins" in the Schuller series.

If we have the computer find versions of the series that have a sort of abstract G chord in the first 6 notes, followed by a D octotonic subset in the second half (notes 7 through 12), there are actually quite a few possibilities. Maybe this is what he means by "cousins".

Search criteria:

?ex any pos0,1,2,3,4,5:eb,f#,c,g#
?ex any pos6,7,8,9,10,11:c#,bb,e,g

finds:

p/9/11:..............A Bb B E G C# D F# Ab F Eb C

r/0/6:...............F E Bb G D C# C Eb F# Ab B A

r/9/6:...............D C# G E B Bb A C Eb F Ab F#

r/9/7:...............C# G E B Bb A C Eb F Ab F# D

i/8/6:...............C# B D E G Bb A Ab Eb C F# F

i/11/6:..............E D F G Bb C# C B F# Eb A Ab

i/9/11:..............B Bb A E C# G F# D C Eb F Ab

ri/8/0:..............Bb G E D B C# F F# C Eb Ab A

ri/11/0:.............C# Bb G F D E Ab A Eb F# B C

ri/9/7:..............G C# E A Bb B Ab F Eb C D F#

from the 5m row:

5m/p/7/6:............E D B C# Bb G C F F# A Eb Ab

5m/p/10/6:...........G F D E C# Bb Eb Ab A C F# B

5m/p/11/11:..........B E A Bb C# G C Ab F# Eb F D

5m/r/7/0:............G Bb C# B D E Ab Eb A F# F C

5m/r/10/0:...........Bb C# E D F G B F# C A Ab Eb

5m/r/11/7:...........G C# Bb A E B D F Eb F# Ab C

5m/i/2/0:............G D C# Bb E B Eb F Ab F# A C

5m/i/5/0:............Bb F E C# G D F# Ab B A C Eb

5m/i/11/11:..........A E B Bb G C# Ab C D F Eb F#

5m/ri/2/6:...........B E Bb C# D G C A F# Ab F Eb

5m/ri/5/6:...........D G C# E F Bb Eb C A B Ab F#

5m/ri/11/7:..........C# G Bb B E A F# Eb F D C Ab
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Old 14th October 2014, 05:27 AM   #163
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Old computer died. It was considered "vintage" (more than 1 minute old), so no one seems to have a replacement power supply. Still looking.

So, new computer. And Logic Pro X.

On the happy-making side:

The computer showed up two days early, and, within 45 minutes of signing for it, Logic Pro X was up and running. Worked right outta the box.

Then, only two days of teeth-gnashing, while I figured out how to get it to do as much as it did before.

In the interest of catering to beginners, they made the defaults be *less* editing power. So the first thing an experienced midi user has to do is figure out how to get to the menu where you turn those features back on.

The literal instructions for getting to that menu -- control-click on the uppermost surface -- didn't work. But I eventually found that menu. It only took a couple of hours of frustration.

Now, back to where I was.

First impressions: Logic Pro X is a cosmetic redesign. The old problems are still there. There are more dumb features for beginners who like big, simple knobs, now.

There is one new thing -- a sort of Melodyne-ish pitch corrector. (Which doesn't interest me, much.)

For a serious microtonalist, the tuning features are still the same -- still completely inadequate.

But there's still Lil' Miss Scale Oven (third party software) to solve that problem, partially.

Logic is still like Target superstore. A heck of a bargain at $200. A huge collection of powerful features, of variable quality, thrown together without much logical consistency. Weird things still happen. Trying to do something that would be fairly simple in other programs might or might not work.

It will do. It won't make this old computer musician happy, but it'll do.
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Old 12th November 2014, 10:38 AM   #164
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https://app.box.com/s/pxig2ql30hmipv4n7o6z

Techno Waltz 80. 11 minutes.

First piece after upgrading to Logic X.

This uses the array here as well as a lot of other stuff:

Code:
p/0/0:...............C  C# Ab Bb F# Eb B  D  G  A  F  E  Good!  Yay!
ri/1/1:..............Ab E  F# B  D  Bb G  Eb F  C  C# A 

p/0/1:...............C# Ab Bb F# Eb B  D  G  A  F  E  C
ri/1/2:..............E  F# B  D  Bb G  Eb F  C  C# A  Ab 

the other one:

p/0/0:...............C  C# Ab Bb F# Eb B  D  G  A  F  E
ri/1/1:..............Ab E  F# B  D  Bb G  Eb F  C  C# A  

p/0/11:..............E  C  C# Ab Bb F# Eb B  D  G  A  F
ri/1/0:..............A  Ab E  F# B  D  Bb G  Eb F  C  C# 

?voc #1:4
?ex forms: 5x 5x5p
?ex har prox3:0,1,2
?ex har:0,3,6
?ex har:0,0,0
?ex har prox2:0,0,0,0
?par uns on
?par 5ths on
?ex har:0,1,2
?inc har:0,1
?inc har:0,6
?har errs: 0 to 2
?har prox errs: 0 to 2
?ex har:0,4,7,9
?ex har:0,4,7,10
?ex har:0,4,7,11
?run

C, Db, Ab, Bb, Gb, Eb, B, D, G, A, F, E,

standard matrix:

C,  Db, Ab, Bb, Gb, Eb, B,  D,  G,  A,  F,  E 1,7,2,8,9,8,3,5,2,8,11,8
B,  C,  G,  A,  F,  D,  Bb, Db, Gb, Ab, E,  Eb
E,  F,  C,  D,  Bb, G,  Eb, Gb, B,  Db, A,  Ab
D,  Eb, Bb, C,  Ab, F,  Db, E,  A,  B,  G,  Gb
Gb, G,  D,  E,  C,  A,  F,  Ab, Db, Eb, B,  Bb
A,  Bb, F,  G,  Eb, C,  Ab, B,  E,  Gb, D,  Db
Db, D,  A,  B,  G,  E,  C,  Eb, Ab, Bb, Gb, F
Bb, B,  Gb, Ab, E,  Db, A,  C,  F,  G,  Eb, D
F,  Gb, Db, Eb, B,  Ab, E,  G,  C,  D,  Bb, A
Eb, E,  B,  Db, A,  Gb, D,  F,  Bb, C,  Ab, G
G,  Ab, Eb, F,  Db, Bb, Gb, A,  D,  E,  C,  B
Ab, A,  E,  Gb, D,  B,  G,  Bb, Eb, F,  Db, C

========================================================
Every 5th note, or "5p" version of series:

0..1...2...3...4...5...6..7..8..9..10.11
C, Db, Ab, Bb, Gb, Eb, B, D, G, A, F, E,

5p:

C,Eb,F,Bb,G,Db,B,E,Gb,A,Ab,D,  

intervals: 3,2,5,9,6,10,5,2,3,11,6,10

Standard Matrix of "5p" series:

C,  Eb, F,  Bb, G,  Db, B,  E,  Gb, A,  Ab, D  3,2,5,9,6,10,5,2,3,11,6,10
A,  C,  D,  G,  E,  Bb, Ab, Db, Eb, Gb, F,  B
G,  Bb, C,  F,  D,  Ab, Gb, B,  Db, E,  Eb, A
D,  F,  G,  C,  A,  Eb, Db, Gb, Ab, B,  Bb, E
F,  Ab, Bb, Eb, C,  Gb, E,  A,  B,  D,  Db, G
B,  D,  E,  A,  Gb, C,  Bb, Eb, F,  Ab, G,  Db
Db, E,  Gb, B,  Ab, D,  C,  F,  G,  Bb, A,  Eb
Ab, B,  Db, Gb, Eb, A,  G,  C,  D,  F,  E,  Bb
Gb, A,  B,  E,  Db, G,  F,  Bb, C,  Eb, D,  Ab
Eb, Gb, Ab, Db, Bb, E,  D,  G,  A,  C,  B,  F
E,  G,  A,  D,  B,  F,  Eb, Ab, Bb, Db, C,  Gb
Bb, Db, Eb, Ab, F,  B,  A,  D,  E,  G,  Gb, C




try backwards, as well:

col: F,  G,  Db, E,  C,  Bb, Gb, Ab, D,  Eb, B,  A
dhv: ********************

C,  Db, Ab, Bb, Gb, Eb, B,  D,  G,  A,  F,  E   quite good.  maybe. yes
Bb, E,  D,  Gb, Ab, B,  A,  Eb, Db, F,  G,  C   simply arpeggiate top four down
Gb, C,  Eb, Ab, D,  A,  F,  B,  E,  G,  Db, Bb
Ab, Bb, B,  D,  Eb, F,  G,  A,  C,  Db, E,  Gb  all rising.2,1,3,1,2,2,2,3,1,3,2,2  

D,  Gb, A,  Eb, B,  G,  Db, F,  Bb, E,  C,  Ab
Eb, Ab, F,  B,  A,  Db, E,  G,  Gb, C,  Bb, D
B,  D,  G,  A,  F,  E,  C,  Db, Ab, Bb, Gb, Eb
A,  Eb, Db, F,  G,  C,  Bb, E,  D,  Gb, Ab, B
F,  B,  E,  G,  Db, Bb, Gb, C,  Eb, Ab, D,  A
G,  A,  C,  Db, E,  Gb, Ab, Bb, B,  D,  Eb, F
Db, F,  Bb, E,  C,  Ab, D,  Gb, A,  Eb, B,  G
E,  G,  Gb, C,  Bb, D,  Eb, Ab, F,  B,  A,  Db



2) Perm matrices as "expansion" generators

columns: C,Db,Eb,G,D,F,B,Bb,Ab,E,A,F#, ais #4

Ab, A,  E,  Gb, D,  B,  G,  Bb, Eb, F,  Db, C
E,  Gb, A,  C,  F,  Bb, D,  Ab, G,  B,  Eb, Db
A,  C,  Gb, Db, B,  Ab, F,  E,  D,  Bb, G,  Eb gd, no 012
Gb, Db, C,  Eb, Bb--E---B---A,  F,  Ab, D,  G not nec fatal
C,  Eb, Db, G,  Ab, A,  Bb, Gb, B,  E,  F,  D
Db, G,  Eb, D,  E,  Gb, Ab, C,  Bb, A,  B,  F
Eb, D,  G,  F,  A,  C,  E,  Db, Ab, Gb, Bb, B
G,  F,  D,  B,  Gb, Db, A,  Eb, E,  C,  Ab, Bb
D,  B,  F,  Bb, C,  Eb, Gb, G,  A,  Db, E,  Ab
F,  Bb, B,  Ab, Db, G,  C,  D,  Gb, Eb, A,  E
B,  Ab, Bb, E,  Eb, D,  Db, F,  C,  G,  Gb, A
Bb, E,  Ab, A,  G,  F,  Eb, B,  Db, D,  C,  Gb







col: F,E,A,G,B,D,Gb,Eb,Bb,Ab,C,Db
dhv: 

C,  Db, Ab, Bb, Gb, Eb, B,  D,  G,  A,  F,  E  **This
Db, F,  C,  Ab, Eb, Bb, D,  Gb, B,  G,  E,  A
F,  E,  Db, C,  Bb, Ab, Gb, Eb, D,  B,  A,  G
E,  A,  F,  Db, Ab, C,  Eb, Bb, Gb, D,  G,  B
A,  G,  E,  F,  C,  Db, Bb, Ab, Eb, Gb, B,  D
G,  B,  A,  E,  Db, F,  Ab, C,  Bb, Eb, D,  Gb
B,  D,  G,  A,  F,  E,  C,  Db, Ab, Bb, Gb, Eb
D,  Gb, B,  G,  E,  A,  Db, F,  C,  Ab, Eb, Bb
Gb, Eb, D,  B,  A,  G,  F,  E,  Db, C,  Bb, Ab
Eb, Bb, Gb, D,  G,  B,  E,  A,  F,  Db, Ab, C
Bb, Ab, Eb, Gb, B,  D,  A,  G,  E,  F,  C,  Db
Ab, C,  Bb, Eb, D,  Gb, G,  B,  A,  E,  Db, F

and retrograde:

col: Db,C,Ab,Bb,Eb,Gb,D,B,G,A,E,F
dhv: 

C,  Db, Ab, Bb, Gb, Eb, B,  D,  G,  A,  F,  E good as 4-voice
Ab, C,  Bb, Eb, D,  Gb, G,  B,  A,  E,  Db, F
Bb, Ab, Eb, Gb, B,  D,  A,  G,  E,  F,  C,  Db
Eb, Bb, Gb, D,  G,  B,  E,  A,  F,  Db, Ab, C

Gb, Eb, D,  B,  A,  G,  F,  E,  Db, C,  Bb, Ab
D,  Gb, B,  G,  E,  A,  Db, F,  C,  Ab, Eb, Bb
B,  D,  G,  A,  F,  E,  C,  Db, Ab, Bb, Gb, Eb
G,  B,  A,  E,  Db, F,  Ab, C,  Bb, Eb, D,  Gb
A,  G,  E,  F,  C,  Db, Bb, Ab, Eb, Gb, B,  D
E,  A,  F,  Db, Ab, C,  Eb, Bb, Gb, D,  G,  B
F,  E,  Db, C,  Bb, Ab, Gb, Eb, D,  B,  A,  G
Db, F,  C,  Ab, Eb, Bb, D,  Gb, B,  G,  E,  A


Inversion of above matrix around C:


C,  B,  E,  D,  Gb, A,  Db, Bb, F,  Eb, G,  Ab
E,  C,  D,  A,  Bb, Gb, F,  Db, Eb, Ab, B,  G
D,  E,  A,  Gb, Db, Bb, Eb, F,  Ab, G,  C,  B
A,  D,  Gb, Bb, F,  Db, Ab, Eb, G,  B,  E,  C
Gb, A,  Bb, Db, Eb, F,  G,  Ab, B,  C,  D,  E
Bb, Gb, Db, F,  Ab, Eb, B,  G,  C,  E,  A,  D
Db, Bb, F,  Eb, G,  Ab, C,  B,  E,  D,  Gb, A
F,  Db, Eb, Ab, B,  G,  E,  C,  D,  A,  Bb, Gb
Eb, F,  Ab, G,  C,  B,  D,  E,  A,  Gb, Db, Bb
Ab, Eb, G,  B,  E,  C,  A,  D,  Gb, Bb, F,  Db
G,  Ab, B,  C,  D,  E,  Gb, A,  Bb, Db, Eb, F
B,  G,  C,  E,  A,  D,  Bb, Gb, Db, F,  Ab, Eb


=========================================================


========================================================
Diagram of derivation of self-similar perms -- which, when done
the second time, yields a rotation of the row.  (Operation produces only
two versions -- original, and variation -- when done more than once.)

0...1...2...3...4...5...6...7...8...9...10..11
C,  Db, Ab, Bb, Gb, Eb, B,  D,  G,  A,  F,  E

....Db..............Eb..............A...........
C.......Ab......Gb..........D...............E...
............Bb..........B.......G.......F.......

========================================================
========================================================
"Designated Perm" series:

Db, Eb, A,  C,  Ab, Gb, D,  E,  Bb, B,  G,  F 1st perm or second row from top

standard matrix of "Designated Perm" series:


Db, Eb, A,  C,  Ab, Gb, D,  E,  Bb, B,  G,  F
B,  Db, G,  Bb, Gb, E,  C,  D,  Ab, A,  F,  Eb
F,  G,  Db, E,  C,  Bb, Gb, Ab, D,  Eb, B,  A
D,  E,  Bb, Db, A,  G,  Eb, F,  B,  C,  Ab, Gb
Gb, Ab, D,  F,  Db, B,  G,  A,  Eb, E,  C,  Bb
Ab, Bb, E,  G,  Eb, Db, A,  B,  F,  Gb, D,  C
C,  D,  Ab, B,  G,  F,  Db, Eb, A,  Bb, Gb, E
Bb, C,  Gb, A,  F,  Eb, B,  Db, G,  Ab, E,  D
E,  Gb, C,  Eb, B,  A,  F,  G,  Db, D,  Bb, Ab
Eb, F,  B,  D,  Bb, Ab, E,  Gb, C,  Db, A,  G
G,  A,  Eb, Gb, D,  C,  Ab, Bb, E,  F,  Db, B
A,  B,  F,  Ab, E,  D,  Bb, C,  Gb, G,  Eb, Db

========================================================


Permutation Matrix showing successive results of this permutation
in each row, from top to bottom.  Third row is rotation 6 positions
and transposition up 4 semitones of first row.  Therefore, this
operation is "closed" with this series, or produces the same 
two series, no matter how many times you do it:

C,  Db, Ab, Bb, Gb, Eb, B,  D,  G,  A,  F,  E  ** mvt or piece: simple in-order t to b.
Db, Eb, A,  C,  Ab, Gb, D,  E,  Bb, B,  G,  F  or maybe better, bottom to top.
Eb, Gb, B,  Db, A,  Ab,|E,  F,  C,  D,  Bb, G
Gb, Ab, D,  Eb, B,  A,  F,  G,  Db, E,  C,  Bb
Ab, A,  E,  Gb, D,  B,  G,  Bb, Eb, F,  Db, C
A,  B,  F,  Ab, E,  D,  Bb, C,  Gb, G,  Eb, Db
B,  D,  G,  A,  F,  E,  C,  Db, Ab, Bb, Gb, Eb
D,  E,  Bb, B,  G,  F,  Db, Eb, A,  C,  Ab, Gb
E,  F,  C,  D,  Bb, G,  Eb, Gb, B,  Db, A,  Ab
F,  G,  Db, E,  C,  Bb, Gb, Ab, D,  Eb, B,  A
G,  Bb, Eb, F,  Db, C,  Ab, A,  E,  Gb, D,  B
Bb, C,  Gb, G,  Eb, Db, A,  B,  F,  Ab, E,  D

1,2,3,2,1,2,3,2,1,2,3,2 not the same as above


========================================================
Hexachord succession of Original version of row:
C,  Db, Ab, Bb, Gb, Eb, to
B,  D,  G,  A,  F,  E:

------------------------------------------------

C,  Db, Ab, Bb, Gb, Eb,

B,  Db, Ab, Bb, Gb, Eb,

B,  D,  Ab, Bb, Gb, Eb,

B,  D,  G,  Bb, Gb, Eb,

B,  D,  G,  A,  Gb, Eb,

B,  D,  G,  A,  F,  Eb,

B,  D,  G,  A,  F,  E

C,  D,  G,  A,  F,  E

C,  Db, G,  A,  F,  E
=
C,  Db, Ab, A,  F,  E

C,  Db, Ab, Bb, F,  E

C,  Db, Ab, Bb, Gb, E

C,  Db, Ab, Bb, Gb, Eb

-------------------------------------------------

5P, also, makes nice hexachord successions:

C,Eb,F,Bb,G,Db,
to
B,E,Gb,A,Ab,D:


C,Eb,F,Bb,G,Db  ** This

B,Eb,F,Bb,G,Db

B,E,F,Bb,G,Db

B,E,F#,Bb,G,Db

B,E,F#,A,G,Db

B,E,F#,A,G#,C#

B,E,F#,A,G#,D

back to

C,E,F#,A,G#,D

C,Eb,F#,A,G#,D

C,Eb,F,A,G#,D

C,Eb,F,Bb,Ab,D

C,Eb,F,Bb,G,D

C,Eb,F,Bb,G,Db
========================================================

 
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Old 16th December 2014, 05:44 AM   #165
calebprime
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I had to abandon a piece after working on it for a little while. The row just wouldn't work for me.

Perhaps a better composer could have made that row work. Bach, after all, wrote a masterpiece based on a theme given to him by Frederick the Great. Boulez and others composed pieces based on a given 6-note set, the so-called "Sacher" hexachord -- or 0,1,2,4,5,7. I would have refused both gigs, in typical cowardly fashion.

http://en.wikipedia.org/wiki/Sacher_hexachord
(Incidentally, I think it's extremely dumb, or wonky, to identify a pitch-set by its Forte number, but not to give the actual set. In the wiki entry above, this set is identified only as "6-z11". I had to look it up. The "11" means -- trivially -- that it's the 11th hexachord in the list, which is not a property of the hexachord. So to know what that hexachord is, you either have to have Forte's list memorized -- which no-one does, except for one or two benighted grad students -- or you have to look it up in Forte's index, or in a similar list. This is a bad kind of reification, if you will. This is rather like calling the banana in the Monty Python "Defense Against Fresh Fruit" sketch something like "fb-27": "How do you defend against an attacker wielding fb-27?".

The wise composer takes what she can from the useful parts of so-called musical "set-theory" and disregards the rest, which is the greater part. There's a little bit of utility, and a whole lot of academic wonk going on there. Music theory suffers from an odd kind of math-and-hard-science envy.)

The row was found by computer search.

It was: C,D,B,E,C#,D#,A,G,Bb,F,Ab,Gb -- or, wonkily, 02B41397A586.

The trichords (3-note chords) are all 013's, and the series is a "tritone nest" -- meaning that the first and last pitches, C and Gb, are a tritone (or augmented fourth, diminished fifth, or 6 semitones), as are the second and next-to-last, D and Ab, then B and F, and so on -- C,Gb D,Ab, B,F, E,Bb, C#,G, D#,A.

I didn't really like the sound of this series, which bored me. So I channelled my inner Michael Gibbs and asked myself what I could do to turn that situation to my own advantage.

http://en.wikipedia.org/wiki/Michael_Gibbs_(composer)

It occurred to me that it would be possible to create a set of other closely-related series that all had the property of consistent trichords.

This seemed to work out really well. I was able to create related series that had every trichord that I wanted. I didn't want 036 or 048.

Here was the result:

012 D,E,D#,G,F,Gb,C,B,C#,A,Bb,Ab original, every-other
013 C,D,B,E,C#,D#,A,G,Bb,F,Ab,Gb original
014 G,Eb,E,D,Gb,F,B,C,Ab,Bb,A,Db every-other of 5p
015 B,D#,Bb,Gb,D,C#,G,Ab,C,E,A,F 5th perm of orig
016 B,Bb,F,A,E,D#,C,C#,Gb,D,G,Ab 6th perm of orig
024 D,C,E,Db,F,Eb|A,B,G,Bb,Gb,Ab rotated ordinal 90
025 C,D,F,E,G,A,Eb,Db,Bb,B,Ab,Gb 5M
026 D#,G,C#,B,F,A,Ab,E,Bb,C,Gb,D second line 2x
027 D,E,A,Db,B,Gb,C,F,G,Eb,Bb,Ab second life 5M every-other perm
037 Db,A,E,D,Gb,B,F,C,Ab,Bb,Eb,G every other 2cnd 5M5p


And here's the thing. I didn't like any of these derived series any more than I did the original!


(If anyone's curious about how I derived any of these, just ask a specific question.)

The reason I didn't like them is that I'm a fussy composer who really only hears tonally and only uses the generative properties of 12-tone theory. That is, I'm completely uninterested in "atonal" hearing, or in producing the "aggregate" -- a pretentious word for all 12 tones all the time. The "aggregate" -- just like all colors at the same time -- is either a fiction or a formula for ugliness.


The series for my current project: C,E,Db,Ab,Eb,F,B,A,D,G,Bb,F# is also a tritone nest. It has an unusual property when you make a table of "every-other" permutations, which some may be able to recognize in the chart below:

Code:
C,  E,  C#, G#, D#, F,  B,  A,  D,  G,  Bb, F#
E,  G#, F,  A,  G,  F#, C,  C#, D#, B,  D,  Bb
G#, A,  F#, C#, B,  Bb, E,  F,  G,  C,  D#, D
A,  C#, Bb, F,  C,  D,  G#, F#, B,  E,  G,  D# 
which immediately gives me the sort of jazzoid chorale of the type I enjoy.
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Old 23rd December 2014, 08:10 AM   #166
calebprime
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I mentioned the generative powers of 12-tone operations (transformations) in my last post.

When is a composer justified in using them?

Answer: When the connection between the original series and the transformed series is made audible in the fabric of the piece, when the transformed series sounds good, and when the composer understands what she is doing.

We might even make this a little more liberal by allowing a sort of Debussy aesthetic: Esoteric connections might be justified if they are somehow ineffably poetic, without those connections being obvious. (This might be just a vague way of saying that some passage following another passage sounds good, but we're not sure exactly why.)

By this standard, the fact that my current series [C E C# Ab Eb F B A D G Bb F#] is identical to a version of itself when you take every fifth note, is only of interest if -- at some point in the piece -- I make it clear that I'm taking every fifth note, and if the music that comes out of that sounds good to me.

By this standard -- my own standard -- my current series (and project) fails.

There isn't anything that justifies the every-other note transformations, and I can't imagine a passage where I use every 5th note in an obvious way. I've tried it.

There are, however, some other transformations that sound fairly good, and are clearly related to the original, if I make it so.

So I haven't completely given up on this project. There may yet be a way to snatch victory from the foul jaws of defeat. Or to rescue quality from the vague tentacles of nerdishness. Maybe just butching it out will work, or sheer insistence, sheer assertion.

Or maybe this piece will simply be very short.

The difficult thing is being in a state of doubt.
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Old 24th December 2014, 09:45 AM   #167
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Here's an artless sketch which shows a way to vary the series, as well as prolong some harmonies.

https://app.box.com/s/66idyy90xjq9jvgwc8u9

called Amoeba motion.

The series is rotated to begin on the fourth note. It's then divided into 2 6-note groups, each an octotonic-scale subset. Each new note of the row then replaces one of the previous notes of the 6-note groups. Result: smoothly, gradually-moving harmonies, adherence to the series, and generation of a handful of new series which are closely related to the original.

It's amazing to me how my psychosomatic stress symptom go away when I'm actually making some music -- as opposed to worrying about making music.





Code:
 

C,  E,  C#, G#, D#, F,  B,  A,  D,  G,  Bb, F#


G#, D#, F,  B,  A,  D,| G,  Bb, F#, C,  E,  C#, (G#/G partition)
7,2,6,10,5,5,3,8,6,4,9,7 



G#, D#, F,  B,  A,  D, [G#,D#,F,B,A,D,G,Bb,F#,C,E,C#]
7,2,6,10,5,5,3,8,6,4,9,7   

G,  D#, F,  B,  A,  D, [G,D#,F,B,A,D,G#,Bb,F#,C,E,C#] 
8,2,6,10,5,6,2,8,6,4,9,6

G,  D#, F,  Bb, A,  D, [G,D#,F,Bb,A,D,G#,B,F#,C,E,C#
8,2,5,11,5,6,3,7,6,4,9,6

G,  D#, F#, Bb, A,  D, [G,D#,F#,Bb,A,D,G#,B,F,C,E,C#]
8,3,4,11,5,6,3,6,7,4,9,6

G,  D#, F#, Bb, C?, D  [G,D#,F#,Bb,C,D,G#,B,F,A,E,C#]
8,3,4,2,2,6,3,6,4,7,9,6

G,  E,  F#, Bb, C,  D  [G,E,F#,Bb,C,D,G#,B,F,A,D#,C#]
9,2,4,2,2,6,3,6,4,6,10,6

G,  E,  F#, Bb, C,  C# [G,E,F#,Bb,C,C#,G#,B,F,A,D#,C] 
9,2,4,2,1,7,3,6,4,6,9,7
----------------------
G#, E,  F#, Bb, C,  C# [G#,E,F#,Bb,C,C#,G,B,F,A,D#,C]
8,2,4,2,1,6,4,6,3,6,9,8

G#, D#, F#, Bb, C,  C# [G#,D#,F#,Bb,C,C#,G,B,F,A,E,C]
7,3,4,2,1,6,4,6,4,7,8,8

G#, D#, F,  Bb, C,  C# [G#,D#,F,Bb,C,C#,G,B,F#,A,E,C]
7,2,5,2,1,6,4,7,3,7,8,8

G#, D#, F,  Bb, B   C# [G#,D#,F,Bb,B,C#,G,C,F#,A,E,D]
7,2,5,1,2,6,5,6,3,7,10,6

G#, D#, F,  A,  B   C# [G#,D#,F,A,B,C#,G,C,F#,Bb,E,D]
7,2,4,2,2,6,5,6,4,6,10,6

G#, D#, F,  B   A   D  [G#,D#,F,B,A,D,G,Bb,F#,C,E,C#]
7,2,6,10,5,5,3,8,6,4,9,7
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Old 31st January 2015, 12:47 PM   #168
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I'm posting here, not because this has much to do with me, or even to bump my thread.

If you've messed around with microtuning, you become aware of an important problem, that -- as Randy Roos might say -- is also an opportunity.

With a conventional instrument -- piano, say -- the overtones are pretty close to integer ratios, even though on the piano they are stretched in the bass.

So if you try to use a piano sound to explore a tuning such as 11 notes per octave, (11 EDO) it just doesn't sound very consonant, at least to me. And the lack of familiar consonances like 3:2 (A "fifth") combined with the familiar sound of a piano produces a, shall way say, gnarly and forlorn result. This pretty much led me to abandon exploring EDOs in favor of JI. In fact, JI with a lot of pitches seemed to be the only way to get what I was after -- a system that encompassed familiar tonality, but did it better, and allowed for exotic sounds as well.

(This introduction is pro forma and I don't really care about it -- it's just a way to set up the topic.)

If one works with 12EDO or JI, one tends to think in what seem like fairly stable categories. An octave is a 2:1 ratio, and so on.

But if you could alter the overtones of the timbres you're using to match the tuning, all those certainties begin to go out the window.

That's why I'm so impressed with the theoretical work of William Sethares, and of course, the work of Wendy Carlos.

Sethares' work has led to some freeware synthesizers that let you match tuning to timbre, more or less automatically.

This is, as they say, a game-changer.

http://www.dynamictonality.com/index.htm

Now, the straight harmonic series, the good ol' 2:1 ratio, and most familiar acoustic instruments are all part of a fairly robust and beautiful thing -- the harmonic world as we've known it.

But if you want to go off-world, responsibly -- I feel -- this is the way to do it.

It's even freeware.

I may never complete a piece with this new information. But I can't say there's nothing new under the sun, musically speaking.

The key point here is that tuning and timbre interact, and have to work well with each other.,
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Old 5th April 2015, 12:49 PM   #169
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Resurrecting this to say that metformin is helping, plus here's an intriguing series, a nice Multiple Order Function (MOF) series.

If anyone is interested in the nuts-and-bolts here, ask me. (I'm not interested in talking philosophy.)

The software search that found it has the following parameters:

M) modulus: 12
P) permutation: 1,3,5,7,9,11,0,2,4,6,8,10
C) center interval of self-similarity: 2
O) minimum number of occurrences of center: 10
D) maximum deviation from center: 1000
S) maximum sum of all deviations: 1000
F) fixed-position notes: 0:0
E) excluded cells within range: 0,3,6,9:4 0,1,2:3
R) excluded intervals within range:
A) filter original solution: on
B) filter permuted solution: on
X) permutation depth: 4
N) number of solutions to print: 1000
W) wrap: on

For anything the computer prints, this means that, under transposition, each series is a near-perfect (10 out of 12) permutation of itself. Or, under every-other permutation (with a 13th-position placeholder), the series is a near-perfect transposition of itself. Up to 4 permutations, there are no 0,1,2's per 3 notes, or 0,3,6,9's per 4 notes.


and the result:

0 2 5 1 6 7 10 3 4 8 11 9 - 10 9 12
0 2 11 7 6 1 10 9 4 8 5 3 - 10 9 12
found 2 solutions.

Which, upon closer examination, is really the same series.

But mainly, I like this motif, found in at least 3 series contiguously: D#,B,A#,F. Real purty.


Putting the motif that I like first -- which is preserved under permutation-- and fiddling with which series is the first row on top (it's a big cycle, so both the horizontal and the vertical starting-points are somewhat arbitrary in principle),
I get the permutation matrix below (not to be confused with the standard 12-tone inversion matrix):

Code:


Starting with this:

C,  D,  B,  G,  F#, C#, Bb, A,  E,  Ab, F,  Eb
D,  G,  C#, A,  Ab, Eb, C,  B,  F#, Bb, E,  F
G,  A,  Eb, B,  Bb, F,  D,  C#, Ab, C,  F#, E
A,  B,  F,  C#, C,  E,  G,  Eb, Bb, D,  Ab, F#
B,  C#, E,  Eb, D,  F#, A,  F,  C,  G,  Bb, Ab
C#, Eb, F#, F,  G,  Ab, B,  E,  D,  A,  C,  Bb
Eb, F,  Ab, E,  A,  Bb, C#, F#, G,  B,  D,  C
F,  E,  Bb, F#, B,  C,  Eb, Ab, A,  C#, G,  D
E,  F#, C,  Ab, C#, D,  F,  Bb, B,  Eb, A,  G
F#, Ab, D,  Bb, Eb, G,  E,  C,  C#, F,  B,  A
Ab, Bb, G,  C,  F,  A,  F#, D,  Eb, E,  C#, B
Bb, C,  A,  D,  E,  B,  Ab, G,  F,  F#, Eb, C#


I derive this by standard rotation:


B,  G,  F#, C#, Bb, A,  E,  G#, F,  Eb, C,  D
C#, A,  G#, Eb, C,  B,  F#, Bb, E,  F,  D,  G
Eb, B,  Bb, F,  D,  C#, G#, C,  F#, E,  G,  A
F,  C#, C,  E,  G,  Eb, Bb, D,  G#, F#, A,  B
E,  Eb, D,  F#, A,  F,  C,  G,  Bb, G#, B,  C#
F#, F,  G,  G#, B,  E,  D,  A,  C,  Bb, C#, Eb
G#, E,  A,  Bb, C#, F#, G,  B,  D,  C,  Eb, F
Bb, F#, B,  C,  Eb, G#, A,  C#, G,  D,  F,  E
C,  G#, C#, D,  F,  Bb, B,  Eb, A,  G,  E,  F#
D,  Bb, Eb, G,  E,  C,  C#, F,  B,  A,  F#, G#
G,  C,  F,  A,  F#, D,  Eb, E,  C#, B,  G#, Bb
A,  D,  E,  B,  G#, G,  F,  F#, Eb, C#, Bb, C


or, another way to see it is like this:

from this:  0 2 11 7 6 1 10 9 4 8 5 3, to this:

row: C,D,B,G,F#,C#,Bb,A,E,G#,F,Eb
col: 
dhv: 

to this:

C,  D,  B,  G,  F#, C#, Bb, A,  E,  G#, F,  Eb
D,  G,  C#, A,  G#, Eb, C,  B,  F#, Bb, E,  F
G,  A,  Eb, B,  Bb, F,  D,  C#, G#, C,  F#, E
A,  B,  F,  C#, C,  E,  G,  Eb, Bb, D,  G#, F#
B,  C#, E,  Eb, D,  F#, A,  F,  C,  G,  Bb, G#
C#, Eb, F#, F,  G,  G#, B,  E,  D,  A,  C,  Bb
Eb, F,  G#, E,  A,  Bb, C#, F#, G,  B,  D,  C
F,  E,  Bb, F#, B,  C,  Eb, G#, A,  C#, G,  D
E,  F#, C,  G#, C#, D,  F,  Bb, B,  Eb, A,  G
F#, G#, D,  Bb, Eb, G,  E,  C,  C#, F,  B,  A
G#, Bb, G,  C,  F,  A,  F#, D,  Eb, E,  C#, B
Bb, C,  A,  D,  E,  B,  G#, G,  F,  F#, Eb, C#
 
This is about as strong a starting-point as is possible. Whether I make a good piece out of it depends on many things -- the most important being persistence, and trying to keep myself in the "compositional bubble" -- a zone where you believe in yourself and the piece, at least enough to keep going.

Quote:
I'm still working on that novel, but I'm just about to quit. 'Cause I'm worried about the future now, or maybe this is it.
There are many reasons why that belief could fail. Common sense is one of them.

Now begins the very enjoyable process of research (or delving) into the properties of the series. (*********** around with it being an important part of the process, but also computer searches, and bringing all my knowledge to bear.)

Oh, just to flesh out what MOF means here, or what embedding means, I've done a computer search of the embedding of the motif I like, B,G,F#,C#.

All these standard transformations of the series have the B,G,F#,C# motif embedded with intervening notes, but within a 6-note range:

Code:
  
 

?new row #1:c,d,b,g,f#,c#,bb,a,e,g#,f,eb
?voc #1:2
?inc all pos0:b
?ex any: b un g ran6
?ex any: g un f# ran6
?ex any:f# un c# ran6
?run
working...
p/9/1:...............B  Ab E  Eb Bb G  F# C# F  D  C  A  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

p/0/2:...............B  G  F# C# Bb A  E  Ab F  Eb C  D  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

p/10/5:..............B  Ab G  D  F# Eb C# Bb C  A  F  E  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

p/7/8:...............B  Eb C  Bb G  A  F# D  C# Ab F  E  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

p/8/11:..............B  Ab Bb G  Eb D  A  F# F  C  E  C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

r/11/11:.............B  D  E  G  Eb Ab A  C  F  F# Bb C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

ri/9/5:..............B  Ab Eb D  Bb G  A  F# E  C# F  C  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

ri/6/8:..............B  G  E  F# Eb C# Bb D  A  Ab F  C  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

ri/10/9:.............B  Ab Bb G  F  D  F# C# C  A  E  Eb 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5p/p/9/5:............B  G  C  Eb F  Ab F# A  Bb D  E  C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5p/p/0/10:...........B  A  C  C# F  G  E  D  Bb Eb F# Ab 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5p/p/2/11:...........B  D  Eb G  A  F# E  C  F  Ab Bb C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5p/r/5/3:............B  Ab Eb G  A  C  Bb F# F  D  E  C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5p/r/7/7:............B  D  C  Ab G  E  F# Eb C# Bb F  A  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5p/r/10/10:..........B  Bb G  A  F# E  C# Ab C  D  F  Eb 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5p/i/0/1:............B  G  F  Ab Bb D  A  F# E  C# Eb C  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5p/i/3/4:............B  C# F  C  A  G  E  F# Eb D  Bb Ab 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5p/ri/10/1:..........B  D  E  G  C  Ab F# Eb F  A  Bb C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x/p/6/5:............B  Ab Eb D  Bb G  A  F# E  C# F  C  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x/p/3/8:............B  G  E  F# Eb C# Bb D  A  Ab F  C  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x/p/7/9:............B  Ab Bb G  F  D  F# C# C  A  E  Eb 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x/i/2/11:...........B  D  E  G  Eb Ab A  C  F  F# Bb C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x/ri/0/1:...........B  Ab E  Eb Bb G  F# C# F  D  C  A  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x/ri/3/2:...........B  G  F# C# Bb A  E  Ab F  Eb C  D  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x/ri/1/5:...........B  Ab G  D  F# Eb C# Bb C  A  F  E  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x/ri/10/8:..........B  Eb C  Bb G  A  F# D  C# Ab F  E  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x/ri/11/11:.........B  Ab Bb G  Eb D  A  F# F  C  E  C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x5p/p/7/9:..........B  D  E  G  C  Ab F# Eb F  A  Bb C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x5p/r/9/5:..........B  G  F  Ab Bb D  A  F# E  C# Eb C  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x5p/r/0/8:..........B  C# F  C  A  G  E  F# Eb D  Bb Ab 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x5p/i/10/3:.........B  D  C  Ab G  E  F# Eb C# Bb F  A  
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x5p/i/1/6:..........B  Bb G  A  F# E  C# Ab C  D  F  Eb 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x5p/i/8/11:.........B  Ab Eb G  A  C  Bb F# F  D  E  C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x5p/ri/3/2:.........B  A  C  C# F  G  E  D  Bb Eb F# Ab 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x5p/ri/5/3:.........B  D  Eb G  A  F# E  C  F  Ab Bb C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 

5x5p/ri/0/9:.........B  G  C  Eb F  Ab F# A  Bb D  E  C# 
p/0/0:...............C  D  B  G  F# C# Bb A  E  Ab F  Eb 



One further note. A quick check shows that the series is equivalent to itself under 5m plus retrograde inversion plus transposition. Meaning that all the things with a "5x" above were redundant.

?inc har:0,0
?run
working...
5x/ri/3/0:...........C D B G F# C# Bb A E Ab F Eb
p/0/0:...............C D B G F# C# Bb A E Ab F Eb


That's actually a good thing, a promising thing.
__________________
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Last edited by calebprime; 5th April 2015 at 02:13 PM.
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Old 1st June 2015, 07:21 AM   #170
calebprime
Somewhat Elitist Parasite
 
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Join Date: Jul 2006
Posts: 11,449
threw out that start, but this is better.

huge file of pre-composition work. some may enjoy the patterns.

Code:

1

Still to try, or do

- Doh a Deer -- sequences   •

- Substitutions based on symmetrical collections

- Hexachordal partitions with substitutions between hexachords

- multiplication

- more review of content already generated

- mappings such as alternating major/minor thirds

- chorale:  all work. suspensions.  linear cont.   Lin cont straddling 2 or more chords.  •

- Correlate D-a-D variations with self-sim (embedded) series

- "Plot"  -- basic order of sections in piece

- another section on contour, based on 5m   •  •  •

- row counterpoint 

- "non-systematic" rows embedded in main foreground row, see section 17

- try thinking in terms of networks of row names -- search for occurances of rows, and note
  interesting recurrences.



2

Contents:

1-To Do

2-Contents

3-Origin as MOF Series

4-Contour

5-Row Segments that work with Main Row Subdivisions (tetrachords, mostly)

5b-Partition into 3 4-note groups, 5m row, with matching row segments

6-Original and 5x Matrices

6b-Self-Similarity of original and 5x line

7-Cells in Series

8-0147 in row?

9-Ordinal Row (90-degree variation)

10-EXPANSIONS of Self-Similar Pattern to Bigger Center Intervals

11-MAIN 4-VOICE CHORALE 
  
12-chorale:  all work.  inversions.  suspensions.  linear cont.

13-Expansions of Row (exp. of vertical grid) retaining contour
(and some cells)

13b- Expansions of 5m Row contour

14-Stagger Chorale: Almost any Dyad will work +-1 position with any other dyad
repetition of 11-Main 4-voice Chorale, but with cells of each chord specified

15-LITERAL ROW-MATCHES to 4-NOTE CHORDS

16-ROWS THAT WORK WITH CHORDS -- AT LEAST 6 NOTES

17-ATTEMPT AT CONTINUING SELF-SIMILAR EMBEDDING

18-Combinations of 5m, I, P, to make Perm Matrices: 

19-"Group-Preserving" Permutation Matrices with orig row as first line

20-Doh a Deer -- sequences

21-Casual Attempts at New Kinds of Alteration


------------------------------------------------------
------------------------------------------------------
3

ORIGIN AS MOF Series

 
0 3 6 8 A 1 4 7 9 B 2 5 	21.237 332233322337


user row: 0,3,6,8,10,1,4,7,9,11,2,5


------------------------------------------------------
 user row: 0  3  6  8  10 1  4  7  9  11 2  5  THIS ONE
 grid row: 7  8  9  10 11 0  1  2  3  4  5  6  
    orbit: 7  0  1  4  11 10 8  3  9  6  5  2  
X-swapped: 1  2  11 7  3  10 9  0  6  8  5  4  
intervals: 1  9  8  8  7  11 3  6  2  9  11 9  

------------------------------------------------------

1  2  11 7  3  10 9  0  6  8  5  4


C#.D..B..G..Eb.Bb.A..C..F#.G#.F..E..
   d........eb.......c.....g#....e..
......b........bb...................
c#.......g........a.....f#....f


C..F#.G#.F..E..C#.D..B..G..Eb.Bb.A..
...............c#.......g........a..
...f#....f........d........eb.......
c.....g#....e........b........bb    


------------------------------------------------------
4

Contour 


c3,f#2,g#2,f2,e2,c#2,d2,b1,g2,eb2,bb2,a2          Original
11 6   8   5  4  1   2  0  7  3   10  9
12 7   9   6  5  2   3  1  8  4   11  10  


C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb    5m

c4, f#3, g#3, b3, e3, g2, d3, f3, c#4, a3, bb3, eb4
9...4....5....8...2...0...1...3...10...6...7....11..


-------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------- 
------------------------------------------------------------------------------------------------------------- 
5

Row Segments that work with Main Row Subdivisions (tetrachords, mostly)


combinations included in primary row:

c,f#,g#,f  -- ex any: g,e  ex pit prox 7: b,c# c#,d b,bb a,bb                                                                                    

c,f,e,c#   -- ex any: eb,f#,d,b

c,d,b,g    -- ex any: c#,bb  ex pit prox 7: f#,g# g#,a f,f# eb,e 

c,d,b,g,eb --

c,bb,a     --
-----------------------------------------------------------------------------------------

c,f#,g#,f  -- ex any: g,e  ex pit prox 7: b,c# c#,d b,bb a,bb :


p/1/2:...............A  F# F  D  Eb C  Ab 		E  B  Bb C# G  
p/4/2:...............C  A  Ab F  F# Eb B  		G  D  C# E  Bb 
p/7/2:...............Eb C  B  Ab A  F# D  		Bb F  E  G  C# 
p/10/2:..............F# Eb D  B  C  A  F  		C# Ab G  Bb E  
   
p/2/8:...............A  F  C  B  D  Ab 			Bb G  F# Eb E  C# 
p/5/8:...............C  Ab Eb D  F  B  			C# Bb A  F# G  E  
p/8/8:...............Eb B  F# F  Ab D  			E  C# C  A  Bb G  
p/11/8:..............F# D  A  Ab B  F  			G  E  Eb C  C# Bb 
   
i/1/2:...............F  Ab A  C  B  D  F# 		Bb Eb E  C# G  
i/4/2:...............Ab B  C  Eb D  F  A  		C# F# G  E  Bb 
i/7/2:...............B  D  Eb F# F  Ab C  		E  A  Bb G  C#
i/10/2:..............D  F  F# A  Ab B  Eb 		G  C  C# Bb E  
   
i/1/3:...............Ab A  C  B  D  F# 			Bb Eb E  C# G  F  
i/4/3:...............B  C  Eb D  F  A  			C# F# G  E  Bb Ab 
i/7/3:...............D  Eb F# F  Ab C  			E  A  Bb G  C# B  
i/10/3:..............F  F# A  Ab B  Eb 			G  C  C# Bb E  D  
   
i/0/8:...............F  A  D  Eb C  F# 			E  G  Ab B  Bb C# 
i/3/8:...............Ab C  F  F# Eb A  			G  Bb B  D  C# E  
i/6/8:...............B  Eb Ab A  F# C  			Bb C# D  F  E  G  
i/9/8:...............D  F# B  C  A  Eb 			C# E  F  Ab G  Bb 
   
5x/p/1/2:............F  D  A  F# B  Ab C  		E  Eb Bb C# G  
5x/p/4/2:............Ab F  C  A  D  B  Eb 		G  F# C# E  Bb 
5x/p/7/2:............B  Ab Eb C  F  D  F# 		Bb A  E  G  C# 
5x/p/10/2:...........D  B  F# Eb Ab F  A  		C# C  G  Bb E  
   
5x/p/10/3:...........B  F# Eb Ab F  A  			C# C  G  Bb E  D  
   
5x/p/7/4:............Eb C  F  D  F# Bb 			A  E  G  C# B  Ab     N.O.
5x/p/10/4:...........F# Eb Ab F  A  C# C  			G  Bb E  D  B         N.O.       
   
5x/p/3/7:............Bb D  F# F  C  Eb 			A  G  E  B  Ab C# 
5x/p/6/7:............C# F  A  Ab Eb F# 			C  Bb G  D  B  E      N.O. 
   
5x/p/0/8:............B  Eb D  A  C  F# 			E  C# Ab F  Bb G  
5x/p/3/8:............D  F# F  C  Eb A  			G  E  B  Ab C# Bb 
5x/p/6/8:............F  A  Ab Eb F# C  			Bb G  D  B  E  C# 
5x/p/9/8:............Ab C  B  F# A  Eb 			C# Bb F  D  G  E  
   
5x/i/1/2:............A  C  F  Ab Eb F# D  		Bb B  E  C# G  
5x/i/4/2:............C  Eb Ab B  F# A  F  		C# D  G  E  Bb 
5x/i/7/2:............Eb F# B  D  A  C  Ab 		E  F  Bb G  C# 
5x/i/10/2:...........F# A  D  F  C  Eb B  		G  Ab C# Bb E  
    
5x/i/2/8:............Eb B  C  F  D  Ab 			Bb C# F# A  E  G  
5x/i/5/8:............F# D  Eb Ab F  B  			C# E  A  C  G  Bb 
5x/i/8/8:............A  F  F# B  Ab D  			E  G  C  Eb Bb C# 
5x/i/11/8:...........C  Ab A  D  B  F  			G  Bb Eb F# C# E  
   
5x/i/9/11:...........C  A  Eb F  Ab C# 			E  B  D  Bb F# G       N.O.

-----------------------------------------------------------------------------------------

c,f,e,c#   -- ex any: eb,f#,d,b

p/8/2:...............E  C# C  A  Bb G  			Eb B  F# F  Ab D     
p/6/4:...............Bb G  Ab F  C# A  			E  Eb F# C  D  B     
p/10/6:..............C  A  F  C# Ab G  			Bb E  F# Eb D  B     
p/4/11:..............C# E  Bb C  A  				Ab F  F# Eb B  G  D  
    
i/9/2:...............C# E  F  Ab G  Bb 			D  F# B  C  A  Eb    
i/11/4:..............G  Bb A  C  E  				Ab C# D  B  F  Eb F#   
i/7/6:...............F  Ab C  E  A  Bb 			G  C# B  D  Eb F#      
i/1/11:..............E  C# G  F  Ab 				A  C  B  D  F# Bb Eb 

5x/p/0/2:............E  C# Ab F  Bb G  			B  Eb D  A  C  F#    
5x/p/2/4:............Bb G  C  A  C# F  E  			B  D  Ab F# Eb   
5x/p/10/6:...........Ab F  A  C# C  				G  Bb E  D  B  F# Eb       
5x/p/4/11:...........C# E  Bb Ab F  C  			A  D  B  Eb G  F#   
5x/i/1/0:............C# G  A  C  F  				Ab Eb F# D  Bb B  E    
5x/i/5/2:............C# E  A  C  G  Bb 			F# D  Eb Ab F  B   
5x/i/3/4:............G  Bb F  Ab E  C  C# 			F# Eb A  B  D       
5x/i/7/6:............A  C  Ab E  F  				Bb G  C# Eb F# B  D       
5x/i/1/11:...........E  C# G  A  C  F  			Ab Eb F# D  Bb B  
   
-----------------------------------------------------------------------------------------

c,d,b,g    -- ex any: c#,bb  ex pit prox 7: f#,g# g#,a f,f# eb,e 


p/3/2:...............B  Ab G  E  F  D  			Bb F# C# C  Eb A  
p/10/2:..............F# Eb D  B  C  A  			F  C# Ab G  Bb E    
p/5/8:...............C  Ab Eb D  F  B  			C# Bb A  F# G  E    

i/4/2:...............Ab B  C  Eb D  F  			A  C# F# G  E  Bb   
i/2/8:...............G  B  E  F  D  Ab 			F# A  Bb C# C  Eb   
i/9/8:...............D  F# B  C  A  Eb 			C# E  F  Ab G  Bb 
   
5x/p/7/2:............B  Ab Eb C  F  D  			F# Bb A  E  G  C# 
5x/p/4/3:............F  C  A  D  B  Eb G  			F# C# E  Bb Ab  
5x/p/9/4:............F  D  G  E  Ab C  B  			F# A  Eb C# Bb   
5x/p/0/7:............G  B  Eb D  A  C  F# 			E  C# Ab F  Bb 
5x/p/5/7:............C  E  Ab G  D  F  B  			A  F# C# Bb Eb 
5x/p/11/11:..........Ab B  F  Eb C  G  			E  A  F# Bb D  C# 
   
5x/i/0/2:............Ab B  E  G  D  F  			C# A  Bb Eb C  F# 
5x/i/7/2:............Eb F# B  D  A  C  			Ab E  F  Bb G  C#
5x/i/10/3:...........A  D  F  C  Eb B  G  			Ab C# Bb E  F#   
5x/i/2/7:............G  Eb B  C  F  D  Ab 			Bb C# F# A  E  
5x/i/3/11:...........F# Eb A  B  D  G  			Bb F  Ab E  C  C# 
5x/i/8/11:...........B  Ab D  E  G  C  			Eb Bb C# A  F  F# 

-----------------------------------------------------------------------------------------

c,bb,a     --
 
p/1/2:...............A  F# F  D  Eb C  			Ab E  B  Bb C# G  
p/8/2:...............E  C# C  A  Bb G  Eb 			B  F# F  Ab D  
p/5/3:...............Bb A  F# G  E  C  			Ab Eb D  F  B  C# 
      
p/2/4:...............F# Eb E  C# A  				F  C  B  D  Ab Bb G  
p/7/6:...............A  F# D  Bb F  				E  G  C# Eb C  B  Ab 
       
p/3/8:...............Bb F# C# C  Eb A  			B  Ab G  E  F  D  
p/9/8:...............E  C  G  F# A  Eb 			F  D  C# Bb B  Ab 
   
i/10/0:..............Bb E  D  F  F# A  			Ab B  Eb G  C  C# 
  
i/2/2:...............F# A  Bb C# C  Eb G  			B  E  F  D  Ab 
i/5/2:...............A  C  C# E  Eb F# Bb 			D  G  Ab F  B  
i/8/2:...............C  Eb E  G  F# A  C# 			F  Bb B  Ab D  
    
i/0/8:...............F  A  D  Eb C  F# 			E  G  Ab B  Bb C# 
i/1/8:...............F# Bb Eb E  C# G  			F  Ab A  C  B  D  
i/4/8:...............A  C# F# G  E  Bb 			Ab B  C  Eb D  F  
   
i/7/8:...............C  E  A  Bb G  C# 			B  D  Eb F# F  Ab 
i/0/9:...............A  D  Eb C  F# E  G  			Ab B  Bb C# F    
i/3/9:...............C  F  F# Eb A  G  Bb 			B  D  C# E  Ab    
  
    
5x/p/2/2:............F# Eb Bb G  C  A  C# 			F E  B  D  Ab 
5x/p/5/2:............A  F# C# Bb Eb C  E  			Ab G  D  F  B  
5x/p/8/2:............C  A  E  C# F# Eb G  			B  Bb F  Ab D  
   
5x/p/7/5:............C  F  D  F# Bb A  			E  G  C# B  Ab Eb    
5x/p/3/7:............Bb D  F# F  C  Eb A  			G  E  B  Ab C#   
5x/p/10/7:...........F  A  C# C  G  Bb E  			D  B  F# Eb Ab 
5x/p/1/8:............C  E  Eb Bb C# G  			F  D  A  F# B  Ab 
   
5x/p/9/11:...........F# A  Eb C# Bb F  			D  G  E  Ab C  B  

5x/i/10/0:...........Bb E  F# A  D  				F  C  Eb B  G  Ab C#   
5x/i/2/2:............Bb C# F# A  E  G  Eb 			B  C  F  D  Ab    
5x/i/8/2:............E  G  C  Eb Bb C# A  			F  F# B  Ab D  
5x/i/5/3:............E  A  C  G  Bb F# D  			Eb Ab F  B  C#       
5x/i/0/7:............F  C# A  Bb Eb C  F# 			Ab B  E  G  D     
5x/i/3/8:............E  C  C# F# Eb A  			B  D  G  Bb F  Ab   
5x/i/9/8:............Bb F# G  C  A  Eb 			F  Ab C# E  B  D     
5x/i/7/9:............E  F  Bb G  C# 				Eb F# B  D  A  C  Ab    
5x/i/6/10:...........E  A  F# C  D  				F  Bb C# Ab B  G  Eb 
5x/i/1/11:...........E  C# G  A  C  F  			Ab Eb F# D  Bb B  
   
---------------------------------------------------------------------------------------------------- 

5m:			C,  F#, G#, B,  		E,  G,  D,  F,  	    C#, A,  Bb, Eb


not killed, 4-note groups:     C,E,F,A,

This is good over A pedal.

C,  F#, G#, B,  		E,  G,  D,  F,  	    C#, A,  Bb, Eb
---------------------------------------------------------
A>------------------------------------------------------>


also, 3-note groups:

C,F#,G#		B,E,G		D,F,C#		A,Bb,Eb
----------------------------------------------- 
A > ---------------------------------->



--------------------------------------------------------------------
5B   --    Partition into 3 4-note groups, 5m row -- see section 19 for group-to-group perm matrix.

group 1              group 2               group 3
C,  F#, G#, B,  		E,  G,  D,  F,  	    C#, A,  Bb, Eb
---------------------------------------------------------
A>------------------------------------------------------> 

group 1
ex any: Bb,C#,G  ex pit prox: E,F 

group 2
ex any: eb,f#,g#   ex pit prox: C#,C   

group 3
ex any: g#,b,d   ex pit prox: e,f


--------------------------------
group 1: C,  F#, G#, B  over A


p/0/11:..............Eb C  F# Ab B  E          G  D  F  C# A  Bb     not oct
p/1/2:...............A  C  F  Ab Eb F# 		D  Bb B  E  C# G     
p/4/2:...............C  Eb Ab B  F# A  		F  C# D  G  E  Bb     subset of not oct
p/10/2:..............F# A  D  F  C  Eb 		B  G  Ab C# Bb E  
p/7/3:...............F# B  D  A  C  Ab E       F  Bb G  C# Eb        not oct   (A Mel Minor)
p/5/8:...............F# D  Eb Ab F  B  		C# E  A  C  G  Bb 
p/8/8:...............A  F  F# B  Ab D  		E  G  C  Eb Bb C# 
p/11/8:..............C  Ab A  D  B  F  		G  Bb Eb F# C# E  

i/4/2:...............Ab F  C  A  D  B  		Eb G  F# C# E  Bb 
i/7/2:...............B  Ab Eb C  F  D  		F# Bb A  E  G  C# 
i/10/3:..............B  F# Eb Ab F  A  		C# C  G  Bb E  D  
i/1/4:...............A  F# B  Ab C  E  		Eb Bb C# G  F  D     not oct
i/0/8:...............B  Eb D  A  C  F# 		E  C# Ab F  Bb G  
i/9/8:...............E  Ab C  B  F# A  Eb 		C# Bb F  D  G        not oct

5x/p/4/2:............Ab B  C  Eb D  F  		A  C# F# G  E  Bb 
5x/p/7/2:............B  D  Eb F# F  Ab 		C  E  A  Bb G  C# 
5x/p/1/3:............Ab A  C  B  D  F# 		Bb Eb E  C# G  F  
5x/p/3/8:............Ab C  F  F# Eb A  		G  Bb B  D  C# E  
5x/p/6/8:............B  Eb Ab A  F# C  		Bb C# D  F  E  G    sub n.o.
  
5x/i/1/2:............A  F# F  D  Eb C  		Ab E  B  Bb C# G  
5x/i/4/2:............C  A  Ab F  F# Eb 		B  G  D  C# E  Bb 
5x/i/10/2:...........F# Eb D  B  C  A  		F  C# Ab G  Bb E  
5x/i/7/3:............C  B  Ab A  F# D  		Bb F  E  G  C# Eb 
5x/i/2/8:............A  F  C  B  D  Ab 		Bb G  F# Eb E  C# 
5x/i/5/8:............C  Ab Eb D  F  B  		C# Bb A  F# G  E  
5x/i/11/8:...........F# D  A  Ab B  F  		G  E  Eb C  C# Bb 
  
-------------------------------------       
group 2:  E,  G,  D,  F, over A

 
p/0/3:...............B  E  G  D  F  C# A  		Bb Eb C  F# Ab 
p/4/7:...............A  F  C# D  G  E  Bb 		C  Eb Ab B  F#  


i/9/2:...............C# Bb F  D  G  E  		Ab C  B  F# A  Eb 
i/2/7:...............A  C# F  E  B  D  		Ab F# Eb Bb G  C  
i/1/11:..............Bb C# G  F  D  A  		F# B  Ab C  E  Eb 


5x/p/3/1:............A  G  Bb B  D  C# E  		Ab C  F  F# Eb 
5x/p/6/2:............Bb C# D  F  E  G  		B  Eb Ab A  F# C  
5x/i/0/3:............F  E  C# D  B  G  		Eb Bb A  C  F# Ab 
5x/i/7/8:............D  Bb F  E  G  C# 		Eb C  B  Ab A  F# 

-------------------------------------  
group 3: C#, A,  Bb, Eb


  
p/2/2:...............Bb C# F# A  E  G  		Eb B  C  F  D  Ab 
p/5/2:...............C# E  A  C  G  Bb 		F# D  Eb Ab F  B  
p/8/2:...............E  G  C  Eb Bb C# 		A  F  F# B  Ab D  
  
p/0/7:...............F  C# A  Bb Eb C  		F# Ab B  E  G  D   n.o.

p/3/8:...............E  C  C# F# Eb A  		B  D  G  Bb F  Ab 
p/6/8:...............G  Eb E  A  F# C  		D  F  Bb C# Ab B  
p/9/8:...............Bb F# G  C  A  Eb 		F  Ab C# E  B  D  
 
i/2/2:...............F# Eb Bb G  C  A  		C# F  E  B  D  Ab 
i/5/2:...............A  F# C# Bb Eb C  		E  Ab G  D  F  B  
i/8/2:...............C  A  E  C# F# Eb 		G  B  Bb F  Ab D  
i/11/2:..............Eb C  G  E  A  F# 		Bb D  C# Ab B  F  
 

i/10/7:..............F  A  C# C  G  Bb 		E  D  B  F# Eb Ab  n.o.
i/1/8:...............C  E  Eb Bb C# G  		F  D  A  F# B  Ab 
i/4/8:...............Eb G  F# C# E  Bb 		Ab F  C  A  D  B  
i/7/8:...............F# Bb A  E  G  C# 		B  Ab Eb C  F  D  
 
 
i/9/11:..............F# A  Eb C# Bb F  		D  G  E  Ab C  B   n.o.
 

5x/p/11/1:...........F  Eb F# G  Bb A  		C  E  Ab C# D  B  

5x/p/2/2:............F# A  Bb C# C  Eb 		G  B  E  F  D  Ab 
5x/p/5/2:............A  C  C# E  Eb F# 		Bb D  G  Ab F  B  
5x/p/8/2:............C  Eb E  G  F# A  		C# F  Bb B  Ab D  
5x/p/11/2:...........Eb F# G  Bb A  C  		E  Ab C# D  B  F  
 
5x/p/1/8:............F# Bb Eb E  C# G  		F  Ab A  C  B  D   
5x/p/4/8:............A  C# F# G  E  Bb 		Ab B  C  Eb D  F   
5x/p/7/8:............C  E  A  Bb G  C# 		B  D  Eb F# F  Ab 
5x/p/10/8:...........Eb G  C  C# Bb E  		D  F  F# A  Ab B  
 
5x/p/3/9:............C  F  F# Eb A  G  		Bb B  D  C# E  Ab not a chord, but nice line
 
5x/i/2/2:............Bb G  F# Eb E  C# 		A  F  C  B  D  Ab 
5x/i/5/2:............C# Bb A  F# G  E  		C  Ab Eb D  F  B  
5x/i/8/2:............E  C# C  A  Bb G  		Eb B  F# F  Ab D  
5x/i/11/2:...........G  E  Eb C  C# Bb 		F# D  A  Ab B  F  
 
5x/i/0/8:............G  Eb Bb A  C  F# 		Ab F  E  C# D  B  
5x/i/3/8:............Bb F# C# C  Eb A  		B  Ab G  E  F  D  
5x/i/6/8:............C# A  E  Eb F# C  		D  B  Bb G  Ab F  
5x/i/9/8:............E  C  G  F# A  Eb 		F  D  C# Bb B  Ab 
 

5x/i/1/11:...........Bb C# G  A  F# F  		D  Eb C  Ab E  B   not a chord, but nice line
 




  
------------------------------------------------------------------------------------------------------------- 
------------------------------------------------------------------------------------------------------------- 

6

Original

C,  F#, G#, F,  E,  C#, D,  B,  G,  Eb, Bb, A            6,2,9,11,9,1,9,8,8,7,11,(3)
F#, C,  D,  B,  Bb, G,  G#, F,  C#, A,  E,  Eb
E,  Bb, C,  A,  G#, F,  F#, Eb, B,  G,  D,  C#
G,  C#, Eb, C,  B,  G#, A,  F#, D,  Bb, F,  E
G#, D,  E,  C#, C,  A,  Bb, G,  Eb, B,  F#, F  
B,  F,  G,  E,  Eb, C,  C#, Bb, F#, D,  A,  G#
Bb, E,  F#, Eb, D,  B,  C,  A,  F,  C#, G#, G
C#, G,  A,  F#, F,  D,  Eb, C,  G#, E,  B,  Bb
F,  B,  C#, Bb, A,  F#, G,  E,  C,  G#, Eb, D
A,  Eb, F,  D,  C#, Bb, B,  G#, E,  C,  G,  F#
D,  G#, Bb, G,  F#, Eb, E,  C#, A,  F,  C,  B
Eb, A,  B,  G#, G,  E,  F,  D,  Bb, F#, C#, C



                                    inversion intervals: 6,10,3,1,3,11,3,4,4,5,1,(9)

------------------------------------------------------

5m                               5m inversion intervals: 6,10,9,7,9,5,9,4,4,11,7,(3)
 
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb   good    6,2,3,5,3,7,3,8,8,1,5,(9)
F#, C,  D,  F,  Bb, C#, G#, B,  G,  Eb, E,  A
E,  Bb, C,  Eb, G#, B,  F#, A,  F,  C#, D,  G
C#, G,  A,  C,  F,  G#, Eb, F#, D,  Bb, B,  E
G#, D,  E,  G,  C,  Eb, Bb, C#, A,  F,  F#, B
F,  B,  C#, E,  A,  C,  G,  Bb, F#, D,  Eb, G#
Bb, E,  F#, A,  D,  F,  C,  Eb, B,  G,  G#, C#
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
B,  F,  G,  Bb, Eb, F#, C#, E,  C,  G#, A,  D
Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
A,  Eb, F,  G#, C#, E,  B,  D,  Bb, F#, G,  C



5m Perm Matrix (Just a column of 5ths)

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
A,  Eb, F,  G#, C#, E,  B,  D,  Bb, F#, G,  C
E,  Bb, C,  Eb, G#, B,  F#, A,  F,  C#, D,  G
B,  F,  G,  Bb, Eb, F#, C#, E,  C,  G#, A,  D
F#, C,  D,  F,  Bb, C#, G#, B,  G,  Eb, E,  A
C#, G,  A,  C,  F,  G#, Eb, F#, D,  Bb, B,  E
G#, D,  E,  G,  C,  Eb, Bb, C#, A,  F,  F#, B
Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
Bb, E,  F#, A,  D,  F,  C,  Eb, B,  G,  G#, C#
F,  B,  C#, E,  A,  C,  G,  Bb, F#, D,  Eb, G#


6b


Self-Similarity of embedded line


C..F#.G#.F..E..C#.D..B..G..Eb.Bb.A..
...............c#.......g........a..
...f#....f........d........eb.......
c.....g#....e........b........bb              


C..F#.G#.B..E..G..D..F..C#.A..Bb.Eb.
...............g........c#.......eb.
...f#....b........d........a........
c.....g#....e........f........bb

------------------------------------------------------
------------------------------------------------------

7

cells: 026, 023, 034, 037, 048, 016,
0137, 0347, 0134, 0235, 0148, 0136, 0236

cells:   026, 025, 037, 025, 014, 048, 016
0146, 0247, 0347, 0358, 0235, 0148, 0235, 0136, 0258

0147 is embedded in 5-note groups, as described below

4-note cells NOT INCLUDED in Orig or 5m:

anything with 012 subset

0145, 0156, 0167, 0135, 0237, 0246, 0257, 0248, 0268, 0369, 

0,1,2:3 0,3,6,9:4 0,1,4,5:4 0,1,5,6:4 0,1,6,7:4 0,1,3,5:4 
0,2,3,7:4 0,2,4,6:4 0,2,5,7:4 0,2,4,8:4 0,2,6,8:4 

=================================================================================

8

ON THE PLACE OF 0147 in the scheme of things

f#,f,c,a


p/4/2:...............C  A  ab F  F# 			Eb B  G  D  C# E  Bb
p/0/11:..............A  C  F# ab F  			E  C# D  B  G  Eb Bb
r/4/5:...............F# F  ab A  C  			Bb E  C# D  G  B  Eb
i/3/9:...............C  F  F# eb A  			G  Bb B  D  C# E  Ab


5x/p/3/9:............F# F  C  eb A  			G  E  B  Ab C# Bb D
5x/i/10/2:...........F# A  d  F  C  			Eb B  G  Ab C# Bb E  
5x/i/6/11:...........A  F# C  d  F  			Bb C# Ab B  G  Eb E  
  
=================================================================================

9

Ord  (90 degree) (Swap pitch and position numbers)
7  0  1  4  11 10 8  3  9  6  5  2
C,  F#, G#, F,  E,  C#, D,  B,  G,  Eb, Bb, A

0   1   2   3   4   5   6   7   8   9   10  11
0   6   8   5   4   1   2   11  7   3   10  9
------------------------------------------------
0   5   6   9   4   3   1   8   2   11  10  7


C,  F,  F#, A,  E,  Eb, Db, Ab, D,  B,  Bb, G
G,  C,  Db, E,  B,  Bb, Ab, Eb, A,  F#, F,  D
F#, B,  C,  Eb, Bb, A,  G,  D,  Ab, F,  E,  Db
Eb, Ab, A,  C,  G,  F#, E,  B,  F,  D,  Db, Bb
Ab, Db, D,  F,  C,  B,  A,  E,  Bb, G,  F#, Eb
A,  D,  Eb, F#, Db, C,  Bb, F,  B,  Ab, G,  E
B,  E,  F,  Ab, Eb, D,  C,  G,  Db, Bb, A,  F#
E,  A,  Bb, Db, Ab, G,  F,  C,  F#, Eb, D,  B
Bb, Eb, E,  G,  D,  Db, B,  F#, C,  A,  Ab, F
Db, F#, G,  Bb, F,  E,  D,  A,  Eb, C,  B,  Ab
D,  G,  Ab, B,  F#, F,  Eb, Bb, E,  Db, C,  A
F,  Bb, B,  D,  A,  Ab, F#, Db, G,  E,  Eb, C


=========================================================

10


EXPANSIONS of Self-Similar Pattern to Bigger Center Intervals

P) permutation: 1,4,7,9,11,2,5,0,3,6,8,10
 
---------------------------------------------------------
0 1 10 6 2 9 8 11 5 7 4 3 - 12 0 0    center interval = 1
C,C#,Bb,F#,D,A,G#,B,F,G,E,Eb
1,9,8,8,7,11,3,6,2,9,11,9
This, is, in fact, the original row.

---------------------------------------------------------
Best 2x Series

0 2 8 11 4 6 3 10 9 1 7 5 - 10 1 2  C,D,Ab,B,E,F#,Eb,Bb,A,C#,G,F          **** cells ok
                           intervals: 2,6,3,5,2,9,7,11,4,6,10,(7)

0,2,3,6  *
0,2,5,8  *
0,2,4,7  *
0,3,4,7  *
0,1,3,7  *
0,1,4,7  *
0,1,4,6  *
0,2,3,6  *
0,2,4,8 
(0,1,5,7)
(0,2,5,7)
(0,2,5,8)        

1,4,7,9,11,2,5,0,3,6,8,10


Permutation Matrix of Best 2x Series

C,  D,  Ab, B,  E,  F#, Eb, Bb, A,  C#, G,  F     2,6,3,5,2,9,7,11,4,6,10,(7)
D,  E,  Bb, C#, F,  Ab, F#, C,  B,  Eb, A,  G     2,6,3,4,3,10,6,11,4,6,10,(7)
E,  F,  C,  Eb, G,  Bb, Ab, D,  C#, F#, B,  A
F,  G,  D,  F#, A,  C,  Bb, E,  Eb, Ab, C#, B
G,  A,  E,  Ab, B,  D,  C,  F,  F#, Bb, Eb, C#
A,  B,  F,  Bb, C#, E,  D,  G,  Ab, C,  F#, Eb
B,  C#, G,  C,  Eb, F,  E,  A,  Bb, D,  Ab, F#
C#, Eb, A,  D,  F#, G,  F,  B,  C,  E,  Bb, Ab
Eb, F#, B,  E,  Ab, A,  G,  C#, D,  F,  C,  Bb
F#, Ab, C#, F,  Bb, B,  A,  Eb, E,  G,  D,  C
Ab, Bb, Eb, G,  C,  C#, B,  F#, F,  A,  E,  D
Bb, C,  F#, A,  D,  Eb, C#, Ab, G,  B,  F,  E

---------------------------------------------------------
Best 4x Series

0 4 5 1 7 2 11 9 8 6 3 10 - 2 1 10   C,E,F,Db,G,D,B,A,Ab,Gb,Eb,Bb,



C,  E,  F,  Db, G,  D,  B,  A,  Ab, Gb, Eb, Bb, 
0   1   2   3   4   5   6   7   8   9   10  11
1   4   7   9   11  2   5   0   3   6   8   10



0   1   2   3   4   5   6   7   8   9   10  11
C,  E,  F,  Db, G,  D,  B,  A,  Ab, Gb, Eb, Bb,   
E   G   A   Gb  Bb  F   D   C   Db  B   Ab  Eb
------------------------------------------------
4   3   4   5   3   3   3   3   5   5   5   5 


0,1,4,5 no
0,2,3,6 *
0,1,4,6 *
0,1,3,7 *
0,2,4,7 *
0,1,3,6 *
0,2,3,5 *
0,1,3,6 *
0,2,4,7 *
0,2,5,8 *
0,1,4,6 *
0,1,5,7 no



C,  E,  F,  Db, G,  D,  B,  A,  Ab, Gb, Eb, Bb
E,  G,  A,  Gb, Bb, F,  D,  C,  Db, B,  Ab, Eb
G,  Bb, C,  B,  Eb, A,  F,  E,  Gb, D,  Db, Ab
Bb, Eb, E,  D,  Ab, C,  A,  G,  B,  F,  Gb, Db
Eb, Ab, G,  F,  Db, E,  C,  Bb, D,  A,  B,  Gb
Ab, Db, Bb, A,  Gb, G,  E,  Eb, F,  C,  D,  B
Db, Gb, Eb, C,  B,  Bb, G,  Ab, A,  E,  F,  D
Gb, B,  Ab, E,  D,  Eb, Bb, Db, C,  G,  A,  F
B,  D,  Db, G,  F,  Ab, Eb, Gb, E,  Bb, C,  A
D,  F,  Gb, Bb, A,  Db, Ab, B,  G,  Eb, E,  C
F,  A,  B,  Eb, C,  Gb, Db, D,  Bb, Ab, G,  E
A,  C,  D,  Ab, E,  B,  Gb, F,  Eb, Db, Bb, G


---------------------------------------------------------
---------------------------------------------------------
Best 6x Series


0 6 2 5 1 9 4 7 10 11 3 8 - 2 1 10   center interval = 6
C,F#,D,F,C#,A,E,G,Bb,B,Eb,Ab


C   F#  D   F   C#  A   E   G   Bb  B   Eb  Ab
0   1   2   3   4   5   6   7   8   9   10  11
1   4   7   9   11  2   5   0   3   6   8   10
F#  C#  G   B   Ab  D   A   C   F   E   Bb  Eb
------------------------------------------------
6   5   7   6   5   7   7   7   5   7   5   5



C,  F#, D,  F,  C#, A,  E,  G,  Bb, B,  Eb, Ab
F#, C#, G,  B,  Ab, D,  A,  C,  F,  E,  Bb, Eb
C#, Ab, C,  E,  Eb, G,  D,  F#, B,  A,  F,  Bb
Ab, Eb, F#, A,  Bb, C,  G,  C#, E,  D,  B,  F
Eb, Bb, C#, D,  F,  F#, C,  Ab, A,  G,  E,  B
Bb, F,  Ab, G,  B,  C#, F#, Eb, D,  C,  A,  E
F,  B,  Eb, C,  E,  Ab, C#, Bb, G,  F#, D,  A
B,  E,  Bb, F#, A,  Eb, Ab, F,  C,  C#, G,  D
E,  A,  F,  C#, D,  Bb, Eb, B,  F#, Ab, C,  G
A,  D,  B,  Ab, G,  F,  Bb, E,  C#, Eb, F#, C
D,  G,  E,  Eb, C,  B,  F,  A,  Ab, Bb, C#, F#
G,  C,  A,  Bb, F#, E,  B,  D,  Eb, F,  Ab, C#


0,1,4,6 *
0,1,4,5 - but close
0,1,4,8 *
0,1,4,8 *
0,2,5,8 *
0,1,3,6 *
0,1,4,7 *
0,1,4,8 *
0,2,3,7 - but close
0,3,4,7 *
0,2,5,8 *
0,2,6,8 - but 026 is good


=========================================================
=========================================================

11

MAIN 4-VOICE CHORALE:

not killed, chord by chord:  none (All are killed)

5x/ri/3/4:...........Ab F  Bb G  D  B  A  Eb F# C# C  E  
p/0/0:...............C  F# Ab F  E  C# D  B  G  Eb Bb A
5x/r/8/10:...........D  Ab F  Bb B  G  Eb F# C# E  A  C  
5x/r/8/8:............A  C  D  Ab F  Bb B  G  Eb F# C# E  
  
                           x                          o


=========================================================
=========================================================

12



chorale:  all work.  inversions.  suspensions.  linear cont.

Inversion of chorale (Inversion around A/Eb)


A  F# E  Bb Db Ab G  B  Eb C  F  D       I don't like this as much
E  Bb Db Ab G  B  Eb C  F  D  A  F#
F# C  Bb C# D  F  E  G  B  Eb G# A
Bb Db Ab B  E  G  A  Eb C  F  F# D 
----------------------------------------------------------------------------------------


Ab F  Bb G  D  B  A  Eb F# C# C  E  
C  F# Ab F  E  C# D  B  G  Eb Bb A
D  Ab F  Bb B  G  Eb F# C# E  A  C  
A  C  D  Ab F  Bb B  G  Eb F# C# E  




chorale: linear continuity, or, continuing each line over other 3 voices:


5x/ri/3/4:...........C  E Ab F  Bb G  D  B  A  	Eb F# C#   
p/0/0:...............C  							F# Ab F  E  C# D  B  G  Eb Bb A
5x/r/8/10:...........D  							Ab F  Bb B  G  Eb F# C# E  A  C  
5x/r/8/8:............A  							C  D  Ab F  Bb B  G  Eb F# C# E  



5x/ri/3/4:...........   Eb F# C# C  E Ab F  Bb 	G  D  B  A    
p/0/0:...............C  F# 						Ab F  E  C# D  B  G  Eb Bb A
5x/r/8/10:...........D  Ab 						F  Bb B  G  Eb F# C# E  A  C  
5x/r/8/8:............A  C  						D  Ab F  Bb B  G  Eb F# C# E  



5x/ri/3/4:...........      C# C  E  Ab F  Bb G  D  B     A  Eb F#   
p/0/0:...............C  F# Ab                            F  E  C# D  B  G  Eb Bb A
5x/r/8/10:...........D  Ab F                             Bb B  G  Eb F# C# E  A  C  
5x/r/8/8:............A  C  D                             Ab F  Bb B  G  Eb F# C# E  


         Eb F# C# C  E  Ab F  Bb G  D  B           A    
C  F# Ab F  										E  C# D  B  G  Eb Bb A
D  Ab F  Bb 										B  G  Eb F# C# E  A  C  
A  C  D  Ab 										F  Bb B  G  Eb F# C# E 


            E Ab F  Bb G  D  B  A  				Eb F# C# C  
C  F# Ab F  E  									C# D  B  G  Eb Bb A
D  Ab F  Bb B  									G  Eb F# C# E  A  C  
A  C  D  Ab F  									Bb B  G  Eb F# C# E  


=========================================================

=========================================================

13


Expansions of Row (exp. of vertical grid) retaining contour
(and some cells)



Contour: 12,7,9,6,5,2,3,1,8,4,11,10


p/0/0:...............C  F# Ab F  E  C# D  B  G  Eb Bb A

c3,f#2,g#2,f2,e2,c#2,d2,b1,g2,eb2,bb2,a2
11 6   8   5  4  1   2  0  7  3   10  9                                          

0,1,2:3 0,3,6,9:4 0,1,4,5:4 0,1,5,6:4 0,1,6,7:4 0,1,3,5:4 
0,2,3,7:4 0,2,4,6:4 0,2,5,7:4 0,2,4,8:4 0,2,6,8:4 

C4,E2,A2,C#2,A#1,D#1,F#1,B0,F2,G#1,G3,D3

C4,B2,F3,G#2,G2,D2,E2,C#2,D#3,F#2,A#3,A3   11,6,3,11,7,2,9,2,3,4,11,(3)

C4,B2,F3,A2,G#2,D2,E2,C#2,D#3,F#2,A#3,G3

0,1,4,7
0,2,3,6
0,1,3,6
0,1,4,6
0,1,3,6
0,1,2,3  xx
0,2,3,5
0,3,5,8
0,1,4,7

=========================================================
exclude certain contiguous pitch-combinations
=========================================================
 
c3,f#2,g#2,f2,e2,c#2,d2,b1,g2,eb2,bb2,a2
11 6   8   5  4  1   2  0  7  3   10  9     

combinations included in primary row:

c,f#,g#,f
c,f,e,c#
c,d,b,g
c,d,b,g,eb
c,bb,a

adjacencies not included:

c#,d
eb,e
g,g#
g#,a
bb,b


===============================================================

C4,A2,B2,F2,E2,G#1,C#2,G1,A#2,D#2,F#3,D3         OK-Good

0,1,3,7  *
0,1,5,7  close
0,1,4,7  *
0,3,4,7  *
0,1,4,7  *
0,1,3,6  *
0,2,5,8  *
0,3,4,7  *
0,1,4,8  *


C4,A2,D3,D#2,B1,F1,F#1,C#1,A#2,G#1,G3,E3    ****** Good Cells by match to row

0,1,3,6  *
0,1,4,6  *
0,2,3,6  *
0,1,3,7  *
0,1,5,7  -
0,2,4,7  *
0,1,3,6  *
0,2,3,6  *
0,1,4,8  *
0,3,5,8  *
0,2,4,7  *


C4,A2,D3,D#2,B1,G1,G#1,E1,C#3,A#1,F#3,F3   good enough

0,1,3,6
0,1,4,6
0,1,4,8
0,1,4,8
0,3,4,7
0,1,4,7  
0,2,5,8
0,2,5,8
0,1,5,8  -
0,1,5,7  -
0,1,4,7   
0,3,5,8


C4,A2,D3,F2,B1,D#1,F#1,C#1,A#2,G#1,G3,E3    g.e.

0,3,5,8  *
0,2,5,8  *
0,2,3,6  *
0,1,3,7  *
0,2,4,7  *
0,3,5,8  -
0,2,4,7  *
0,1,3,6  *
0,2,3,6  *
0,1,4,8  -
0,3,5,8  -
0,2,4,7  *


C4,B2,D3,F#2,E2,A1,A#1,G1,C#3,D#2,G#3,F3

0,1,3,7
0,2,4,7
0,2,4,7
0,1,4,6
0,1,3,6
0,2,3,6
0,2,5,8
0,1,5,7
0,2,4,7
0,3,5,8
0,1,4,7
0,1,3,6


C4,C#3,E3,G#2,F2,G1,A#1,F#1,D3,D#2,B3,A3   ok-good

0,1,4,8
0,3,4,7
0,1,3,4
0,2,3,5
0,1,2,5  -
0,1,4,8
0,1,4,8
0,3,4,7
0,1,4.6
0,2,3,6
0,1,2,4  -
0,3,4,7


C4,C#3,F3,G#2,E2,G1,A#1,F#1,D3,D#2,B3,A3       *** Good cells

0,1,5,8   -
0,3,4,7   *
0,1,3,4   *
0,2,3,6   *
0,2,3,6   *
0,1,4,8   *
0,1,4,8   *
0,3,4,7   *
0,1,4,6   *
0,2,3,6   *
0,1,2,4   -
0,1,4,8   *

===============================================================

C4,C#3,F#3,A2,D#2,G1,A#1,F1,E3,D2,B3,G#3

0,1,4,7
0,2,5,8
0,2,3,6
0,1,3,7
0,2,4,7
0,1,3,6
0,2,5,8
0,2,3,6
0,1,2,5   -
0,1,5,7   -

==============================================================
==============================================================


13B




5m with assigned contour:


C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb    

c4, f#3, g#3, b3, e3, g2, d3, f3, c#4, a3, bb3, eb4
9...4....5....8...2...0...1...3...10...6...7....11..
10  5    6    9   3   1   2   4   11   7   8    12



not killed, 3-note groups total:
c,d,e,a,




C4,A2,D3,B3,F#2,D#1,A#1,G2,C#4,F3,G#3,E4      ok
C4,A2,D#3,B3,F#2,D1,A#1,G2,C#4,F3,G#3,E4

C4,A#2,C#3,A3,F2,F#1,B1,G#2,D4,E3,G3,D#4      ok- (too much E7?)

C4,C#3,D#3,A#3,E2,D1,G1,B2,F4,G#3,A3,F#4      don't like middle G, etc.

C4,C#3,D#3,A#3,F#2,B1,E2,G#2,D4,F3,G3,A4      ok-
C4,C#3,D#3,A#3,F#2,B1,E2,G#2,D4,F3,A3,G4

C4,C#3,D#3,A#3,G2,B1,E2,G#2,D4,F3,F#3,A4      ok-

C4,C#3,E3,G#3,F2,D1,A1,B2,D#4,F#3,G3,A#4

C4,D3,D#3,A3,G2,A#1,F#2,C#3,E4,F3,G#3,B4

C4,D#3,F#3,A#3,E2,G1,D2,C#3,F4,G#3,A3,B4

C4,E3,F#3,B3,G#2,A1,F2,D3,C#4,G3,A#3,D#4

C4,F#3,G#3,B3,E3,G2,D3,F3,C#4,A3,A#3,D#4    original 5m row




===============================================================
cells: 026, 023, 034, 037, 048, 016,
0137, 0347, 0134, 0235, 0148, 0136, 0236
•           •     •     •     •     •
cells: 026, 025, 037, 025, 014, 048, 016
0146, 0247, 0347, 0358, 0235, 0148, 0235, 0136, 0258
•                             •           •     •

NOT INCLUDED:

-- anything with 012 subset

-- 0145, 0156, 0167, 0135, 0237, 0246, 0257, 0248, 0268, 0369, 0147, 0157?,
===============================================================


14

Stagger Chorale: Almost any Dyad will work +-1 position with any other dyad

                     0  1  2  3  4  5  6  7  8  9  10 11
5x/ri/3/4:...........Ab F  Bb G  D  B--A  Eb F# C# C  E   
p/0/0:...............C  F# Ab F  E  C# D  B  G  Eb Bb A
5x/r/8/10:...........D  Ab F  Bb B  G  Eb F# C# E  A  C  
5x/r/8/8:............A  C  D  Ab F  Bb B  G  Eb F# C# E  


0 -- a,d,c,ab  -- 0,1,4,6/

1 -- c,ab,f#,f -- 0,1,3,7/

2 -- d,f,ab,bb -- 0,2,5,8\

3 -- ab,bb,f,g -- 0,2,3,5/

4 -- f,b,e,d   -- 0,1,3,6\

5 -- bb,g,c#,b -- 0,2,3,6\

6 -- b,eb,d,a  -- 0,1,4,6\

7 -- g,f#,b,eb -- 0,1,4,8\

8 -- eb,c#,g,f#-- 0,1,4,6\

9 -- f#,e,eb,c#-- 0,2,3,5\

10 --c#,a,bb,c -- 0,1,3,4/

11 --e,c,a,e   -- 0,3,7/

=========================================================
=========================================================

15


LITERAL ROW-MATCHES to 4-NOTE CHORDS

0 -- a,d,c,ab  -- 0,1,4,6/

5x/p/8/0:............Ab D  C  A  		E  C# F# Eb G  B  Bb F
5x/i/7/5:............D  A  C  Ab 		E  F  Bb G  C# Eb F# B 
5x/i/11/8:...........C  Ab A  D  		B  F  G  Bb Eb F# C# E 
---------------------------------------------------------

1 -- c,ab,f#,f -- 0,1,3,7/

r/0/8:...............F  Ab F# C  		A  Bb Eb G  B  D  C# E
i/7/5:...............F# F  Ab C  		E  A  Bb G  C# B  D  Eb
i/3/8:...............Ab C  F  F# 		Eb A  G  Bb B  D  C# E

---------------------------------------------------------

2 -- d,f,ab,bb -- 0,2,5,8\

5x/p/8/10:...........Bb F  Ab D  		C  A  E  C# F# Eb G  B 
5x/i/2/11:...........F  D  Ab Bb 		C# F# A  E  G  Eb B  C


---------------------------------------------------------

3 -- ab,bb,f,g -- 0,2,3,5/

p/6/4:...............Bb G  Ab F  		C# A  E  Eb F# C  D  B
i/9/4:...............F  Ab G  Bb 		D  F# B  C  A  Eb C# E 

5x/p/0/4:............Ab F  Bb G  		B  Eb D  A  C  F# E  C# 
5x/i/3/4:............G  Bb F  Ab 		E  C  C# F# Eb A  B  

---------------------------------------------------------

4 -- f,b,e,d   -- 0,1,3,6\

i/2/9:...............B  E  F  D  		Ab F# A  Bb C# C  Eb G 

5x/p/2/9:............F  E  B  D  		Ab F# Eb Bb G  C  A  C#

---------------------------------------------------------

5 -- bb,g,c#,b -- 0,2,3,6\


p/1/10:..............B  Bb C# G  		A  F# F  D  Eb C  Ab E 
i/7/11:..............Bb G  C# B  		D  Eb F# F  Ab C  E  A

5x5p/i/0/1:..........G  Bb B  C# 		F# D  Eb E  A  Ab F  C


---------------------------------------------------------

6 -- b,eb,d,a  -- 0,1,4,6\

5x/p/4/5:............A  D  B  Eb 		G  F# C# E  Bb Ab F  C
5x/p/0/8:............B  Eb D  A  		C  F# E  C# Ab F  Bb G
5x/i/3/0:............Eb A  B  D  		G  Bb F  Ab E  C  C# F# 

---------------------------------------------------------

7 -- g,f#,b,eb -- 0,1,4,8\    ***** not octotonic

p/4/6:...............F# Eb B  G  		D  C# E  Bb C  A  Ab F
p/8/7:...............G  Eb B  F# 		F  Ab D  E  C# C  A  Bb

5x/p/8/6:............F# Eb G  B  		Bb F  Ab D  C  A  E  C#
5x/p/4/7:............B  Eb G  F# 		C# E  Bb Ab F  C  A  D

---------------------------------------------------------

8 -- eb,c#,g,f#-- 0,1,4,6\

5x/p/8/5:............C# F# Eb G  		B  Bb F  Ab D  C  A  E 
5x/p/4/8:............Eb G  F# C# 		E  Bb Ab F  C  A  D  B
5x/i/7/0:............G  C# Eb F# 		B  D  A  C  Ab E  F  Bb

---------------------------------------------------------

9 -- f#,e,eb,c#-- 0,2,3,5\


p/2/4:...............F# Eb E  C# 		A  F  C  B  D  Ab Bb G
i/5/4:...............C# E  Eb F# 		Bb D  G  Ab F  B  A  C 

5x/p/8/4:............E  C# F# Eb 		G  B  Bb F  Ab D  C  A
5x/i/11/4:...........Eb F# C# E  		C  Ab A  D  B  F  G  Bb 

---------------------------------------------------------

10 --c#,a,bb,c -- 0,1,3,4/

p/8/3:...............C# C  A  Bb 		G  Eb B  F# F  Ab D  E

i/2/3:...............A  Bb C# C  		Eb G  B  E  F  D  Ab F#

---------------------------------------------------------

11 --e,c,a,e   -- 0,3,7/

i/11/6:..............A  C  E  		Ab C# D  B  F  Eb F# G  Bb
i/7/8:...............C  E  A  		Bb G  C# B  D  Eb F# F  Ab 

5x/p/8/2:............C  A  E  		C# F# Eb G  B  Bb F  Ab D  
5x/i/5/3:............E  A  C  		G  Bb F# D  Eb Ab F  B  C# 

=========================================================
=========================================================

16


ROWS THAT WORK WITH CHORDS -- AT LEAST 6 NOTES                                      

0 -- a,d,c,ab  -- 0,1,4,6/
                                             
5x/p/8/0:............Ab D  C  A  		E  C# F# Eb G  B  Bb F
5x/i/7/5:............D  A  C  Ab 		E  F  Bb G  C# Eb F# B 
5x/i/11/8:...........C  Ab A  D  		B  F  G  Bb Eb F# C# E 


ex any pos:g,bb,c#    ex pit prox:b,bb  &  eb,e


5x/p/9/7:............E  Ab C  B  F# A  	Eb C# Bb F  D  G          **NOT OCT

5x/i/7/2:............F# B  D  A  C  Ab E	F Bb G  C# Eb             **NOTOCT

---------------------------------------------------------

1 -- c,ab,f#,f -- 0,1,3,7/

ex any pos0,1,2,3,4,5: g,e,  b-c#, bb,b, c#,d a,bb 
 
5x/i/9/11:...........C  A  Eb F  Ab C# 	E  B  D  Bb F# G          *N-O 

---------------------------------------------------------

2 -- d,f,ab,bb -- 0,2,5,8\

5x/p/8/10:...........Bb F  Ab D  		C  A  E  C# F# Eb G  B 
5x/i/2/11:...........F  D  Ab Bb 		C# F# A  E  G  Eb B  C

ex any: a 
ex pit prox:  f#,g  c#,c  c#,eb eb,e  e,f#


5x/p/10/2:...........D  B  F# Eb Ab F  		A  C# C  G  Bb E   
d,f,ab,bb & d,eb,f,f#,g#,b,= d,eb,f,f#,ab,bb,b,
  
5x/p/7/3:............Ab Eb C  F  D  F# Bb 	A  E  G  C# B  

  
5x/p/0/4:............Ab F  Bb G  B  Eb D  		A  C  F# E  C#        * eb har maj.
5x/p/3/4:............B  Ab C# Bb D  F# F  		C  Eb A  G  E         * f# har maj.
5x/p/7/4:............Eb C  F  D  F# Bb 		A E  G  C# B  Ab      * bb har maj.
5x/p/9/4:............F  D  G  E  Ab C  		B  F# A  Eb C# Bb     c har maj.
 
5x/p/0/5:............F  Bb G  B  Eb D  		A  C  F# E  C# Ab 
5x/p/3/5:............Ab C# Bb D  F# F  		C  Eb A  G  E  B      bb phryg b4
   
5x/p/3/7:............Bb D  F# F  C  Eb 		A  G  E  B  Ab C# 

5x/p/5/7:............C  E  Ab G  D  F  		B  A  F# C# Bb Eb 
5x/p/8/7:............Eb G  B  Bb F  Ab 		D  C  A  E  C# F# 
5x/p/11/7:...........F# Bb D  C# Ab B  		F  Eb C  G  E  A  
 
--------------------------------

5x/p/2/8:............C# F  E  B  D  Ab 		F# Eb Bb G  C  A  OCT
5x/p/5/8:............E  Ab G  D  F  B  		A  F# C# Bb Eb C  
5x/p/8/8:............G  B  Bb F  Ab D  		C  A  E  C# F# Eb 
5x/p/11/8:...........Bb D  C# Ab B  F  		Eb C  G  E  A  F# 
     
5x/p/2/11:...........B  D  Ab F# Eb Bb 		G  C  A  C# F  E  not oct
  
5x/i/0/2:............Ab B  E  G  D  F  		C# A  Bb Eb C  F# oct
5x/i/3/2:............B  D  G  Bb F  Ab 		E  C  C# F# Eb A  
5x/i/6/2:............D  F  Bb C# Ab B  		G  Eb E  A  F# C  
5x/i/9/2:............F  Ab C# E  B  D  		Bb F# G  C  A  Eb 
  
5x/i/0/3:............B  E  G  D  F  C# 		A  Bb Eb C  F# Ab oct
5x/i/1/3:............C  F  Ab Eb F# D  		Bb B  E  C# G  A  not oct
5x/i/3/3:............D  G  Bb F  Ab E  		C  C# F# Eb A  B  at intersection
5x/i/6/3:............F  Bb C# Ab B  G  		Eb E  A  F# C  D 
5x/i/9/3:............Ab C# E  B  D  Bb 		F# G  C  A  Eb F  
   
5x/i/1/4:............F  Ab Eb F# D  Bb 		B  E  C# G  A  C  not oct
5x/i/3/4:............G  Bb F  Ab E  C  		C# F# Eb A  B  D  not oct  
5x/i/1/5:............Ab Eb F# D  Bb B  		E  C# G  A  C  F  not oct
5x/i/5/7:............Bb F# D  Eb Ab F  		B  C# E  A  C  G  not oct  
5x/i/7/7:............C  Ab E  F  Bb G  		C# Eb F# B  D  A  not oct
5x/i/1/8:............D  Bb B  E  C# G  		A  C  F  Ab Eb F# intersect of type 3 and oct
     
5x/i/4/8:............F  C# D  G  E  Bb 		C  Eb Ab B  F# A  oct

5x/i/5/8:............F# D  Eb Ab F  B  		C# E  A  C  G  Bb not oct

5x/i/7/8:............Ab E  F  Bb G  C# 		Eb F# B  D  A  C  oct
5x/i/10/8:...........B  G  Ab C# Bb E  		F# A  D  F  C  Eb oct
   
5x/i/2/11:...........F  D  Ab Bb C# F# 		A  E  G  Eb B  C  not oct
  
5x/i/11/11:..........D  B  F  G  Bb Eb 		F# C# E  C  Ab A  * not oct

---------------------------------------------------------
---------------------------------------------------------

3 -- ab,bb,f,g -- 0,2,3,5/

p/6/4:...............Bb G  Ab F  		C# A  E  Eb F# C  D  B
i/9/4:...............F  Ab G  Bb 		D  F# B  C  A  Eb C# E 

5x/p/0/4:............Ab F  Bb G  		B  Eb D  A  C  F# E  C# 
5x/i/3/4:............G  Bb F  Ab 		E  C  C# F# Eb A  B  

p/0/2:...............Ab F  E  C# D  B  		G  Eb Bb A  C  F#
p/3/2:...............B  Ab G  E  F  D  		Bb F# C# C  Eb A

i/6/3:...............C# D  F  E  G  B  		Eb Ab A  F# C  Bb 
i/3/5:...............D  C# E  Ab C  F  		F# Eb A  G  Bb B  
i/2/8:...............G  B  E  F  D  Ab 		F# A  Bb C# C  Eb 
i/11/8:..............E  Ab C# D  B  F  		Eb F# G  Bb A  C  
 
5x/p/6/3:............G  D  B  E  C# F  		A  Ab Eb F# C  Bb 
5x/p/9/4:............F  D  G  E  Ab C  		B  F# A  Eb C# Bb  not oct Lyd b7
5x/p/5/7:............C  E  Ab G  D  F  		B  A  F# C# Bb Eb  not oct
5x/p/2/8:............C# F  E  B  D  Ab 		F# Eb Bb G  C  A  
5x/p/5/8:............E  Ab G  D  F  B  		A  F# C# Bb Eb C  
   
5x/i/0/2:............Ab B  E  G  D  F  		C# A  Bb Eb C  F# 
5x/i/9/2:............F  Ab C# E  B  D  		Bb F# G  C  A  Eb 
5x/i/0/3:............B  E  G  D  F  C# 		A  Bb Eb C  F# Ab 
  
---------------------------------------------------------

4 -- f,b,e,d   -- 0,1,3,6\

i/2/9:...............B  E  F  D  		Ab F# A  Bb C# C  Eb G 
5x/p/2/9:............F  E  B  D  		Ab F# Eb Bb G  C  A  C#

ex any:eb,f#  ex pit prox bb,c bb,a c,c# 

p/0/2:...............Ab F  E  C# D  B  G  		Eb Bb A  C  F# 
p/3/2:...............B  Ab G  E  F  D  Bb 		F# C# C  Eb A
p/6/2:...............D  B  Bb G  Ab F  C# 		A  E  Eb F# C  
p/9/2:...............F  D  C# Bb B  Ab E  		C  G  F# A  Eb 
p/1/8:...............Ab E  B  Bb C# G  		A  F# F  D  Eb C

p/2/8:...............A  F  C  B  D  Ab 		Bb G  F# Eb E  C#  not oct
p/4/8:...............B  G  D  C# E  Bb 		C  A  Ab F  F# Eb
p/7/8:...............D  Bb F  E  G  C# 		Eb C  B  Ab A  F#
p/10/8:..............F  C# Ab G  Bb E  		F# Eb D  B  C  A
 
i/0/2:...............E  G  Ab B  Bb C# F  		A  D  Eb C  F#
i/1/2:...............F  Ab A  C  B  D  		F# Bb Eb E  C# G  not oct
i/3/2:...............G  Bb B  D  C# E  Ab 		C  F  F# Eb A  
i/6/2:...............Bb C# D  F  E  G  B  		Eb Ab A  F# C  
i/9/2:...............C# E  F  Ab G  Bb D  		F# B  C  A  Eb 


i/2/8:...............G  B  E  F  D  Ab 		F# A  Bb C# C  Eb 
i/5/8:...............Bb D  G  Ab F  B  		A  C  C# E  Eb F# 
i/8/8:...............C# F  Bb B  Ab D  		C  Eb E  G  F# A  
i/11/8:..............E  Ab C# D  B  F  		Eb F# G  Bb A  C 
 
5x/p/0/2:............E  C# Ab F  Bb G  B  		Eb D  A  C  F# 
5x/p/3/2:............G  E  B  Ab C# Bb D  		F# F  C  Eb A  
5x/p/4/2:............Ab F  C  A  D  B  		Eb G  F# C# E  Bb N.O.
5x/p/6/2:............Bb G  D  B  E  C# F  		A  Ab Eb F# C  
5x/p/9/2:............C# Bb F  D  G  E  Ab 		C  B  F# A  Eb 
5x/p/0/3:............C# Ab F  Bb G  B  		Eb D  A  C  F# E   

5x/p/9/5:............D  G  E  Ab C  B  		F# A  Eb C# Bb F  Not OCT
5x/p/2/7:............A  C# F  E  B  D  		Ab F# Eb Bb G  C  N.O. 
5x/p/5/7:............C  E  Ab G  D  F  B  		A  F# C# Bb Eb    N.O. 
5x/p/8/8:............G  B  Bb F  Ab D  		C  A  E  C# F# Eb 
5x/p/11/8:...........Bb D  C# Ab B  F  		Eb C  G  E  A  F# 
5x/p/7/10:...........A  E  G  C# B  Ab 		Eb C  F  D  F# Bb 
5x/p/8/11:...........F  Ab D  C  A  E  		C# F# Eb G  B  Bb N.O.
   
5x/i/3/2:............B  D  G  Bb F  Ab E  		C  C# F# Eb A  
5x/i/6/2:............D  F  Bb C# Ab B  G  		Eb E  A  F# C 
5x/i/9/2:............F  Ab C# E  B  D  Bb 		F# G  C  A  Eb   
5x/i/0/3:............B  E  G  D  F  C# A  		Bb Eb C  F# Ab      N.O.
  
5x/i/0/4:............E  G  D  F  C# A  Bb 		Eb C  F# Ab B       NOT OCT
5x/i/7/4:............B  D  A  C  Ab E  F  		Bb G  C# Eb F#      NOT OCT 
5x/i/4/7:............A  F  C# D  G  E  		Bb C  Eb Ab B  F#   N.O.
5x/i/11/7:...........E  C  Ab A  D  B  F  		G  Bb Eb F# C#      N.O.
5x/i/1/8:............D  Bb B  E  C# G  		A  C  F  Ab Eb F#   
 
5x/i/7/8:............Ab E  F  Bb G  C# 		Eb F# B  D  A  C  
5x/i/10/8:...........B  G  Ab C# Bb E  		F# A  D  F  C  Eb 
5x/i/11/8:...........C  Ab A  D  B  F  G  		Bb Eb F# C# E  
    
5x/i/5/11:...........Ab F  B  C# E  A  		C  G  Bb F# D  Eb   
5x/i/8/11:...........B  Ab D  E  G  C  		Eb Bb C# A  F  F#  N.O.
  
---------------------------------------------------------

5 -- bb,g,c#,b -- 0,2,3,6\


p/1/10:..............B  Bb C# G  		A  F# F  D  Eb C  Ab E 
i/7/11:..............Bb G  C# B  		D  Eb F# F  Ab C  E  A
5x5p/i/0/1:..........G  Bb B  C# 		F# D  Eb E  A  Ab F  C


ex any:a,c     ex pit prox f,f#, f#,g# d,d# 

 
p/2/2:...............Bb G  F# Eb E  C# 		A  F  C  B  D  Ab      N.O.

p/0/2:...............Ab F  E  C# D  B  G  		Eb Bb A  C  F#   
p/3/2:...............B  Ab G  E  F  D  Bb 		F# C# C  Eb A  
p/6/2:...............D  B  Bb G  Ab F  C# 		A  E  Eb F# C  
p/9/2:...............F  D  C# Bb B  Ab E  		C  G  F# A  Eb 
   
p/1/8:...............Ab E  B  Bb C# G  		A  F# F  D  Eb C  
p/4/8:...............B  G  D  C# E  Bb 		C  A  Ab F  F# Eb 
p/7/8:...............D  Bb F  E  G  C# 		Eb C  B  Ab A  F# 
p/10/8:..............F  C# Ab G  Bb E  		F# Eb D  B  C  A  

i/0/2:...............E  G  Ab B  Bb C# F  		A  D  Eb C  F# 
i/3/2:...............G  Bb B  D  C# E  Ab 		C  F  F# Eb A  
i/6/2:...............Bb C# D  F  E  G  B  		Eb Ab A  F# C  
i/9/2:...............C# E  F  Ab G  Bb D  		F# B  C  A  Eb 
   
i/1/8:...............F# Bb Eb E  C# G  		F  Ab A  C  B  D       N.O. 
   
i/2/8:...............G  B  E  F  D  Ab 		F# A  Bb C# C  Eb 
i/5/8:...............Bb D  G  Ab F  B  		A  C  C# E  Eb F# 
i/8/8:...............C# F  Bb B  Ab D  		C  Eb E  G  F# A  
i/11/8:..............E  Ab C# D  B  F  		Eb F# G  Bb A  C  
   
5x/p/0/2:............E  C# Ab F  Bb G  B  		Eb D  A  C  F# 
5x/p/3/2:............G  E  B  Ab C# Bb D  		F# F  C  Eb A  
5x/p/6/2:............Bb G  D  B  E  C# F  		A  Ab Eb F# C  
5x/p/9/2:............C# Bb F  D  G  E  Ab 		  B  F# A  Eb 
    
5x/p/8/4:............E  C# F# Eb G  B  Bb 		F  Ab D  C  A           N.O.
      
5x/p/4/7:............B  Eb G  F# C# E  Bb 		Ab F  C  A  D           N.O.
5x/p/8/7:............Eb G  B  Bb F  Ab 		D  C  A  E  C# F#       N.O.
   
5x/p/2/8:............C# F  E  B  D  Ab 		F# Eb Bb G  C  A  
5x/p/5/8:............E  Ab G  D  F  B  		A  F# C# Bb Eb C  
5x/p/8/8:............G  B  Bb F  Ab D  		C  A  E  C# F# Eb 
5x/p/11/8:...........Bb D  C# Ab B  F  		Eb C  G  E  A  F# 
      
5x/p/7/11:...........E  G  C# B  Ab Eb 		C  F  D  F# Bb A  
5x/p/10/11:..........G  Bb E  D  B  F# 		Eb Ab F  A  C# C  
      
5x/i/0/2:............Ab B  E  G  D  F  C# 		A  Bb Eb C  F# 
5x/i/3/2:............B  D  G  Bb F  Ab E  		C  C# F# Eb A  
5x/i/6/2:............D  F  Bb C# Ab B  G  		Eb E  A  F# C     
5x/i/11/2:...........G  Bb Eb F# C# E  		C  Ab A  D  B  F  
   
5x/i/9/3:............Ab C# E  B  D  Bb F# 	G  	C  A  Eb F 		
     
5x/i/1/7:............F# D  Bb B  E  C# G  		A  C  F  Ab Eb         N.O. 
5x/i/10/7:...........Eb B  G  Ab C# Bb E  		F# A  D  F             N.O.  
    
5x/i/4/8:............F  C# D  G  E  Bb 		C  Eb Ab B  F# A  
5x/i/7/8:............Ab E  F  Bb G  C# 		Eb F# B  D  A  C  
      
5x/i/7/11:...........Bb G  C# Eb F# B  		D  A  C  Ab E  F       N.O. 
   
---------------------------------------------------------

6 -- b,eb,d,a  -- 0,1,4,6\

5x/p/4/5:............A  D  B  Eb 		G  F# C# E  Bb Ab F  C
5x/p/0/8:............B  Eb D  A  		C  F# E  C# Ab F  Bb G
5x/i/3/0:............Eb A  B  D  		G  Bb F  Ab E  C  C# F# 


ex any: c#,e,bb       ex pit prox7: g#,g 
   
p/4/2:...............C  A  Ab F  F# Eb 		B  G  D  C# E  Bb 
p/7/2:...............Eb C  B  Ab A  F# 		D  Bb F  E  G  C# 
p/10/2:..............F# Eb D  B  C  A  		F  C# Ab G  Bb E  
   
p/10/3:..............Eb D  B  C  A  F  		C# Ab G  Bb E  F#  
   
p/2/8:...............A  F  C  B  D  Ab 		Bb G  F# Eb E  C# 
p/5/8:...............C  Ab Eb D  F  B  		C# Bb A  F# G  E  
p/8/8:...............Eb B  F# F  Ab D  		E  C# C  A  Bb G  
p/11/8:..............F# D  A  Ab B  F  		G  E  Eb C  C# Bb 
     
i/1/2:...............F  Ab A  C  B  D  F# 		Bb Eb E  C# G  
i/4/2:...............Ab B  C  Eb D  F  A  		C# F# G  E  Bb 
i/7/2:...............B  D  Eb F# F  Ab C  		E  A  Bb G  C#   
i/10/2:..............D  F  F# A  Ab B  Eb 		G  C  C# Bb E  
   
i/1/3:...............Ab A  C  B  D  F# 		Bb Eb E  C# G  F  
i/4/3:...............B  C  Eb D  F  A  		C# F# G  E  Bb Ab 
i/7/3:...............D  Eb F# F  Ab C  		E  A  Bb G  C# B  
i/10/3:..............F  F# A  Ab B  Eb 		G  C  C# Bb E  D  
   
i/0/8:...............F  A  D  Eb C  F# 		E  G  Ab B  Bb C# 
i/3/8:...............Ab C  F  F# Eb A  		G  Bb B  D  C# E  
i/6/8:...............B  Eb Ab A  F# C  		Bb C# D  F  E  G  
i/9/8:...............D  F# B  C  A  Eb 		C# E  F  Ab G  Bb 
   
   
5x/p/1/2:............F  D  A  F# B  Ab C  		E  Eb Bb C# G  
5x/p/4/2:............Ab F  C  A  D  B  Eb 		G  F# C# E  Bb 
5x/p/7/2:............B  Ab Eb C  F  D  F# 		Bb A  E  G  C# 
5x/p/10/2:...........D  B  F# Eb Ab F  A  		C# C  G  Bb E  
   
5x/p/1/3:............D  A  F# B  Ab C  		E  Eb Bb C# G  F  
5x/p/4/3:............F  C  A  D  B  Eb 		G  F# C# E  Bb Ab 
5x/p/7/3:............Ab Eb C  F  D  F# 		Bb A  E  G  C# B  
5x/p/10/3:...........B  F# Eb Ab F  A  		C# C  G  Bb E  D  
   
5x/p/4/4:............C  A  D  B  Eb G  F# 		C# E  Bb Ab F  N.O.
   
5x/p/0/7:............G  B  Eb D  A  C  F# 		E  C# Ab F  Bb  N.O.
   
5x/p/3/8:............D  F# F  C  Eb A  		G  E  B  Ab C# Bb 
5x/p/6/8:............F  A  Ab Eb F# C  		Bb G  D  B  E  C# 
5x/p/9/8:............Ab C  B  F# A  Eb 		C# Bb F  D  G  E  
      
5x/i/1/2:............A  C  F  Ab Eb F# D  		Bb B  E  C# G  
5x/i/4/2:............C  Eb Ab B  F# A  F  		C# D  G  E  Bb 
5x/i/7/2:............Eb F# B  D  A  C  Ab 		E  F  Bb G  C# 
5x/i/10/2:...........F# A  D  F  C  Eb B  		G  Ab C# Bb E  
   
5x/i/1/3:............C  F  Ab Eb F# D  		Bb B  E  C# G  A  
5x/i/4/3:............Eb Ab B  F# A  F  		C# D  G  E  Bb C  
5x/i/7/3:............F# B  D  A  C  Ab 		E  F  Bb G  C# Eb 
5x/i/10/3:...........A  D  F  C  Eb B  G  		Ab C# Bb E  F#     N.O.
  
5x/i/2/7:............G  Eb B  C  F  D  		Ab Bb C# F# A  E   N.O.
   
5x/i/2/8:............Eb B  C  F  D  Ab 		Bb C# F# A  E  G  
5x/i/5/8:............F# D  Eb Ab F  B  		C# E  A  C  G  Bb 
5x/i/8/8:............A  F  F# B  Ab D  		E  G  C  Eb Bb C# 
5x/i/11/8:...........C  Ab A  D  B  F  		G  Bb Eb F# C# E  
   
5x/i/3/11:...........F# Eb A  B  D  G  		Bb F  Ab E  C  C#   N.O.
   
---------------------------------------------------------

7 -- g,f#,b,eb -- 0,1,4,8\    ***** not octotonic

p/4/6:...............F# Eb B  G  		D  C# E  Bb C  A  Ab F
p/8/7:...............G  Eb B  F# 		F  Ab D  E  C# C  A  Bb

5x/p/8/6:............F# Eb G  B  		Bb F  Ab D  C  A  E  C#
5x/p/4/7:............B  Eb G  F# 		C# E  Bb Ab F  C  A  D

ex any: f,ab ex pit prox: bb,c d,e bb,a d,c# c,c#

p/2/2:...............Bb G  F# Eb E  C# 		A F  C  B  D  Ab 
p/10/2:..............F# Eb D  B  C  A  		F  C# Ab G  Bb E  
p/9/8:...............E  C  G  F# A  Eb 		F  D  C# Bb B  Ab 
   
i/8/2:...............C  Eb E  G  F# A  		C# 	F  Bb B  Ab D   
i/1/8:...............F# Bb Eb E  C# G  		F  Ab A  C  B  D  
i/9/8:...............D  F# B  C  A  Eb 		C# E  F  Ab G  Bb 

7 -- g,f#,b,eb 

5x/p/11/2:...........Eb C  G  E  A  F# 		Bb D  C# Ab B  F  
5x/p/8/3:............A  E  C# F# Eb G  B  		Bb F  Ab D  C  
5x/p/4/4:............C  A  D  B  Eb G  F# 		C# E  Bb Ab F  
5x/p/0/7:............G  B  Eb D  A  C  F# 		E  C# Ab F  Bb 
5x/p/4/7:............B  Eb G  F# C# E  Bb 		Ab F  C  A  D      
5x/p/3/11:...........C  Eb A  G  E  B  		Ab C# Bb D  F# F  
   

5x/i/7/2:............Eb F# B  D  A  C  		Ab E  F  Bb G  C#
5x/i/7/11:...........Bb G  C# Eb F# B  D  		A  C  Ab E  F  
5x/i/11/2:...........G  Bb Eb F# C# E  C  		Ab A  D  B  F  
5x/i/2/3:............C# F# A  E  G  Eb B  		C  F  D  Ab Bb 
5x/i/6/7:............B  G  Eb E  A  F# C  		D  F  Bb C# Ab 
5x/i/3/11:...........F# Eb A  B  D  G  Bb 		F  Ab E  C  C# 
  
---------------------------------------------------------

8 -- eb,c#,g,f#-- 0,1,4,6\

5x/p/8/5:............C# F# Eb G  		B  Bb F  Ab D  C  A  E 
5x/p/4/8:............Eb G  F# C# 		E  Bb Ab F  C  A  D  B
5x/i/7/0:............G  C# Eb F# 		B  D  A  C  Ab E  F  Bb


ex any: d,f,ab ex pit prox:


p/2/2:...............Bb G  F# Eb E  C# A  		F  C  B  D  Ab 
p/5/2:...............C# Bb A  F# G  E  C  		Ab Eb D  F  B  
p/8/2:...............E  C# C  A  Bb G  Eb 		B  F# F  Ab D  
p/11/2:..............G  E  Eb C  C# Bb F# 		D  A  Ab B  F  
   

p/2/3:...............G  F# Eb E  C# A  		F  C  B  D  Ab Bb 
p/5/3:...............Bb A  F# G  E  C  		Ab Eb D  F  B  C# 
p/8/3:...............C# C  A  Bb G  Eb 		B  F# F  Ab D  E  
p/11/3:..............E  Eb C  C# Bb F# 		D  A  Ab B  F  G  
   

p/8/4:...............C  A  Bb G  Eb B  F# 		F  Ab D  E  C# 
p/8/5:...............A  Bb G  Eb B  F# 		F  Ab D  E  C# C  

p/0/8:...............G  Eb Bb A  C  F# 		Ab F  E  C# D  B  
p/3/8:...............Bb F# C# C  Eb A  		B  Ab G  E  F  D  
p/6/8:...............C# A  E  Eb F# C  		D  B  Bb G  Ab F  
p/9/8:...............E  C  G  F# A  Eb 		F  D  C# Bb B  Ab 
   
p/1/9:...............E  B  Bb C# G  			A  F# F  D  Eb C  Ab 
p/3/9:...............F# C# C  Eb A  			B  Ab G  E  F  D  Bb   
p/7/11:..............E  G  C# Eb C  			B  Ab A  F# D  Bb F  
    
i/2/2:...............F# A  Bb C# C  Eb G  		B  E  F  D  Ab 
i/5/2:...............A  C  C# E  Eb F# Bb 		D  G  Ab F  B  
i/8/2:...............C  Eb E  G  F# A  C# 		F  Bb B  Ab D  
   
i/11/2:..............Eb F# G  Bb A  C  E  		Ab C# D  B  F  
i/2/3:...............A  Bb C# C  Eb G  B  		E  F  D  Ab F# 
i/5/3:...............C  C# E  Eb F# Bb D  		G  Ab F  B  A  
i/8/3:...............Eb E  G  F# A  C# 		F Bb B  Ab D  C  
   
i/1/8:...............F# Bb Eb E  C# G  		F  Ab A  C  B  D  
i/4/8:...............A  C# F# G  E  Bb 		Ab B  C  Eb D  F  
i/7/8:...............C  E  A  Bb G  C# 		B  D  Eb F# F  Ab 
i/10/8:..............Eb G  C  C# Bb E  		D  F  F# A  Ab B  
   
i/7/9:...............E  A  Bb G  C# 			B  D  Eb F# F  Ab C  
i/9/9:...............F# B  C  A  Eb 			C# E  F  Ab G  Bb D  
i/3/11:..............F# Eb A  G  Bb 			B  D  C# E  Ab C  F  


8 -- eb,c#,g,f#-- 0,1,4,6\
   

5x/p/5/1:............B  A  F# C# Bb Eb 		C  E  Ab G  D  F  
5x/p/2/2:............F# Eb Bb G  C  A  C# 		F  E  B  D  Ab 
5x/p/5/2:............A  F# C# Bb Eb C  E  		Ab G  D  F  B  
5x/p/8/2:............C  A  E  C# F# Eb G  		B  Bb F  Ab D  
   
5x/p/11/2:...........Eb C  G  E  A  F# Bb 		D  C# Ab B  F  
  
5x/p/2/3:............Eb Bb G  C  A  C# F  		E  B  D  Ab F# 
5x/p/5/3:............F# C# Bb Eb C  E  Ab G  	D  F  B  A  
5x/p/8/3:............A  E  C# F# Eb G  B  		Bb F  Ab D  C  
5x/p/11/3:...........C  G  E  A  F# Bb 		D C# Ab B  F  Eb 
  
5x/p/4/7:............B  Eb G  F# C# E  Bb 		Ab F  C  A  D  

5x/p/1/8:............C  E  Eb Bb C# G  		F  D  A  F# B  Ab 
5x/p/4/8:............Eb G  F# C# E  Bb 		Ab F  C  A  D  B  
5x/p/7/8:............F# Bb A  E  G  C# 		B  Ab Eb C  F  D  
5x/p/10/8:...........A  C# C  G  Bb E  		D  B  F# Eb Ab F  
   
   
5x/i/2/2:............Bb C# F# A  E  G  Eb B  	C  F  D  Ab  
5x/i/8/2:............E  G  C  Eb Bb C# A  		F  F# B  Ab D  
 
5x/i/11/2:...........G  Bb Eb F# C# E  C  		Ab A  D  B  F 
5x/i/6/7:............B  G  Eb E  A  F# C  		D  F  Bb C# Ab 
	
5x/i/0/8:............C# A  Bb Eb C  F# 		Ab B  E  G  D  F  
5x/i/3/8:............E  C  C# F# Eb A  		B  D  G  Bb F  Ab 
5x/i/9/8:............Bb F# G  C  A  Eb 		F  Ab C# E  B  D     
5x/i/1/9:............Bb B  E  C# G  A  C  		F  Ab Eb F# D  
5x/i/3/9:............C  C# F# Eb A  B  		D  G  Bb F  Ab E  
5x/i/7/11:...........Bb G  C# Eb F# B  		D  A  C  Ab E  F  
   

---------------------------------------------------------

9 -- f#,e,eb,c#-- 0,2,3,5\


p/2/4:...............F# Eb E  C# 		A  F  C  B  D  Ab Bb G
i/5/4:...............C# E  Eb F# 		Bb D  G  Ab F  B  A  C 

5x/p/8/4:............E  C# F# Eb 		G  B  Bb F  Ab D  C  A
5x/i/11/4:...........Eb F# C# E  		C  Ab A  D  B  F  G  Bb 

 
p/2/2:...............Bb G  F# Eb E  C# A  		F  C  B  D  Ab 
p/5/2:...............C# Bb A  F# G  E  C  		Ab Eb D  F  B  
p/8/2:...............E  C# C  A  Bb G  Eb 		B  F# F  Ab D  
p/11/2:..............G  E  Eb C  C# Bb F# 		D  A  Ab B  F  
   
p/0/8:...............G  Eb Bb A  C  F# 		Ab F  E  C# D  B  
p/3/8:...............Bb F# C# C  Eb A  		B  Ab G  E  F  D  
p/6/8:...............C# A  E  Eb F# C  		D  B  Bb G  Ab F  
p/9/8:...............E  C  G  F# A  Eb 		F  D  C# Bb B  Ab 
    
p/1/9:...............E  B  Bb C# G  			A  F# F  D  Eb C  Ab 
p/6/9:...............A  E  Eb F# C  			D  B  Bb G  Ab F  C# 
p/9/9:...............C  G  F# A  Eb 			F  D  C# Bb B  Ab E  
    
p/4/11:..............C# E  Bb C  A  			Ab F  F# Eb B  G  D  
p/10/11:.............G  Bb E  F# Eb 			D  B  C  A  F  C# Ab 
    
i/5/2:...............A  C  C# E  Eb F# Bb 		D  G  Ab F  B  
i/8/2:...............C  Eb E  G  F# A  C# 		F  Bb B  Ab D  
i/11/2:..............Eb F# G  Bb A  C  E  		b C# D  B  F  
   
i/1/8:...............F# Bb Eb E  C# G  		F  Ab A  C  B  D  
i/4/8:...............A  C# F# G  E  Bb 		Ab B  C  Eb D  F  
i/7/8:...............C  E  A  Bb G  C# 		B  D  Eb F# F  Ab 
i/10/8:..............Eb G  C  C# Bb E  		D  F  F# A  Ab B  
   
i/1/9:...............Bb Eb E  C# G  			F  Ab A  C  B  D  F# 
i/6/9:...............Eb Ab A  F# C  			Bb C# D  F  E  G  B  
i/7/9:...............E  A  Bb G  C# 			B  D  Eb F# F  Ab C  
i/10/9:..............G  C  C# Bb E  			D  F  F# A  Ab B  Eb 
     
i/3/11:..............F# Eb A  G  Bb B  		D  C# E  Ab C  F  
i/6/11:..............A  F# C  Bb C# 			D  F  E  G  B  Eb Ab 
i/9/11:..............C  A  Eb C# E  F  		Ab G  Bb D  F# B  
   

9 -- f#,e,eb,c#-- 0,2,3,5\



5x/p/2/2:............F# Eb Bb G  C  A  C# 		F  E  B  D  Ab 
5x/p/5/2:............A  F# C# Bb Eb C  E  		Ab G  D  F  B  
5x/p/8/2:............C  A  E  C# F# Eb G  		B  Bb F  Ab D  
5x/p/11/2:...........Eb C  G  E  A  F# Bb 		D  C# Ab B  F  
  
5x/p/3/3:............E  B  Ab C# Bb 			D  F# F  C  Eb A  G  
   
5x/p/2/4:............Bb G  C  A  C# 			F  E  B  D  Ab F# Eb 
5x/p/5/4:............C# Bb Eb C  E  Ab 		G  D  F  B  A  F# 
5x/p/8/4:............E  C# F# Eb G  B  Bb 		F  Ab D  C  A  
5x/p/11/4:...........G  E  A  F# Bb 			D  C# Ab B  F  Eb C  
   
5x/p/1/7:............Ab C  E  Eb Bb C# 		G  F  D  A  F# B     N.O.
5x/p/4/7:............B  Eb G  F# C# E  Bb 		Ab F  C  A  D        N.O. 
   
5x/p/1/8:............C  E  Eb Bb C# G  		F  D  A  F# B  Ab 
5x/p/4/8:............Eb G  F# C# E  Bb 		Ab F  C  A  D  B  
5x/p/7/8:............F# Bb A  E  G  C# 		B  Ab Eb C  F  D  
5x/p/10/8:...........A  C# C  G  Bb E  		D  B  F# Eb Ab F  
   
5x/p/6/9:............A  Ab Eb F# C  			Bb G  D  B  E  C# F  N.O.
5x/p/7/9:............Bb A  E  G  C# 			B Ab Eb C  F  D  F#  nice side-step pair with above
5x/p/10/9:...........C# C  G  Bb E  			D  B  F# Eb Ab F  A  
   
5x/p/4/10:...........F# C# E  Bb Ab 			F  C  A  D  B  Eb G  N.O.
5x/p/9/10:...........B  F# A  Eb C# 			Bb F  D  G  E  Ab C  N.O.
   
5x/p/0/11:...........A  C  F# E  C# Ab 		F  Bb G  B  Eb D     N.O.
5x/p/6/11:...........Eb F# C  Bb G  			D  B  E  C# F  A  Ab 
5x/p/9/11:...........F# A  Eb C# Bb 			F  D  G  E  Ab C  B  
   
5x/i/7/0:............G  C# Eb F# B  			D  A  C  Ab E  F  Bb N.O.
   
5x/i/2/2:............Bb C# F# A  E  G  Eb 		B  C  F  D  Ab 
5x/i/5/2:............C# E  A  C  G  Bb F# 		D  Eb Ab F  B  
5x/i/8/2:............E  G  C  Eb Bb C# A  		F  F# B  Ab D  
5x/i/11/2:...........G  Bb Eb F# C# E  C  		Ab A  D  B  F  
   
5x/i/4/3:............Eb Ab B  F# A  			F  C# D  G  E  Bb C   N.O.

5x/i/2/4:............F# A  E  G  Eb B  		C  F  D  Ab Bb C#     N.O.
5x/i/5/4:............A  C  G  Bb F# 			D  Eb Ab F  B  C# E  
5x/i/8/4:............C  Eb Bb C# A  			F  F# B  Ab D  E  G  
5x/i/11/4:...........Eb F# C# E  C  Ab A  		D  B  F  G  Bb        N.O.
   
5x/i/11/5:...........F# C# E  C  Ab A  		D  B  F  G  Bb Eb 
5x/i/3/7:............Ab E  C  C# F# Eb A  		B  D  G  Bb F  
5x/i/6/7:............B  G  Eb E  A  F# C  		D  F  Bb C# Ab 
   
5x/i/0/8:............C# A  Bb Eb C  F# 		Ab B  E  G  D  F  
5x/i/3/8:............E  C  C# F# Eb A  		B  D  G  Bb F  Ab 
5x/i/6/8:............G  Eb E  A  F# C  		D  F  Bb C# Ab B  
5x/i/9/8:............Bb F# G  C  A  Eb 		F  Ab C# E  B  D  
   
5x/i/0/9:............A  Bb Eb C  F# 			Ab B  E  G  D  F  C# 
5x/i/1/9:............Bb B  E  C# G  			A  C  F  Ab Eb F# D  
5x/i/6/9:............Eb E  A  F# C  			D  F  Bb C# Ab B  G  
5x/i/9/9:............F# G  C  A  Eb 			F  Ab C# E  B  D  Bb 
   
5x/i/3/10:...........C# F# Eb A  B  			D  G  Bb F  Ab E  C    N.O.
5x/i/10/10:..........Ab C# Bb E  F# 			A  D  F  C  Eb B  G    N.O.
5x/i/1/11:...........E  C# G  A  C  			F Ab Eb F# D  Bb B  
5x/i/7/11:...........Bb G  C# Eb F# B  		D  A  C  Ab E  F       N.O.
5x/i/10/11:..........C# Bb E  F# A  			D  F  C  Eb B  G  Ab 
   

---------------------------------------------------------

10 --c#,a,bb,c -- 0,1,3,4/

p/8/3:...............C# C  A  Bb 		G  Eb B  F# F  Ab D  E
i/2/3:...............A  Bb C# C  		Eb G  B  E  F  D  Ab F#


p/2/2:...............Bb G  F# Eb E  C# A  		F  C  B  D  Ab 
p/5/2:...............C# Bb A  F# G  E  C  		Ab Eb D  F  B  
p/8/2:...............E  C# C  A  Bb G  Eb 		B  F# F  Ab D  
p/11/2:..............G  E  Eb C  C# Bb F# 		D  A  Ab B  F  
   	
p/0/8:...............G  Eb Bb A  C  F# 		Ab F  E  C# D  B  
p/3/8:...............Bb F# C# C  Eb A  		B  Ab G  E  F  D  
p/6/8:...............C# A  E  Eb F# C  		D  B  Bb G  Ab F  
p/9/8:...............E  C  G  F# A  Eb 		F  D  C# Bb B  Ab 
      
p/7/10:..............F  E  G  C# Eb C  		B  Ab A  F# D  Bb   not good cell, but nice line
p/1/11:..............Bb C# G  A  F# F  		D  Eb C  Ab E  B  
   
   
i/2/2:...............F# A  Bb C# C  Eb G  		B  E  F  D  Ab 
i/5/2:...............A  C  C# E  Eb F# Bb 		D  G  Ab F  B  
i/8/2:...............C  Eb E  G  F# A  C# 		F  Bb B  Ab D  
i/11/2:..............Eb F# G  Bb A  C  E  		Ab C# D  B  F  
   
i/1/8:...............F# Bb Eb E  C# G  		F  Ab A  C  B  D  
i/4/8:...............A  C# F# G  E  Bb 		Ab B  C  Eb D  F  
i/7/8:...............C  E  A  Bb G  C# 		B  D  Eb F# F  Ab 
i/10/8:..............Eb G  C  C# Bb E  		D  F  F# A  Ab B  
    
i/9/11:..............C  A  Eb C# E  			F  Ab G  Bb D  F# B  
   

5x/p/2/2:............F# Eb Bb G  C  A  C# 		F  E  B  D  Ab 
5x/p/5/2:............A  F# C# Bb Eb C  E  		Ab G  D  F  B  
5x/p/8/2:............C  A  E  C# F# Eb G  		B  Bb F  Ab D  
   
5x/p/10/7:...........F  A  C# C  G  Bb E  		D  B  F# Eb Ab 
   

5x/p/1/8:............C  E  Eb Bb C# G  		F  D  A  F# B  Ab 
5x/p/4/8:............Eb G  F# C# E  Bb 		Ab F  C  A  D  B  
5x/p/7/8:............F# Bb A  E  G  C# 		B  Ab Eb C  F  D  
5x/p/10/8:...........A  C# C  G  Bb E  		D  B  F# Eb Ab F  
   

5x/p/1/9:............E  Eb Bb C# G  			F  D  A  F# B  Ab C  
5x/p/3/9:............F# F  C  Eb A  			G  E  B  Ab C# Bb D  
   
5x/p/9/11:...........F# A  Eb C# Bb F  		D  G  E  Ab C  B  N.O.
   

5x/i/2/2:............Bb C# F# A  E  G  Eb 		B  C  F  D  Ab 
5x/i/5/2:............C# E  A  C  G  Bb F# 		D  Eb Ab F  B  
5x/i/8/2:............E  G  C  Eb Bb C# A  		F  F# B  Ab D  
5x/i/11/2:...........G  Bb Eb F# C# E  C  		Ab A  D  B  F  
   

5x/i/2/3:............C# F# A  E  G  Eb 		B  C  F  D  Ab Bb 
5x/i/5/3:............E  A  C  G  Bb F# 		D  Eb Ab F  B  C# 
5x/i/8/3:............G  C  Eb Bb C# A  F  		F# B  Ab D  E  
5x/i/11/3:...........Bb Eb F# C# E  C  		Ab A  D  B  F  G  
 

10 --c#,a,bb,c -- 0,1,3,4/

  

5x/i/8/4:............C  Eb Bb C# A  			F  F# B  Ab D  E  G  
	
 
5x/i/0/7:............F  C# A  Bb Eb C  F# 		Ab B  E  G  D  
 
   
5x/i/3/8:............E  C  C# F# Eb A  		B  D  G  Bb F  Ab 
5x/i/6/8:............G  Eb E  A  F# C  		D  F  Bb C# Ab B  
5x/i/9/8:............Bb F# G  C  A  Eb 		F Ab C# E  B  D      Nice line down to F
   

5x/i/1/11:...........E  C# G  A  C  F  		Ab Eb F# D  Bb B  
   
---------------------------------------------------------

11 --e,c,a,e   -- 0,3,7/

i/11/6:..............A  C  E  		Ab C# D  B  F  Eb F# G  Bb
i/7/8:...............C  E  A  		Bb G  C# B  D  Eb F# F  Ab 

5x/p/8/2:............C  A  E  		C# F# Eb G  B  Bb F  Ab D  
5x/i/5/3:............E  A  C  		G  Bb F# D  Eb Ab F  B  C# 

 
p/2/8:...............A  F  C  B  D  Ab 		Bb G  F# Eb E  C#




Complete cycles that (mostly) spare A-C-E.

These have non-harm tones that approach harm tones, rather
than crossing over them:   Bb--A, rather than Bb-Ab.



?ex forms: 5p 5x5p r ri

?ex pit prox7 pos0,1,2,3,4,5:g#,a#
?ex pit prox7 pos0,1,2,3,4,5:b,c#
?ex pit prox7 pos0,1,2,3,4,5:d#,f
?ex pit prox7 pos0,1,2,3,4,5:g#,g
?ex pit prox7 pos0,1,2,3,4,5:b,bb
?ex pit prox7 pos0,1,2,3,4,5:d#,d
?ex pit prox7 pos0,1,2,3,4,5:f,f# 
?ex pit prox7 pos0,1,2,3,4,5:c#,d

 
p/7/2:...............Eb C  B  Ab A  F# D  Bb F  E  G  C# 
   
p/8/2:...............E  C# C  A  Bb G  Eb B  F# F  Ab D  

p/11/2:..............G  E  Eb C  C# Bb F# D  A  Ab B  F  
   
p/0/8:...............G  Eb Bb A  C  F# Ab F  E  C# D  B  
     
i/2/3:...............A  Bb C# C  Eb G  B  E  F  D  Ab F#   borderline?
   
5x/p/2/2:............F# Eb Bb G  C  A  C# F  E  B  D  Ab   maybe
 
5x/p/8/2:............C  A  E  C# F# Eb G  B  Bb F  Ab D  
    
5x/p/1/8:............C  E  Eb Bb C# G  F  D  A  F# B  Ab 
   
5x/p/0/11:...........A  C  F# E  C# Ab F  Bb G  B  Eb D  

5x/p/3/11:...........C  Eb A  G  E  B  Ab C# Bb D  F# F  
    
5x/i/4/2:............C  Eb Ab B  F# A  F  C# D  G  E  Bb 
        
5x/i/8/3:............G  C  Eb Bb C# A  F  F# B  Ab D  E  
   
5x/i/5/4:............A  C  G  Bb F# D  Eb Ab F  B  C# E  
 
5x/i/11/7:...........E  C  Ab A  D  B  F  G  Bb Eb F# C#   
   
5x/i/6/7:............B  G  Eb E  A  F# C  D  F  Bb C# Ab   
   
5x/i/0/8:............C# A  Bb Eb C  F# Ab B  E  G  D  F  
 
5x/i/3/8:............E  C  C# F# Eb A  B  D  G  Bb F  Ab
   
5x/i/1/11:...........E  C# G  A  C  F  Ab Eb F# D  Bb-B  


=========================================================
=========================================================
=========================================================
=========================================================
=========================================================


17

ATTEMPT AT CONTINUING SELF-SIMILAR EMBEDDING




C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb   good    6,2,3,5,3,7,3,8,8,1,5,(9)
F#, C,  D,  F,  Bb, C#, G#, B,  G,  Eb, E,  A
E,  Bb, C,  Eb, G#, B,  F#, A,  F,  C#, D,  G
C#, G,  A,  C,  F,  G#, Eb, F#, D,  Bb, B,  E
G#, D,  E,  G,  C,  Eb, Bb, C#, A,  F,  F#, B
F,  B,  C#, E,  A,  C,  G,  Bb, F#, D,  Eb, G#
Bb, E,  F#, A,  D,  F,  C,  Eb, B,  G,  G#, C#
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
B,  F,  G,  Bb, Eb, F#, C#, E,  C,  G#, A,  D
Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
A,  Eb, F,  G#, C#, E,  B,  D,  Bb, F#, G,  C




C..F#.G#.B..E..G..D..F..C#.A..Bb.Eb.
...............g........c#.......eb.
...f#....b........d........a........
c.....g#....e........f........bb



..................D.................
......G#......................Bb....
........................C#..........
...F#......................A........
............E.......................
...............G.................Eb.
.........B..........................
C....................F



...............D........G#.......Bb.........
G  C# Eb F# B  D  A  C  G# E  F  Bb      |G   
d  a  c  g# e  f  bb       g  c# eb f# b |d
f  bb       g  c# eb f# b  d  a  c  g# e |f



...C#....F#.......A........E................
G  C# Eb F# B  D  A  C  G# E  F  Bb      |G   
d  a  c  g# e  f  bb       g  c# eb f# b |d
f  bb       g  c# eb f# b  d  a  c  g# e |f



G.....Eb....B........C........F
G  C# Eb F# B  D  A  C  G# E  F  Bb      |G   
d  a  c  g# e  f  bb       g  c# eb f# b |d
f  bb       g  c# eb f# b  d  a  c  g# e |f





------------------------------------------------------------------------------------------------------------------
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
a,  eb, f,  g#, c#, e,  b,  d,  bb, f#, g,  c


C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, a,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb                                    
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb                                            
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb  C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb




C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb    
F#, C,  D,  F,  Bb, C#, G#, B,  G,  Eb, E,  A
E,  Bb, C,  Eb, G#, B,  F#, A,  F,  C#, D,  G
C#, G,  A,  C,  F,  G#, Eb, F#, D,  Bb, B,  E
G#, D,  E,  G,  C,  Eb, Bb, C#, A,  F,  F#, B
F,  B,  C#, E,  A,  C,  G,  Bb, F#, D,  Eb, G#
Bb, E,  F#, A,  D,  F,  C,  Eb, B,  G,  G#, C#
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
B,  F,  G,  Bb, Eb, F#, C#, E,  C,  G#, A,  D
Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
A,  Eb, F,  G#, C#, E,  B,  D,  Bb, F#, G,  C


------------------------------------------------------------------------------------------------------------------



1  2  3  4  5  6  7  8  9  10 11 12    (36 beats total)
13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36 
C..F#.G#.B..E..G..D..F..C#.A..Bb.Eb.
...............g........c#.......eb.
...f#....b........d........a........
c.....g#....e........f........bb




6  9  12 14 16 19 22 25 27 29  32  35  (108 beats total)
42 45 48 50 52 55 58 61 63 65  68  71
78 81 84 86 88 91 94 97 99 101 104 107
G..C#.D#.F#.B..D..A..C..G#.E...F...Bb.
...............d........g#.........bb.
...c#....f#.......a........e..........
g.....d#....b........c.........f......



19  27  35  45  50  58  65  78  84  88  97  104  (324 beats total)
D...G#..Bb..C#..F#..A...E...G...D#..B...C...F..
....................a...........d#..........f..
....g#......c#..........e...........b..........
d.......bb......f#..........g...........c......



58  84  104 135 153 173 196 235 251 266 294 313  (972 beats total) 
A...D#..F...G#..C#..E...B...D...A#..F#..G...C..
....................e...........a#..........c..
....d#......g#..........b...........f#.........
a.......f.......c#..........d...........g......




RI:

C..F#.G#.B..E..G..D..F..C#.A..Bb.Eb.
...f#....b.........................
c.....g#....e..g..d..f........bb


C..F#.G#.B..E..G..D..F..C#.A..Bb.Eb.
.........b..e........f..c#.a........
c..............g..............bb.eb.
...f#.g#..........d

=========================================================
=========================================================
=========================================================
=========================================================
=========================================================
Original

C,  F#, G#, F,  E,  C#, D,  B,  G,  Eb, Bb, A            6,2,9,11,9,1,9,8,8,7,11,(3)
F#, C,  D,  B,  Bb, G,  G#, F,  C#, A,  E,  Eb
E,  Bb, C,  A,  G#, F,  F#, Eb, B,  G,  D,  C#
G,  C#, Eb, C,  B,  G#, A,  F#, D,  Bb, F,  E
G#, D,  E,  C#, C,  A,  Bb, G,  Eb, B,  F#, F  
B,  F,  G,  E,  Eb, C,  C#, Bb, F#, D,  A,  G#
Bb, E,  F#, Eb, D,  B,  C,  A,  F,  C#, G#, G
C#, G,  A,  F#, F,  D,  Eb, C,  G#, E,  B,  Bb
F,  B,  C#, Bb, A,  F#, G,  E,  C,  G#, Eb, D
A,  Eb, F,  D,  C#, Bb, B,  G#, E,  C,  G,  F#
D,  G#, Bb, G,  F#, Eb, E,  C#, A,  F,  C,  B
Eb, A,  B,  G#, G,  E,  F,  D,  Bb, F#, C#, C



                                    inversion intervals: 6,10,3,1,3,11,3,4,4,5,1,(9)

------------------------------------------------------

5m                               5m inversion intervals: 6,10,9,7,9,5,9,4,4,11,7,(3)
 
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb   good    6,2,3,5,3,7,3,8,8,1,5,(9)
F#, C,  D,  F,  Bb, C#, G#, B,  G,  Eb, E,  A
E,  Bb, C,  Eb, G#, B,  F#, A,  F,  C#, D,  G
C#, G,  A,  C,  F,  G#, Eb, F#, D,  Bb, B,  E
G#, D,  E,  G,  C,  Eb, Bb, C#, A,  F,  F#, B
F,  B,  C#, E,  A,  C,  G,  Bb, F#, D,  Eb, G#
Bb, E,  F#, A,  D,  F,  C,  Eb, B,  G,  G#, C#
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
B,  F,  G,  Bb, Eb, F#, C#, E,  C,  G#, A,  D
Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
A,  Eb, F,  G#, C#, E,  B,  D,  Bb, F#, G,  C

------------------------------------------------------------------------------

18

Combinations of 5m, I, P, to make Perm Matrices:  



Some Ok results:


C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
F,  D,  Eb, E,  C#, A,  Bb, G#, G,  C,  B,  F#
G#, Bb, F#, C#, G,  C,  B,  Eb, A,  F,  E,  D
Eb, B,  D,  G,  A,  F,  E,  F#, C,  G#, C#, Bb
F#, E,  Bb, A,  C,  G#, C#, D,  F,  Eb, G,  B
D,  C#, B,  C,  F,  Eb, G,  Bb, G#, F#, A,  E
Bb, G,  E,  F,  G#, F#, A,  B,  Eb, D,  C,  C#
B,  A,  C#, G#, Eb, D,  C,  E,  F#, Bb, F,  G
E,  C,  G,  Eb, F#, Bb, F,  C#, D,  B,  G#, A
C#, F,  A,  F#, D,  B,  G#, G,  Bb, E,  Eb, C
G,  G#, C,  D,  Bb, E,  Eb, A,  B,  C#, F#, F
A,  Eb, F,  Bb, B,  C#, F#, C,  E,  G,  D,  G#



C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
G,  D,  F,  C#, A,  Bb, Eb, B,  E,  C,  F#, G#
Bb, Eb, B,  E,  C,  F#, G#, C#, A,  G,  D,  F
F#, G#, C#, A,  G,  D,  F,  E,  C,  Bb, Eb, B
D,  F,  E,  C,  Bb, Eb, B,  A,  G,  F#, G#, C#
Eb, B,  A,  G,  F#, G#, C#, C,  Bb, D,  F,  E
G#, C#, C,  Bb, D,  F,  E,  G,  F#, Eb, B,  A
F,  E,  G,  F#, Eb, B,  A,  Bb, D,  G#, C#, C
B,  A,  Bb, D,  G#, C#, C,  F#, Eb, F,  E,  G
C#, C,  F#, Eb, F,  E,  G,  D,  G#, B,  A,  Bb
E,  G,  D,  G#, B,  A,  Bb, Eb, F,  C#, C,  F#
A,  Bb, Eb, F,  C#, C,  F#, G#, B,  E,  G,  D



col: Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
C#, Eb, E,  D,  C,  Bb, G,  G#, F#, B,  F,  A
F#, A,  C,  G,  C#, F,  Bb, E,  Eb, D,  G#, B
Eb, B,  C#, Bb, F#, G#, F,  C,  A,  G,  E,  D
A,  D,  F#, F,  Eb, E,  G#, C#, B,  Bb, C,  G
B,  G,  Eb, G#, A,  C,  E,  F#, D,  F,  C#, Bb
D,  Bb, A,  E,  B,  C#, C,  Eb, G,  G#, F#, F
G,  F,  B,  C,  D,  F#, C#, A,  Bb, E,  Eb, G#
Bb, G#, D,  C#, G,  Eb, F#, B,  F,  C,  A,  E
F,  E,  G,  F#, Bb, A,  Eb, D,  G#, C#, B,  C
G#, C,  Bb, Eb, F,  B,  A,  G,  E,  F#, D,  C#
E,  C#, F,  A,  G#, D,  B,  Bb, C,  Eb, G,  F#



col: F,B,A,F#,C#,Bb,Eb,C,E,G#,G,D
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
E,  C#, G,  A,  G#, D,  F,  B,  Bb, F#, Eb, C
G#, Bb, D,  F#, G,  F,  B,  A,  Eb, C#, C,  E
G,  Eb, F,  C#, D,  B,  A,  F#, C,  Bb, E,  G#
D,  C,  B,  Bb, F,  A,  F#, C#, E,  Eb, G#, G
F,  E,  A,  Eb, B,  F#, C#, Bb, G#, C,  G,  D
B,  G#, F#, C,  A,  C#, Bb, Eb, G,  E,  D,  F
A,  G,  C#, E,  F#, Bb, Eb, C,  D,  G#, F,  B
F#, D,  Bb, G#, C#, Eb, C,  E,  F,  G,  B,  A
C#, F,  Eb, G,  Bb, C,  E,  G#, B,  D,  A,  F#
Bb, B,  C,  D,  Eb, E,  G#, G,  A,  F,  F#, C#
Eb, A,  E,  F,  C,  G#, G,  D,  F#, B,  C#, Bb



col: A,Eb,C#,Bb,F,D,G,E,G#,C,B,F#
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb    ********   This one is good.
B,  A,  C,  F#, G#, E,  G,  D,  Bb, Eb, F,  C#
F#, Eb, B,  A,  C,  G#, E,  G,  F,  C#, D,  Bb
A,  C#, F#, Eb, B,  C,  G#, E,  D,  Bb, G,  F
Eb, Bb, A,  C#, F#, B,  C,  G#, G,  F,  E,  D
C#, F,  Eb, Bb, A,  F#, B,  C,  E,  D,  G#, G
Bb, D,  C#, F,  Eb, A,  F#, B,  G#, G,  C,  E
F,  G,  Bb, D,  C#, Eb, A,  F#, C,  E,  B,  G#
D,  E,  F,  G,  Bb, C#, Eb, A,  B,  G#, F#, C
G,  G#, D,  E,  F,  Bb, C#, Eb, F#, C,  A,  B
E,  C,  G,  G#, D,  F,  Bb, C#, A,  B,  Eb, F#
G#, B,  E,  C,  G,  D,  F,  Bb, Eb, F#, C#, A



col: Bb,E,D,B,F#,Eb,G#,F,A,C#,C,G
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
G,  Eb, F,  F#, D,  Bb, B,  A,  C,  C#, E,  G#
Bb, G#, A,  Eb, B,  E,  F#, C#, G,  C,  D,  F
E,  F,  C#, G#, F#, D,  Eb, C,  Bb, G,  B,  A
D,  A,  C,  F,  Eb, B,  G#, G,  E,  Bb, F#, C#
B,  C#, G,  A,  G#, F#, F,  Bb, D,  E,  Eb, C
F#, C,  Bb, C#, F,  Eb, A,  E,  B,  D,  G#, G
Eb, G,  E,  C,  A,  G#, C#, D,  F#, B,  F,  Bb
G#, Bb, D,  G,  C#, F,  C,  B,  Eb, F#, A,  E
F,  E,  B,  Bb, C,  A,  G,  F#, G#, Eb, C#, D
A,  D,  F#, E,  G,  C#, Bb, Eb, F,  G#, C,  B
C#, B,  Eb, D,  Bb, C,  E,  G#, A,  F,  G,  F#


=========================================================
=========================================================
=========================================================
=========================================================
=========================================================

19


"Group-Preserving" Permutation Matrices with orig row as first line



*4-note groups*

?pit errs: 0 to 3
?ex forms: 5p 5x5p
?inc all pos0,3,6,9:c,f#,g#,b
?inc all pos1,4,7,10:e,g,d,f
?inc all pos2,5,8,11:c#,a,bb,eb


p/5/2:...............c# E  A  C  G  Bb F# D  Eb Ab F  b   -- good swap -- b,c#

ri/4/1:..............F# G  Eb B  D  A  C  F  ab ab E  C#  -- good swap -- ab,bb


5x/p/7/2:............B  D  Eb F# F  ab C  E  A  bb G  C# 
5x/ri/2/1:...........C  F  A  c# E  Eb F# G  Bb Ab D  b  




col: B,E,A,C,G,Bb,F#,D,Eb,G#,F,C#
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
G,  D,  F,  E,  A,  Bb, Eb, C#, B,  C,  F#, G#
Bb, Eb, C#, A,  C,  F#, G#, B,  E,  G,  D,  F
F#, G#, B,  C,  G,  D,  F,  E,  A,  Bb, Eb, C#  •
D,  F,  E,  G,  Bb, Eb, C#, A,  C,  F#, G#, B
Eb, C#, A,  Bb, F#, G#, B,  C,  G,  D,  F,  E
G#, B,  C,  F#, D,  F,  E,  G,  Bb, Eb, C#, A   •
F,  E,  G,  D,  Eb, C#, A,  Bb, F#, G#, B,  C
C#, A,  Bb, Eb, G#, B,  C,  F#, D,  F,  E,  G
B,  C,  F#, G#, F,  E,  G,  D,  Eb, C#, A,  Bb  •
E,  G,  D,  F,  C#, A,  Bb, Eb, G#, B,  C,  F#
A,  Bb, Eb, C#, B,  C,  F#, G#, F,  E,  G,  D

=========================================================
=========================================================
------------------------------------------------------
------------------------------------------------------


20


Doh a Deer -- sequences

5m
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb   good    6,2,3,5,3,7,3,8,8,1,5,(9)

----------------------------------------------------------------------------------

5m     G,  D,  F,  C#, A,  Bb,		Eb, C,  F#, G#, B,  E,    This is ok.
       (g,a,bb,c#,d,f)                (f#,g#,b,c,d#,e)


G,  D,  F,  C#, A,  Bb,		Eb, C,  F#, G#, B,  E,

A,  F,  G,  D,  Bb, C#,		E,  D#, G#, B,  C,  F#,

Bb, G,  A,  F,  C#, D,        F#, E,  B,  C,  D#, G#,

C#, A,  Bb, G,  D,  F,        G#, F#, C,  D#, E,  B,

D,  Bb, C#, A,  F,  G,        B,  G#, D#, E,  F#, C,

F,  C#, D,  Bb, G,  A,        C,  B,  E,  F#, G#, Eb

----------------------------------------------------------------------------------

----------------------------------------------------------------------------------
Let's try to get the desired effect by 6-note group-to-group


C,  F#, G#, B,  E,  G,  			D,  F,  C#, A,  Bb, Eb 


column?  g#,bb,c,d,e,f,g,a,b,c#,f#,eb?


f#,eb


p/1/1:...............G  A  C  F  Ab Eb F# D  bb-b  E  C#   great -- just exp. with swap


i/8/0:...............Ab D  C  A  E  C# F# Eb G  b--bb F


1) as is
2) bb-b swapped for complete group-to-group


1)as is: p/1/1

col: G,A,C,F,G#,Eb,F#,D,Bb,B,E,C#
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
F,  D,  Eb, E,  C#, A,  Bb, G#, G,  C,  B,  F#
G#, Bb, F#, C#, G,  C,  B,  Eb, A,  F,  E,  D
Eb, B,  D,  G,  A,  F,  E,  F#, C,  G#, C#, Bb
F#, E,  Bb, A,  C,  G#, C#, D,  F,  Eb, G,  B
D,  C#, B,  C,  F,  Eb, G,  Bb, G#, F#, A,  E
Bb, G,  E,  F,  G#, F#, A,  B,  Eb, D,  C,  C#
B,  A,  C#, G#, Eb, D,  C,  E,  F#, Bb, F,  G
E,  C,  G,  Eb, F#, Bb, F,  C#, D,  B,  G#, A
C#, F,  A,  F#, D,  B,  G#, G,  Bb, E,  Eb, C
G,  G#, C,  D,  Bb, E,  Eb, A,  B,  C#, F#, F
A,  Eb, F,  Bb, B,  C#, F#, C,  E,  G,  D,  G#

--------------------
2) bb-b swapped for complete group-to-group

col: G,A,C,F,G#,Eb,F#,D,B,Bb,E,C#
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
F,  D,  Eb, Bb, C#, A,  B,  G#, G,  C,  E,  F#
G#, B,  F#, E,  G,  C,  Bb, Eb, A,  F,  C#, D
Eb, Bb, D,  C#, A,  F,  E,  F#, C,  G#, G,  B
F#, E,  B,  G,  C,  G#, C#, D,  F,  Eb, A,  Bb
D,  C#, Bb, A,  F,  Eb, G,  B,  G#, F#, C,  E
B,  G,  E,  C,  G#, F#, A,  Bb, Eb, D,  F,  C#
Bb, A,  C#, F,  Eb, D,  C,  E,  F#, B,  G#, G
E,  C,  G,  G#, F#, B,  F,  C#, D,  Bb, Eb, A
C#, F,  A,  Eb, D,  Bb, G#, G,  B,  E,  F#, C
G,  G#, C,  F#, B,  E,  Eb, A,  Bb, C#, D,  F
A,  Eb, F,  D,  Bb, C#, F#, C,  E,  G,  B,  G#



1) as is: i/8/0:

col: G#,D,C,A,E,C#,F#,Eb,G,B,Bb,F                           
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
A,  Eb, D,  Bb, C#, B,  C,  G#, F#, E,  F,  G
E,  G,  C,  F,  F#, Bb, A,  D,  Eb, C#, G#, B
C#, B,  A,  G#, Eb, F,  E,  C,  G,  F#, D,  Bb
F#, Bb, E,  D,  G,  G#, C#, A,  B,  Eb, C,  F
Eb, F,  C#, C,  B,  D,  F#, E,  Bb, G,  A,  G#
G,  G#, F#, A,  Bb, C,  Eb, C#, F,  B,  E,  D
B,  D,  Eb, E,  F,  A,  G,  F#, G#, Bb, C#, C
Bb, C,  G,  C#, G#, E,  B,  Eb, D,  F,  F#, A
F,  A,  B,  F#, D,  C#, Bb, G,  C,  G#, Eb, E
G#, E,  Bb, Eb, C,  F#, F,  B,  A,  D,  G,  C#
D,  C#, F,  G,  A,  Eb, G#, Bb, E,  C,  B,  F#


2) bb-b swapped


col: G#,D,C,A,E,C#,F#,Eb,G,Bb,B,F
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
A,  Eb, D,  F,  C#, Bb, C,  G#, F#, E,  B,  G
E,  G,  C,  G#, F#, B,  A,  D,  Eb, C#, F,  Bb
C#, Bb, A,  D,  Eb, F,  E,  C,  G,  F#, G#, B
F#, B,  E,  C,  G,  G#, C#, A,  Bb, Eb, D,  F
Eb, F,  C#, A,  Bb, D,  F#, E,  B,  G,  C,  G#
G,  G#, F#, E,  B,  C,  Eb, C#, F,  Bb, A,  D
Bb, D,  Eb, C#, F,  A,  G,  F#, G#, B,  E,  C
B,  C,  G,  F#, G#, E,  Bb, Eb, D,  F,  C#, A
F,  A,  Bb, Eb, D,  C#, B,  G,  C,  G#, F#, E
G#, E,  B,  G,  C,  F#, F,  Bb, A,  D,  Eb, C#
D,  C#, F,  Bb, A,  Eb, G#, B,  E,  C,  G,  F#


===================================================
attempt at g-to-g with smooth interval sizes  
 

*  maybe see if limited-interval cycles can be partitioned into group-to-group?


user row: 0,3,6,8,10,1,4,7,9,11,2,5


C,Eb,F#,G#,Bb,C#,E,G,A,B,D,F

5m     G,  D,  F,  C#, A,  Bb,		Eb, C,  F#, G#, B,  E,    This is ok.


p/2/1:...............F  Ab Bb C  eb F# A  B  C# E  G  d

p/6/1:...............A  C  D  E  G  bb C# Eb F  Ab b  F# 

i/7/0:...............G  E  C# B  A  F# eb C  Bb Ab F  d

i/11/0:..............b  Ab F  Eb C# bb G  E  D  C  A  F# 


G,  D,  F,  C#, A,  Bb, Eb, C,  F#, G#, B,  E
Eb, F#, G#, E,  B,  C,  F,  D,  A,  Bb, C#, G
F,  A,  Bb, G,  C#, D,  G#, F#, B,  C,  E,  Eb
G#, B,  C,  Eb, E,  F#, Bb, A,  C#, D,  G,  F
Bb, C#, D,  F,  G,  A,  C,  B,  E,  F#, Eb, G#
C,  E,  F#, G#, Eb, B,  D,  C#, G,  A,  F,  Bb
D,  G,  A,  Bb, F,  C#, F#, E,  Eb, B,  G#, C
F#, Eb, B,  C,  G#, E,  A,  G,  F,  C#, Bb, D
A,  F,  C#, D,  Bb, G,  B,  Eb, G#, E,  C,  F#
B,  G#, E,  F#, C,  Eb, C#, F,  Bb, G,  D,  A
C#, Bb, G,  A,  D,  F,  E,  G#, C,  Eb, F#, B
E,  C,  Eb, B,  F#, G#, G,  Bb, D,  F,  A,  C#



col: A,C,D,E,G,B,C#,Eb,F,G#,Bb,F#
dhv: 

G,  D,  F,  C#, A,  Bb, Eb, C,  F#, G#, B,  E
B,  E,  G#, Eb, C,  F#, F,  D,  A,  Bb, C#, G
C#, G,  Bb, F,  D,  A,  G#, E,  C,  F#, Eb, B
Eb, B,  F#, G#, E,  C,  Bb, G,  D,  A,  F,  C#
F,  C#, A,  Bb, G,  D,  F#, B,  E,  C,  G#, Eb
G#, Eb, C,  F#, B,  E,  A,  C#, G,  D,  Bb, F
Bb, F,  D,  A,  C#, G,  C,  Eb, B,  E,  F#, G#
F#, G#, E,  C,  Eb, B,  D,  F,  C#, G,  A,  Bb
A,  Bb, G,  D,  F,  C#, E,  G#, Eb, B,  C,  F#
C,  F#, B,  E,  G#, Eb, G,  Bb, F,  C#, D,  A
D,  A,  C#, G,  Bb, F,  B,  F#, G#, Eb, E,  C
E,  C,  Eb, B,  F#, G#, C#, A,  Bb, F,  G,  D




G,  D,  F,  C#, A,  Bb, Eb, C,  F#, G#, B,  E
E,  C,  Eb, B,  F#, G#, G,  Bb, D,  F,  A,  C#
C#, Bb, G,  A,  D,  F,  E,  G#, C,  Eb, F#, B
B,  G#, E,  F#, C,  Eb, C#, F,  Bb, G,  D,  A
A,  F,  C#, D,  Bb, G,  B,  Eb, G#, E,  C,  F#
F#, Eb, B,  C,  G#, E,  A,  G,  F,  C#, Bb, D
D,  G,  A,  Bb, F,  C#, F#, E,  Eb, B,  G#, C
C,  E,  F#, G#, Eb, B,  D,  C#, G,  A,  F,  Bb
Bb, C#, D,  F,  G,  A,  C,  B,  E,  F#, Eb, G#
G#, B,  C,  Eb, E,  F#, Bb, A,  C#, D,  G,  F
F,  A,  Bb, G,  C#, D,  G#, F#, B,  C,  E,  Eb
Eb, F#, G#, E,  B,  C,  F,  D,  A,  Bb, C#, G



col: Bb,G#,F,Eb,C#,B,G,E,D,C,A,F#
dhv: 

G,  D,  F,  C#, A,  Bb, Eb, C,  F#, G#, B,  E
E,  C,  Eb, B,  F#, G#, C#, A,  Bb, F,  G,  D
D,  A,  C#, G,  Bb, F,  B,  F#, G#, Eb, E,  C
C,  F#, B,  E,  G#, Eb, G,  Bb, F,  C#, D,  A
A,  Bb, G,  D,  F,  C#, E,  G#, Eb, B,  C,  F#
F#, G#, E,  C,  Eb, B,  D,  F,  C#, G,  A,  Bb
Bb, F,  D,  A,  C#, G,  C,  Eb, B,  E,  F#, G#
G#, Eb, C,  F#, B,  E,  A,  C#, G,  D,  Bb, F
F,  C#, A,  Bb, G,  D,  F#, B,  E,  C,  G#, Eb
Eb, B,  F#, G#, E,  C,  Bb, G,  D,  A,  F,  C#
C#, G,  Bb, F,  D,  A,  G#, E,  C,  F#, Eb, B
B,  E,  G#, Eb, C,  F#, F,  D,  A,  Bb, C#, G



 
------------------------------------------------------
------------------------------------------------------

21

Casual Attempts at New Kinds of Alteration





Grid and User row the same:  Both are p/0.  Makes complete orbit with itself
 user row: C  F# G# B  E  G  D  F  C# A  Bb Eb 
 grid row: F# G# B  E  G  D  F  C# A  Bb Eb C  
    orbit: F# C  Eb Bb A  C# F  D  G  E  B  G# 
X-swapped: C# F  G  D  A  F# C  G# B  E  Eb Bb 
intervals: 4  2  7  7  9  6  8  3  5  11 7  3  


Row is original, column is "x-swapped" from above -- column is result of
x-swapped orbit of original with itself

col: C# F  G  D  A  F# C  G# B  E  Eb Bb
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
G#, C,  B,  E,  Eb, D,  A,  G,  F,  F#, C#, Bb
B,  G#, E,  Eb, Bb, A,  F#, D,  G,  C,  F,  C#
E,  B,  Eb, Bb, C#, F#, C,  A,  D,  G#, G,  F
Eb, E,  Bb, C#, F,  C,  G#, F#, A,  B,  D,  G
Bb, Eb, C#, F,  G,  G#, B,  C,  F#, E,  A,  D
C#, Bb, F,  G,  D,  B,  E,  G#, C,  Eb, F#, A
F,  C#, G,  D,  A,  E,  Eb, B,  G#, Bb, C,  F#
G,  F,  D,  A,  F#, Eb, Bb, E,  B,  C#, G#, C
D,  G,  A,  F#, C,  Bb, C#, Eb, E,  F,  B,  G#
A,  D,  F#, C,  G#, C#, F,  Bb, Eb, G,  E,  B
F#, A,  C,  G#, B,  F,  G,  C#, Bb, D,  Eb, E


-------------------------------------------------

output becomes input.  input is previous output plus 1 chromatic row

user row: C,C#,D,Eb,E,F,F#,G,G#,A,Bb,B

 user row: C  C# D  Eb E  F  F# G  G# A  Bb B  
 grid row: Eb Bb A  C# F  D  G  E  B  G# F# C  7,11,4,4,9,5,9,7,9,10,6,3  original
    orbit: Eb C  B  G# A  D  F  E  G  F# Bb C# 
X-swapped: C# B  F  C  G  F# A  G# Eb E  Bb D  10,6,7,7,11,3,11,7,1,6,4,11
intervals: 10 6  7  7  11 3  11 7  1  6  4  11 

----------
 user row: C  C# D  D# E  F  F# G  G# A  A# B  
 grid row: A# E  D# G# A  F# G  C  F  B  C# D  
    orbit: A# C  G  F# F  G# D# D  B  A  E  C# 
X-swapped: C# B  G  F# A# E  D# D  F  A  C  G# 
intervals: 10 8  11 4  6  11 11 3  4  3  8  5  


-------------
grid row: C#,B,G,F#,A#,E,D#,D,F,A,C,G#
user row: C,C#,D,D#,E,F,F#,G,G#,A,A#,B

 user row: C  C# D  D# E  F  F# G  G# A  A# B  
 grid row: F  D  D# E  A# F# G  B  C# G# C  A  
    orbit: F  C  A# E  D# D  C# G# A  B  G  F# 
X-swapped: C# F# F  E  D# C  B  A# G  G# D  A  
intervals: 5  11 11 11 9  11 11 9  1  6  7  4  

--------------


grid row: C#,F#,F,E,D#,C,B,A#,G,G#,D,A
user row: C,C#,D,D#,E,F,F#,G,G#,A,A#,B

 user row: C  C# D  D# E  F  F# G  G# A  A# B  
 grid row: E  D# C  B  A# G  G# D  A  C# F# F  
    orbit: E  C  D  G  F  B  D# C# A  G# F# A# 
X-swapped: C# G  D  F# C  E  A# D# A  G# B  F  
intervals: 6  7  4  6  4  6  5  6  11 3  6  8  

 user row: C  C# D  D# E  F  F# G  G# A  A# B  
 grid row: D  G# G  A# B  C  D# E  F  F# C# A  
    orbit: D  C  F  G# C# A# D# F# A  B  E  G  
X-swapped: C# E  C  F# A# D  G  B  D# G# F  A  
intervals: 3  8  6  4  4  5  4  4  5  9  4  4  

 user row: C  C# D  D# E  F  F# G  G# A  A# B  
 grid row: B  C  D# E  F  F# C# A  D  G# G  A# 
    orbit: B  C  C# F# F  E  D# D  G# A  G  A# 
X-swapped: C# D  G  F# F  E  D# A# G# A  B  C  
intervals: 1  5  11 11 11 11 7  10 1  2  1  1  

 user row: C  C# D  D# E  F  F# G  G# A  A# B  
 grid row: F  F# C# A  D  G# G  A# B  C  D# E  
    orbit: F  C  A  D# A# G  F# C# D  E  B  G# 
X-swapped: C# G  G# D# A  C  F# F  B  D  E  A# 
intervals: 6  1  7  6  3  6  11 6  3  2  6  3  


--------------












--------------
--------------
--------------
--------------
MORE SCREWING AROUND



0 3 6 8 A 1 4 7 9 B 2 5 	21.237 332233322337


user row: 0,3,6,8,10,1,4,7,9,11,2,5


------------------------------------------------------
 user row: 0  3  6  8  10 1  4  7  9  11 2  5  THIS ONE
 grid row: 7  8  9  10 11 0  1  2  3  4  5  6  
    orbit: 7  0  1  4  11 10 8  3  9  6  5  2  
X-swapped: 1  2  11 7  3  10 9  0  6  8  5  4  
intervals: 1  9  8  8  7  11 3  6  2  9  11 9  

------------------------------------------------------

C,Eb,F#,G#,Bb,C#,E,G,A,B,D,F



grid row: C,Eb,F#,G#,Bb,C#,E,G,A,B,D,F
user row: C,Eb,F#,G#,Bb,C#,E,G,A,B,D,F

 user row: C  Eb F# G# Bb C# E  G  A  B  D  F  
 grid row: Eb F# G# Bb C# E  G  A  B  D  F  C  
    orbit: Eb C  F  D  B  A  G  E  C# Bb G# F# 
X-swapped: C# G# Eb C  G  D  B  F# Bb F  A  E  
intervals: 7  7  9  7  7  9  7  4  7  4  7  9  

 user row: C  Eb F# G# Bb C# E  G  A  B  D  F  
 grid row: C# E  G  A  B  D  F  C  Eb F# G# Bb 
    orbit: C# C  G  F# B  Bb F  E  Eb A  G# D  
X-swapped: C# C  B  G# G  F# Eb D  Bb A  F  E  
intervals: 11 11 9  11 11 9  11 8  11 8  11 9  

 user row: C  Eb F# G# Bb C# E  G  A  B  D  F  
 grid row: G  A  B  D  F  C  Eb F# G# Bb C# E  
    orbit: G  C  C# D  G# A  Eb E  F  Bb B  F# 
X-swapped: C# D  Eb F# G  G# B  C  E  F  A  Bb 
intervals: 1  1  3  1  1  3  1  4  1  4  1  3  

 user row: C  Eb F# G# Bb C# E  G  A  B  D  F  
 grid row: F  C  Eb F# G# Bb C# E  G  A  B  D  
    orbit: F  C  Eb F# G# Bb C# E  G  A  B  D  
X-swapped: C# F# B  D  G  C  Eb G# E  A  F  Bb    This is input to second iteration
intervals: 5  5  3  5  5  3  5  8  5  8  5  3  


--------


grid row: F  C  Eb F# G# Bb C# E  G  A  B  D
user row: C# F# B  D  G  C  Eb G# E  A  F  Bb

 user row: C# F# B  D  G  C  Eb G# E  A  F  Bb 
 grid row: F# G# Bb C# E  G  A  B  D  F  C  Eb 
    orbit: F# C# D  E  G  C  F  A  Eb Bb B  G# 
X-swapped: F  C# D  G# Eb F# C  E  B  G  A  Bb 
intervals: 8  1  6  7  3  6  4  7  8  2  1  7  

 user row: C# F# B  D  G  C  Eb G# E  A  F  Bb 
 grid row: E  G  A  B  D  F  C  Eb F# G# Bb C# 
    orbit: E  C# Bb F  C  Eb G# A  B  D  G  F#   This is input to third iteration
X-swapped: E  C# A  F  C  Eb B  Bb F# G  D  G# 
intervals: 9  8  8  7  3  8  11 8  1  7  6  8  


--------


grid row: E  C# Bb F  C  Eb G# A  B  D  G  F# 
user row: E  C# A  F  C  Eb B  Bb F# G  D  G# 

 user row: E  C# A  F  C  Eb B  Bb F# G  D  G# 
 grid row: D  G  F# E  C# Bb F  C  Eb G# A  B  
    orbit: D  E  F  B  G# G  C# C  Bb Eb F# A  
X-swapped: G  F# C  A  C# D  Bb F  E  B  G# Eb 
intervals: 11 6  9  4  1  8  7  11 7  9  7  4  

--------

grid row: D  E  F  B  G# G  C# C  Bb Eb F# A 
user row: G  F# C  A  C# D  Bb F  E  B  G# Eb

 user row: G  F# C  A  C# D  Bb F  E  B  G# Eb 
 grid row: B  G# G  C# C  Bb Eb F# A  D  E  F  
    orbit: B  G  C  C# A  E  G# F# F  Eb Bb D  
X-swapped: D  Eb B  A  F  G# G  C# F# E  Bb C  
intervals: 1  8  10 8  3  11 6  5  10 6  2  2  

 user row: G  F# C  A  C# D  Bb F  E  B  G# Eb 
 grid row: C# G  G# B  F  E  D  A  F# Eb Bb C  
    orbit: C# G  F# E  D  Bb G# C  Eb B  A  F  input
X-swapped: G  C  E  G# Eb B  D  C# F# Bb F  A  
intervals: 5  4  4  7  8  3  11 5  4  7  4  10 

 user row: G  F# C  A  C# D  Bb F  E  B  G# Eb 
 grid row: G# B  F  E  D  A  F# Eb Bb C  C# G  
    orbit: G# G  Eb F  C  B  F# Bb E  A  D  C# 
X-swapped: E  B  Bb D  G# Eb F# C# C  A  G  F  
intervals: 7  11 4  6  7  3  7  11 9  10 10 11 


--------

grid row: C# G  F# E  D  Bb G# C  Eb B  A  F
user row: G  C  E  G# Eb B  D  C# F# Bb F  A

 user row: G  C  E  G# Eb B  D  C# F# Bb F  A  
 grid row: B  A  F  C# G  F# E  D  Bb G# C  Eb 
    orbit: B  G  Eb A  C  F  E  D  C# G# Bb F# 
X-swapped: E  G# G  D  F# F  B  C# A  Eb Bb C  
intervals: 4  11 7  4  11 6  2  8  6  7  2  4  

 user row: G  C  E  G# Eb B  D  C# F# Bb F  A  
 grid row: G# Bb D  E  F# G  C# F  A  B  Eb C  
    orbit: G# G  B  Bb C  A  F# Eb F  C# D  E  
X-swapped: E  A  Bb G  B  G# F# C# C  F  Eb D  
intervals: 5  1  9  4  9  10 7  11 5  10 11 2  

 user row: G  C  E  G# Eb B  D  C# F# Bb F  A  
 grid row: D  E  F# G  C# F  A  B  Eb C  G# Bb 
    orbit: D  G  G# F  B  C# Eb F# E  C  Bb A  
X-swapped: A  F  C  F# G# Eb G  C# D  B  Bb E  
intervals: 8  7  6  2  7  4  6  1  9  11 6  5  



=============================================================
More Screwing Around -- 2


--------------
--------------
--------------
--------------



0 3 6 8 A 1 4 7 9 B 2 5 	21.237 332233322337


user row: 0,3,6,8,10,1,4,7,9,11,2,5


------------------------------------------------------
 user row: 0  3  6  8  10 1  4  7  9  11 2  5  THIS ONE
 grid row: 7  8  9  10 11 0  1  2  3  4  5  6  
    orbit: 7  0  1  4  11 10 8  3  9  6  5  2  
X-swapped: 1  2  11 7  3  10 9  0  6  8  5  4  
intervals: 1  9  8  8  7  11 3  6  2  9  11 9  


Original

C,  F#, G#, F,  E,  C#, D,  B,  G,  Eb, Bb, A            6,2,9,11,9,1,9,8,8,7,11,(3)
F#, C,  D,  B,  Bb, G,  G#, F,  C#, A,  E,  Eb
E,  Bb, C,  A,  G#, F,  F#, Eb, B,  G,  D,  C#
G,  C#, Eb, C,  B,  G#, A,  F#, D,  Bb, F,  E
G#, D,  E,  C#, C,  A,  Bb, G,  Eb, B,  F#, F  
B,  F,  G,  E,  Eb, C,  C#, Bb, F#, D,  A,  G#
Bb, E,  F#, Eb, D,  B,  C,  A,  F,  C#, G#, G
C#, G,  A,  F#, F,  D,  Eb, C,  G#, E,  B,  Bb
F,  B,  C#, Bb, A,  F#, G,  E,  C,  G#, Eb, D
A,  Eb, F,  D,  C#, Bb, B,  G#, E,  C,  G,  F#
D,  G#, Bb, G,  F#, Eb, E,  C#, A,  F,  C,  B
Eb, A,  B,  G#, G,  E,  F,  D,  Bb, F#, C#, C



                                    inversion intervals: 6,10,3,1,3,11,3,4,4,5,1,(9)

------------------------------------------------------

5m                               5m inversion intervals: 6,10,9,7,9,5,9,4,4,11,7,(3)
 
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb   good    6,2,3,5,3,7,3,8,8,1,5,(9)
F#, C,  D,  F,  Bb, C#, G#, B,  G,  Eb, E,  A
E,  Bb, C,  Eb, G#, B,  F#, A,  F,  C#, D,  G
C#, G,  A,  C,  F,  G#, Eb, F#, D,  Bb, B,  E
G#, D,  E,  G,  C,  Eb, Bb, C#, A,  F,  F#, B
F,  B,  C#, E,  A,  C,  G,  Bb, F#, D,  Eb, G#
Bb, E,  F#, A,  D,  F,  C,  Eb, B,  G,  G#, C#
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
B,  F,  G,  Bb, Eb, F#, C#, E,  C,  G#, A,  D
Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
A,  Eb, F,  G#, C#, E,  B,  D,  Bb, F#, G,  C





0  1  2  3  4  5  6  7  8  9  10  11
1  4  7  9  11 2  5  0  3  6  8   10


C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb

c#  f   eb  bb  b   c   g   d   e   f#  ab  a


C,C#,E,B,Bb,G#,Eb,A,F#,F,D,G



C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb     6,2,3,5,3,7,3,8,8,1,5,9
C#, F,  Eb, Bb, B,  C,  G,  D,  E,  F#, G#, A      4,10,7,1,1,7,7,2,2,2,1,4
E,  D,  A,  G#, Bb, C#, C,  G,  B,  F,  Eb, F#     10,7,11,2,3,11,7,4,6,10,3,10
B,  G,  F#, Eb, G#, E,  C#, C,  Bb, D,  A,  F      8,11,9,5,8,9,11,10,4,7,8,6
Bb, C,  F,  A,  Eb, B,  E,  C#, G#, G,  F#, D      2,5,4,6,8,5,9,7,11,11,8,8
G#, C#, D,  F#, A,  Bb, B,  E,  Eb, C,  F,  G
Eb, E,  G,  F,  F#, G#, Bb, B,  A,  C#, D,  C
A,  B,  C,  D,  F,  Eb, G#, Bb, F#, E,  G,  C#
F#, Bb, C#, G,  D,  A,  Eb, G#, F,  B,  C,  E
F,  G#, E,  C,  G,  F#, A,  Eb, D,  Bb, C#, B
D,  Eb, B,  C#, C,  F,  F#, A,  G,  G#, E,  Bb
G,  A,  Bb, E,  C#, D,  F,  F#, C,  Eb, B,  G#
__________________
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Last edited by calebprime; 1st June 2015 at 07:36 AM.
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Old 18th June 2015, 12:47 PM   #171
calebprime
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a nice 5-voice array, not yet voiced, but the tritones work for me on the bottom.



Code:
ri/5/8:..............F# A  B  F  D  G  Ab E  C  Eb Bb C# 
ri/3/1:..............F  F# D  Bb C# Ab B  E  G  A  Eb C  
i/5/6:...............Eb C  E  Ab G  D  F  B  A  F# C# Bb 
r/2/7:...............F# C# Bb Ab D  F  C  B  Eb G  E  A  
p/0/0:...............C  F# Ab B  E  G  D  F  C# A  Bb Eb 


and these are a couple of 4-voice family-resemblance arrays, which I just
 learned a new little method to make.

I can use one of my limited-interval series:

Limited-Interval Scales (FOR MAPPING AND PERMUTATION) SERIES ID# INTERVALS 0 2 3 4 5 6 7 8 9 A B 1 1.12B 21111111112B 0 2 4 5 6 7 8 9 A B 1 3 2.129 221111111229 0 1 4 5 6 7 8 9 A B 2 3 3.139 131111111319 0 2 4 6 7 8 9 A B 1 3 5 4.127 222111112227 0 2 4 6 8 9 A B 1 3 5 7 5.125 222211122225 0 1 4 5 8 9 A B 2 3 6 7 6.135 131311131315 0 2 4 5 7 8 A B 1 3 6 9 7.123 221212122333 0 2 3 5 7 8 A B 1 4 6 9 8.123 212213123233 0 1 3 5 7 8 A B 2 4 6 9 9.123 122213132233 0 1 3 4 7 8 A B 2 5 6 9 10.123 121313133133 0 1 3 5 6 8 A B 2 4 7 9 11.123 122123122323 0 2 4 6 8 A B 1 3 5 7 9 12.123 222221222223 2^n mod 13, mallalieu, standard perm 0 1 3 6 8 A B 2 4 5 7 9 13.123 123231321223 0 2 3 5 8 A B 1 4 6 7 9 14.123 212331232123 0 1 3 4 6 7 A B 2 5 8 9 15.123 121213133313 0 1 3 6 7 A B 2 4 5 8 9 16.123 123131321313 0 1 3 5 7 A B 2 4 6 8 9 17.123 122231222213 span=24 0 3 5 7 9 B 2 4 6 8 A 1 18.23B 32222222233B span=36 0 3 4 7 8 B 2 5 6 9 A 1 19.13B 31313331313B 0 3 6 9 A 1 4 7 8 B 2 5 20.137 333133313337 0 3 6 8 A 1 4 7 9 B 2 5 21.237 332233322337 0 3 5 8 A 1 4 6 9 B 2 7 22.235 323333232355 0 3 6 9 B 2 5 8 A 1 4 7 23.235 333233333335 0 2 4 7 9 B 3 6 A 1 5 8 24.234 223224343434 0 2 4 6 9 B 3 7 A 1 5 8 25.234 222324433434 0 2 4 7 A 1 5 9 B 3 6 8 26.234 223334424324 0 2 5 7 A 3 6 8 B 1 4 9 27.235 232353232353 0 2 5 7 A 3 8 1 6 B 4 9 28.235 232355555553 0 2 4 6 8 B 3 7 A 1 5 9 29.234 222234433443 0 2 4 7 B 3 6 8 A 1 5 9 30.234 223443223443 0 1 4 8 B 3 6 7 A 2 5 9 31.134 133343134343 0 2 4 7 A 3 5 8 B 1 6 9 32.235 223352332533 0 1 4 5 8 B 3 7 A 2 6 9 33.134 131334434433 0 2 5 8 A 1 4 7 B 3 6 9 34.234 233233344333 0 2 5 7 A 1 4 8 B 3 6 9 35.234 232333434333 0 2 4 7 A 1 5 8 B 3 6 9 36.234 223334334333 0 2 8 B 1 3 5 7 A 4 6 9 37.236 263222236233 borderline case 0 2 5 7 A 1 3 8 B 4 6 9 38.235 232332535233 0 2 8 B 1 4 6 9 3 5 7 A 39.236 263232362232 borderline case 0 3 6 9 1 4 7 A 2 5 8 B 40.134 333433343331 span=36 0 4 7 A 2 5 8 B 3 6 9 1 41.34B 43343334334B span=48 0 3 6 9 2 5 8 B 4 7 A 1 42.35B 33353335333B 0 4 7 A 2 6 9 1 5 8 B 3 43.349 433443443349 0 4 8 B 3 7 A 2 6 9 1 5 44.347 443443443447 0 3 8 B 4 7 A 1 6 9 2 5 45.357 353533353537 0 3 6 9 2 5 8 B 4 A 1 7 46.356 333533356365 0 3 6 A 1 5 8 B 4 9 2 7 47.345 334443355555 0 3 7 A 2 5 9 1 6 B 4 8 48.345 343434455544 0 3 6 9 1 5 A 2 7 B 4 8 49.345 333445454544 0 3 6 A 2 7 B 4 9 1 5 8 50.345 334454554434 0 5 8 1 4 9 2 7 A 3 6 B 51.135 335355535351 0 4 8 1 5 9 2 6 A 3 7 B 52.145 445445445441 span=48 0 5 9 2 6 A 3 7 B 4 8 1 53.45B 54544544545B span=60 0 5 9 2 7 B 4 8 1 6 A 3 54.459 545545455459 0 5 8 1 6 B 4 9 2 7 A 3 55.359 535555555359 0 5 9 1 6 A 2 7 B 3 8 4 56.458 544544544588 0 3 8 B 5 A 4 9 2 7 1 6 57.356 353556555656 0 3 9 2 8 B 5 A 4 7 1 6 58.356 365636553656 0 4 9 2 7 B 5 A 3 8 1 6 59.456 455546555556 0 4 8 2 7 B 5 A 3 9 1 6 60.456 444546556456 0 4 9 1 7 B 5 A 3 8 2 6 61.456 454646555646 0 4 8 1 7 B 5 A 3 9 2 6 62.456 445646556546 0 2 8 3 A 5 B 1 7 9 4 6 63.267 267776262726 (borderline case) 0 3 6 B 5 A 4 9 2 8 1 7 64.356 335654556565 0 4 9 1 6 B 5 A 3 8 2 7 65.456 454556555655 0 4 8 1 6 B 5 A 3 9 2 7 66.456 445556556555 0 4 9 3 8 1 6 B 5 A 2 7 67.456 456555565455 0 5 A 3 8 2 7 1 6 B 4 9 68.356 555565655553 0 2 8 3 5 B 6 1 7 9 4 A 69.267 267267762762 (borderline case) 0 5 A 4 9 3 8 2 7 1 6 B 70.156 556565656551 span=60 0 6 B 5 A 4 9 3 8 2 7 1 71.56B 65656565656B span=72 0 5 B 6 1 8 3 A 4 9 2 7 72.567 567777767555 span=72 0 5 A 2 9 4 B 6 1 8 3 7 73.457 574777777745
to make them: B) C, F#, G#, B, E, G, D, F, C#, A, Bb, Eb T) G, D, F, C#, A, Bb, C, F#, Eb, G#, B, E A) Bb, C, F#, Eb, G#, B, G, D, E, F, C#, A S) B, G, D, E, F, C#, Bb, C, A, F#, Eb, G# Sounded good to C#, Bb, C, A, F#, Eb, B, G, G#, D, E, F read top line bass Eb, B, G, G#, D, E, C#, Bb, F, C, A, F# scnd - tenor 3rd-alto E, C#, Bb, F, C, A, Eb, B, F#, G, G#, D A, Eb, B, F#, G, G#, E, C#, D, Bb, F, C G#, E, C#, D, Bb, F, A, Eb, C, B, F#, G F, A, Eb, C, B, F#, G#, E, G, C#, D, Bb F#, G#, E, G, C#, D, F, A, Bb, Eb, C, B D, F, A, Bb, Eb, C, F#, G#, B, E, G, C# S) B, G, D, E, F, C#, Bb, C, A, F#, Eb, G# A) Bb, C, F#, Eb, G#, B, G, D, E, F, C#, A T) G, D, F, C#, A, Bb, C, F#, Eb, G#, B, E B) C, F#, G#, B, E, G, D, F, C#, A, Bb, Eb T) G, D, F, C#, A, Bb, C, F#, Eb, G#, B, E S) C, G, D, E, F, C#, Bb, C, A, F#, Eb, G# A) Bb, C, F#, Eb, G#, B, G, D, E, F, C#, A B) C, F#, G#, B, E, G, D, F, C#, A, Bb, Eb ============================================================ Originally called: Should Sound Better than it Does. C, F#, G#, B, E, G, D, F, C#, A, Bb, Eb * ************************** E, G, Eb, D, F, C#, A, Bb, C, F#, G#, B F, C#, B, A, Bb, C, F#, G#, E, G, Eb, D Bb, C, D, F#, G#, E, G, Eb, F, C#, B, A G#, E, A, G, Eb, F, C#, B, Bb, C, D, F# Eb, F, F#, C#, B, Bb, C, D, G#, E, A, G B, Bb, G, C, D, G#, E, A, Eb, F, F#, C# D, G#, C#, E, A, Eb, F, F#, B, Bb, G, C A, Eb, C, F, F#, B, Bb, G, D, G#, C#, E F#, B, E, Bb, G, D, G#, C#, A, Eb, C, F G, D, F, G#, C#, A, Eb, C, F#, B, E, Bb C#, A, Bb, Eb, C, F#, B, E, G, D, F, G#
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Last edited by calebprime; 18th June 2015 at 12:53 PM.
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Old 17th August 2015, 05:58 AM   #172
calebprime
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Same project. Thought I'd post the current state of things. I'm allowing myself unlimited time to generate and test everything I can think of. I'm reaching the point of diminishing returns, though. Soon it will be time to start trying things out on the sequencer.

This post loses the font sizes and occasional colors, but it would be hours of work to add them back in. Also, some alignments are off. Oh well. Better to document than not document at all.

I've worked with self-similar rows long enough now, and this row long enough, to be sure that this row generates its own counterpoint or accompaniment, and that it sounds good when it does generate those things. A solid foundation. Without the right foundation, the process seems to peter out, but this one has held my interest.

In a long process like this, I start to wonder whether I'm turning into an elderly Joseph Mitchell (writer for The New Yorker) who took longer and longer to finish his work, until he wasn't writing anything at all. He suffered from increasing perfectionism, but also he was working on more ambitious stories.

Nah. Not to worry. I've written fast, I've written slow, and everything in between.

Generating, choosing the best of what you've generated, and memorizing it: That process starts to grow geometrically.

In such a process, pairing down is necessary, and brings a feeling of relief.






Code:
============================================================

SUMMARY OF MAIN STRUCTURES WITHOUT AS MUCH CLUTTER:


                                
5m                               5m inversion intervals: 6,10,9,7,9,5,9,4,4,11,7,(3)


good    6,2,3,5,3,7,3,8,8,1,5,(9)  [very nice over F pedal]

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb   
F#, C,  D,  F,  Bb, C#, G#, B,  G,  Eb, E,  A
E,  Bb, C,  Eb, G#, B,  F#, A,  F,  C#, D,  G
C#, G,  A,  C,  F,  G#, Eb, F#, D,  Bb, B,  E
G#, D,  E,  G,  C,  Eb, Bb, C#, A,  F,  F#, B
F,  B,  C#, E,  A,  C,  G,  Bb, F#, D,  Eb, G#
Bb, E,  F#, A,  D,  F,  C,  Eb, B,  G,  G#, C#
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
B,  F,  G,  Bb, Eb, F#, C#, E,  C,  G#, A,  D
Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
A,  Eb, F,  G#, C#, E,  B,  D,  Bb, F#, G,  C


"Natural" contour of this:  c3,f#3,g#3,b3,e3,g3,d3,f3,c#3,a2,bb2,eb3
............................3..9...11..12.7..10.5..8..4...1..2...6..

5m Perm Matrix (Just a column of 5ths)

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
A,  Eb, F,  G#, C#, E,  B,  D,  Bb, F#, G,  C
E,  Bb, C,  Eb, G#, B,  F#, A,  F,  C#, D,  G
B,  F,  G,  Bb, Eb, F#, C#, E,  C,  G#, A,  D
F#, C,  D,  F,  Bb, C#, G#, B,  G,  Eb, E,  A
C#, G,  A,  C,  F,  G#, Eb, F#, D,  Bb, B,  E
G#, D,  E,  G,  C,  Eb, Bb, C#, A,  F,  F#, B
Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
Bb, E,  F#, A,  D,  F,  C,  Eb, B,  G,  G#, C#
F,  B,  C#, E,  A,  C,  G,  Bb, F#, D,  Eb, G#


2x rotated to match original-row rotation:

A,  Ab, C,  F#, E,  B,  C#, G,  Bb, Eb, F,  D     * Main match with original p/0/0
Bb, A,  C#, G,  F,  C,  D,  Ab, B,  E,  F#, Eb
F#, F,  A,  Eb, C#, Ab, Bb, E,  G,  C,  D,  B
C,  B,  Eb, A,  G,  D,  E,  Bb, C#, F#, Ab, F      Matching trans at t9 relation
D,  C#, F,  B,  A,  E,  F#, C,  Eb, Ab, Bb, G
G,  F#, Bb, E,  D,  A,  B,  F,  Ab, C#, Eb, C
F,  E,  Ab, D,  C,  G,  A,  Eb, F#, B,  C#, Bb
B,  Bb, D,  Ab, F#, C#, Eb, A,  C,  F,  G,  E
Ab, G,  B,  F,  Eb, Bb, C,  F#, A,  D,  E,  C#
Eb, D,  F#, C,  Bb, F,  G,  C#, E,  A,  B,  Ab
C#, C,  E,  Bb, Ab, Eb, F,  B,  D,  G,  A,  F#
E,  Eb, G,  C#, B,  F#, Ab, D,  F,  Bb, C,  A

 


-----------------------------------------------------------
=======================================================================
2x against original series:


p/11/0:..............a  Ab C  F# E  B  		   C# G  Bb Eb F  D    2x series makes good diatonic match
p/0/0:...............C  F# Ab B  E  			G  D  F  C# A  Bb Eb   with original p/0/0 series


6 becomes 11
2 b       4
3 b       6
5 b       10
3 b       6
7 b       2
3 b       6   (d to f becomes c# to g) 
8 b       3
8 b       5
1 b       2
5 b       9
9 b       7      
 
This, to my relief, actually makes sense.






================================================================================
=======================================================================



Revised 4x:



Eb, C#, A,  Ab, E,  G,  B,  Bb, F,  D,  F#, C
F,  Eb, B,  Bb, F#, A,  C#, C,  G,  E,  Ab, D
A,  G,  Eb, D,  Bb, C#, F,  E,  B,  Ab, C,  F#
Bb, Ab, E,  Eb, B,  D,  F#, F,  C,  A,  C#, G
D,  C,  Ab, G,  Eb, F#, Bb, A,  E,  C#, F,  B
B,  A,  F,  E,  C,  Eb, G,  F#, C#, Bb, D,  Ab
G,  F,  C#, C,  Ab, B,  Eb, D,  A,  F#, Bb, E
Ab, F#, D,  C#, A,  C,  E,  Eb, Bb, G,  B,  F
C#, B,  G,  F#, D,  F,  A,  Ab, Eb, C,  E,  Bb
E,  D,  Bb, A,  F,  Ab, C,  B,  F#, Eb, G,  C#
C,  Bb, F#, F,  C#, E,  Ab, G,  D,  B,  Eb, A
F#, E,  C,  B,  G,  Bb, D,  C#, Ab, F,  A,  Eb   best match


Best diatonic match against orig p/0/0:    C,F#,G#,B,            E,G,D,F,C#,A,Bb,Eb


octotonic:
                           start:

p/2/11:..............G# D |F  D# B          Bb F# A  C# C  G  E  
p/5/11:..............B  F |G# F# D          C# A  C  E  Eb Bb G   
p/8/11:..............D  G#|B  A  F          E  C  D# G  F# C# Bb 
p/11/11:.............F  B |D  C  G#         G  D# F# Bb A  E  C# 

r of this:


 
nice side-slip!
p/2/11:..............G# D |F  D# B 
to:
p/3/11:..............A  Eb|F# E  C  B       G  Bb D  C# Ab F  


 
===================================================================

======================================================================================

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb          (5m)

A,  Ab, C,  F#, E,  B,  C#, G,  Bb, Eb, F,  D            2x 

F#, E,  C,  B,  G,  Bb, D,  C#, Ab, F,  A,  Eb           4x



** try straight substitution of pitches in various structures: chorales, arrays, etc.
You could do as text-substitution with textedit.
===========================================================================

=====================================================================================
==================================================================================================
4

Contour 


c3,f#2,g#2,f2,e2,c#2,d2,b1,g2,eb2,bb2,a2          Original
11 6   8   5  4  1   2  0  7  3   10  9
12 7   9   6  5  2   3  1  8  4   11  10  


C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb    5m

c4, f#3, g#3, b3, e3, g2, d3, f3, c#4, a3, bb3, eb4
9...4....5....8...2...0...1...3...10...6...7....11..

=========================================================================================

NEW CONTOUR, BASED ON THE WAY I USUALLY PLAY the BASIC 5m Row.

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb    5m
3   3   3   3   3   3   3   3   3   2   2   3
3...9...11..12..7...10..5...8...4...1...2...6.          6,2,3,5,3,7,3,8,8,1,5,(9)


C2,D#3,B3,G#4,A2,F3,D2,A#2,C#2,G0,F#1,E2  up an octave, or make adj.(bad Bb triad?)   3,8,9,1,8,9,8,3,6,11,10,(8)
C2,D#3,B3,G#4,A2,F3,D2,A#2,C#2,F#1,G1,E2                    3,8,9,1,8,9,8,3,5,1,9,(8)
                                   watch for NBC


C2,G#3,F4,F#4,D3,B3,G2,D#3,E2,A#0,C#1,A2   adjust C2 to C3  8,9,1,8,9,8,8,1,6,3,8,(3)

C2,G#3,F4,C#5,D3,A#3,F#2,D#3,E2,G1,A1,B2                    8,9,8,1,8,8,9,1,3,2,2,1
C2,G#3,F4,C#5,D3,A#3,F#2,D#3,E2,G1,B1,A2                    8,9,8,1,8,8,9,1,3,4,10,(3)

C2,A3,F4,C#5,D3,A#3,G2,D#3,E2,F#1,G#1,B2
C2,A3,F4,C#5,D3,A#3,G2,D#3,F#2,E1,G#1,B2  E triad too bald?

C2,B3,D#4,G4,E3,C#4,F2,A#3,D2,F#1,A1,G#2  D triad too bald?
C2,B3,G#4,A4,F3,D4,A#2,F#3,G2,C#1,E1,D#3



--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
13B



5m with assigned contour:


C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb    

c4, f#3, g#3, b3, e3, g2, d3, f3, c#4, a3, bb3, eb4
9...4....5....8...2...0...1...3...10...6...7....11..
10  5    6    9   3   1   2   4   11   7   8    12



not killed, 3-note groups total:
c,d,e,a,

========================================
Contour:  10  5    6    9   3   1   2   4   11   7   8    12

C4,A2,D3,B3,F#2,D#1,A#1,G2,C#4,F3,G#3,E4      ok      9,5,9,7,9,7,9,6,4,3,8,8
C4,C#3,E3,G#3,F2,D1,A1,B2,D#4,F#3,G3,A#4      ok

C4,D3,D#3,A3,G2,A#1,F#2,C#3,E4,F3,G#3,B4      ok


C4,F#2,A2,B3,D2,G#0,E1,F2,C#4,D#3,A#3,G4      ok

C4,G#2,B2,F#3,D2,G1,A#1,D#2,C#4,E3,F3,A4      ok

C4,G#2,B2,F#3,D2,G1,A#1,F2,D#4,C#3,E3,A4      ok

C4,G#2,B2,F#3,D#2,D1,A#1,G2,F4,C#3,E3,A4      minor 9th is weird

C4,G#2,B2,A3,D2,F#1,A#1,G2,F4,C#3,E3,D#5      ok

C4,G#2,B2,A3,F#2,D1,A#1,G2,F4,C#3,E3,D#5      ok

C4,A2,B2,F#3,D#2,D1,A#1,G2,F4,C#3,E3,G#4


C4,F#2,G#2,B3,D2,E1,G1,D#2,C#4,A#2,F3,A4    c,f#,g#,b     good-


-------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------


++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
** Don't forget "too obvious" constructions like progression:

** How to gradually change pitches in these arrays?
 

C,  F#, G#, F,               
F#, C,  D,  B,   
E,  Bb, C,  A,   
G,  C#, Eb, C,   
  


D,  C,  Ab, G,  Eb,               
Bb, Ab, E,  Eb, B,
A,  G,  Eb, D,  Bb,
F,  Eb, B,  Bb, F#,
Eb, C#, A,  Ab, E,   

====================================================
====================================================
====================================================
An attempt at a gradual subtitution in row giving different arrays

  
C,  F#, G#, B,  E,| G D F C# A Bb Eb (C)
F#, C,  D,  F,  Bb
E,  Bb, C,  Eb, G#,  
C#, G,  A,  C,  F,   
G#, D,  E,  G,  C,


9   8    10   11  12  6   7   2   1    3   4    5
C#, F,   A,   Bb, Eb, G,  D,  F#, C,   G#, B,   E      4,4,1,5,4,7,4,6,8,3,5,(9)           *******
0,1,4,8  0,1,4,5

vs.

original:
C,  F#,  G#,  B,  E,  G,  D,  F,  C#,  A,  Bb,  Eb,
1   2    3    4   5   6   7   8   9    10  11   12


C#  F#  G#  B   E
G#  C#  D#  F#  B
F#  B   C#  E   A
D#  G#  A#  C#  F#
A#  D#  F   G#  C#

and

G   D   F   C   A   Bb  Eb
C   G   Bb  F   D   Eb  Ab
A   E   G   D   B   C   F
D   A   C   G   E   F   Bb
F   C   Eb  Bb  G   Ab  Db
E   B   D   A   F#  G   C
B   F#  A   E   C#  D   G

=------------------------------------------------


C#  F   G#   B   E
A   C#  E    G   C
F#  Bb  C#   E   A
D#  G   A#   C#  F#
A#  D   F    G#  C#

and

G,  D,  F#, C,  A,  Bb, Eb
C   G   B   F   D   Eb  Ab
Ab  Eb  G   Db  Bb  B   E
D   A   C#  G   E   F   Bb
F   C   E   Bb  G   Ab  Db
E   B   Eb  A   F#  G   C
B   F#  Bb  E   C#  D   G

=------------------------------------------------


C#  F   A   B   E
A   C#  F   G   C
F   Bb  C#  Eb  Ab
Eb  G   B   Db  Gb
Bb  D   F#  Ab  Db 

and

G,  D,  F#, C, G#, Bb, Eb
C   G   B   F  C#  Eb  Ab
Ab  Eb  G   Db A   B   E
D   A   C#  G  D#  F   Bb
F#  C#  F   B  G   A   D
E   B   Eb  A  F   G   C
B   F#  Bb  E  C   D   G

=------------------------------------------------


C#  F   A   Bb  E
A   C#  F   F#  C
F   A   C#  D   G#
E   G#  C   C#  G
Bb  D   F#  G   C#

and

G,  D,  F#,  C,  G#, B,  Eb
C   G   B    F   C#  E   Ab
Ab  Eb  G    Db  A   C   E
D   A   C#   G   D#  F#  Bb
F#  C#  F    B   G   Bb  D
Eb  Bb  D    Ab  E   G   B
B   F#  Bb   E   C   Eb  G

=------------------------------------------------

C#  F   A   Bb  Eb
A   C#  F   F#  B
F   A   C#  D   G
E   G#  C   C#  F#
B   D#  G   G#  C#

and

G,  D,  F#,  C,  G#,  B,  E
C   G   B    F   C#   E   A
Ab  Eb  G    Db  A    C   F
D   A   C#   G   D#   F#  B
F#  C#  F    B   G    Bb  Eb
Eb  Bb  D    Ab  E    G   C
Bb  F   A    Eb  B    D   G

=------------------------------------------------


====================================================
==============================================================================================
==============================================================================================

 
=------------------------------------------------
G#, B,  E,  G,  D,          This is less effective, because octotonic
F,  G#, C#, E,  B,   
C,  Eb, G#, B,  F#,  
A,  C,  F,  G#, Eb,  
D,  F,  Bb, C#, G#, 


=------------------------------------------------
A,  B,  E,  G,  D,
G   A   D   F   C
D   E   A   C   G
B   C#  F#  A   E
E   F#  B   D   A


=------------------------------------------------
A,  Bb, E,  G,  D,
G#  A   D#  F#  C#
D   Eb  A   C   G
B   C   F#  A   E
E   F   B   D   A


=------------------------------------------------
A,  Bb, Eb, G,  D,
G#  A   D   F#  C#
Eb  E   A   C#  G#
B   C   F   A   E
E   F   Bb  D   A

=------------------------------------------------
Ab, Bb, Eb, G,  D,
Gb  Ab  Db  F   C
Db  Eb  Ab  C   G
A   B   E   Ab  Eb
D   E   A   Db  Ab


=------------------------------------------------
=------------------------------------------------


 


 
B,  E,  G,  D,  F,   nice this as bottom
F#, B,  D,  A,  C,   
Eb, G#, B,  F#, A,   
G#, C#, E,  B,  D,   
F,  Bb, C#, G#, B,   

=------------------------------------------------
Bb E  G  D  F
E  Bb Db Ab B
C# G  Bb F  Ab
F# C  Eb Bb Db
Eb A  C  G  Bb

=------------------------------------------------
B  E  G  D  F
F# B  D  A  C
D# G# B  F# A
G# C# E  B  D
F  Bb C# G# B

=------------------------------------------------
B  Eb G  D  F
G  B  Eb Bb Db
Eb G  B  F# A
Ab C  E  B  D
F  A  Db Ab B
=------------------------------------------------
B  Eb G  D  F#
G  B  Eb Bb D
Eb G  B  F# Bb
Ab C  E  B  Eb
E  Ab C  G  B

=------------------------------------------------
=------------------------------------------------

 
=------------------------------------------------
E,  G,  D,  F,  C#,  
C#, E,  B,  D,  Bb,  
F#, A,  E,  G,  Eb,  
Eb, F#, C#, E,  C,   
G,  Bb, F,  G#, E,   


=------------------------------------------------
Eb  G   D   F   C#
B   Eb  Bb  Db  A
E   Ab  Eb  Gb  D
Db  F   C   Eb  B
F   A   E   G   D#
=------------------------------------------------
Eb  G   D   F#  C#
B   Eb  Bb  D   A
E   Ab  Eb  G   D
C   E   B   Eb  Bb
F   A   E   Ab  Eb

=------------------------------------------------
Eb  G   D   F#  C
B   Eb  Bb  D   Ab
E   Ab  Eb  G   Db
C   E   B   Eb  A
F#  Bb  F   A   Eb

=------------------------------------------------
=------------------------------------------------

=------------------------------------------------




G,  D,  F,  C#, A,     * nice
C,  G,  Bb, F#, D,   
A,  E,  G,  Eb, B,   
C#, G#, B,  G,  Eb,  
F,  C,  Eb, B,  G,   


=------------------------------------------------
G   D,  F   Db  Ab
C   G   Bb  Gb  Db
A   E   G   Eb  Bb
C#  G#  B   G   D
F#  C#  E   C   G

=------------------------------------------------
G,  D,  F,  c,  g#
C   G   Bb  F   C#
A   E   G   D   A#
D   A   C   G   D#
F#  C#  E   B   G

=------------------------------------------------
f#, D,  F,  c,  g#
Bb  F#  A   E   C
G   Eb  F#  C#  A
C   G#  B   F#  D
E   C   Eb  Bb  F#
=------------------------------------------------


=------------------------------------------------
=------------------------------------------------


D,  F,  C#, A,  Bb,  
B,  D,  Bb, F#, G,   
Eb, F#, D,  Bb, B,   
G,  Bb, F#, D,  Eb,  voice these two as major seventh 
F#, A,  F,  C#, D,   



=------------------------------------------------
D,  F,  C#,  A,  B
B   D   Bb   F#  G#
Eb  F#  D    Bb  C
G   Bb  F#   D   E
Ab  B   G    Eb  F
=------------------------------------------------
D,  F,  C#,  G#, B
B   D   Bb   F   G#
Eb  F#  D    A   C
Ab  B   G    D   F
F   G#  E    B   D

=------------------------------------------------
D,  F,  C,   G#, B
B   D   A    F   G#
E   G   D    Bb  C#
G#  B   F#   D   F
F   G#  Eb   B   D
=------------------------------------------------
D,  F#, C,   G#, B
Bb  D   Ab   E   G
E   G#  D    Bb  C#
Ab  C   F#   D   F
F   A   Eb   B   D
=------------------------------------------------

=------------------------------------------------
=------------------------------------------------



=------------------------------------------------

F,  C#, A,  Bb, Eb,  
A,  F,  C#, D,  G,   
C#, A,  F,  F#, B,   
C,  G#, E,  F,  Bb,  
G,  Eb, B,  C,  F,   



=------------------------------------------------
f#,  C#, A,  Bb, Eb
B    F#  D   Eb  Ab
Eb   Bb  F#  G   C
D    A   F   F#  B
A    E   C   C#  F#
=------------------------------------------------
f#,  c,  A,  Bb, Eb
C    F#  Eb  E   A
Eb   A   F#  G   C
D    Ab  F   F#  B
A    Eb  C   C#  F#
=------------------------------------------------
f#,  c,  g#, b,  Eb
C    F#  D   F   A
E    Bb  F#  A   Db
C#   G   D#  F#  Bb
A    Eb  B   D   F#
=------------------------------------------------
f#,  c,  g#, b,  e,
C    F#  D   F   Bb
E    Bb  F#  A   D
C#   G   D#  F#  B
G#   D   A#  C#  F#
=------------------------------------------------
=------------------------------------------------

=------------------------------------------------
=------------------------------------------------





=------------------------------------------------
C#, A,  Bb, Eb, C,   
F,  C#, D,  G,  E,   
E,  C,  C#, F#, Eb,  
B,  G,  G#, C#, Bb,  
D,  Bb, B,  E,  C#,  


=------------------------------------------------
C#,  A,  Bb, e,  C,
F    C#  D   G#  E
E    C   C#  G   Eb
Bb   F#  G   C#  A   
D    Bb  B   F   C#
=------------------------------------------------
C#,  A,  b,  e,  C
F    C#  D#  G#  E
Eb   B   C#  F#  D
Bb   F#  G#  C#  A
D    Bb  C   F   C#
=------------------------------------------------
C#,  g#, b,  e,  C
F#   C#  E   A   F
G#   D#  F#  B   G
A#   F   G#  C#  Bb
D    A   C   F   C#
=------------------------------------------------
c,   g#, b,  e,  c#,
E    C   D#  G#  F
C#   A   C   F   D
G#   E   G   C   A
B    G   Bb  Eb  C


=------------------------------------------------
=------------------------------------------------





=------------------------------------------------



A,  Bb, Eb, C,  F#,  Dim
G#, A,  D,  B,  F,   
Eb, E,  A,  F#, C,   
F#, G,  C,  A,  Eb,  
C,  C#, F#, Eb, A,   


=------------------------------------------------
=------------------------------------------------
G#, Bb, Eb, C,  F#
F#  G#  C#  Bb  E
C#  Eb  Ab  F   B
E   F#  B   Ab  D
A#  C   F   D   G#

=------------------------------------------------
Ab, B,  Eb, C,  F#
F   G#  C   A   Eb
C#  E   Ab  F   B
E   G   B   Ab  D
A#  C#  F   D   Ab

=------------------------------------------------
G#, B,  E,  C,  F#
F   G#  C#  A   Eb
C   D#  G#  E   Bb
E   G   C   G#  D
A#  C#  F#  D   G#

=------------------------------------------------
G#, B,  E,  C#, F#
F   G#  C#  A#  Eb
C   D#  G   F   Bb
D#  F#  B   G#  C#
A#  C#  F#  D#  G#

=------------------------------------------------
G#, B,  E,  C#, F,
F   G#  C#  A#  D
C   D#  G#  F   A
D#  F#  B   G#  C
B   D   G   E   G#

=------------------------------------------------



=------------------------------------------------



9   8    10   11  12  6   7   2   1    3   4    5
C#, F,   A,   Bb, Eb, G,  D,  F#, C,   G#, B,   E      4,4,1,5,4,7,4,6,8,3,5,(9)           *******
0,1,4,8  0,1,4,5

vs.

original:
C,  F#,  G#,  B,  E,  G,  D,  F,  C#,  A,  Bb,  Eb,
1   2    3    4   5   6   7   8   9    10  11   12




Bb, Eb, C,  F#, G#,  
F,  Bb, G,  C#, Eb,  
G#, C#, Bb, E,  F#,  
D,  G,  E,  Bb, C,   
C,  F,  D,  G#, Bb,  



b,  Eb, C,  F#,  G#,
G   B   G#  D    E
Bb  D   B   F    G
E   Ab  F   B    C#
D   F#  Eb  A    B

b,  e,  C,  F#,  G#,
F#  B   G   C#   D#
Bb  D#  B   F    G
E   A   F   B    C#
D   G   Eb  A    B

b,  e,  C,  F#,  g,
F#  B   G   C#   D
Bb  D#  B   F    F#
E   A   F   B    C
D#  G#  E   Bb   B

b,  e   d,  f,   g,
F#  B   A   C    D
G#  C#  B   D    E
F   Bb  Ab  B    Db
D#  Ab  Gb  A    B

b,  e,  c#, f,   g
F#  B   G#  C    D
A   D   B   Eb   F
F   Bb  G   B    C#
Eb  Ab  F   A    B









=------------------------------------------------
Eb, C,  F#, G#, B,    
F#, Eb, A,  B,  D,   
C,  A,  Eb, F,  G#,  
Bb, G,  C#, Eb, F#,  
G,  E,  Bb, C,  Eb,  


e,  C,  F#, G#,  B
G#  E   Bb  C    D#
D   Bb  E   F#   A
C   Ab  D   E    G
A   F   B   C#   E

e,  c#, F#, G#,  B
G   E   A   B    D
D   B   E   F#   A
C   A   D   E    G
A   F#  B   C#   E

e,  c#, f,  G#,  B
G   E   G#  B    D
Eb  C   E   G    Bb
C   A   C#  E    G
A   F#  Bb  C#   E

e,  c#, f,  a,   B
G   E   G#  C    D
Eb  C   E   G#   Bb
B   G#  C   E    F#
A   F#  Bb  D    E

e,  c#, f,  a,   bb,
G   E   G#  C    C#
Eb  C   E   G#   A
B   G#  C   E    F
Bb  G   B   Eb   E



=------------------------------------------------
------------------------------------------
-------------------------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------------

BASIC CHORALE:

5x/ri/3/4:...........Ab F  Bb G  D  B  A  Eb F# C# C  E  
p/0/0:...............C  F# Ab F  E  C# D  B  G  Eb Bb A
5x/r/8/10:...........D  Ab F  Bb B  G  Eb F# C# E  A  C  
5x/r/8/8:............A  C  D  Ab F  Bb B  G  Eb F# C# E  


  nice alternation:         [:Bb B:]G  Eb
                              Ab F  Bb B   
...................................................C7 to F maj 7!

2x of Basic Chorale:

5x/ri/3/4:...........c  g  f  b  c# f# eb d  ab bb a  e 
p/0/0:...............a  ab c  g  e  bb c# f# b  d  f  eb
5x/r/8/10:...........c# c  g  f  f# b  d  ab bb e  eb a  
5x/r/8/8:............eb a  c# c  g  f  f# b  d  ab bb e


  









Retrograde of Inversion 

D  F  C  Eb B  G  Ab Db Bb E  F# A               
F# A  D  F  C  Eb B  G  Ab Db Bb E        
A  G# Eb B  G  E  F  D  C# Bb C  F# 
D  F# F  C  Eb A  G  E  B  Ab Db Bb       

d>..........g>.......db>............

-------------------------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------------
PERM CHORALES:

1)   PERM CHORALE:  

D3,F#3,D#3,B3,C3,E3,G#3,C#3,F3,A3,A#3,G3

loop just upper two voices:

[:C,  F#, G#:]B,  E,  G,  D,  F,  C#, A,  Bb, Eb    
  E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
  G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
  C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

  C#-------------->   G-------------------->

not killed, chord-by-chord:  [c,a]



C#, D, F, F#, A, B, D#, G, E, C, G#, Bb



=============================================================================

2) 

D#3,B3,C3,E3,G#3,F3,C#3,D3,A3,A#3,F#3,G3

col: Eb,B,C,E,G#,F,C#,D,A,Bb,F#,G
dhv: 

C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb        not killed, chord-by-chord:  
E,  G,  F,  C,  G#, Eb, A,  C#, D,  Bb, F#, B         [e,g,a] 
G#, Eb, C#, E,  F,  B,  Bb, D,  A,  F#, G,  C         
F,  B,  D,  G#, C#, C,  F#, A,  Bb, G,  Eb, E


as compared to 1):

C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E


=============================================================================
3) A and C not killed

C,  F#, G#,-B,  E,  G,  D,  F,  C#, A,  Bb, Eb   -Yeah, mon.
A,  B, -C, -G#, F#, D,  E,  G,  Bb, C#, Eb, F
C#, G#,-A, -C,  B,  E,  F#, D,  Eb, Bb, F,  G    -second take good
Bb, C, -C#, A,  G#, F#, B,  E,  F,  Eb, G,  D    -3rd take good enough

A>..............E>..............Eb>..........
or, different!:
....G#>.............

Here's a 2x of this #3 perm chorale that seemed ok:

c#, c,  f,  bb, ab, eb, e,  b,  d,  f#, a,  g,       Ok+
f#, bb, c#, f,  c,  e,  ab, eb, a,  d,  g,  b,
d,  f,  f#, c#, bb, ab, c,  e,  g,  a,  b,  eb,
a,  c#, d,  f#, f,  c,  bb, ab, b,  g,  eb, e,




Here's a 4x of this #3 perm chorale that seemed ok:

f,  eb, c#, c,  ab, g,  b,  d,  a,  e,  bb, f#    OK good-
e,  c,  f,  c#, eb, b,  ab, g,  bb, a,  f#, d,
a,  c#, e,  f,  c,  ab, eb, b,  f#, bb, d,  g,
bb, f,  a,  e,  c#, eb, c,  ab, d,  f#, g,  b,


===================================================================================
4) ** not killed, chord-by-chord:  [d,d#,f#,a] ** possibly interesting            *

C,  F#, G#, B,[ E,  G,  D,  F,] C#, A,  Bb, Eb      6,2,3,5,3,7,3,8,8,1,5,(9)              
G,  D,  F,  E,[ A,  Bb, Eb, C#] B,  C,  F#, G#      7,3,11,5,1,5,10,10,1,6,2,(11)                  
Bb, Eb, C#, A,[ C,  F#, G#, B,] E,  G,  D,  F
F#, G#, B,  C,[ G,  D,  F,  E,] A,  Bb, Eb, C#  •       
.................................................. 

* this sounds great with a high D#, despite 012.

B,E,A,C,G,Bb,F#,D,Eb,G#,F,C#   --- modified p/5  (b and c# swapped)

5,5,3,7,3,8,8,1,5,9,8,10

p/5/8:...............F# D  Eb Ab F  B  C# E  A  C  G  Bb 



===================================================================================
=============================================================================
5) use  -- definite

comment:  play wide and sweet, esp. 9th chord -- c,d,f#,c#
comment2:  no idea where this series came from
                                *
C,  F#, G#, B,  E, -G,  D,  F,  C#, A,  Bb, Eb      **** WHOLE-TONE 
E,  D,  F,  C#, Bb,-A, -C,  Eb, F#, B,  G#, G
Bb, C,  Eb, F#, G#- B-- E,  G,  D,  C#, F,  A
G#, E,  G,  D,  F,  C#- Bb, A,  C,  F#, Eb, B       Fam Res 

G#>.................G>..............G#......V of G#



=============================================================================


END of PERM CHORALES 
=============================================================================
=============================================================================
=============================================================================


0146 and 0347 array:

ri/5/10:.............B  F  D {G  Ab}E  C  Eb Bb C# F# A           good-
i/5/6:...............Eb C  E  Ab G  D  F  B  A  F# C# Bb 

p/0/0:...............C  F# Ab B  E  G  D  F  C# A  Bb Eb 
r/0/4:...............F  D  G  E  B  Ab F# C  Eb Bb A  C# 


================================================================
End of 4-voice, beginning of 5-or-more-voice section

============================================================================================


5-Note Array:



LOOP LAST TWO CHORDS, V to I !!


ri/11/4:.............F# A  E  G  C  Eb F  B  Ab C# D  Bb        
p/6/6:...............Ab B  G  Eb E  A  F# C  D  F  Bb C# 
p/5/1:...............B  C# E  A  C  G  Bb F# D  Eb Ab F   Next level up from p/0/0!s

ri/5/10:.............B  F  D  G  Ab E  C  Eb Bb C# F# A             
p/0/0:...............C  F# Ab B  E  G  D  F  C# A  Bb Eb 
........................N.....N..N.....N........N..N..N

                        B--E--?--E--A--D
                                 c--b--bb-a--ab-g--f#-f

--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
6-note array:


revoiced, slightly:

5x/i/6/11:...........Eb}{F# C} D  B  Bb G  Ab F  C# A {E  
p/0/0:...............C   F# Ab B  E  G  D  F  C# A  Bb Eb 
5x/p/6/7:............G   B  Eb Ab A  F# C  Bb C# D  F  E  
5x/p/2/5:............C#  C  Eb G  B  E  F  D  Ab F# A  Bb 
p/1/2:...............A   C  F  Ab Eb F# D  Bb B  E  C# G  
p/0/1:...............F#  Ab B  E  G  D  F  C# A  Bb Eb C  




-------------------------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------------
Seven-Note Arrays, with mostly no 3-or-more-note octotonic fields.  

Max of 2-note oct. fields, mostly.



5x/ri/2/11:..........D  B |C |F |A |C# E |Eb|F# G  Bb|Ab        Good flow
p/7/5:...............D  A |C |Ab|E |F  Bb|G |C# Eb F#|B

5x/i/0/2:............Ab F |E |C#|D |B  G |Eb|Bb A  C |F# 
5x/r/0/0:............Eb D |A |F |C#|Bb B |Ab|G  E  F#|C  
  
p/0/0:...............C  F#|Ab|B |E |G  D |F |C# A  Bb|Eb 
p/4/4:...............Ab B |F#|A |F |C# D |G |E  Bb C |Eb 
p/0/1:...............F# Ab|B |E |G |D  F |C#|A  Bb Eb|C  

...........................N..N..N........N.......


========================================================================
Good:

5x/ri/2/10:..........Ab|D  B |C |F |A |C#|E| Eb|F# G  Bb       Less Oct than most.
5x/r/1/2:............Bb|F# D |B  C  A  Ab F  G |C# E  Eb 
5x/p/11/5:...........Bb|A  C |E  Ab C# D  B  F |Eb F# G  
ri/1/4:..............Ab|B  F#|A  D  F  G  C# Bb|Eb E  C  
p/5/9:...............D |Eb Ab|F  B  C# E  A  C |G  Bb F# 
p/0/1:...............F#|Ab B |E  G  D  F  C# A |Bb Eb C  
p/0/0:...............C |F# Ab|B  E  G  D  F  C#|A  Bb Eb

.....................N........N..N..N.....N..N...........



========================================================================
-------------------------------------------------------------------------------------------------------------------




1  2  11 7  3  10 9  0  6  8  5  4


C#.D..B..G..Eb.Bb.A..C..F#.G#.F..E..
   d........eb.......c.....g#....e..
......b........bb...................
c#.......g........a.....f#....f


C..F#.G#.F..E..C#.D..B..G..Eb.Bb.A..
...............c#.......g........a..
...f#....f........d........eb.......
c.....g#....e........b........bb    

------------------------------------------------------

------------------------------------------------------
------------------------------------------------------
------------------------------------------------------
------------------------------------------------------


5B  Groupings and Pedals

I tend to hear this series in E! (irrespective of this choice of pedal)


5m:			C,  F#, G#, B,  		E,  G,  D,  F,  	    C#, A,  Bb, Eb


not killed, 4-note groups:     C,E,F,A,

This is good over A pedal.

C,  F#, G#, B,  		E,  G,  D,  F,  	    C#, A,  Bb, Eb
---------------------------------------------------------
A>------------------------------------------------------>


also, 3-note groups:

C,F#,G#		B,E,G		D,F,C#		A,Bb,Eb
----------------------------------------------- 
A > ---------------------------------->


F Pedal is nice!
F,C#,A,Bb				Eb,C,F#,G#,	    B,E,G,D




5C   --    Partition into 3 4-note groups, 5m row -- see section 19 for group-to-group perm matrix.

group 1              group 2               group 3
C,  F#, G#, B,  		E,  G,  D,  F,  	    C#, A,  Bb, Eb
---------------------------------------------------------
A>------------------------------------------------------> 


--------------------------------
group 1: C,  F#, G#, B  over A


p/0/11:..............Eb C  F# Ab B  E          G  D  F  C# A  Bb     not oct

p/1/2:...............A  C  F  Ab Eb F# 		D  Bb B  E  C# G     
p/4/2:...............C  Eb Ab B  F# A  		F  C# D  G  E  Bb     subset of not oct
p/10/2:..............F# A  D  F  C  Eb 		B  G  Ab C# Bb E      Link to Retro of Inversion

p/7/3:...............F# B  D  A  C  Ab E       F  Bb G  C# Eb        not oct   (A Mel Minor)


i/4/2:...............Ab F  C  A  D  B  		Eb G  F# C# E  Bb 
i/7/2:...............B  Ab Eb C  F  D  		F# Bb A  E  G  C# 
i/10/3:..............B  F# Eb Ab F  A  		C# C  G  Bb E  D  

i/1/4:...............A  F# B  Ab C  E  		Eb Bb C# G  F  D     not oct

i/0/8:...............B  Eb D  A  C  F# 		E  C# Ab F  Bb G  
i/9/8:...............E  Ab C  B  F# A  Eb 		C# Bb F  D  G        not oct

5x/p/4/2:............Ab B  C  Eb D  F  		A  C# F# G  E  Bb 
5x/p/7/2:............B  D  Eb F# F  Ab 		C  E  A  Bb G  C# 
5x/p/1/3:............Ab A  C  B  D  F# 		Bb Eb E  C# G  F  
5x/p/3/8:............Ab C  F  F# Eb A  		G  Bb B  D  C# E  
5x/p/6/8:............B  Eb Ab A  F# C  		Bb C# D  F  E  G    sub n.o.
  
  
-------------------------------------       
group 2:  E,  G,  D,  F, over A

 
p/0/3:...............B  E  G  D  F  C# A  		Bb Eb C  F# Ab 
p/4/7:...............A  F  C# D  G  E  Bb 		C  Eb Ab B  F#  


i/9/2:...............C# Bb F  D  G  E  		Ab C  B  F# A  Eb 
i/2/7:...............A  C# F  E  B  D  		Ab F# Eb Bb G  C  
i/1/11:..............Bb C# G  F  D  A  		F# B  Ab C  E  Eb 


  
5x/p/6/2:............Bb C# D  F  E  G  		B  Eb Ab A  F# C  
5x/i/0/3:............F  E  C# D  B  G  		Eb Bb A  C  F# Ab 
5x/i/7/8:............D  Bb F  E  G  C# 		Eb C  B  Ab A  F# 

-------------------------------------  
group 3: C#, A,  Bb, Eb


  
p/0/7:...............F  C# A  Bb Eb C  		F# Ab B  E  G  D   n.o.


i/10/7:..............F  A  C# C  G  Bb 		E  D  B  F# Eb Ab  n.o.

 
 
i/9/11:..............F# A  Eb C# Bb F  		D  G  E  Ab C  B   n.o.
 


5x/i/1/11:...........Bb C# G  A  F# F  		D  Eb C  Ab E  B   not a chord, but nice line
 

  
------------------------------------------------------------------------------------------------------------- 
------------------------------------------------------------------------------------------------------------- 
5C   Straddling Two 4-note groups --  

5m:			C,  F#, G#, B,  		E,  G,  D,  F,  	    C#, A,  Bb, Eb


Comment:  Sounds much better if end of c,f#,g#,b  pitches work on next (continuity)


Ex any:      Bb,G,C#               Eb,F#,                Ab,B,D
Ex pit prox: F,E,                  Ab,A  C#,C            E,F   

                     C,  F#, G#, B             E,  G,  D,  F 

p/1/2:...............A  C  F  Ab eb f# 		D  Bb B  E  C# G
p/4/2:...............C  Eb Ab B  f# A  	       F  C# D  G  E  Bb 
p/7/2:...............Eb F# B  D  A  C          Ab E  F  Bb G  C# 
p/10/2:..............F# A  D  F  C  eb         B  G  Ab C# Bb E       Link to Retro of Inversion

p/5/8:...............F# D  Eb Ab F  B  	       C# E  A  C  G  Bb      (c#-c against D)
 
p/6/9:...............Eb E  A  F# C  D  	       F  Bb C# Ab B  G  
 
p/0/11:..............Eb C  F# Ab B  E          G  D  F  C# A  Bb      Not oct.
 
i/10/1:..............E  D  B  f# eb ab 	       F  A  C# C  G  Bb      (c#-c against D) 
i/10/2:..............D  B  F# eb ab F          A  C# C  G  Bb E       (c#-c against D) 
i/10/3:..............B  F# Eb Ab F  A          C# C  G  Bb E  D       (c#-c against D)  

i/7/3:...............Ab Eb C  F  D  f#         Bb A  E  G  C# B  
 
i/1/5:...............F# B  Ab C  E  eb         Bb C# G  F  D  A       Not oct. 
  
i/0/9:...............Eb D  A  C  f# E          C# Ab F  Bb G  B  
 
i/2/10:..............E  B  D  Ab f# eb 	       Bb G  C  A  C# F  
 
 
5x/i/1/3:............F# F  D  Eb C  Ab         E  B  Bb C# G  A       b-bb-a 
5x/i/4/3:............A  Ab F  F# Eb B          G  D  C# E  Bb C       d-c#-c 
 

5x/i/8/8:............Eb B  F# F  Ab D          E  C# C  A  Bb G       (c#-c against D)
 

 
 					E,  G,  D,  F               C#, A, Bb, Eb

 
p/2/9:...............B  C  F  D  ab Bb 		  C# F# A  E  G  Eb 
 
p/8/11:..............B  Ab D  E  G  C  		  Eb Bb C# A  F  F#        Not Oct.
 
i/9/5:...............D  G  E  Ab C  b            F# A  Eb C# Bb F         Not Oct.
 
5x/p/3/3:............Bb B  D  C# E  ab           C  F  F# Eb A  G         Not Oct. 
 
5x/i/2/9:............F  C  B  D  ab Bb            G  F# Eb E  C# A        First hex not oct.
 

                      C#, A, Bb, Eb                C,  F#, G#, B 

 
p/2/2:...............Bb C# F# A  E  g  			Eb B  C  F  D  Ab 
p/5/2:...............C# E  A  C  g  bb 			F# D  Eb Ab F  B  
p/8/2:...............E  G  C  Eb bb c# 			A  F  F# B  Ab D  
p/11/2:..............G  Bb Eb F# c# E  			C  Ab A  D  B  F  
 
 
i/1/8:...............C  E  Eb Bb c# g  			F  D  A  F# B  Ab 
i/4/8:...............Eb G  F# C# E  bb 			Ab F  C  A  D  B  
i/7/8:...............F# Bb A  E  g  c# 			B  Ab Eb C  F  D  
i/10/8:..............A  C# C  G  bb E  			D  B  F# Eb Ab F  
 

5x/p/1/8:............F# Bb Eb E  c# g  			F  Ab A  C  B  D  
5x/p/4/8:............A  C# F# G  E  bb 			Ab B  C  Eb D  F  
5x/p/7/8:............C  E  A  Bb g  c# 			B  D  Eb F# F  Ab 
5x/p/10/8:...........Eb G  C  C# bb E  			D  F  F# A  Ab B  
 

5x/i/2/2:............Bb G  F# Eb E  c# 			A  F  C  B  D  Ab 
5x/i/5/2:............C# Bb A  F# g  E  			C  Ab Eb D  F  B  
5x/i/8/2:............E  C# C  A  bb g  			Eb B  F# F  Ab D  
5x/i/11/2:...........G  E  Eb C  c# bb 			F# D  A  Ab B  F  
 

------------------------------------------------------------------------------------------------------------- 
------------------------------------------------------------------------------------------------------------- 
 
6b


Self-Similarity of embedded line


C..F#.G#.F..E..C#.D..B..G..Eb.Bb.A..
...............c#.......g........a..
...f#....f........d........eb.......
c.....g#....e........b........bb              


C..F#.G#.B..E..G..D..F..C#.A..Bb.Eb.
...............g........c#.......eb.
...f#....b........d........a........
c.....g#....e........f........bb

------------------------------------------------------
------------------------------------------------------



=========================================================

15


LITERAL ROW-MATCHES to 4-NOTE CHORDS

0 -- a,d,c,ab  -- 0,1,4,6/

5x/p/8/0:............Ab D  C  A  		E  C# F# Eb G  B  Bb F
5x/i/7/5:............D  A  C  Ab 		E  F  Bb G  C# Eb F# B 
5x/i/11/8:...........C  Ab A  D  		B  F  G  Bb Eb F# C# E 
---------------------------------------------------------

1 -- c,ab,f#,f -- 0,1,3,7/

r/0/8:...............F  Ab F# C  		A  Bb Eb G  B  D  C# E
i/7/5:...............F# F  Ab C  		E  A  Bb G  C# B  D  Eb
i/3/8:...............Ab C  F  F# 		Eb A  G  Bb B  D  C# E

---------------------------------------------------------

2 -- d,f,ab,bb -- 0,2,5,8\

5x/p/8/10:...........Bb F  Ab D  		C  A  E  C# F# Eb G  B 
5x/i/2/11:...........F  D  Ab Bb 		C# F# A  E  G  Eb B  C


---------------------------------------------------------

3 -- ab,bb,f,g -- 0,2,3,5/

p/6/4:...............Bb G  Ab F  		C# A  E  Eb F# C  D  B
i/9/4:...............F  Ab G  Bb 		D  F# B  C  A  Eb C# E 

5x/p/0/4:............Ab F  Bb G  		B  Eb D  A  C  F# E  C# 
5x/i/3/4:............G  Bb F  Ab 		E  C  C# F# Eb A  B  

---------------------------------------------------------

4 -- f,b,e,d   -- 0,1,3,6\

i/2/9:...............B  E  F  D  		Ab F# A  Bb C# C  Eb G 

5x/p/2/9:............F  E  B  D  		Ab F# Eb Bb G  C  A  C#

---------------------------------------------------------

5 -- bb,g,c#,b -- 0,2,3,6\


p/1/10:..............B  Bb C# G  		A  F# F  D  Eb C  Ab E 
i/7/11:..............Bb G  C# B  		D  Eb F# F  Ab C  E  A

5x5p/i/0/1:..........G  Bb B  C# 		F# D  Eb E  A  Ab F  C


---------------------------------------------------------

6 -- b,eb,d,a  -- 0,1,4,6\

5x/p/4/5:............A  D  B  Eb 		G  F# C# E  Bb Ab F  C
5x/p/0/8:............B  Eb D  A  		C  F# E  C# Ab F  Bb G
5x/i/3/0:............Eb A  B  D  		G  Bb F  Ab E  C  C# F# 

---------------------------------------------------------

7 -- g,f#,b,eb -- 0,1,4,8\    ***** not octotonic

p/4/6:...............F# Eb B  G  		D  C# E  Bb C  A  Ab F
p/8/7:...............G  Eb B  F# 		F  Ab D  E  C# C  A  Bb

5x/p/8/6:............F# Eb G  B  		Bb F  Ab D  C  A  E  C#
5x/p/4/7:............B  Eb G  F# 		C# E  Bb Ab F  C  A  D

---------------------------------------------------------

8 -- eb,c#,g,f#-- 0,1,4,6\

5x/p/8/5:............C# F# Eb G  		B  Bb F  Ab D  C  A  E 
5x/p/4/8:............Eb G  F# C# 		E  Bb Ab F  C  A  D  B
5x/i/7/0:............G  C# Eb F# 		B  D  A  C  Ab E  F  Bb

---------------------------------------------------------

9 -- f#,e,eb,c#-- 0,2,3,5\


p/2/4:...............F# Eb E  C# 		A  F  C  B  D  Ab Bb G
i/5/4:...............C# E  Eb F# 		Bb D  G  Ab F  B  A  C 

5x/p/8/4:............E  C# F# Eb 		G  B  Bb F  Ab D  C  A
5x/i/11/4:...........Eb F# C# E  		C  Ab A  D  B  F  G  Bb 

---------------------------------------------------------

10 --c#,a,bb,c -- 0,1,3,4/

p/8/3:...............C# C  A  Bb 		G  Eb B  F# F  Ab D  E

i/2/3:...............A  Bb C# C  		Eb G  B  E  F  D  Ab F#

---------------------------------------------------------

11 --e,c,a,e   -- 0,3,7/

i/11/6:..............A  C  E  		Ab C# D  B  F  Eb F# G  Bb
i/7/8:...............C  E  A  		Bb G  C# B  D  Eb F# F  Ab 

5x/p/8/2:............C  A  E  		C# F# Eb G  B  Bb F  Ab D  
5x/i/5/3:............E  A  C  		G  Bb F# D  Eb Ab F  B  C# 

=========================================================
=========================================================

16


ROWS THAT WORK WITH CHORDS -- AT LEAST 6 NOTES                                      

0 -- a,d,c,ab  -- 0,1,4,6/
                                             
5x/p/8/0:............Ab D  C  A  		E  C# F# Eb G  B  Bb F
5x/i/7/5:............D  A  C  Ab 		E  F  Bb G  C# Eb F# B 
5x/i/11/8:...........C  Ab A  D  		B  F  G  Bb Eb F# C# E 

5x/p/9/7:............E  Ab C  B  F# A  	Eb C# Bb F  D  G          **NOT OCT

5x/i/7/2:............F# B  D  A  C  Ab E	F Bb G  C# Eb             **NOT OCT

---------------------------------------------------------

1 -- c,ab,f#,f -- 0,1,3,7/
 
5x/i/9/11:...........C  A  Eb F  Ab C# 	E  B  D  Bb F# G          *N-O 

---------------------------------------------------------

2 -- d,f,ab,bb -- 0,2,5,8\

5x/p/8/10:...........Bb F  Ab D  		C  A  E  C# F# Eb G  B 
5x/i/2/11:...........F  D  Ab Bb 		C# F# A  E  G  Eb B  C



5x/p/10/2:...........D  B  F# Eb Ab F  		A  C# C  G  Bb E   
d,f,ab,bb & d,eb,f,f#,g#,b,= d,eb,f,f#,ab,bb,b,
  
5x/p/7/3:............Ab Eb C  F  D  F# 		Bb 	A  E  G  C# B  

  
5x/p/0/4:............Ab F  Bb G  B  Eb D  		A  C  F# E  C#        * eb har maj.
5x/p/3/4:............B  Ab C# Bb D  F# F  		C  Eb A  G  E         * f# har maj.
5x/p/7/4:............Eb C  F  D  F# Bb 		A E  G  C# B  Ab      * bb har maj.
5x/p/9/4:............F  D  G  E  Ab C  		B  F# A  Eb C# Bb     c har maj.
 
5x/p/0/5:............F  Bb G  B  Eb D  		A  C  F# E  C# Ab 
5x/p/3/5:............Ab C# Bb D  F# F  		C  Eb A  G  E  B      bb phryg b4     Match to main
   
5x/p/3/7:............Bb D  F# F  C  Eb 		A  G  E  B  Ab C# 

5x/p/5/7:............C  E  Ab G  D  F  		B  A  F# C# Bb Eb 
5x/p/8/7:............Eb G  B  Bb F  Ab 		D  C  A  E  C# F# 
5x/p/11/7:...........F# Bb D  C# Ab B  		F  Eb C  G  E  A  
 
--------------------------------
     
5x/p/2/11:...........B  D  Ab F# Eb Bb 		G  C  A  C# F  E  not oct
  
5x/i/0/2:............Ab B  E  G  D  F  		C# A  Bb Eb C  F# oct
5x/i/3/2:............B  D  G  Bb F  Ab 		E  C  C# F# Eb A  
5x/i/6/2:............D  F  Bb C# Ab B  		G  Eb E  A  F# C  
5x/i/9/2:............F  Ab C# E  B  D  		Bb F# G  C  A  Eb 
  
5x/i/0/3:............B  E  G  D  F  C# 		A  Bb Eb C  F# Ab oct
5x/i/1/3:............C  F  Ab Eb F# D  		Bb B  E  C# G  A  not oct
5x/i/3/3:............D  G  Bb F  Ab E  		C  C# F# Eb A  B  at intersection
5x/i/6/3:............F  Bb C# Ab B  G  		Eb E  A  F# C  D 
5x/i/9/3:............Ab C# E  B  D  Bb 		F# G  C  A  Eb F  
   
5x/i/1/4:............F  Ab Eb F# D  Bb 		B  E  C# G  A  C  not oct
5x/i/3/4:............G  Bb F  Ab E  C  		C# F# Eb A  B  D  not oct  
5x/i/1/5:............Ab Eb F# D  Bb B  		E  C# G  A  C  F  not oct
5x/i/5/7:............Bb F# D  Eb Ab F  		B  C# E  A  C  G  not oct  
5x/i/7/7:............C  Ab E  F  Bb G  		C# Eb F# B  D  A  not oct
5x/i/1/8:............D  Bb B  E  C# G  		A  C  F  Ab Eb F# intersect of type 3 and oct
     
5x/i/4/8:............F  C# D  G  E  Bb 		C  Eb Ab B  F# A  oct

5x/i/5/8:............F# D  Eb Ab F  B  		C# E  A  C  G  Bb inter?

5x/i/7/8:............Ab E  F  Bb G  C# 		Eb F# B  D  A  C  oct
5x/i/10/8:...........B  G  Ab C# Bb E  		F# A  D  F  C  Eb oct        Link to Retro of Inversion
   
5x/i/2/11:...........F  D  Ab Bb C# F# 		A  E  G  Eb B  C  not oct
  
5x/i/11/11:..........D  B  F  G  Bb Eb 		F# C# E  C  Ab A  * not oct

---------------------------------------------------------
---------------------------------------------------------

3 -- ab,bb,f,g -- 0,2,3,5/

p/6/4:...............Bb G  Ab F  		C# A  E  Eb F# C  D  B
i/9/4:...............F  Ab G  Bb 		D  F# B  C  A  Eb C# E 

5x/p/0/4:............Ab F  Bb G  		B  Eb D  A  C  F# E  C# 
5x/i/3/4:............G  Bb F  Ab 		E  C  C# F# Eb A  B  

p/0/2:...............Ab F  E  C# D  B  		G  Eb Bb A  C  F#
p/3/2:...............B  Ab G  E  F  D  		Bb F# C# C  Eb A

i/6/3:...............C# D  F  E  G  B  		Eb Ab A  F# C  Bb 
i/3/5:...............D  C# E  Ab C  F  		F# Eb A  G  Bb B  
i/2/8:...............G  B  E  F  D  Ab 		F# A  Bb C# C  Eb 
i/11/8:..............E  Ab C# D  B  F  		Eb F# G  Bb A  C  
 
5x/p/6/3:............G  D  B  E  C# F  		A  Ab Eb F# C  Bb 
5x/p/9/4:............F  D  G  E  Ab C  		B  F# A  Eb C# Bb  not oct Lyd b7
5x/p/5/7:............C  E  Ab G  D  F  		B  A  F# C# Bb Eb  not oct
5x/p/2/8:............C# F  E  B  D  Ab 		F# Eb Bb G  C  A  
5x/p/5/8:............E  Ab G  D  F  B  		A  F# C# Bb Eb C  
   
5x/i/0/2:............Ab B  E  G  D  F  		C# A  Bb Eb C  F# 
5x/i/9/2:............F  Ab C# E  B  D  		Bb F# G  C  A  Eb 
5x/i/0/3:............B  E  G  D  F  C# 		A  Bb Eb C  F# Ab 
  
---------------------------------------------------------

4 -- f,b,e,d   -- 0,1,3,6\

i/2/9:...............B  E  F  D  		Ab F# A  Bb C# C  Eb G 
5x/p/2/9:............F  E  B  D  		Ab F# Eb Bb G  C  A  C#


p/0/2:...............Ab F  E  C# D  B  G  		Eb Bb A  C  F#                   links to main
p/3/2:...............B  Ab G  E  F  D  Bb 		F# C# C  Eb A
p/6/2:...............D  B  Bb G  Ab F  C# 		A  E  Eb F# C  
p/9/2:...............F  D  C# Bb B  Ab E  		C  G  F# A  Eb 
p/1/8:...............Ab E  B  Bb C# G  		A  F# F  D  Eb C

p/2/8:...............A  F  C  B  D  Ab 		Bb G  F# Eb E  C#  not oct
p/4/8:...............B  G  D  C# E  Bb 		C  A  Ab F  F# Eb
p/7/8:...............D  Bb F  E  G  C# 		Eb C  B  Ab A  F#
p/10/8:..............F  C# Ab G  Bb E  		F# Eb D  B  C  A
 
i/0/2:...............E  G  Ab B  Bb C# F  		A  D  Eb C  F#
i/1/2:...............F  Ab A  C  B  D  		F# Bb Eb E  C# G  not oct
i/3/2:...............G  Bb B  D  C# E  Ab 		C  F  F# Eb A  
i/6/2:...............Bb C# D  F  E  G  B  		Eb Ab A  F# C  
i/9/2:...............C# E  F  Ab G  Bb D  		F# B  C  A  Eb 

 
5x/p/0/2:............E  C# Ab F  Bb G  B  		Eb D  A  C  F# 
5x/p/3/2:............G  E  B  Ab C# Bb D  		F# F  C  Eb A  
5x/p/4/2:............Ab F  C  A  D  B  		Eb G  F# C# E  Bb N.O.
5x/p/6/2:............Bb G  D  B  E  C# F  		A  Ab Eb F# C  
5x/p/9/2:............C# Bb F  D  G  E  Ab 		C  B  F# A  Eb 
5x/p/0/3:............C# Ab F  Bb G  B  		Eb D  A  C  F# E   

5x/p/9/5:............D  G  E  Ab C  B  		F# A  Eb C# Bb F  Not OCT
5x/p/2/7:............A  C# F  E  B  D  		Ab F# Eb Bb G  C  N.O. 
5x/p/5/7:............C  E  Ab G  D  F  B  		A  F# C# Bb Eb    N.O. 
5x/p/8/8:............G  B  Bb F  Ab D  		C  A  E  C# F# Eb 
5x/p/11/8:...........Bb D  C# Ab B  F  		Eb C  G  E  A  F# 
5x/p/7/10:...........A  E  G  C# B  Ab 		Eb C  F  D  F# Bb 
5x/p/8/11:...........F  Ab D  C  A  E  		C# F# Eb G  B  Bb N.O.
   

5x/i/0/3:............B  E  G  D  F  C# A  		Bb Eb C  F# Ab      N.O.
  
5x/i/0/4:............E  G  D  F  C# A  Bb 		Eb C  F# Ab B       NOT OCT
5x/i/7/4:............B  D  A  C  Ab E  F  		Bb G  C# Eb F#      NOT OCT 
5x/i/4/7:............A  F  C# D  G  E  		Bb C  Eb Ab B  F#   N.O.
5x/i/11/7:...........E  C  Ab A  D  B  F  		G  Bb Eb F# C#      N.O.
5x/i/1/8:............D  Bb B  E  C# G  		A  C  F  Ab Eb F#   
 
5x/i/7/8:............Ab E  F  Bb G  C# 		Eb F# B  D  A  C  
5x/i/10/8:...........B  G  Ab C# Bb E  		F# A  D  F  C  Eb       Link to Retro of Inversion
5x/i/11/8:...........C  Ab A  D  B  F  G  		Bb Eb F# C# E  
    
5x/i/5/11:...........Ab F  B  C# E  A  		C  G  Bb F# D  Eb   
5x/i/8/11:...........B  Ab D  E  G  C  		Eb Bb C# A  F  F#  N.O.
  
---------------------------------------------------------

5 -- bb,g,c#,b -- 0,2,3,6\


p/1/10:..............B  Bb C# G  		A  F# F  D  Eb C  Ab E 
i/7/11:..............Bb G  C# B  		D  Eb F# F  Ab C  E  A
5x5p/i/0/1:..........G  Bb B  C# 		F# D  Eb E  A  Ab F  C


ex any:a,c     ex pit prox f,f#, f#,g# d,d# 

 
p/2/2:...............Bb G  F# Eb E  C# 		A  F  C  B  D  Ab      N.O.

p/0/2:...............Ab F  E  C# D  B  G  		Eb Bb A  C  F#     links to main 
p/3/2:...............B  Ab G  E  F  D  Bb 		F# C# C  Eb A  
p/6/2:...............D  B  Bb G  Ab F  C# 		A  E  Eb F# C  
p/9/2:...............F  D  C# Bb B  Ab E  		C  G  F# A  Eb 
      
i/1/8:...............F# Bb Eb E  C# G  		F  Ab A  C  B  D       N.O. 
   
    
5x/p/8/4:............E  C# F# Eb G  B  Bb 		F  Ab D  C  A           N.O.
      
5x/p/4/7:............B  Eb G  F# C# E  Bb 		Ab F  C  A  D           N.O.
5x/p/8/7:............Eb G  B  Bb F  Ab 		D  C  A  E  C# F#       N.O.
   
   
5x/i/9/3:............Ab C# E  B  D  Bb F# 	G  	C  A  Eb F 		
     
5x/i/1/7:............F# D  Bb B  E  C# G  		A  C  F  Ab Eb         N.O. 
5x/i/10/7:...........Eb B  G  Ab C# Bb E  		F# A  D  F             N.O.  
    
5x/i/4/8:............F  C# D  G  E  Bb 		C  Eb Ab B  F# A  
5x/i/7/8:............Ab E  F  Bb G  C# 		Eb F# B  D  A  C  
      
5x/i/7/11:...........Bb G  C# Eb F# B  		D  A  C  Ab E  F       N.O. 
   
---------------------------------------------------------

6 -- b,eb,d,a  -- 0,1,4,6\

   
p/10/3:..............Eb D  B  C  A  F  		C# Ab G  Bb E  F#  
   
   
5x/p/4/4:............C  A  D  B  Eb G  F# 		C# E  Bb Ab F  N.O.
   
5x/p/0/7:............G  B  Eb D  A  C  F# 		E  C# Ab F  Bb  N.O.
   
      
5x/i/1/2:............A  C  F  Ab Eb F# D  		Bb B  E  C# G  
5x/i/4/2:............C  Eb Ab B  F# A  F  		C# D  G  E  Bb 
5x/i/7/2:............Eb F# B  D  A  C  Ab 		E  F  Bb G  C# 
5x/i/10/2:...........F# A  D  F  C  Eb B  		G  Ab C# Bb E               Links to Retro of Inversion
   
5x/i/1/3:............C  F  Ab Eb F# D  		Bb B  E  C# G  A  
5x/i/4/3:............Eb Ab B  F# A  F  		C# D  G  E  Bb C  
5x/i/7/3:............F# B  D  A  C  Ab 		E  F  Bb G  C# Eb 
5x/i/10/3:...........A  D  F  C  Eb B  G  		Ab C# Bb E  F#     N.O.      Match to main  
  
5x/i/2/7:............G  Eb B  C  F  D  		Ab Bb C# F# A  E   N.O.
      
5x/i/3/11:...........F# Eb A  B  D  G  		Bb F  Ab E  C  C#   N.O.
   
---------------------------------------------------------

7 -- g,f#,b,eb -- 0,1,4,8\    ***** not octotonic

p/4/6:...............F# Eb B  G  		D  C# E  Bb C  A  Ab F
p/8/7:...............G  Eb B  F# 		F  Ab D  E  C# C  A  Bb

5x/p/8/6:............F# Eb G  B  		Bb F  Ab D  C  A  E  C#
5x/p/4/7:............B  Eb G  F# 		C# E  Bb Ab F  C  A  D

ex any: f,ab ex pit prox: bb,c d,e bb,a d,c# c,c#

p/2/2:...............Bb G  F# Eb E  C# 		A F  C  B  D  Ab 
p/10/2:..............F# Eb D  B  C  A  		F  C# Ab G  Bb E  
p/9/8:...............E  C  G  F# A  Eb 		F  D  C# Bb B  Ab 
   
i/8/2:...............C  Eb E  G  F# A  		C# 	F  Bb B  Ab D   
i/1/8:...............F# Bb Eb E  C# G  		F  Ab A  C  B  D  
i/9/8:...............D  F# B  C  A  Eb 		C# E  F  Ab G  Bb 

7 -- g,f#,b,eb 

5x/p/11/2:...........Eb C  G  E  A  F# 		Bb D  C# Ab B  F  
5x/p/8/3:............A  E  C# F# Eb G  B  		Bb F  Ab D  C  
5x/p/4/4:............C  A  D  B  Eb G  F# 		C# E  Bb Ab F  
5x/p/0/7:............G  B  Eb D  A  C  F# 		E  C# Ab F  Bb 
5x/p/4/7:............B  Eb G  F# C# E  Bb 		Ab F  C  A  D      
5x/p/3/11:...........C  Eb A  G  E  B  		Ab C# Bb D  F# F      Match to main
   

5x/i/7/2:............Eb F# B  D  A  C  		Ab E  F  Bb G  C#
5x/i/7/11:...........Bb G  C# Eb F# B  D  		A  C  Ab E  F  
5x/i/11/2:...........G  Bb Eb F# C# E  C  		Ab A  D  B  F  
5x/i/2/3:............C# F# A  E  G  Eb B  		C  F  D  Ab Bb 
5x/i/6/7:............B  G  Eb E  A  F# C  		D  F  Bb C# Ab 
5x/i/3/11:...........F# Eb A  B  D  G  Bb 		F  Ab E  C  C# 
  
---------------------------------------------------------

8 -- eb,c#,g,f#-- 0,1,4,6\

5x/p/8/5:............C# F# Eb G  		B  Bb F  Ab D  C  A  E 
5x/p/4/8:............Eb G  F# C# 		E  Bb Ab F  C  A  D  B
5x/i/7/0:............G  C# Eb F# 		B  D  A  C  Ab E  F  Bb


p/8/4:...............C  A  Bb G  Eb B  F# 		F  Ab D  E  C# 
p/8/5:...............A  Bb G  Eb B  F# 		F  Ab D  E  C# C  

   
p/1/9:...............E  B  Bb C# G  			A  F# F  D  Eb C  Ab 
p/3/9:...............F# C# C  Eb A  			B  Ab G  E  F  D  Bb   
p/7/11:..............E  G  C# Eb C  			B  Ab A  F# D  Bb F  
    


8 -- eb,c#,g,f#-- 0,1,4,6\
   

  
5x/p/2/3:............Eb Bb G  C  A  C# 		F  E  B  D  Ab F# 
5x/p/5/3:............F# C# Bb Eb C  E  Ab G  	D  F  B  A  
5x/p/8/3:............A  E  C# F# Eb G  B  		Bb F  Ab D  C     N .O.   **** Nice line
5x/p/11/3:...........C  G  E  A  F# Bb 		D C# Ab B  F  Eb 
  
5x/p/4/7:............B  Eb G  F# C# E  Bb 		Ab F  C  A  D        N.O.  Bb sounds dorky, sadly.

   
5x/i/2/2:............Bb C# F# A  E  G  Eb B  	C  F  D  Ab  
5x/i/8/2:............E  G  C  Eb Bb C# A  		F  F# B  Ab D  
 
5x/i/11/2:...........G  Bb Eb F# C# E  C  		Ab A  D  B  F 
5x/i/6/7:............B  G  Eb E  A  F# C  		D  F  Bb C# Ab 
	
5x/i/1/9:............Bb B  E  C# G  A  C  		F  Ab Eb F# D  
5x/i/3/9:............C  C# F# Eb A  B  		D  G  Bb F  Ab E  
5x/i/7/11:...........Bb G  C# Eb F# B  		D  A  C  Ab E  F  
   

---------------------------------------------------------

9 -- f#,e,eb,c#-- 0,2,3,5\


p/2/4:...............F# Eb E  C# 		A  F  C  B  D  Ab Bb G
i/5/4:...............C# E  Eb F# 		Bb D  G  Ab F  B  A  C 

5x/p/8/4:............E  C# F# Eb 		G  B  Bb F  Ab D  C  A
5x/i/11/4:...........Eb F# C# E  		C  Ab A  D  B  F  G  Bb 

   
p/1/9:...............E  B  Bb C# G  			A  F# F  D  Eb C  Ab 
p/6/9:...............A  E  Eb F# C  			D  B  Bb G  Ab F  C# 
p/9/9:...............C  G  F# A  Eb 			F  D  C# Bb B  Ab E  
    
p/4/11:..............C# E  Bb C  A  			Ab F  F# Eb B  G  D  
p/10/11:.............G  Bb E  F# Eb 			D  B  C  A  F  C# Ab 
        
   
i/1/9:...............Bb Eb E  C# G  			F  Ab A  C  B  D  F# 
i/6/9:...............Eb Ab A  F# C  			Bb C# D  F  E  G  B  
i/7/9:...............E  A  Bb G  C# 			B  D  Eb F# F  Ab C  
i/10/9:..............G  C  C# Bb E  			D  F  F# A  Ab B  Eb 
        

9 -- f#,e,eb,c#-- 0,2,3,5\


5x/p/3/3:............E  B  Ab C# Bb 			D  F# F  C  Eb A  G  
   
   
5x/p/1/7:............Ab C  E  Eb Bb C# 		G  F  D  A  F# B     N.O.
5x/p/4/7:............B  Eb G  F# C# E  Bb 		Ab F  C  A  D        N.O. 
   
   
5x/p/6/9:............A  Ab Eb F# C  			Bb G  D  B  E  C# F  N.O.
5x/p/7/9:............Bb A  E  G  C# 			B Ab Eb C  F  D  F#  nice side-step pair with above
5x/p/10/9:...........C# C  G  Bb E  			D  B  F# Eb Ab F  A  
   
5x/p/4/10:...........F# C# E  Bb Ab 			F  C  A  D  B  Eb G  N.O.
5x/p/9/10:...........B  F# A  Eb C# 			Bb F  D  G  E  Ab C  N.O.
     
5x/i/7/0:............G  C# Eb F# B  			D  A  C  Ab E  F  Bb N.O.
   
   
5x/i/4/3:............Eb Ab B  F# A  			F  C# D  G  E  Bb C   N.O.

5x/i/2/4:............F# A  E  G  Eb B  		C  F  D  Ab Bb C#     N.O.
5x/i/5/4:............A  C  G  Bb F# 			D  Eb Ab F  B  C# E  
5x/i/8/4:............C  Eb Bb C# A  			F  F# B  Ab D  E  G  
5x/i/11/4:...........Eb F# C# E  C  Ab A  		D  B  F  G  Bb        N.O.
   
5x/i/11/5:...........F# C# E  C  Ab A  		D  B  F  G  Bb Eb 
5x/i/3/7:............Ab E  C  C# F# Eb A  		B  D  G  Bb F  
5x/i/6/7:............B  G  Eb E  A  F# C  		D  F  Bb C# Ab 
   
   
5x/i/0/9:............A  Bb Eb C  F# 			Ab B  E  G  D  F  C# 
5x/i/1/9:............Bb B  E  C# G  			A  C  F  Ab Eb F# D  
5x/i/6/9:............Eb E  A  F# C  			D  F  Bb C# Ab B  G  
5x/i/9/9:............F# G  C  A  Eb 			F  Ab C# E  B  D  Bb 
   
5x/i/3/10:...........C# F# Eb A  B  			D  G  Bb F  Ab E  C    N.O.
5x/i/10/10:..........Ab C# Bb E  F# 			A  D  F  C  Eb B  G    N.O.      Match to main
5x/i/1/11:...........E  C# G  A  C  			F Ab Eb F# D  Bb B  
5x/i/7/11:...........Bb G  C# Eb F# B  		D  A  C  Ab E  F       N.O.
5x/i/10/11:..........C# Bb E  F# A  			D  F  C  Eb B  G  Ab            Match to main
   

---------------------------------------------------------

10 --c#,a,bb,c -- 0,1,3,4/

p/8/3:...............C# C  A  Bb 		G  Eb B  F# F  Ab D  E
i/2/3:...............A  Bb C# C  		Eb G  B  E  F  D  Ab F#

      
p/7/10:..............F  E  G  C# Eb C  		B  Ab A  F# D  Bb   not good cell, but nice line
p/1/11:..............Bb C# G  A  F# F  		D  Eb C  Ab E  B  
      
i/9/11:..............C  A  Eb C# E  			F  Ab G  Bb D  F# B  
   

5x/p/2/2:............F# Eb Bb G  C  A  C# 		F  E  B  D  Ab 
5x/p/5/2:............A  F# C# Bb Eb C  E  		Ab G  D  F  B  
5x/p/8/2:............C  A  E  C# F# Eb G  		B  Bb F  Ab D  
   
5x/p/10/7:...........F  A  C# C  G  Bb E  		D  B  F# Eb Ab     Not Oct.   
   

5x/p/1/9:............E  Eb Bb C# G  			F  D  A  F# B  Ab C  
5x/p/3/9:............F# F  C  Eb A  			G  E  B  Ab C# Bb D  
   
5x/p/9/11:...........F# A  Eb C# Bb F  		D  G  E  Ab C  B  N.O.
   

10 --c#,a,bb,c -- 0,1,3,4/

  
5x/i/8/4:............C  Eb Bb C# A  			F  F# B  Ab D  E  G  
	
 
5x/i/0/7:............F  C# A  Bb Eb C  F# 		Ab B  E  G  D      N.O. F-F# seems, sometimes, counterintuitive on an A chord
 
   
5x/i/3/8:............E  C  C# F# Eb A  		B  D  G  Bb F  Ab 
5x/i/6/8:............G  Eb E  A  F# C  		D  F  Bb C# Ab B  
5x/i/9/8:............Bb F# G  C  A  Eb 		F Ab C# E  B  D      Nice line down to F
   

5x/i/1/11:...........E  C# G  A  C  F  		Ab Eb F# D  Bb B  
   
---------------------------------------------------------

11 --e,c,a,e   -- 0,3,7/

i/11/6:..............A  C  E  		Ab C# D  B  F  Eb F# G  Bb
i/7/8:...............C  E  A  		Bb G  C# B  D  Eb F# F  Ab 

5x/p/8/2:............C  A  E  		C# F# Eb G  B  Bb F  Ab D  
5x/i/5/3:............E  A  C  		G  Bb F# D  Eb Ab F  B  C#  nice

 
p/2/8:...............A  F  C  B  D  Ab 		Bb G  F# Eb E  C#


Complete cycles that (mostly) spare A-C-E.

These have non-harm tones that approach harm tones, rather
than crossing over them:   Bb--A, rather than Bb-Ab.


p/7/2:...............Eb C  B  Ab A  F# D  Bb F  E  G  C#   my fave






p/8/2:...............E  C# C  A  Bb G  Eb B  F# F  Ab D  

p/11/2:..............G  E  Eb C  C# Bb F# D  A  Ab B  F  
   
p/0/8:...............G  Eb Bb A  C  F# Ab F  E  C# D  B    match to main
      
5x/p/2/2:............F# Eb Bb G  C  A  C# F  E  B  D  Ab   maybe  
    
5x/p/1/8:............C  E  Eb Bb C# G  F  D  A  F# B  Ab 
   
5x/p/0/11:...........A  C  F# E  C# Ab F  Bb G  B  Eb D  

5x/p/3/11:...........C  Eb A  G  E  B  Ab C# Bb D  F# F      Match to main
    
5x/i/4/2:............C  Eb Ab B  F# A  F  C# D  G  E  Bb   ? better in the bass below the chord ??
        
5x/i/8/3:............G  C  Eb Bb C# A  F  F# B  Ab D  E  
 
5x/i/11/7:...........E  C  Ab A  D  B  F  G  Bb Eb F# C#     **  Quite nice over A minor
   
5x/i/6/7:............B  G  Eb E  A  F# C  D  F  Bb C# Ab   
   
5x/i/0/8:............C# A  Bb Eb C  F# Ab B  E  G  D  F  
 
5x/i/3/8:............E  C  C# F# Eb A  B  D  G  Bb F  Ab
   
5x/i/1/11:...........E  C# G  A  C  F  Ab Eb F# D  Bb-B  


=========================================================
=========================================================



The Results are weird, and not entirely satisfactory:


G,  D,  F,  C#, A,  Bb,		D#, C,  F#, G#, B,  E,     7,3,8,8,1,5,9,6,2,3,5,(3)  G on bottom 5/8 groove, very nice

A,  F,  G,  D,  Bb, C#,       E,  D#, G#, B,  C,  F#,    8,2,7,8,3,3,11,5,3,1,6,(3)          

Bb, F,  A,  G,  C#, D,        F#, E,  C,  B,  D#, G#,    7,4,10,6,1,4,10,8,11,4,5,(2)                  

C,  G,  Bb, F,  D,  Eb,       G#, F#, B,  C#, E,  a,     7,3,7,9,1,5,10,5,2,3,5,(3) 

C#, G,  Bb, F,  D,  E,        G#, F#, B,  C,  Eb, a,     6,3,7,9,2,4,10,5,1,3,6,(4)                                       

D,  A,  C,  G#, e,  F,        Bb, G,  C#, D#, F#, B,     7,3,8,8,1,5,9,6,2,3,5,(3)          

e,  Bb, D,  C#, F,  G,        B,  A,  D#, F#, G#, C,     6,4,11,4,2,4,10,6,3,2,4,(4)          

F,  C#, e,  Bb, G,  A,        C,  B,  D,  F#, G#, D#,    8,3,6,9,2,3,11,3,4,2,7,(2)           



-----------------------------------------------------------------------------------------  
====================================================================================================

Summary of self-sim embedding done so far.

factors in choosing row successions:

-embedding pattern
-first six notes of new with last 6 notes of old
-tones not killed -- tones in common between two rows



ok. we have 

p/0/:...............C  F# Ab B  E  G  D  F  C# A  Bb Eb 



-------------------------------------------------------------------
===================================================================
not killed by 4-note | 3-note groups of below row:  a | d,eb,f#,g,a,bb
p/5/:...............C  G  Bb F# D  Eb Ab F  B  C# E  A  


not killed by 4-note | 3-note groups of below row:  b | e,f,g#,a,b,c
p/7/4:...............B  D  A  C  Ab E  F  Bb G  C# Eb F# 
.....................b..............e........g...........
........................d..............F........C# 



not killed by 4-note | 3-note groups of below row:  a | d,eb,f#,g,a,bb                           
p/5/:...............C  G  Bb F# D  Eb Ab F  B  C# E  A 
...............................................C#....A
..........................Bb.......Eb...................    



C,G,Bb,F# to D,Eb,Ab,F to B,C#,E,A,C

not killed:  a, |  ab,a,c,e,f
5x/ri/7/8:...........C  Eb C# G  E  F  Bb D  F# A  Ab B  
.....................c........g........bb....f#.......... 

not killed by 4-note | 3-note groups of below row:  a  |  ab,a,b,c,eb,e 
ri/1/8:..............D  F  G  C# Bb Eb E  C  Ab B  F# A  
.....................d..............eb.......ab...........
........................f....

not killed:  a, |  ab,a,c,e,f
5x/ri/7/7:...........B  C  Eb C# G  E  F  Bb D  F# A  Ab 
.....................b........c#....e..............a......
........................c...... 


C,Eb,Db,G  to E,F,Bb,D to F#,A,G#,B


ri/6/10:.............C  F# Eb Ab A  F  C# E  B  D  G  Bb 
.....................c.....eb..........db..........g.......


5x/ri/8/9:...........E  D  Ab F  F# B  Eb G  Bb A  C  C# 
.....................e........f..............bb.........
........................d 


5x/ri/6/11:..........F# Eb E  A  C# F  Ab G  Bb B  D  C  
.....................f#.......a........g#.......b......... 
      
--------------------------------------------------------------------
--------------------------------------------------------------------

STRAIGHT 4ths (Each new row is a 4th above the old one)

G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb


C  F# G# B  E  G  D  F  C# A  Bb Eb          C
...............g........c#.......eb..
...f#....b........d........a.........
c.....g#....e........f........bb
 


C  G# E  F  Bb G  C# Eb F# B  D  A           G
c........f....................d.....
...g#.......bb....c#....f#.......a..
......e........g.....eb....b........ 


C  F  D  G# Bb C# F# A  E  G  Eb B           D
c....................a........eb....
...f.....g#....c#.......e........b..
......d.....bb....f#.......g........


C  A  Eb F  G# C# E  B  D  Bb F# G           A 
c.....eb....g#.......b........f#....
...a.....f.....c#.......d........g..
..................e........bb.......

 
C  Eb G# B  F# A  F  C# D  G  E  Bb          E
c.....g#.......a........d............
.........b........f........g.....bb..
...eb.......f#.......c#.......e......


C  G# A  D  B  F  G  Bb Eb F# C# E           B
c........d.....f.....bb.......c#....
...g#.......b.....g.....eb.......e..
......a....................f#.......


C  D  F  Bb C# G# B  G  Eb E  A  F#          F#
c.....f........g#.......eb.......f#..
...d.....bb.......b........e.........
............c#.......g........a......


C  F  G# Eb F# D  Bb B  E  C# G  A           Db
......G#.......D........E.....G.....
C........Eb.......Bb.......C#....A..
...F........F#.......B..............


C  Eb Bb C# A  F  F# B  G# D  E  G           Ab
c........c#.......f#................
...eb.......a........b.....d.....g..
......bb.......f........g#....e.....


C  Db F# Eb A  B  D  G  Bb F  G# E           Eb
c........eb....b.....g........g#...
...db...................bb.......e. 
......f#....a.....d........f.......


C  Eb B  G  Ab Db Bb E  F# A  D  F           Bb 
c........g........bb....f#....d.....
...eb.......ab...................f..
......b........db....e.....a


C  G  Bb F# D  Eb Ab F  B  C# E  A           F
c........f#.......g#....b.....e......
...g........d........f.....c#....a
......bb.......eb


C  F# G# B  E  G  D  F  C# A  Bb Eb          C
...............g........c#.......eb..
...f#....b........d........a.........
c.....g#....e........f........bb


C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb   
F#, C,  D,  F,  Bb, C#, G#, B,  G,  Eb, E,  A
E,  Bb, C,  Eb, G#, B,  F#, A,  F,  C#, D,  G
C#, G,  A,  C,  F,  G#, Eb, F#, D,  Bb, B,  E
G#, D,  E,  G,  C,  Eb, Bb, C#, A,  F,  F#, B
F,  B,  C#, E,  A,  C,  G,  Bb, F#, D,  Eb, G#
Bb, E,  F#, A,  D,  F,  C,  Eb, B,  G,  G#, C#
G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb
B,  F,  G,  Bb, Eb, F#, C#, E,  C,  G#, A,  D
Eb, A,  B,  D,  G,  Bb, F,  G#, E,  C,  C#, F#
D,  G#, Bb, C#, F#, A,  E,  G,  Eb, B,  C,  F
A,  Eb, F,  G#, C#, E,  B,  D,  Bb, F#, G,  C


=================================================================
 
-------------------------------------------------------------------

26

HEXACHORDAL SUBSTITUTION, FOLLOWING ROW

p/0/0:...............C |F# Ab B  E  G  D| F  C# A  Bb Eb  6,2,3,5,3,7,3,7,3 | 8,8,1,5,(9)

these are new rows:

f,c#,a,bb,eb,c			 F# Ab B  E  G  D   8,8,1,5,9,6,2,3,5,3,7,(3)

f#,c#,a,bb,eb,c            f ab  b  e  g  d   7,8,1,5,9,5,3,3,5,3,7,(4)

f#,c#,g#,bb,eb,c           f a   b  e  g  d   7,7,2,5,9,5,4,2,5,3,7,(4)

f#,c#,g#,bb,eb,b           f  a  c  e  g  d   7,7,2,5,8,6,4,3,4,3,7,(4)

f#,c#,g#,bb,e,b            f  a  c  eb g  d   7,7,2,6,7,6,4,3,3,4,7,(4)

g, c#,g#,bb,e,b  			  f a---c--eb-f# d   6,7,2,6,7,6,4,3,3,3,8,(5)

g, c#,g#,f,e,b              bb a c  eb f# d    6,7,9,11,7,11,11,3,3,3,8,(5)

g, c#,a, f, e, b            bb ab c eb f# d    6,8,8,11,7,11,10,4,3,3,8,(5)


g, c#, a, f, e, bb			 b, ab, c, eb, f#, d   6,8,8,11,6,1,9,4,3,3,8,(5)


g, c#, a, f eb, bb			b, ab c, e, f#, d,     6,8,8,10,7,1,9,4,3,3,8,(5)


c, c#,  a, f eb, bb        b, ab, g, e, f#, d,    1,8,8,10,7,1,9,11,9,2,8,(10)  Nice dark chord to end, over C.
=========================================================

It seems to have gone wrong....




Hexachordal substitution another attempt


G,  D,  F,  C#, A,  Bb,

Eb replaces D

G,  Eb, F,  C#, A,  Bb,		D,  C,  F#, G#, B,  E,

C replaces C#

G,  Eb, F,  C,  A,  Bb,		D,  C#, F#, G#, B,  E,		

F# replaces F				...keep this low, lest it be shrill

G,  Eb, F#, C,  A,  Bb, 		D,  C#, F,  G#, B,  E,       

Ab replaces G, and B replaces Bb

Ab, Eb, F#, C,  A,  B			D,  C#, F,  G,  Bb, E,  

oddly enough, E replaces A

Ab, Eb, F#, C,  E,  B


=======================================================

=========================================================================
G#,B,E,G,D,F,

to:

C#,A,Bb,Eb,C,F#,


Start:   G#,B,E,G,D,F,


C# replaces D:   G#,B,E,G,C#,F

A replaces G#:   A,B,E,G,C#,F

Bb replaces B:   A,Bb,E,G,C#,F

Eb replaces E:   A,Bb,Eb,G,C#,F

C replaces C#:   A,Bb,Eb,G,C,F

F# replaces F:   A,Bb,Eb,G,C,F#

----------------------------------

G# replaces A:  G#,Bb,Eb,G,C,F
F replaces F#

B replaces Bb: G#,B,Eb,G,C,F

E replaces Eb:  G#,B,E,G,C,F

entire G,D,F,C#,A replaces!

=========================================================================

===============================================================================================================================================
======================================================
C,F#,G#,B,E,G,D,F,C#,A,Bb,Eb

0,1,4,6
0,3,4,7
0,2,3,5
0,1,4,8
0,1,3,6
======================================================
C,  F#,  G#,  B,  E,  G,  D,  F,  C#,  A,  Bb,  Eb,    6,2,3,5,3,7,3,8,8,1,5,(9)

Hear as:

======================================================

Call this "Switch Re: G Row"

alternation thought of in relation to tonal center of G:
 
numbered in relation to original row:

Switch Re: G Row

9   8    10   11  12  6   7   2   1    3   4    5
C#, F,   A,   Bb, Eb, G,  D,  F#, C,   G#, B,   E      4,4,1,5,4,7,4,6,8,3,5,(9)           *******
0,1,4,8  0,1,4,5

vs.

original:
C,  F#,  G#,  B,  E,  G,  D,  F,  C#,  A,  Bb,  Eb,
1   2    3    4   5   6   7   8   9    10  11   12


9   8   10  11  12  6   7   2   1   3   4   5       
C#, F,  A,  Bb, Eb, G,  D,| F#, C,  G#, B,  E          4,4,1,5,4,7,4,6,8,3,5,(9)
A,  C#, F,  F#, B,  Eb, Bb, D,  G#, E,  G,  C
F,  A,  C#, D,  G,  B,  F#, Bb, E,  C,  Eb, G#
E,  G#, C,  C#, F#, Bb, F,  A,  Eb, B,  D,  G
B,  Eb, G,  G#, C#, F,  C,  E,  Bb, F#, A,  D
G,  B,  Eb, E,  A,  C#, G#, C,  F#, D,  F,  Bb
C,  E,  G#, A,  D,  F#, C#, F,  B,  G,  Bb, Eb
G#, C,  E,  F,  Bb, D,  A,  C#, G,  Eb, F#, B
D,  F#, Bb, B,  E,  G#, Eb, G,  C#, A,  C,  F
F#, Bb, D,  Eb, G#, C,  G,  B,  F,  C#, E,  A
Eb, G,  B,  C,  F,  A,  E,  G#, D,  Bb, C#, F#
Bb, D,  F#, G,  C,  E,  B,  Eb, A,  F,  G#, C#


perm matrix?

C#, F,  A,  Bb, Eb, G,  D, F#, C,  G#, B,  E

MOF Properties of "Switch Re: G Row"

?new row #1:c#,f,a,bb,eb,g,d,f#,c,g#,b,e
?inc all pos0:c#
?ex any pos0:c# un f ran5
?ex any: f un a ran5
?ex any:a un bb ran5
?ex any:bb un eb ran5

p/0/0:...............C# F  A  Bb Eb G  D  F# C  Ab B  E 


ri/5/4:..............C# F  C  E  A  Bb D  F# Eb Ab B  G  
 
ri/8/9:..............C# F  A  F# B  D  Bb E  Ab Eb G  C  




5x/p/1/8:............C# F  Ab A  F# D  Bb Eb E  C  B  G  
 
======================================================================
5x/r/4/9:............C# F  A  C  B  Ab E  Bb D  Eb G  F# 

p/0/0:...............C# F  A  Bb Eb G  D  F# C  Ab B  E 



-----------------------------------------
this one, (the above 5x/r/4/9) seems to continue well.

C# F  A  C  B  Ab E  Bb D  Eb G  F#

c#.f..a..............bb....eb.g......    this is p/0/0
........................d........f#..
.........c..b..g#.e


HM, don't get hung up on it.  Nothing so great, as of yet.


======================================================================


==================================================================================================================================================================
==================================================================================================================================================================

 
-------------------------------------------------------------------------------------------------------------------



Retrograde of Inversion: Fitting Row segs

D  F  C  Eb B  G  Ab Db Bb E  F# A               
F# A  D  F  C  Eb B  G  Ab Db Bb E       Second take, yes, definite.
A  G# Eb B  G  E  F  D  C# Bb C  F# 
D  F# F  C  Eb A  G  E  B  Ab Db Bb      Third:  Good

d>..........g>.......db>............





===========================================================================
==============
D,A,F#,D
0,3,7\
==============

p/1/2:...............A  C  F  Ab Eb F# 		D  Bb B  E  C# G  
p/4/2:...............C  Eb Ab B  F# A  		F  C# D  G  E  Bb 
p/7/2:...............Eb F# B  D  A  C  		Ab E  F  Bb G  C#
p/10/2:..............F# A  D  F  C  Eb 		B  G  Ab C# Bb E 

p/2/2:...............Bb C# F# A  E  G  		Eb B  C  F  D  Ab    N.O.
 
p/1/3:...............C  F  Ab Eb F# D  		Bb B  E  C# G  A  
p/4/3:...............Eb Ab B  F# A  F  		C# D  G  E  Bb C  
p/7/3:...............F# B  D  A  C  Ab 		E  F  Bb G  C# Eb  
p/10/3:..............A  D  F  C  Eb B  		G  Ab C# Bb E  F# 

p/5/3:...............E  A  C  G  Bb F# 		D  Eb Ab F  B  C#    N.O.
 
p/8/7:...............C# A  F  F# B  Ab 		D  E  G  C  Eb Bb 
p/11/7:..............E  C  Ab A  D  B  		F  G  Bb Eb F# C# 

p/9/7:...............D  Bb F# G  C  A  		Eb F  Ab C# E  B     N.O.

p/3/11:..............F# Eb A  B  D  G  		Bb F  Ab E  C  C# 
p/6/11:..............A  F# C  D  F  Bb 		C# Ab B  G  Eb E  
 
p/10/11:.............C# Bb E  F# A  D  		F  C  Eb B  G  Ab    N.O.
 

i/1/2:...............F  D  A  F# B  Ab 		C  E  Eb Bb C# G  


i/2/2:...............F# Eb Bb G  C  A  		C# F  E  B  D  Ab 

i/11/3:..............C  G  E  A  F# Bb 		D  C# Ab B  F  Eb 
 
i/0/7:...............G  B  Eb D  A  C  		F# E  C# Ab F  Bb 
i/3/7:...............Bb D  F# F  C  Eb 		A  G  E  B  Ab C# 
i/9/7:...............E  Ab C  B  F# A  		Eb C# Bb F  D  G  
 
i/6/8:...............F  A  Ab Eb F# C  		Bb G  D  B  E  C# 
 

i/5/11:..............D  F  B  A  F# C# 		Bb Eb C  E  Ab G  

 
5x/p/11/2:...........Eb F# G  Bb A  C  		E  Ab C# D  B  F  
 
 
5x/p/4/8:............A  C# F# G  E  Bb 		Ab B  C  Eb D  F  


5x/i/5/2:............C# Bb A  F# G  E  		C  Ab Eb D  F  B  
 
5x/i/0/8:............G  Eb Bb A  C  F# 		Ab F  E  C# D  B  
 
===========================================================================
==============
F#,G#,A,F
0,1,3,4  -- ex any: g,e,bb
==============

   

p/8/7:...............C# A  F  F# B  Ab 		D  E  G  C  Eb Bb   N.O.

p/2/8:...............Eb B  C  F  D  Ab 		Bb C# F# A  E  G  
p/5/8:...............F# D  Eb Ab F  B  		C# E  A  C  G  Bb 
p/11/8:..............C  Ab A  D  B  F  		G  Bb Eb F# C# E  
 

p/9/11:..............C  A  Eb F  Ab C# 		E  B  D  Bb F# G    N.O.
 
 

i/5/11:..............D  F  B  A  F# C# 		Bb Eb C  E  Ab G     N.O.
 

 

===========================================================================
==============
F,Eb,D,C
0,2,3,5   -- ex any:c#,e  ex pit prox: b,bb prox:f#,g
==============


 
p/6/11:..............A  F# C  D  F  Bb 		C# Ab B  G  Eb E      N.O.  
 

 
i/0/7:...............G  B  Eb D  A  C  		F# E  C# Ab F  Bb     N.O.

i/3/7:...............Bb D  F# F  C  Eb 		A  G  E  B  Ab C#     N.O.
 

i/6/8:...............F  A  Ab Eb F# C  		Bb G  D  B  E  C# 
i/9/8:...............Ab C  B  F# A  Eb 		C# Bb F  D  G  E  
 
 
i/11/11:.............Ab B  F  Eb C  G  		E  A  F# Bb D  C#     N.O.
 
 
===========================================================================

==============
==============
C,B,F,Eb  -- ex any: c#,bb,e prox:f#,g
0,1,4,6/



i/11/11:.............Ab B  F  Eb C  G  		E  A  F# Bb D  C#     N.O.
 

5x/p/1/2:............F  Ab A  C  B  D  		F# Bb Eb E  C# G  
5x/p/4/2:............Ab B  C  Eb D  F  		A  C# F# G  E  Bb 
5x/p/7/2:............B  D  Eb F# F  Ab 		C  E  A  Bb G  C# 
5x/p/10/2:...........D  F  F# A  Ab B  		Eb G  C  C# Bb E  
 

 
===========================================================================
==============
Eb,G,C,B  -- ex any:c#,bb prox:f#,f ab,a e,f 
0,1,4,8/
==============

p/7/2:...............Eb F# B  D  A  C  		Ab E  F  Bb G  C# 
 
p/10/3:..............A  D  F  C  Eb B  		G  Ab C# Bb E  F# 
 
p/2/4:...............F# A  E  G  Eb B  		C  F  D  Ab Bb C# 
 
p/6/7:...............B  G  Eb E  A  F# 		C  D  F  Bb C# Ab 
 
p/3/11:..............F# Eb A  B  D  G  		Bb F  Ab E  C  C# 
 
p/8/11:..............B  Ab D  E  G  C  		Eb Bb C# A  F  F# 
 
i/7/2:...............B  Ab Eb C  F  D  		F# Bb A  E  G  C# 
 
i/11/2:..............Eb C  G  E  A  F# 		Bb D  C# Ab B  F  
 
i/4/3:...............F  C  A  D  B  Eb 		G  F# C# E  Bb Ab 
 
i/9/5:...............D  G  E  Ab C  B  		F# A  Eb C# Bb F  
 
i/0/7:...............G  B  Eb D  A  C  		F# E  C# Ab F  Bb 
 
i/3/11:..............C  Eb A  G  E  B  		Ab C# Bb D  F# F  
 
i/11/11:.............Ab B  F  Eb C  G  		E  A  F# Bb D  C# 
 
5x/p/4/2:............Ab B  C  Eb D  F  		A  C# F# G  E  Bb 
 
5x/p/9/8:............D  F# B  C  A  Eb 		C# E  F  Ab G  Bb 
    
5x/i/9/8:............E  C  G  F# A  Eb 		F  D  C# Bb B  Ab 
 

=========================================================================== 
==============
A,E,Eb,G  -- ex any:d,f,ab prox: bb,b d,c# 
0,1,4,6/
==============


 
p/6/7:...............B  G  Eb E  A  F# 		C  D  F  Bb C# Ab      N.O.
 
 
 
i/4/7:...............B  Eb G  F# C# E  		Bb Ab F  C  A  D       N.O.
 
i/1/8:...............C  E  Eb Bb C# G  		F  D  A  F# B  Ab 
i/10/8:..............A  C# C  G  Bb E  		D  B  F# Eb Ab F  
 
i/3/11:..............C  Eb A  G  E  B  		Ab C# Bb D  F# F       N.O.
 
 
 
=========================================================================== 
==============

G,F,B,Ab  -- ex: f#,a  prox: e,eb  c,c# bb,c
0,2,3,6/
==============

 
p/10/4:..............D  F  C  Eb B  G  		Ab C# Bb E  F# A         N.O. 
 
p/2/7:...............G  Eb B  C  F  D  		Ab Bb C# F# A  E         N.O.

p/4/8:...............F  C# D  G  E  Bb 		C  Eb Ab B  F# A  
p/7/8:...............Ab E  F  Bb G  C# 		Eb F# B  D  A  C  
p/10/8:..............B  G  Ab C# Bb E  		F# A  D  F  C  Eb 
p/1/8:...............D  Bb B  E  C# G  		A  C  F  Ab Eb F# 
 
p/8/11:..............B  Ab D  E  G  C  		Eb Bb C# A  F  F# 
p/11/11:.............D  B  F  G  Bb Eb 		F# C# E  C  Ab A         N.O.
 
i/0/2:...............E  C# Ab F  Bb G  		B  Eb D  A  C  F# 
i/3/2:...............G  E  B  Ab C# Bb 		D  F# F  C  Eb A  
i/6/2:...............Bb G  D  B  E  C# 		F  A  Ab Eb F# C  
i/9/2:...............C# Bb F  D  G  E  		Ab C  B  F# A  Eb  

i/7/2:...............B  Ab Eb C  F  D  		F# Bb A  E  G  C#        N.O.
 


5x/p/4/2:............Ab B  C  Eb D  F  		A  C# F# G  E  Bb         N.O. 

 

5x/i/0/5:............C# D  B  G  Eb Bb 		A  C  F# Ab F  E  
 

5x/i/5/8:............C  Ab Eb D  F  B  		C# Bb A  F# G  E         N.O.
 

=========================================================================== 
==============
E,D,G,Db  -- ex: eb,c  prox:f,f#  g#,a
0,1,3,6/
==============

 

p/2/2:...............Bb C# F# A  E  G  		Eb B  C  F  D  Ab 
  
 
p/10/11:.............C# Bb E  F# A  D  		F  C  Eb B  G  Ab        N.O.
 
 
i/11/4:..............G  E  A  F# Bb D  		C# Ab B  F  Eb C         N.O.
 
i/2/7:...............A  C# F  E  B  D  		Ab F# Eb Bb G  C         N.O.
 
i/7/7:...............D  F# Bb A  E  G  		C# B  Ab Eb C  F         N.O. 
 

i/1/11:..............Bb C# G  F  D  A  		F# B  Ab C  E  Eb        N.O.
 
i/10/11:.............G  Bb E  D  B  F# 		Eb Ab F  A  C# C         N.O.
 
 
5x/p/4/9:............C# F# G  E  Bb Ab 		B  C  Eb D  F  A  
 
 
5x/i/0/2:............Ab F  E  C# D  B  		G  Eb Bb A  C  F# 
 
 
5x/i/5/2:............C# Bb A  F# G  E  		C  Ab Eb D  F  B        N.O.


=========================================================================== 
==============
B,C#,Ab,Bb   --  ex. c,a,   prox: g,f#,  d,d#
0,2,3,5/
==============
 
p/0/2:...............Ab B  E  G  D  F  		C# A  Bb Eb C  F# 
p/3/2:...............B  D  G  Bb F  Ab 		E  C  C# F# Eb A  
p/6/2:...............D  F  Bb C# Ab B  		G  Eb E  A  F# C  
p/9/2:...............F  Ab C# E  B  D  		Bb F# G  C  A  Eb 
 

p/1/8:...............D  Bb B  E  C# G  		A  C  F  Ab Eb F# 
p/4/8:...............F  C# D  G  E  Bb 		C  Eb Ab B  F# A  
p/7/8:...............Ab E  F  Bb G  C# 		Eb F# B  D  A  C  
p/10/8:..............B  G  Ab C# Bb E  		F# A  D  F  C  Eb 
 

p/2/11:..............F  D  Ab Bb C# F# 		A  E  G  Eb B  C         N.O.
 

i/0/2:...............E  C# Ab F  Bb G  		B  Eb D  A  C  F# 
i/3/2:...............G  E  B  Ab C# Bb 		D  F# F  C  Eb A  
i/6/2:...............Bb G  D  B  E  C# 		F  A  Ab Eb F# C  
i/9/2:...............C# Bb F  D  G  E  		Ab C  B  F# A  Eb 
 

i/2/8:...............C# F  E  B  D  Ab 		F# Eb Bb G  C  A  
i/5/8:...............E  Ab G  D  F  B  		A  F# C# Bb Eb C  
i/8/8:...............G  B  Bb F  Ab D  		C  A  E  C# F# Eb 
i/11/8:..............Bb D  C# Ab B  F  		Eb C  G  E  A  F# 
 

i/7/11:..............E  G  C# B  Ab Eb 		C  F  D  F# Bb A         N.O.
 


=========================================================================== 
==============
Ab,Bb,Db,E  -- ex: A  ex pit prox: B,C  C,D  G,F#, F,F# Eb,D Eb,F, 
0,2,5,8/
==============

p/0/2:...............Ab B  E  G  D  F  		C# A  Bb Eb C  F# 
p/3/2:...............B  D  G  Bb F  Ab 		E  C  C# F# Eb A  
p/6/2:...............D  F  Bb C# Ab B  		G  Eb E  A  F# C  
p/9/2:...............F  Ab C# E  B  D  		Bb F# G  C  A  Eb  

p/8/2:...............E  G  C  Eb Bb C# 		A  F  F# B  Ab D  
 
p/11/3:..............Bb Eb F# C# E  C  		Ab A  D  B  F  G  
 
 
p/1/7:...............F# D  Bb B  E  C# 		G  A  C  F  Ab Eb 
p/7/7:...............C  Ab E  F  Bb G  		C# Eb F# B  D  A
p/10/7:..............Eb B  G  Ab C# Bb 		E  F# A  D  F  C  

p/3/7:...............Ab E  C  C# F# Eb 		A  B  D  G  Bb F  
 
  
p/4/8:...............F  C# D  G  E  Bb 		C  Eb Ab B  F# A  
p/7/8:...............Ab E  F  Bb G  C# 		Eb F# B  D  A  C  
p/10/8:..............B  G  Ab C# Bb E  		F# A  D  F  C  Eb 
 


i/5/3:...............F# C# Bb Eb C  E  		Ab G  D  F  B  A  
 
i/1/7:...............Ab C  E  Eb Bb C# 		G  F  D  A  F# B  
 
i/11/7:..............F# Bb D  C# Ab B  		F  Eb C  G  E  A  
 

i/2/8:...............C# F  E  B  D  Ab 		F# Eb Bb G  C  A  
i/8/8:...............G  B  Bb F  Ab D  		C  A  E  C# F# Eb 
 
 
i/4/11:..............C# E  Bb Ab F  C  		A  D  B  Eb G  F# 
i/7/11:..............E  G  C# B  Ab Eb 		C  F  D  F# Bb A  
 



5x/p/5/3:............C  C# E  Eb F# Bb 		D  G  Ab F  B  A  
 


5x/p/10/8:...........Eb G  C  C# Bb E  		D  F  F# A  Ab B  
  


5x/i/11/2:...........G  E  Eb C  C# Bb 		F# D  A  Ab B  F  
 
=========================================================================== 
==============
Db,C,Bb,F#  -- ex. B,D    prox: A,Ab  F,G   F,E   G,Ab 
0,1,3,7\
==============


 

i/5/4:...............C# Bb Eb C  E  Ab 		G  D  F  B  A  F#     N.O.
 

i/1/7:...............Ab C  E  Eb Bb C# 		G  F  D  A  F# B      N.O.
 
i/1/8:...............C  E  Eb Bb C# G  		F  D  A  F# B  Ab 
 

i/4/8:...............Eb G  F# C# E  Bb 		Ab F  C  A  D  B  
i/7/8:...............F# Bb A  E  G  C# 		B  Ab Eb C  F  D  
i/10/8:..............A  C# C  G  Bb E  		D  B  F# Eb Ab F  
 
i/9/11:..............F# A  Eb C# Bb F  		D  G  E  Ab C  B       N.O.
 

5x/p/1/8:............F# Bb Eb E  C# G  		F  Ab A  C  B  D  
5x/p/4/8:............A  C# F# G  E  Bb 		Ab B  C  Eb D  F  
5x/p/7/8:............C  E  A  Bb G  C# 		B  D  Eb F# F  Ab 
5x/p/10/8:...........Eb G  C  C# Bb E  		D  F  F# A  Ab B  
 
 
5x/i/0/8:............G  Eb Bb A  C  F# 		Ab F  E  C# D  B  
5x/i/3/8:............Bb F# C# C  Eb A  		B  Ab G  E  F  D  
5x/i/6/8:............C# A  E  Eb F# C  		D  B  Bb G  Ab F  
5x/i/9/8:............E  C  G  F# A  Eb 		F  D  C# Bb B  Ab 
 


=========================================================================== 
==============
Bb,F#,E,A  -- ex: ab,b,f  prox:eb,d 
0,1,4,6\

==============

  
p/0/8:...............C# A  Bb Eb C  F# 		Ab B  E  G  D  F  
p/3/8:...............E  C  C# F# Eb A  		B  D  G  Bb F  Ab 
p/6/8:...............G  Eb E  A  F# C  		D  F  Bb C# Ab B  
p/9/8:...............Bb F# G  C  A  Eb 		F  Ab C# E  B {D  
 
p/10/11:.............C# Bb E  F# A  D  		F  C  Eb B  G  Ab    N.O.
 
i/2/2:...............F# Eb Bb G  C  A  		C# F  E  B  D  Ab 
i/5/2:...............A  F# C# Bb Eb C  		E  Ab G  D  F  B  
i/8/2:...............C  A  E  C# F# Eb 		G  B  Bb F  Ab D  
i/11/2:..............Eb C  G  E  A  F# 		Bb D  C# Ab B  F  
 
 
5x/p/2/2:............F# A  Bb C# C  Eb 		G  B  E  F  D  Ab 
5x/p/5/2:............A  C  C# E  Eb F# 		Bb D  G  Ab F  B  
5x/p/8/2:............C  Eb E  G  F# A  		C# F  Bb B  Ab D  
5x/p/11/2:...........Eb F# G  Bb A  C  		E  Ab C# D  B  F  
 
 
5x/i/2/2:............Bb G  F# Eb E  C# 		A  F  C  B  D  Ab 
5x/i/5/2:............C# Bb A  F# G  E  		C  Ab Eb D  F  B  
5x/i/8/2:............E  C# C  A  Bb G  		Eb B  F# F  Ab D  
5x/i/11/2:...........G  E  Eb C  C# Bb 		F# D  A  Ab B  F  
 
5x/i/0/8:............G  Eb Bb A  C  F# 		Ab F  E  C# D  B  
5x/i/3/8:............Bb F# C# C  Eb A  		B  Ab G  E  F  D  
5x/i/6/8:............C# A  E  Eb F# C  		D  B  Bb G  Ab F  
5x/i/9/8:............E  C  G  F# A  Eb 		F  D  C# Bb B  Ab 
 
-------------------------------------------------------------------------------------------------------------------
1)   PERM CHORALE: FITTING ROW SEGS

D3,F#3,D#3,B3,C3,E3,G#3,C#3,F3,A3,A#3,G3

loop just upper two voices:

[:C,  F#, G#:]B,  E,  G,  D,  F,  C#, A,  Bb, Eb    Very good, surprisingly, rightside up
  E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
  G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
  C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

  C#-------------->   G-------------------->

not killed, chord-by-chord:  [c,a]


C#,G#,E,C  --
0,1,4,8/

C,B,Eb,F#  --
0,1,4,7/

A,F,C#,G#  --
0,1,4,8\

G#,E,C,B   --
0,1,4,8\

F,C#,G#,E  --
0,3,4,7

Eb,F#,D,G  --
0,1,4,5

B,Eb,F#,D  --
0,3,4,7

G,Bb,A,F   --
0,1,3,5\

Bb,A,F,C#  --
0,1,4,8\

D,G,Bb,A   --
0,2,3,7/

F#,D,G,Bb  --
0,1,4,8\

E,C,B,Eb   --
0,1,4,5


C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

p/11/6:..............C# E  C  Ab A  D  B  F  G  Bb Eb F# 
p/3/7:...............Ab E  C  C# F# Eb A  B  D  G  Bb F  
 
-----------------------------------------------
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

p/4/2:...............C  Eb Ab B  F# A  F  C# D  G  E  Bb 
p/0/11:..............Eb C  F# Ab B  E  G  D  F  C# A (Bb) 
i/9/9:...............C  B  F# A  Eb C# Bb F  D  G  E  Ab 

----------------------------------------------- 
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

i/10/5:..............Ab F  A  C# C  G  Bb E  D  B  F# Eb 
i/6/6:...............C# F  A  Ab Eb F# C  Bb G  D  B  E  
 
-----------------------------------------------
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

p/9/2:...............F  Ab C# E  B  D  Bb F# G  C  A  Eb 
i/0/2:...............E  C# Ab F  Bb G  B  Eb D  A  C  F# 
 
-----------------------------------------------
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

p/5/6:...............G  Bb F# D  Eb Ab F  B  C# E  A  C  
i/4/6:...............D  B  Eb G  F# C# E  Bb Ab F  C  A  

-----------------------------------------------
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

p/7/2:...............Eb F# B  D  A  C  Ab E  F  Bb G  C# 
 
i/10/2:..............D  B  F# Eb ab F  A  C# C  G  Bb E  
  
-----------------------------------------------
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

i/1/11:..............Bb c# G  F  d  A  F# B  Ab C  E  Eb 

-----------------------------------------------
C,  F#, G#, B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

p/5/6:...............G  Bb F# D  Eb Ab F  B  C# E  A  C  
 
p/9/7:...............D  Bb F# G  C  A  Eb F  Ab C# E  B  
 
-----------------------------------------------


==============================================================================

2x:  A,  Ab, C,  F#, E,  B,  C#, G,  Bb, Eb, F,  D 

2x, 4x series on original segments and chorales

C,  F#, G#, B,                 E,  G,  D,  F,                    C#, A,  Bb, Eb 


2x

p/5/3:...............B  A  E  F# C  Eb Ab                            Bb G  D  C# F  

p/1/5:...............C  D  Ab B  E  F# Eb                            Bb A  C# G  F  

p/6/8:...............E  A  B  Ab Eb D  F# C                          Bb F  G  C# 

p/0/10:..............F  D |A  Ab C  F# E  B                          C# G  Bb Eb 

i/2/0:...............B  C  Ab D  E  A                                G  C# Bb F  Eb F# 

i/9/2:...............Eb A  B  E  D  Ab F  C                          Bb C# F# G  

i/4/3:...............E  F# B  A  Eb C  G  F  Ab                      C# D  Bb 

i/1/4:...............Eb Ab F# C  A  E  D  F  Bb B                    G  C# 

i/2/10:..............Eb F# B  C  Ab D  E  A                          G  C# Bb F  
i/5/10:..............F# A  D  Eb B  F  G  C                          Bb E  C# Ab 
i/8/10:..............A  C  F  F# D  Ab Bb Eb                         C# G  E  B  
i/11/10:.............C  Eb Ab A  F  B  C# F# E                       Bb G  D  
-----------------------------------------------
4x



p/7/2:...............Ab E  Eb B  D  F# F  C  A                       C# G  Bb 

p/1/4:...............A  F  Ab C  B  F# Eb                            G  C#|E  D  Bb 
p/4/4:...............C  Ab B  Eb D  A  F#                            Bb E  G  F  C# 
p/7/4:...............Eb B  D  F# F  C  A                             C# G  Bb Ab E  
p/10/4:..............F# D  F  A  Ab Eb C  E                          Bb C# B  G  

p/6/8:...............E  B  Ab C  F#|A                                G  Eb D  Bb C# F  

p/3/11:..............A  Eb|F# E  C  B                                G  Bb D  C# Ab F  

i/0/0:...............C |A  B  Eb E  Ab F                             C# D  G  Bb F# 

i/1/4:...............F  A  F# D  Eb Ab B                             G  C#|Bb C  E  
i/4/4:...............Ab C  A  F  F# B  D                             Bb E  C# Eb G  
i/7/4:...............B  Eb C  Ab A  D  F                             C# G  E  F# Bb 
i/10/4:..............D  F# Eb B  C  F  Ab E                          Bb G  A  C# 


i/2/7:...............Eb E  A  C  Ab D  B                             C# F  F# Bb G  

i/0/11:..............F# C  A  B  Eb E  Ab F                          C# D  G  Bb 

-----------------------------------------------

================================================================================================
================================================================================================


IDEA OF 3 or 4-voice chorales on top of 
slower basic chorales.   ================================================================================================
1    2    3     4    5    6    7    8    9    10   11    12
C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

================================================================================================
================================================================================================
================================================================================================

Method is to generate all mechanical variations on existing chorales/arrays,

then look for fits to 2-chord combinations of chords of an existing chorale,

that is, a straddle.  The two chords can also come from "obvious combinations", above.


================================================================================================
=================================================================

First chord against 6 chords from this chorale, up a major third:
1     
C,
E,
G#,
C#,


G,  E,  Bb, C,  Eb, Ab,  very nice, 'tho doesn't lead to next chord
Eb, Ab, G,  F,  E,  C,
E,  C,  D#, A,  G#, F,
Ab, F,  E,  C#, C,  A,


=================================================================

Second chord against 6 chords from this chorale, ?


2                          3
F#,                |(G#)
Eb,                |(C#)
B,                 |(F )
C,                 |(A )

E,  G,  D#, B,  C, |F,
B,  Eb, E,  C,  G#,|C#,
C,  E,  B,  G#, A, |D
G#  B,  C,  A,  F, |F#
=================================================================

1    2    3     4    5    6    7    8    9    10   11    12
C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E



3              4
B  E  C#  G# |-F-(E)-Eb   (careful with Eb-F-Eb over E)
C# G# F   Eb-| A  C
D  G  G#  F  | B  A
E  F  C#  A  | C  B

=================================================================

1    2    3     4    5    6    7    8    9    10   11    12
C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

Retrograde of perm chorale 2:
4                         5
C   B   D#  G   E | A
G#  C   E   D#  B | F
A   G#  B   E   C | C#
F   A   C   B   G#| D

=================================================================

1    2    3     4    5    6    7    8    9    10   11    12
C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

R of T7 perm chorale 2:


5                  6

F   E   G# C   A  |D
C#  F   A  G#  E  |Bb
D   C#  E  A   F  |F#
Bb  D   F  E   C# |G

=================================================================
1    2    3     4    5    6    7    8    9    10   11    12
C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E

R again             6               7
                    G   Bb  F#  D   Eb   
                    D   F#  G   Eb  B    
                    Eb  G   D   B   C    
                    B   D   Eb  C   Ab                      


=================================================================


1    2    3     4    5    6    7    8    9    10   11    12
C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E
                           (f#?)

Retrograde of #1: 
7                         8
Bb  F   D   C   F#  A
D   F#  G   A   Bb  F
G   Bb  B   F   D   f# (G)
B   D   Eb  F#  G   Bb
                 
                 
                 
==========================================================================
1    2    3     4    5    6    7    8    9    10   11    12
C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E


any of this on the G,Bb,A,F: 

Eb, A,  B,  D,  G, [Bb, F]  Ab,[E,  C,  C#, E] [] are good sideslips on G
C   D   Eb  B   A  [F   G]  Bb  C#  E   F#  G#    but not good over pedal
E,  B   C   Eb  D  [G   A]  F   F#  C#  G#  B
C#  Eb  E   C   B  [A   D]  G   G#  F#  A#  F

plus:              [         ]
and:[ any size               ]

This extends to 9,10,11, and back to 4,5,6,7,8 but 12 has its own ending flourish:

As elaborations of G, basically.


1    2    3     4    5    6    7    8    9    10   11    12
C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E


to do: investigate combos between these and the ones above. quick find.


1    2    3     4    5    6    7    8    9    10   11    12
C,  F#, G#  B,  E,  G,  D,  F,  C#, A,  Bb, Eb     
E,  Eb, C#, C,  G#, D,  F#, A,  F,  Bb, G,  B
G#, B,  F,  E,  C#, F#, Eb, Bb, A,  G,  D,  C
C#, C,  A,  G#, F,  Eb, B,  G,  Bb, D,  F#, E



x   *   x   x    x   *   *   x   -   *   *   -
A,  Eb, F,  G#,  C#, E,  B,  D,  Bb, F#, G,  C,
C#, E,  D,  A,   F,  C,  F#, Bb, B,  G,  Eb, G#,
F,  C,  Bb, C#,  D,  G#, G,  B,  F#, Eb, E,  A,
D,  G#, B,  F,   Bb, A,  Eb, F#, G,  E,  C,  C# 
  retrograde of:    [                      ]

12
G   F#  Bb  D    B  [E     G ]
Eb  G   B   Bb   F#  C     Eb
E   Eb  F#  B    G   G#    E
C   E   G   F#   Eb  A     C
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Old 7th December 2015, 11:58 AM   #173
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https://app.box.com/s/e6dzmg3k8ix93mik0dj2dw8pe0mq78e3

First sketch, to see if one of the versions of the series makes a nice
loop for perpetual motion. It's going to be ok.

And, after two tries -- two different series -- that had me despairing, this third try
sounds like a series I can work with for this kind of loop/generator.

Started doing pre-composition on this June 1. Around 5 months, I guess. Glad to be on to the next phase.
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Old 9th December 2015, 11:39 AM   #174
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https://app.box.com/s/kzmw2c3s3js9rhkpbwphejfuoqtow3qw

Sketch extended and layered a little more.

With this series, this generating technique seems to make everything fall into
place nicely, and it generates all these syncopated rhythms.

While the effect is sort of cooly indifferent, the notes have to sound good somehow, and I think these do. It's a little mysterious why.

This could be video-game suspense music, when it gets going.
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Old 11th December 2015, 04:29 AM   #175
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https://app.box.com/s/01485k9w67949i770a1wctlqo0tymnc9

Third version of this sketch, nearly 10 minutes. oops, more like 7 and change. I uploaded the wrong version.

This is too mechanical and indifferent to be lovable, but -- considering that it was very easy to do -- it's surprisingly effective, just to hear textural changes, different instruments coming in and out.

Next sketches: variable loop -- gradually changing into different versions of series, and polyrhythms.
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Old 17th December 2015, 12:03 PM   #176
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Originally Posted by calebprime View Post
...
Next sketches: variable loop -- gradually changing into different versions of series, and polyrhythms.
https://app.box.com/s/fe45k1v28cny4asx25s89xc0inv6s78y

Here it is, with just enough filling-in to test the idea.

The lesson here was that a two-note motive hitting the beginning and end of the bars makes the meter clear, makes the chunking clear -- and this turns an endless stream of undifferentiated notes (too much work for the listener) into something much more enjoyable.

Auto polyrhythms at every 2, 3, and 5 16th-notes.

I'm not sure if I should add more stuff for now, or move on to the next sketch.

This is basically a working out of this:

Code:

STRAIGHT 4ths (Each new row is a 4th above the old one)

G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb


to add notes, move up the array chain


C  F# G# B  E  G  D  F  C# A  Bb Eb          C
...............g........c#.......eb..
...f#....b........d........a.........
c.....g#....e........f........bb



C  G# E  F  Bb G  C# Eb F# B  D  A
to
C  F# G# B  E  G  D  F  C# A  Bb Eb



C  G# E  F  Bb G  C# Eb F# B  D  A  3x

C  F#|G# E  F  Bb G  C# Eb F# B  D  A

C  F# G# B  E |F  Bb G  C# Eb F# B  D  A 
 
C  F# G# B  E  G  D  F  Bb G  C# Eb F# B  D  A

C  F# G# B  E  G  D  F  C# Eb F# B  D  A

C  F# G# B  E  G  D  F  C# A  Bb Eb  many times

 

* Nice Ost: C,Ab,E,F,Bb,G     Nice Ost from EMBEDDINGS


THIS:  C  F  D  G# Bb C# F# A  E  G  Eb B

TO THIS"

C  G# E  F  Bb G  C# Eb F# B  D  A           G    
c........f....................d.....
...g#.......bb....c#....f#.......a..
......e........g.....eb....b........ 




C  A  Eb F  G# C# E  B  D  Bb F# G

C  F# A  Eb F  G# C# E  B  D  Bb F# G

C  C# F# A  Eb F  G# C# E  B  D  Bb F# G

C  Bb C# F# A  Eb F  G# C# E  B  D  Bb F# G

C  G# Bb C# F# A  Eb F  G# C# E  B  D  Bb F# G

C  D  G# Bb C# F# A  Eb F  G# C# E  B  D  Bb F# G

C  F  D  G# Bb C# F# A  E  G  Eb B




C  F  D  G# Bb C# F# A  E  G  Eb B           D     F#-A--E--G
c....................a........eb....
...f.....g#....c#.......e........b..
......d.....bb....f#.......g........


C  A  Eb F  G# C# E  B  D  Bb F# G           A 
c.....eb....g#.......b........f#....
...a.....f.....c#.......d........g..
..................e........bb.......


C  Eb G# B  F# A  F  C# D  G  E  Bb

C  A  Eb G# B  F# A  F  C# D  G  E  Bb

C  A  Eb F  G# B  F# A  F  C# D  G  E  Bb

C  A  Eb F  G# C# E  B  F# A  F  C# D  G  E  Bb

C  A  Eb F  G# C# E  B  D  Bb F# A  F  C# D  G  E  Bb

C  A  Eb F  G# C# E  B  D  Bb F# G

 
C  Eb G# B  F# A  F  C# D  G  E  Bb          E
c.....g#.......a........d............
.........b........f........g.....bb..
...eb.......f#.......c#.......e......



C  G# A  D  B  F  G  Bb Eb F# C# E

C  Eb G# A  D  B  F  G  Bb Eb F# C# E

C  Eb G# B  F# A  D  B  F  G  Bb Eb F# C# E

C  Eb G# B  F# A  F  C# D  B  F  G  Bb Eb F# C# E

C  Eb G# B  F# A  F  C# D  G  Eb E  A  F#

C  Eb G# B  F# A  F  C# D  G  E  Bb

C  G# A  D  B  F  G  Bb Eb F# C# E           B
c........d.....f.....bb.......c#....
...g#.......b.....g.....eb.......e..
......a....................f#.......


C  D  F  Bb C# G# B  G  Eb E  A  F#

C  G# A  D  F  Bb C# G# B  G  Eb E  A  F#

C  G# A  D  B  F  Bb C# G# B  G  Eb E  A  F#

C  G# A  D  B  F  G  Bb C# G# B  G  Eb E  A  F#

C  G# A  D  B  F  G  Bb Eb F# C# G# B  G  Eb E  A  F#

C  G# A  D  B  F  G  Bb Eb F# C# E





C  D  F  Bb C# G# B  G  Eb E  A  F#          F#          D  F  Bb C#
c.....f........g#.......eb.......f#..
...d.....bb.......b........e.........
............c#.......g........a......




current tempo: 78

C--D--F  G# Eb F# D  Bb B  E  C# G  A

C--D--F--Bb-C#-G# Eb F# D  Bb B  E  C# G  A

C--D--F--Bb-C#-G#-B--G--Eb F# D  Bb B  E  C# G  A

C--D--F--Bb-C#-G#-B--G--Eb-E--A--F#


C  F  G# Eb F# D  Bb B  E  C# G  A           Db
......G#.......D........E.....G.....
C........Eb.......Bb.......C#....A..
...F........F#.......B..............


C  F  G# Eb Bb C# A  F  F# B  G# D  E  G

C  F  G# Eb F# D  Bb C# A  F  F# B  G# D  E  G 

C  F  G# Eb F# D  Bb B  E  C# A  F  F# B  G# D  E  G

C  F  G# Eb F# D  Bb B  E  C# G  A 






C  Eb Bb C# A  F  F# B  G# D  E  G           Ab
c........c#.......f#................
...eb.......a........b.....d.....g..
......bb.......f........g#....e.....


C  Eb Bb C# F# Eb A  B  D  G  Bb F  G# E 

C  Eb Bb C# A  B  D  G  Bb F  G# E

C  Eb Bb C# A  F  F# Eb A  B  D  G  Bb F  G# E 

C  Eb Bb C# A  F  F# B  D  G  Bb F  G# E 

C  Eb Bb C# A  F  F# B  G# D  G  Bb F  G# E

C  Eb Bb C# A  F  F# B  G# D  E  G



C  Db F# Eb A  B  D  G  Bb F  G# E           Eb
c........eb....b.....g........g#...
...db...................bb.......e. 
......f#....a.....d........f.......


C  Eb B  G  Ab Db Bb E  F# A  D  F           Bb 
c........g........bb....f#....d.....
...eb.......ab...................f..
......b........db....e.....a


C  G  Bb F# D  Eb Ab F  B  C# E  A           F
c........f#.......g#....b.....e......
...g........d........f.....c#....a
......bb.......eb


C  F# G# B  E  G  D  F  C# A  Bb Eb          C
...............g........c#.......eb..
...f#....b........d........a.........
c.....g#....e........f........bb

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Last edited by calebprime; 17th December 2015 at 12:06 PM.
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Old 3rd January 2016, 11:18 AM   #177
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a spacey realization of this "basic chorale", from above:

Code:
  
r/3/4:...............Ab F  Bb G  D  B  A  Eb F# C# C  E  
5x/i/0/0:............C  F# Ab F  E  C# D  B  G  Eb Bb A
ri/8/10:.............D  Ab F  Bb B  G  Eb F# C# E  A  C  
ri/8/8:..............A  C  D  Ab F  Bb B  G  Eb F# C# E  

https://app.box.com/s/o9ws7rjwx863m83qyrnmz9whw9rl4t3i


I improvised with these lines, then resynthesised those tracks with Alchemy, then twiddled with that sound.

Going to try stretching out even further, using Soundhack.

eta: I'm not sure if it's acceptable how far ahead the violin gets. It sounds mostly ok, if a little, um, Ivesian.
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Last edited by calebprime; 3rd January 2016 at 11:32 AM.
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Old 3rd January 2016, 12:32 PM   #178
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I think the stretched version sounds great. (It's very long, 24 minutes.)

I'm thinking of composing over it, using it as a background bed and guide.

The stretch function I used rapidly goes to about 5x, then approaches 1x, that is, gets less and less stretched over the full 24 minutes duration.

https://app.box.com/s/kkijaruvmm4fuw5s46uiqn6ndno6eglg
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Old 4th January 2016, 02:03 PM   #179
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https://app.box.com/s/6hp9adx6w2tb4uvb02cp2bgndmk621tt

Same thing.

A little stretched, so it's 12 minutes long.
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Old 13th January 2016, 07:27 AM   #180
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Over that bed I've added a continuous motor, a generator part that will be the source of all the other parts. It sounds sort of like robo-Ralph Towner here. I very much like the interaction of a part like this with the harmonies of the bed -- that is, a low chord-scale guitar arpeggiation that has a motoric groove. When pitches in the guitar part agree with pitches in the bed, it sets up a very nice resonance.

So while ordinarily the motor part might not be heard at all, I think I'll use it literally, and layer polyrhythms on top of it that will make its effect less monotonous.

https://app.box.com/s/emoeo90ra6iaxj5klilj2vzui5c1c3qa

It has the virtue of a sort of single-minded monotony and simplicity. robo-Ralph.

The motor part that is repeated so much is the series 10,5,6,9,3,1,2,4,11,7,8,12 picking out notes of diatonic or octotonic scales -- picking out a contour. Diatonic serialism.

I've chosen this contour from the pre-composition work above, but I did so somewhat blindly. I don't know all of its possibilities for deriving self-similar shapes. Fortunately, chord-scales are a forgiving sound. You can fudge things a little to get a self-similar effect, and, because the note is still in the scale, it will still sound good.

There is an abrupt shift into a 12-tone ostinato in a crazy part of the piece -- in the middle -- that I have to make work somehow. Right now I'd be happy to get rid of it, but the challenge is good. A little risk.

The bed: The effect of stretching the wind parts is partly to make them sort of mid-fi electronicky, partly just the delicious smear of notes, maybe that strange passing notes or strange overtones will be emphasized. The violin part, added last, charges ahead, and sets up more of a polytonal clash later in the piece (from 8:30) than the original array would have suggested. The violin is way up in the upper register, playing bittersweet wrong notes. If the array is a little ruined, well, ruins are romantic.

I may try filtering the bed in time with the new ostinato, but it has enough processing already. It's already borderline rough and ugly.
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Old 14th January 2016, 08:37 AM   #181
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With the filtering, and now tricked out for stereo instrumental hocketing:

https://app.box.com/s/qfkp1h4n2gdrjo1totbsmk5koc7t74n3

Caution: There's some low bass later on toward the end of the piece that could overload your speakers if you're playing it too loud.



This was thrown together quickly. Compared to the past, this is absurdly efficient and stress-free composition and production. There's something to be said for middle age.
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Old 15th January 2016, 09:36 PM   #182
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I've listened to several of your pieces. They are fascinating. I can't honestly say I understand 1 percent of your theory as my musical training ended in 7th grade. But keep up the good work and I'll keep listening
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Old 16th January 2016, 04:15 AM   #183
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Thank you, KwamiFabu.
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Old 17th January 2016, 05:12 AM   #184
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That sketch achieved 85% of the effect without much effort, but it has some flaws.

--violin gets ahead, starts to sound a little weird at around 8 minutes. I like this, but it has nothing to do with original plan.

--aggressive filtering at beginning makes for thick, goopy effect -- bad mix, pumping the compression. The first impression a piece makes is important, and this isn't very good.

--filtering pretty much massacres the background part in general. You can't really hear the original instruments. There are maybe some good things in that part that should be preserved.

--most important: There isn't any real polyrhythm effect or any independence of voices in this version. This is where all the work is.

Verdict: It has maybe a dozen good things in it as it is, despite flaws and superficiality. Leave it as is. Do a different sketch with related material.
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Old 18th January 2016, 01:21 PM   #185
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Originally Posted by calebprime View Post
a spacey realization of this "basic chorale", from above:

Code:
  
r/3/4:...............Ab F  Bb G  D  B  A  Eb F# C# C  E  
5x/i/0/0:............C  F# Ab F  E  C# D  B  G  Eb Bb A
ri/8/10:.............D  Ab F  Bb B  G  Eb F# C# E  A  C  
ri/8/8:..............A  C  D  Ab F  Bb B  G  Eb F# C# E  
...
Same pitches, new background, 8 minutes.

https://app.box.com/s/vonjcgoy40e2l75llc9v52wxc0o09sn6
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Old 20th January 2016, 11:00 AM   #186
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That background is going to be fun to work with.

Here I've added automatic self-similar counterpoint in a speed ratio of 1:3:9

(guitar:harp:bass) over the first chord, chord-scale of A harmonic minor as one possible scale to choose for the chord (A,D,C,G#)

And the very heartening thing is that 1:3:9 works great. So I'm guaranteed a decent piece if I do nothing right but just hammer away at that.

first thirty seconds of sketch:

https://app.box.com/s/ih6z76wng4g2hodoh4et46lc02s9u0i5
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Old 23rd January 2016, 01:03 PM   #187
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https://app.box.com/s/2j0pzk5ls3s5hyj5m2l88fyl0jy7ybyi

Whole thing, basic sketch. 8 minutes. A lot of music from that little
4x12 array! I was quite pleased with this. Then my wife put on Bach's
St. Matthew Passion. His music is a lot better than mine is.
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Old 24th January 2016, 09:08 AM   #188
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Listening to that today, the harp figure is way too insistent and simple-minded. It's probably more than just a mix issue, though it's that. The piece is currently more boring than before because of the mechanical stuff -- which at best is supposed to be a sort of delightful clockworks effect, wheels-within-wheels.

Here the harp is bordering on being a bit of a torture.

Needs more richness, more change, even for a boring minimalist sketch, and something must be done about the harp part.

Also the background is just blaring in some spots -- that's contributing to the problem.
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Old 24th January 2016, 11:49 AM   #189
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Well, quick-and-dirty solutions to above problems, including the Too Long problem.

https://app.box.com/s/v35pi7zv9ln2yrpim8qda6mjj0najzx5

further research is needed.

This is sort of Strawberry Fields.
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Old 1st February 2016, 07:08 AM   #190
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Originally Posted by calebprime View Post
https://app.box.com/s/fe45k1v28cny4asx25s89xc0inv6s78y

Here it is, with just enough filling-in to test the idea.

The lesson here was that a two-note motive hitting the beginning and end of the bars makes the meter clear, makes the chunking clear -- and this turns an endless stream of undifferentiated notes (too much work for the listener) into something much more enjoyable.

Auto polyrhythms at every 2, 3, and 5 16th-notes.

I'm not sure if I should add more stuff for now, or move on to the next sketch.

This is basically a working out of this:

Code:

STRAIGHT 4ths (Each new row is a 4th above the old one)

G,  C#, Eb, F#, B,  D,  A,  C,  G#, E,  F,  Bb


to add notes, move up the array chain


C  F# G# B  E  G  D  F  C# A  Bb Eb          C
...............g........c#.......eb..
...f#....b........d........a.........
c.....g#....e........f........bb



C  G# E  F  Bb G  C# Eb F# B  D  A
to
C  F# G# B  E  G  D  F  C# A  Bb Eb



C  G# E  F  Bb G  C# Eb F# B  D  A  3x

C  F#|G# E  F  Bb G  C# Eb F# B  D  A

C  F# G# B  E |F  Bb G  C# Eb F# B  D  A 
 
C  F# G# B  E  G  D  F  Bb G  C# Eb F# B  D  A

C  F# G# B  E  G  D  F  C# Eb F# B  D  A

C  F# G# B  E  G  D  F  C# A  Bb Eb  many times

 

* Nice Ost: C,Ab,E,F,Bb,G     Nice Ost from EMBEDDINGS


THIS:  C  F  D  G# Bb C# F# A  E  G  Eb B

TO THIS"

C  G# E  F  Bb G  C# Eb F# B  D  A           G    
c........f....................d.....
...g#.......bb....c#....f#.......a..
......e........g.....eb....b........ 




C  A  Eb F  G# C# E  B  D  Bb F# G

C  F# A  Eb F  G# C# E  B  D  Bb F# G

C  C# F# A  Eb F  G# C# E  B  D  Bb F# G

C  Bb C# F# A  Eb F  G# C# E  B  D  Bb F# G

C  G# Bb C# F# A  Eb F  G# C# E  B  D  Bb F# G

C  D  G# Bb C# F# A  Eb F  G# C# E  B  D  Bb F# G

C  F  D  G# Bb C# F# A  E  G  Eb B




C  F  D  G# Bb C# F# A  E  G  Eb B           D     F#-A--E--G
c....................a........eb....
...f.....g#....c#.......e........b..
......d.....bb....f#.......g........


C  A  Eb F  G# C# E  B  D  Bb F# G           A 
c.....eb....g#.......b........f#....
...a.....f.....c#.......d........g..
..................e........bb.......


C  Eb G# B  F# A  F  C# D  G  E  Bb

C  A  Eb G# B  F# A  F  C# D  G  E  Bb

C  A  Eb F  G# B  F# A  F  C# D  G  E  Bb

C  A  Eb F  G# C# E  B  F# A  F  C# D  G  E  Bb

C  A  Eb F  G# C# E  B  D  Bb F# A  F  C# D  G  E  Bb

C  A  Eb F  G# C# E  B  D  Bb F# G

 
C  Eb G# B  F# A  F  C# D  G  E  Bb          E
c.....g#.......a........d............
.........b........f........g.....bb..
...eb.......f#.......c#.......e......



C  G# A  D  B  F  G  Bb Eb F# C# E

C  Eb G# A  D  B  F  G  Bb Eb F# C# E

C  Eb G# B  F# A  D  B  F  G  Bb Eb F# C# E

C  Eb G# B  F# A  F  C# D  B  F  G  Bb Eb F# C# E

C  Eb G# B  F# A  F  C# D  G  Eb E  A  F#

C  Eb G# B  F# A  F  C# D  G  E  Bb

C  G# A  D  B  F  G  Bb Eb F# C# E           B
c........d.....f.....bb.......c#....
...g#.......b.....g.....eb.......e..
......a....................f#.......


C  D  F  Bb C# G# B  G  Eb E  A  F#

C  G# A  D  F  Bb C# G# B  G  Eb E  A  F#

C  G# A  D  B  F  Bb C# G# B  G  Eb E  A  F#

C  G# A  D  B  F  G  Bb C# G# B  G  Eb E  A  F#

C  G# A  D  B  F  G  Bb Eb F# C# G# B  G  Eb E  A  F#

C  G# A  D  B  F  G  Bb Eb F# C# E





C  D  F  Bb C# G# B  G  Eb E  A  F#          F#          D  F  Bb C#
c.....f........g#.......eb.......f#..
...d.....bb.......b........e.........
............c#.......g........a......




current tempo: 78

C--D--F  G# Eb F# D  Bb B  E  C# G  A

C--D--F--Bb-C#-G# Eb F# D  Bb B  E  C# G  A

C--D--F--Bb-C#-G#-B--G--Eb F# D  Bb B  E  C# G  A

C--D--F--Bb-C#-G#-B--G--Eb-E--A--F#


C  F  G# Eb F# D  Bb B  E  C# G  A           Db
......G#.......D........E.....G.....
C........Eb.......Bb.......C#....A..
...F........F#.......B..............


C  F  G# Eb Bb C# A  F  F# B  G# D  E  G

C  F  G# Eb F# D  Bb C# A  F  F# B  G# D  E  G 

C  F  G# Eb F# D  Bb B  E  C# A  F  F# B  G# D  E  G

C  F  G# Eb F# D  Bb B  E  C# G  A 






C  Eb Bb C# A  F  F# B  G# D  E  G           Ab
c........c#.......f#................
...eb.......a........b.....d.....g..
......bb.......f........g#....e.....


C  Eb Bb C# F# Eb A  B  D  G  Bb F  G# E 

C  Eb Bb C# A  B  D  G  Bb F  G# E

C  Eb Bb C# A  F  F# Eb A  B  D  G  Bb F  G# E 

C  Eb Bb C# A  F  F# B  D  G  Bb F  G# E 

C  Eb Bb C# A  F  F# B  G# D  G  Bb F  G# E

C  Eb Bb C# A  F  F# B  G# D  E  G



C  Db F# Eb A  B  D  G  Bb F  G# E           Eb
c........eb....b.....g........g#...
...db...................bb.......e. 
......f#....a.....d........f.......


C  Eb B  G  Ab Db Bb E  F# A  D  F           Bb 
c........g........bb....f#....d.....
...eb.......ab...................f..
......b........db....e.....a


C  G  Bb F# D  Eb Ab F  B  C# E  A           F
c........f#.......g#....b.....e......
...g........d........f.....c#....a
......bb.......eb


C  F# G# B  E  G  D  F  C# A  Bb Eb          C
...............g........c#.......eb..
...f#....b........d........a.........
c.....g#....e........f........bb

that link was wrong. Is this different?

https://app.box.com/s/fe45k1v28cny4asx25s89xc0inv6s78y

It was asking for log in before, but it seems to be working now, even after I logged out.

I'm sick of that harp sound in that register, otherwise I like the piece.
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Old 1st February 2016, 07:41 AM   #191
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Boy, these sketches don't sound that great after a break. That's too bad, I'd hoped they'd sound better.

I think it's time I moved on from the chord & figuration basic design. There have been a few good pieces, so it hasn't been a total failure. Now it's time to try some different approaches. I can't do much better than what I've already done.

One thing I've learned, I think, is that if you're going to do one of these self-similar polyrhythmic pieces, you might as well use a "perfect" pattern -- that is, sadly, one of the well-known ones.

For example, below is the indices of 2 ^ n mod 11, and so it will have perfect self-similarity at every other note starting on the second note, every third notes starting on the third note, every 4th starting on the 4th, etc. all the way out.

So all of those polyrhythms are available in the framework of an intelligible composition:

Code:
10, 1,  8,  2,  4,  9,  7,  3,  6,  5
1,  2,  9,  3,  5,  10, 8,  4,  7,  6
2,  3,  10, 4,  6,  1,  9,  5,  8,  7
3,  4,  1,  5,  7,  2,  10, 6,  9,  8
4,  5,  2,  6,  8,  3,  1,  7,  10, 9
5,  6,  3,  7,  9,  4,  2,  8,  1,  10
6,  7,  4,  8,  10, 5,  3,  9,  2,  1
7,  8,  5,  9,  1,  6,  4,  10, 3,  2
8,  9,  6,  10, 2,  7,  5,  1,  4,  3
9,  10, 7,  1,  3,  8,  6,  2,  5,  4
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Old 6th February 2016, 04:19 AM   #192
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Projects for 2016

The great thing about the study of music is that there is always something to work on. Can't compose? Practice. Can't practice? Do theory. Can't do theory? Do some listening. Don't feel like listening? Write your memoirs.

Composing is my first-tier project. I hope to keep doing that, mainly. But if I can't do that...


Practice:

- 43-pitch scale. The goal is to become as fluent as in 12-tone, to know where all the pitches are without thinking. Then to find the unique sounds of this "scale" and learn to compose with it.

- Quarter-tone scales. W. D. Clinger helped me by writing a program that found the relatively consonant scales and chords with at least one quarter tone. Again, learn the layout. Learn to understand the connections between quarter-tone structures just as you understand them with 12 tones.

This is sort of the opposite of learning repertoire -- that is, pieces -- so it's about long-term understanding, not getting something ready for performance.


Theory:

I have use for nuts-and-bolts writing by composers for composers.
This is necessarily a small set of texts.

I can benefit from a close reading of:

_Composition with Pitch-Classes_ by Robert Morris.

https://en.wikipedia.org/wiki/Robert_Morris_(composer)

and

_Self-Similar Melodies_ by Tom Johnson.

https://en.wikipedia.org/wiki/Tom_Johnson_(composer)
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Old 8th February 2016, 11:53 AM   #193
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Originally Posted by calebprime View Post
...
Practice:

...
- Quarter-tone scales. W. D. Clinger helped me by writing a program that found the relatively consonant scales and chords with at least one quarter tone. Again, learn the layout. Learn to understand the connections between quarter-tone structures just as you understand them with 12 tones.

This is sort of the opposite of learning repertoire -- that is, pieces -- so it's about long-term understanding, not getting something ready for performance.

...
I've done some work on the list of 65 scales. Each of these can be transposed to 24 starting-points. To practice that, the most useful entry for me is the one on the far right, that shows relative fingering.

Code:
 A sorting of 65 quarter-tone scales by left-most pack to right-most pack


Scale pitch-names, scale names                    Fingering, abs.     Fingering, relative

A,Bb,C,C#,D#,E,G- close to "A oct"                A,B,D#,F,A,B,E      0,2,6,8,|0,2,7
A,Bb,C,Db,Eb,F,G- like Bbhar. min.                A,B,D#,F,A,C#,E     0,2,6,8,|0,4,7

A,Bb,C,D-,Eb,F,Gb like Bb har. maj/min.           A,B,D#,F#,A,C#,D#   0,2,6,9,|0,4,6
A,Bb,C,D-,Eb,F,G- like Bb Ion.                    A,B,D#,F#,A,C#,E    0,2,6,9,|0,4,7
A,Bb,C,D-,Eb,F,G like Bb Ion.                     A,B,D#,F#,A,C#,F    0,2,6,9,|0,4,8

A,Bb,C,D-,E,F,G like F har. maj.                  A,B,D#,F#,B,C#,F    0,2,6,9,|2,4,8

A,Bb,C,D,Eb,F,G- like Bb har. maj.                A,B,D#,G,A,C#,E     0,2,6,10,|0,4,7             
A,Bb,C,D,Eb,F#-,G like G har. min.                A,B,D#,G,A,D,F      0,2,6,10,|0,5,8

A,Bb,C,D,E,F#-,G like Bb Lyd.,like G mel.min.     A,B,D#,G,B,D,F      0,2,6,10,|2,5,8

A,Bb,C#-,D,E,F,G like D har. min.                 A,B,E,G,B,C#,F      0,2,7,10,|2,4,8
A,Bb,C#-,D,E,F#-,G like D har maj/min.            A,B,E,G,B,D,F       0,2,7,10,|2,5,8
A,Bb,C#-,D,E,F#,G like D har. maj.                A,B,E,G,B,D#,F      0,2,7,10,|2,6,8
A,Bb,C#-,D#,E,F#,G close to "A oct"               A,B,E,A,B,D#,F      0,2,7,|0,2,6,8

A,Bb,C#,D,E,F#-,G Hijaz like D harmonic maj/min.  A,B,F,G,B,D,F       0,2,8,10,|2,5,8

A,B-,C,D,Eb,F,G like Eb Lyd., like C mel. min.    A,C,D#,G,A,C#,F     0,3,6,10,|0,4,8
A,B-,C,D,Eb,F#-,G                                 A,C,D#,G,A,D,F      0,3,6,10,|0,5,8
A,B-,C,D,Eb,F#,G like G har. maj/min.             A,C,D#,G,A,D#,F     0,3,6,10,|0,6,8

A,B-,C,D,E,F,G like C Ion.                        A,C,D#,G,B,C#,F     0,3,6,10,|2,4,8
A,B-,C,D,E,F#-,G                                  A,C,D#,G,B,D,F      0,3,6,10,|2,5,8
A,B-,C,D,E,F#,G like G Ion.                       A,C,D#,G,B,D#,F     0,3,6,10,|2,6,8    

A B-,C#-,D-,E,F#-,G#-                             A,C,E,F#,B,D,F#     0,3,7,9,|2,5,9
A,B-,C#-,D,E,F#-,G                                A,C,E,G,B,D,F       0,3,7,10,|2,5,8
A,B-,C#-,D,E,F#-,G#-                              A,C,E,G,B,D,F#      0,3,7,10,|2,5,9

A,B-,C#-,D#-,E,F#-,G#- Sikah/Nahawand             A,C,E,G#,B,D,F#     0,3,7,11,|2,5,9
 
A,B-,C#,D,E,F,G Mustaar like D har. min.          A,C,F,G,B,C#,F      0,3,8,10,|2,4,8    
A,B-,C#,D,E,F#-,G like D Ion                      A,C,F,G,B,D,F       0,3,8,10,|2,5,8
A,B-,C#,D,E,F#,G like C#har. maj.                 A,C,F,G,B,D#,F      0,3,8,10,|2,6,8  

A,B,C,D,Eb,F#-,G like G har. maj.                 A,C#,D#,G,A,D,F#    0,4,6,10,|0,5,9
A,B,C,D,Eb,F#-,G# close to "D oct"                A,C#,D#,G,A,D,G     0,4,6,10,|0,5,10

A,B,C,D,E,F,G#- like A har. min.                  A,C#,D#,G,B,C#,F#   0,4,6,10,|2,4,9 
A,B,C,D,E,F#-,G like G Ion.                       A,C#,D#,G,B,D,F     0,4,6,10,|2,5,8
A,B,C,D,E,F#-,G# like A har. min.                 A,C#,D#,G,B,D,G     0,4,6,10,|2,5,10
A,B,C,D,E,F#,G#- like A mel. min. up              A,C#,D#,G,B,D#,F#   0,4,6,10,|2,6,9

A,B,C,D#-,E,F#,G like E har. min.                 A,C#,D#,G#,B,D#,F   0,4,6,11,|2,6,8
A,B,C,D#-,E,F#,G#-                                A,C#,D#,G#,B,D#,F#  0,4,6,11,|2,6,9
A,B,C,D#-,E,F#,G# like E har. maj.                A,C#,D#,G#,B,D#,G   0,4,6,11,|2,6,10
A,B,C,D#-,F,F#,G# close to "D oct"                A,C#,D#,G#,C#,D#,G  0,4,6,11,|4,6,10

A,B,C,D#,E,F#,G#- like E harmonic maj/min.        A,C#,D#,A,B,D#,F#   0,4,6,|0,2,6,9

A,B,C#-,D,E,F,G like F Lyd., like D mel. min. up  A,C#,E,G,B,C#,F     0,4,7,10|2,4,8
A,B,C#-,D,E,F,G#-                                 A,C#,E,G,B,C#,F#    0,4,7,10|2,4,9    
A,B,C#-,D,E,F,G# like A harmonic maj/min.         A,C#,E,G,B,C#,G     0,4,7,10|2,4,10      
A,B,C#-,D,E,F#-,G Bayati                          A,C#,E,G,B,D,F      0,4,7,10|2,5,8
A,B,C#-,D,E,F#-,G#-                               A,C#,E,G,B,D,F#     0,4,7,10|2,5,9
A,B,C#-,D,E,F#-,G# like A Ion.                    A,C#,E,G,B,D,G      0,4,7,10|2,5,10    
A,B,C#-,D,E,F#,G Rast like D Ion.                 A,C#,E,G,B,D#,F     0,4,7,10|2,6,8
A,B,C#-,D,E,F#,G#- Rast (Wiki)                    A,C#,E,G,B,D#,F#    0,4,7,10|2,6,9
A,B,C#-,D,E,F#,G# like A Ion.                     A,C#,E,G,B,D#,G     0,4,7,10|2,6,10    

A,B,C#-,D#-,E,F#-,G#-                             A,C#,E,G#,B,D,F#    0,4,7,11|2,5,9
A,B,C#-,D#-,E,F#,G#-                              A,C#,E,G#,B,D#,F#   0,4,7,11|2,6,9

A,B,C#-,D#,E,F#,G like E har. min.                A,C#,E,A,B,D#,F     0,4,7,|0,2,6,8
A,B,C#-,D#,E,F#,G#- like E Ion.                   A,C#,E,A,B,D#,F#    0,4,7,|0,2,6,9   
A,B,C#-,D#,E,F#,G# like E har. maj.               A,C#,E,A,B,D#,G     0,4,7,|0,2,6,10

A,B,C#,D,E,F,G#- like A har. maj.                 A,C#,F,G,B,C#,F#    0,4,8,10,|2,4,9
A,B,C#,D,E,F#-,G like D Ion.                      A,C#,F,G,B,D,F      0,4,8,10,|2,5,8
A,B,C#,D,E,F#-,G# like A har. maj.                A,C#,F,G,B,D,G      0,4,8,10,|2,5,10
A,B,C#,D,E,F#,G#- Jiharkah/Ajam like A Ion.       A,C#,F,G,B,D#,F#    0,4,8,10,|2,6,9

A,B,C#,D#-,E,F#,G like G Lyd., like E mel. min.   A,C#,F,G#,B,D#,F    0,4,8,11,|2,6,8   
A,B,C#,D#-,E,F#,G#- like E Ion.                   A,C#,F,G#,B,D#,F#   0,4,8,11,|2,6,9
A,B,C#,D#-,E,F#,G# like E Ion.                    A,C#,F,G#,B,D#,G    0,4,8,11,|2,6,10
A,B,C#,D#-,F,F#,G# like F#har. min.               A,C#,F,G#,C#,D#,G   0,4,8,11,|4,6,10    

A,B,C#,D#,E,F#,G#- like E Ion.                    A,C#,F,A,B,D#,F#    0,4,8,|0,2,6,9

A,C-,C#-,D#-,E,F#-,G#-                            A,D,F,G#,B,D,F#     0,5,8,11,|2,5,9
A,C-,C#,D#,E,F#,G#  like C# har. min.             A,D,F,A,B,D#,G      0,5,8,|0,2,6,10            
A,C-,C#,D#,F,F#,G#  like C# har. maj.             A,D,F,A,C#,D#,G     0,5,8,|0,4,6,10
A,C-,D,Eb,F,F#,G#   close to "D oct"              A,D,G,A,C#,D#,G     0,5,10,|0,4,6,10
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Old 9th February 2016, 06:39 AM   #194
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And here is the same relative-position list (or "fingering, relative") for the 5- and 6-note structures that have no "wolf" -- or 650-cent or 750-cent -- intervals.

With that relative-position list I can already begin to improvise a little, seeking common-tones between different structures. The goal is to learn to be able to move smoothly and freely between different harmonies in this quarter-tone world -- without that slightly nauseating feeling of discordant and arbitrary tonal flavors.

More generally, the goal is beautiful freshness and strangeness, without Exoticism or Orientalism (so to speak.) I don't want my music to sound like Kimono Wednesday, or Burka Thursday.

I'm years from fluency. It might be possible to compose without competence or fluency in the scale -- but...I don't swing that way. I play for the Competents, not the Charlatans. Maybe they'll let me off the bench some day.

Code:
Five and Six-Note "No-Wolf" chord/scales.  Relative fingering on right.

A, D,  E,  F#-, G#:  10,4,3,5,2      0,10,|2,5,10
A, B-, C#, D,   G:   3,5,2,10,4      0,3,8,10,|8                                  
A, Bb, D#, F,   G-:  2,10,4,3,5      0,2,|0,4,7           
A, C-, C#-,F#-, G#-: 5,2,10,4,3      0,5,7,|5,9                
A, B,  C#-,D#,  E:   4,3,5,2,10      0,4,7,|0,2             
=================================
A, D,  D#, F#-, G:   10,2,5,3,4      0,10,|0,5,8               
A, C-, C#, D#,  G#:  5,3,4,10,2      0,5,8,|0,10               
A, B,  E,  F,   G#-: 4,10,2,5,3      0,4,|2,4,9              
A, B-, C#-,F#-, G-;  3,4,10,2,5      0,3,7,|5,7              
A, Bb, C#-,D,   E:   2,5,3,4,10      0,2,7,10,|2              


A, C-, D,  D#,  F#-, G#: 5,5,2,5,5,2   0,5,10,|0,5,10       
A, C-, C#-,D#,  F#-,G-:  5,2,5,5,2,5   0,5,7,|0,5,7               
A, Bb, C#-,D#,  E,  G-:  2,5,5,2,5,5   0,2,7,|0,2,7                


A, B,  F,  F#,  G#-: 4,12,2,3,3        0,4,|4,6,9                   
A, Bb, C-, C#, D#:   2,3,3,4,12        0,2,5,8,|0                  
===============================
A, B-, C-, F#-, G#-: 3,2,12,4,3        0,3,5,|5,9


A, B,  E,  F#,  G#-: 4,10,4,3,3        0,4,|2,6,9
A, D,  E,  F#-, G:   10,4,3,3,4        0,10,|2,5,8
A, B-, C#-,F#-, G#-: 3,4,10,4,3        0,3,7,|5,8
A, B-, C,  D, G:     3,3,4,10,4        0,3,6,10,|8
A, B,  C#-,D, E:     4,3,3,4,10        0,4,7,10,|2


A, C#-,E,  F#-, G#-: 7,7,3,4,3         0,7,|2,5,8
A, B,  C#-,E,   G#-: 4,3,7,7,3         0,4,7,|2,9
A, B-, D,  F#-, G:   3,7,7,3,4         0,3,10,|5,
A, C#-,D,  E,   F#-: 7,3,4,3,7         0,7,10,|2,5
A, B-, C#-,D,   F#-: 3,4,3,7,7         0,3,7,10,|5


these two are against the "rules", but I like them

A, Bb, C-, C#-, D#, G-: 2,3,2,5,7,5    0,2,5,7,|0,7
A, Bb, C-, D, D#:       2,3,5,2,12     0,2,5,10,|0


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Old 14th February 2016, 07:58 AM   #195
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Code:


Scales / Modes

5-note

2 8 3 6 5  Anchihoye: Ethiopia   A,Bb,D,E-,G-  0,2,10, | 1,7
Has 650-cent "5th"

5 5 4 5 5  Quasi-equal Pentatonic              0,5,10, | 2,7   

5 5 5 5 4  Hába's Pentatonic -                 0,5,10, | 3,8 

------------------------------------------------------------------
7-note

3 3 4 3 3 4 4 Ouchairan-Hussaini, Bayatan,  

3 4 3 3 4 4 3 Dastgah-e Sehgah,  0,3,7,10,|1,5,9   Has 650-cent "5th"

4 3 3 4 4 3 3 Rast,              0,4,7,10,|2,6,9   same as above

3 3 4 4 3 3 4 Hussaini, Ushaq,   0,3,6,10,|2,5,8   same as above

3 4 4 3 3 4 3 Sikah (Segah),     0,3,7,11,|2,5,9,  same as above

4 4 3 3 4 3 3

4 3 3 4 3 3 4 Miha'il Musaqa: Egypt  0,4,7,10,|2,5,8  called Bayati

3 4 3 3 4 3 4
 
4 3 3 4 3 4 3
 
3 3 4 3 4 3 4
 
3 4 3 4 3 4 3 Sikah Baladi 

4 3 4 3 4 3 3
 
3 4 3 4 3 3 4
 
4 3 4 3 3 4 3
 
3 5 2 4 3 5 2 Dastgah-e Chahargah

4 2 4 4 3 3 4 Dastgah-e Nava, Maqam Ushaq Masri

3 3 4 4 2 4 4 Maqam 'Ushshaq Turki, Urfa, Isfahan, Dastgah-e Shur

3 3 4 4 4 2 4 Maqam Nahfat

3 3 2 6 2 4 4 Maqam Saba

3 3 2 6 2 6 2 Maqam Sabr Jadid

4 3 3 4 2 6 2 Maqam Suznak (Soznak)

4 3 3 4 4 4 2 Maqam Mahur

3 3 4 2 6 2 4 Maqam Qarjighar, Bayati Shuri

3 4 2 6 2 4 3 Maqam Hizam (Huzam, El Houzam), Rahat al Arouah

2 4 4 4 3 3 4 Maqam Nawa

2 5 3 4 2 5 3 Maqam Higaz-kar

3 4 4 2 4 4 3 Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari

4 4 2 4 4 3 3 Maqam Jahargah (Jiharkah), Naghmeh Bayat-e Tork, Naghmeh Dashti

3 5 2 4 2 4 4 Dastgah-e Homayun

4 2 4 4 3 5 2 Naghmeh Esfahan

3 6 1 5 2 6 1 Maqam 'Awg 'ara (Aug-ara)  0,3,9,10, | 3,5,11

4 1 5 4 2 6 2 Maqam Buselik

4 2 6 2 2 5 3 Maqam Neuter

------------------------------------------------------------------

8-note

3 3 3 3 3 3 3 3  8-equal, Wyschnegradsky's octatonic

3 3 4 4 2 1 3 4  Maqam Bayati

3 3 2 6 2 4 2 2  Maqam Saba

4 3 1 2 4 4 2 4  Maqam Suzidil 'ara

3 3 2 2 4 3 3 4  Maqam Mansuri

4 3 3 4 4 2 1 3  Maqam Rast, Dilkashidah, Dilnishin

3 4 2 6 2 4 2 1  Maqam Rahat al-Arwah

3 4 3 3 4 4 2 1  Maqam Iraq

2 6 2 4 2 1 3 4  Maqam Hijaz

3 4 4 2 1 3 4 3  Maqam Musta'ar

3 4 4 4 2 4 2 1  Maqam Farahnak

3 4 3 3 2 6 2 1  Maqam Bastanikar, Tarz Nuin

4 2 6 2 4 2 1 3  Maqam Farah Faza, Maqam Nakriz

3 1 2 4 4 2 4 4  Maqam Jabburi
------------------------------------------------------------------
9-note

 
3 4 2 2 2 2 2 4 3    Maqam Huzam

4 4 2 1 3 2 2 4 2    Maqam Shawq Afza
------------------------------------------------------------------
10-note
  
 
2 3 2 2 3 2 3 2 2 3   Oljare Decatonic -  

2 1 3 2 2 4 2 4 2 2   Maqam Shawq Tarab

4 2 1 3 2 2 4 2 1 3   Maqam Basandida

4 3 1 2 1 3 4 2 1 3   Maqam Yakah
------------------------------------------------------------------
11-note

4 2 1 3 2 2 2 2 3 1 2 Maqam Hayyan
------------------------------------------------------------------



The collection of quarter-tone material I'm trying to learn is enlarged by this:

http://xenharmonic.wikispaces.com/24edo

As always, the xenharmonic folks provide the richest, most useful information.

I've selected most of it, rejected some because it makes no sense to me, or seems unreasonable. When in doubt, I've accepted anything with an Arabic-sounding label, on the grounds that it's at least sanctioned by tradition (which in musical terms means it's not complete junk). Further winnowing may be necessary. If the contributor of those Arabic maqam names is who I think it is, he's a master, and I trust his judgment enough to try whatever he proposes.

In particular, some of the quarter-tone scales with lots of actual quarter-tone intervals (1's, here) seem worthless to me. I'd defend this rejection, if pressed, with a distinction between structural/harmonic pitches and pitches which are only for melodic elaborations. I'm interested in the former. Decorations come after the foundations are secure. Also, someone's naming of some of these scales with reference to modes made no sense to me.

We ought to be using the standard, contemporary naming of modes, even though the names have changed over the centuries. Dorian, in contemporary terms, should always be 1,2,b3,4,5,6,b7 -- ( say, Ab,Bb,Cb,Db,Eb,F,Gb) -- not whatever the term meant to the ancient Greeks. Standardization is more important the history. These terms are only aids to understanding. They do not represent the delicious mysterious Eternal Wisdom of the Ancients.

Also, I'm unmoved by the Moment of Symmetry concept.

A lot of theory consists of working-out of premises that may or may not really be that important:
In 12-tone theory, for instance, the "aggregate" (simply, all 12 tones) and "combinatoriality" have been worked out to amazing degrees of sophistication. But neither of those concepts sounds like much to me, so I don't study them.

Another somewhat-dubious-but-provisionally-useful concept is the pitch-class-set, and musical "set theory". Guerilla set-theory -- say, knowing what an 014 sounds like -- seems useful to me. The complete working-out (as in Forte's _The Structure of Atonal Music_) shades off into pure mathematical abstraction, and shouldn't be treated like it's really something all that musical.

What I'm looking for here is a relatively euphonious, invertible, modal quarter-tone sound, that can modulate freely via common-tone structures.
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Last edited by calebprime; 14th February 2016 at 08:50 AM.
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Old 14th February 2016, 01:38 PM   #196
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Originally Posted by calebprime View Post
Code:


Scales / Modes

5-note

2 8 3 6 5  Anchihoye: Ethiopia   A,Bb,D,E-,G-  0,2,10, | 1,7
Has 650-cent "5th"

5 5 4 5 5  Quasi-equal Pentatonic              0,5,10, | 2,7   

5 5 5 5 4  Hába's Pentatonic -                 0,5,10, | 3,8 

------------------------------------------------------------------
7-note

3 3 4 3 3 4 4 Ouchairan-Hussaini, Bayatan,  

3 4 3 3 4 4 3 Dastgah-e Sehgah,  0,3,7,10,|1,5,9   Has 650-cent "5th"

4 3 3 4 4 3 3 Rast,              0,4,7,10,|2,6,9   same as above

3 3 4 4 3 3 4 Hussaini, Ushaq,   0,3,6,10,|2,5,8   same as above

3 4 4 3 3 4 3 Sikah (Segah),     0,3,7,11,|2,5,9,  same as above

4 4 3 3 4 3 3

4 3 3 4 3 3 4 Miha'il Musaqa: Egypt  0,4,7,10,|2,5,8  called Bayati

3 4 3 3 4 3 4
 
4 3 3 4 3 4 3
 
3 3 4 3 4 3 4
 
3 4 3 4 3 4 3 Sikah Baladi 

4 3 4 3 4 3 3
 
3 4 3 4 3 3 4
 
4 3 4 3 3 4 3
 
3 5 2 4 3 5 2 Dastgah-e Chahargah

4 2 4 4 3 3 4 Dastgah-e Nava, Maqam Ushaq Masri

3 3 4 4 2 4 4 Maqam 'Ushshaq Turki, Urfa, Isfahan, Dastgah-e Shur

3 3 4 4 4 2 4 Maqam Nahfat

3 3 2 6 2 4 4 Maqam Saba

3 3 2 6 2 6 2 Maqam Sabr Jadid

4 3 3 4 2 6 2 Maqam Suznak (Soznak)

4 3 3 4 4 4 2 Maqam Mahur

3 3 4 2 6 2 4 Maqam Qarjighar, Bayati Shuri

3 4 2 6 2 4 3 Maqam Hizam (Huzam, El Houzam), Rahat al Arouah

2 4 4 4 3 3 4 Maqam Nawa

2 5 3 4 2 5 3 Maqam Higaz-kar

3 4 4 2 4 4 3 Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari

4 4 2 4 4 3 3 Maqam Jahargah (Jiharkah), Naghmeh Bayat-e Tork, Naghmeh Dashti

3 5 2 4 2 4 4 Dastgah-e Homayun

4 2 4 4 3 5 2 Naghmeh Esfahan

3 6 1 5 2 6 1 Maqam 'Awg 'ara (Aug-ara)  0,3,9,10, | 3,5,11

4 1 5 4 2 6 2 Maqam Buselik

4 2 6 2 2 5 3 Maqam Neuter

------------------------------------------------------------------

8-note

3 3 3 3 3 3 3 3  8-equal, Wyschnegradsky's octatonic

3 3 4 4 2 1 3 4  Maqam Bayati

3 3 2 6 2 4 2 2  Maqam Saba

4 3 1 2 4 4 2 4  Maqam Suzidil 'ara

3 3 2 2 4 3 3 4  Maqam Mansuri

4 3 3 4 4 2 1 3  Maqam Rast, Dilkashidah, Dilnishin

3 4 2 6 2 4 2 1  Maqam Rahat al-Arwah

3 4 3 3 4 4 2 1  Maqam Iraq

2 6 2 4 2 1 3 4  Maqam Hijaz

3 4 4 2 1 3 4 3  Maqam Musta'ar

3 4 4 4 2 4 2 1  Maqam Farahnak

3 4 3 3 2 6 2 1  Maqam Bastanikar, Tarz Nuin

4 2 6 2 4 2 1 3  Maqam Farah Faza, Maqam Nakriz

3 1 2 4 4 2 4 4  Maqam Jabburi
------------------------------------------------------------------
9-note

 
3 4 2 2 2 2 2 4 3    Maqam Huzam

4 4 2 1 3 2 2 4 2    Maqam Shawq Afza
------------------------------------------------------------------
10-note
  
 
2 3 2 2 3 2 3 2 2 3   Oljare Decatonic -  

2 1 3 2 2 4 2 4 2 2   Maqam Shawq Tarab

4 2 1 3 2 2 4 2 1 3   Maqam Basandida

4 3 1 2 1 3 4 2 1 3   Maqam Yakah
------------------------------------------------------------------
11-note

4 2 1 3 2 2 2 2 3 1 2 Maqam Hayyan
------------------------------------------------------------------



The collection of quarter-tone material I'm trying to learn is enlarged by this:

http://xenharmonic.wikispaces.com/24edo

As always, the xenharmonic folks provide the richest, most useful information.

I've selected most of it, rejected some because it makes no sense to me, or seems unreasonable. When in doubt, I've accepted anything with an Arabic-sounding label, on the grounds that it's at least sanctioned by tradition (which in musical terms means it's not complete junk). Further winnowing may be necessary. If the contributor of those Arabic maqam names is who I think it is, he's a master, and I trust his judgment enough to try whatever he proposes.

In particular, some of the quarter-tone scales with lots of actual quarter-tone intervals (1's, here) seem worthless to me. I'd defend this rejection, if pressed, with a distinction between structural/harmonic pitches and pitches which are only for melodic elaborations. I'm interested in the former. Decorations come after the foundations are secure. ...
Case in point: Under the 8-note list, we have a Maqam Bayati scale given as: 3 3 4 4 2 1 3 4.

This would be, in C: C, D-, Eb, F, | G, Ab, A-, Bb

Clearly the Ab and A- (the pitches separated by a quarter-tone, or 1) are alternate versions of the same note. (Spelling aside. Spelling is verbal convenience here, not that important.)

So it's really a 7-note scale with a variable 6th degree. Not mysterious.

The Ab and A- would never occur together in a chord.

There really isn't a structural 1 in the scale, any more than in the conventional notion of a "melodic minor" scale the two versions of the 6th degree are both simultaneous scale-degrees. They're not. One's for going up, the other's for going down.

I don't hear a lot of actual 50-cent melodic or harmonic intervals in Arabic music or any other kind of music. It's whiny like a mosquito as melody, horrible like a toothache as harmony. Too close to the unison for comfort.

So, as always with the xenharmonic stuff, you have to use your own ears, and read between the lines a little. I don't think of this stuff as a holiday from convention, a world where all bets are off, and anything's possible.

The fundamental things in life apply, as time goes by.
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Last edited by calebprime; 14th February 2016 at 01:44 PM.
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Old 15th February 2016, 09:56 AM   #197
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Absolute pitch, relative pitch

I've been wanting to write a little post about this, to bring my experience from music school to bear, to clear up a few of the common misconceptions.

This wiki page seems fairly accurate and enlightened:

https://en.wikipedia.org/wiki/Absolute_pitch

My main points:

1) The general public (the "civilian") is slightly too impressed with absolute pitch.

1a.) The public isn't really that interested in how best to train musicians or what goes into the process. I like a sausage, I don't care what goes into it.

1b.) A lot of what I'm digging up on the Net from non-experts is just wrong.

1c.) Music is one of those areas where everyone feels entitled to his opinion, no matter how misinformed.

1d.) Some in the public seem to want to experience musical performance as if it were some kind of Proof of Virtuosity, or gladiatorial combat, or Triumph over Adversity. For some, Only the Best Will Do. That is silly.


2) Absolute pitch is a definite advantage -- especially for improvisers and conductors. Not so much for composers.

2a.) Conservatory training is a weird mix of ridiculous unexamined archaic notions -- often making a virtue of a necessity -- that, nevertheless, do work to make good musicians. One of these notions is that composers should compose "head to paper" without checking on piano, as if they had absolute pitch. Sure, and painters shouldn't have to look at their canvases when they paint, either. That would be cheating.


3) Absolute pitch is a much better, more accurate term than perfect pitch.

4) You really can't develop absolute pitch. After early childhood, that door closes. The courses that claim otherwise are scams, just like penis enlargement.

5) Absolute pitch often seems to come with unusual memory abilities -- what people call "photographic memory". (Stan Getz, Susan, David Fulmer, Kevin Gibbs, Keith Jarrett.)

6) People hear someone singing with good intonation ("in tune") and they think that's "perfect pitch", or absolute pitch. No. You can have absolute pitch and sing out of tune, a little flat or sharp. You can lack it, and sing perfectly in tune. They are two different things, but related.

7) People with only relative pitch rely more on schemas, on concepts, on understanding, because they have to. This can be good for a composer.

8) Having absolute pitch doesn't mean you have a great ability to perceive fine gradations of pitch.

9) Absolute pitch is long-term memory lookup. About 1 in 10,000 people have the ability.

10) People with absolute pitch don't perceive as great a difference in difficulty between tonal and "atonal" music. Some feel no difference at all. For me, there's a huge difference.

11) Musicians without absolute pitch have to work a little, or a lot, harder. This can be a good thing, or it can crush them.


People I knew at NEC who had absolute pitch for sure:

David Fulmer. Kevin Gibbs. Susan (former girlfriend). Student in class whose name I can't remember.

People I knew at NEC and around Boston who didn't, who were just as good:
George Schuller. Nancy Zeltsman. Don Byron. Rachel Z. Gunther Schuller. Clayton Hoener.

People who were frickin' geniuses. Not sure, but I don't think so:
Lorraine Hunt Lieberson. David Rakowski. Joel Smirnoff.

A friend with a great ear, but not absolute pitch: Andy Fox.
Someone who consistently said perceptive things, despite seeming not to have a great ear for pitch: Blobru.

Composers with absolute pitch:
Mozart. Boulez. Shostakovich.

Composers without absolute pitch, (probably):
Stravinsky. Beethoven. Schoenberg. Haydn

Great jazz players with absolute pitch, (and it showed)
Stan Getz. Keith Jarrett. Ornett Coleman

Great jazz players without absolute pitch:
Coltrane. Miles. Bill Evans. ( I'm not sure about these)


Differences in taste based on differences in hearing between AP and RP? One story:

I wrote a piece for violin and tape (I'm now calling it Clay's Way, in honor of Clayton Hoener, who played it really well.) It was praised by a number of my musical friends -- none of whom had absolute pitch.

https://app.box.com/s/q9dknyphurezkxy7z5bj

It wasn't at all well-received by the two musicians who had absolute pitch. I think it was because the underlying structure was repetitive, although the melodic elaboration (the foreground) was not repetitive.

This has pained me and confused me. Should I go with the way I hear it? Or should I go with the possibly superior judgment of those with absolute pitch?
As a composer, you can't go around second-guessing yourself. You have to trust your own ear. There isn't anything else you can rely on.

Two photographic memory stories:

David Fulmer -- by his own account to me -- played the premier of Thomas Ades' Violin Concerto at Lincoln Center without having practiced it and without having looked at the score or the part much. Was a little depressed at the time. He looked it over, had it memorized in his head. Showed up, played it. Felt a little stiff at first, he said. Otherwise it went alright.

I think this is the piece:

https://www.youtube.com/watch?v=CVG5R6sIobo

Kevin Gibbs hears a horrible atonal electronic fake samba in a film shown once at NEC in class. A year later, he plays it perfectly from memory, with the composer in attendance.

These feats are just completely out of reach for even good musicians.

Absolute pitch can be a component, it seems, of a bullet-proof talent. Stan Getz could be drunk off his ass and still play beautifully. Shostakovich -- well, there are many stories, like Tea for Two.

Or, listen to Keith Jarrett playing live with Miles in 1971. Or more recently, improvising with moving harmonies that sound like Hindemith. No schemas can make that possible. Only absolute pitch makes that possible.






------------------------------------
Oh, and while I'm trying to clear up popular misconceptions, there's the notion that the best musicians "can do it all". Someone here who worked in music publishing even said that explicitly.

Well, problem is, that woud rule out 99.9% of musicians.

Nobody can do it all. Not Gunther Schuller, not Keith Jarrett, not Chick Corea, not Andre Previn, not William Thomas McKinley. They were (or are) much better at some things than others.

Everyone does some things well, gets by or fakes it with other things.

Jarrett doesn't seem to have the patience or attitude to make a really good composer, for instance.
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Old 16th February 2016, 04:17 AM   #198
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Originally Posted by calebprime View Post
Code:


Scales / Modes

5-note

2 8 3 6 5  Anchihoye: Ethiopia   A,Bb,D,E-,G-  0,2,10, | 1,7
Has 650-cent "5th"

5 5 4 5 5  Quasi-equal Pentatonic              0,5,10, | 2,7   

5 5 5 5 4  Hába's Pentatonic -                 0,5,10, | 3,8 

------------------------------------------------------------------
7-note

3 3 4 3 3 4 4 Ouchairan-Hussaini, Bayatan,  

3 4 3 3 4 4 3 Dastgah-e Sehgah,  0,3,7,10,|1,5,9   Has 650-cent "5th"

4 3 3 4 4 3 3 Rast,              0,4,7,10,|2,6,9   same as above

3 3 4 4 3 3 4 Hussaini, Ushaq,   0,3,6,10,|2,5,8   same as above

3 4 4 3 3 4 3 Sikah (Segah),     0,3,7,11,|2,5,9,  same as above

4 4 3 3 4 3 3

4 3 3 4 3 3 4 Miha'il Musaqa: Egypt  0,4,7,10,|2,5,8  called Bayati

3 4 3 3 4 3 4
 
4 3 3 4 3 4 3
 
3 3 4 3 4 3 4
 
3 4 3 4 3 4 3 Sikah Baladi 

4 3 4 3 4 3 3
 
3 4 3 4 3 3 4
 
4 3 4 3 3 4 3
 
3 5 2 4 3 5 2 Dastgah-e Chahargah

4 2 4 4 3 3 4 Dastgah-e Nava, Maqam Ushaq Masri

3 3 4 4 2 4 4 Maqam 'Ushshaq Turki, Urfa, Isfahan, Dastgah-e Shur

3 3 4 4 4 2 4 Maqam Nahfat

3 3 2 6 2 4 4 Maqam Saba

3 3 2 6 2 6 2 Maqam Sabr Jadid

4 3 3 4 2 6 2 Maqam Suznak (Soznak)

4 3 3 4 4 4 2 Maqam Mahur

3 3 4 2 6 2 4 Maqam Qarjighar, Bayati Shuri

3 4 2 6 2 4 3 Maqam Hizam (Huzam, El Houzam), Rahat al Arouah

2 4 4 4 3 3 4 Maqam Nawa

2 5 3 4 2 5 3 Maqam Higaz-kar

3 4 4 2 4 4 3 Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari

4 4 2 4 4 3 3 Maqam Jahargah (Jiharkah), Naghmeh Bayat-e Tork, Naghmeh Dashti

3 5 2 4 2 4 4 Dastgah-e Homayun

4 2 4 4 3 5 2 Naghmeh Esfahan

3 6 1 5 2 6 1 Maqam 'Awg 'ara (Aug-ara)  0,3,9,10, | 3,5,11

4 1 5 4 2 6 2 Maqam Buselik

4 2 6 2 2 5 3 Maqam Neuter

------------------------------------------------------------------

8-note

3 3 3 3 3 3 3 3  8-equal, Wyschnegradsky's octatonic

3 3 4 4 2 1 3 4  Maqam Bayati

3 3 2 6 2 4 2 2  Maqam Saba

4 3 1 2 4 4 2 4  Maqam Suzidil 'ara

3 3 2 2 4 3 3 4  Maqam Mansuri

4 3 3 4 4 2 1 3  Maqam Rast, Dilkashidah, Dilnishin

3 4 2 6 2 4 2 1  Maqam Rahat al-Arwah

3 4 3 3 4 4 2 1  Maqam Iraq

2 6 2 4 2 1 3 4  Maqam Hijaz

3 4 4 2 1 3 4 3  Maqam Musta'ar

3 4 4 4 2 4 2 1  Maqam Farahnak

3 4 3 3 2 6 2 1  Maqam Bastanikar, Tarz Nuin

4 2 6 2 4 2 1 3  Maqam Farah Faza, Maqam Nakriz

3 1 2 4 4 2 4 4  Maqam Jabburi
------------------------------------------------------------------
9-note

 
3 4 2 2 2 2 2 4 3    Maqam Huzam

4 4 2 1 3 2 2 4 2    Maqam Shawq Afza
------------------------------------------------------------------
10-note
  
 
2 3 2 2 3 2 3 2 2 3   Oljare Decatonic -  

2 1 3 2 2 4 2 4 2 2   Maqam Shawq Tarab

4 2 1 3 2 2 4 2 1 3   Maqam Basandida

4 3 1 2 1 3 4 2 1 3   Maqam Yakah
------------------------------------------------------------------
11-note

4 2 1 3 2 2 2 2 3 1 2 Maqam Hayyan
------------------------------------------------------------------



The collection of quarter-tone material I'm trying to learn is enlarged by this:

http://xenharmonic.wikispaces.com/24edo

As always, the xenharmonic folks provide the richest, most useful information.

I've selected most of it, rejected some because it makes no sense to me, or seems unreasonable. When in doubt, I've accepted anything with an Arabic-sounding label, on the grounds that it's at least sanctioned by tradition (which in musical terms means it's not complete junk). Further winnowing may be necessary. If the contributor of those Arabic maqam names is who I think it is, he's a master, and I trust his judgment enough to try whatever he proposes.

In particular, some of the quarter-tone scales with lots of actual quarter-tone intervals (1's, here) seem worthless to me. I'd defend this rejection, if pressed, with a distinction between structural/harmonic pitches and pitches which are only for melodic elaborations. I'm interested in the former. Decorations come after the foundations are secure. Also, someone's naming of some of these scales with reference to modes made no sense to me.

We ought to be using the standard, contemporary naming of modes, even though the names have changed over the centuries. Dorian, in contemporary terms, should always be 1,2,b3,4,5,6,b7 -- ( say, Ab,Bb,Cb,Db,Eb,F,Gb) -- not whatever the term meant to the ancient Greeks. Standardization is more important the history. These terms are only aids to understanding. ...

What I'm looking for here is a relatively euphonious, invertible, modal quarter-tone sound, that can modulate freely via common-tone structures.
Originally Posted by calebprime View Post
Case in point: Under the 8-note list, we have a Maqam Bayati scale given as: 3 3 4 4 2 1 3 4.

This would be, in C: C, D-, Eb, F, | G, Ab, A-, Bb

Clearly the Ab and A- (the pitches separated by a quarter-tone, or 1) are alternate versions of the same note. (Spelling aside. Spelling is verbal convenience here, not that important.)

So it's really a 7-note scale with a variable 6th degree. Not mysterious.

The Ab and A- would never occur together in a chord.

There really isn't a structural 1 in the scale, any more than in the conventional notion of a "melodic minor" scale the two versions of the 6th degree are both simultaneous scale-degrees. They're not. One's for going up, the other's for going down.

I don't hear a lot of actual 50-cent melodic or harmonic intervals in Arabic music or any other kind of music. It's whiny like a mosquito as melody, horrible like a toothache as harmony. Too close to the unison for comfort.

So, as always with the xenharmonic stuff, you have to use your own ears, and read between the lines a little. I don't think of this stuff as a holiday from convention, a world where all bets are off, and anything's possible.

The fundamental things in life apply, as time goes by.


Broad strokes here, to make a distinction.

It's as I thought. I've gone through all the maqams in the list that have 8 notes or more. They are all hybrids with two versions of the same note, so they're not really "scales" the way I think of them.

For musicians who rely on schemas, having the best schemas is crucial.

1) A scale is a whole. It's complete. No pitch can be added without conflicting with what's already there.

2) A scale is equally a source of melody and harmony. Any note can be combined with any other note in the scale to make some kind of chord.

3) Following from 2, every note in a scale can be a starting-point, and can work harmonically, so they have almost equal status in the collection.

The very slight drawback to this approach is that 5-note (pentatonic) scales are considered subsets of more complete scales, not really things in themselves. Or they are considered to be more like chords -- for most pentatonic scales, collections of fourths. They are incomplete (and often fairly static, though that doesn't really matter here.) So, pentatonic scales are practiced under a different heading, kept in a different mental drawer. No biggie.

Same with the so-called "blues scale", which isn't really a scale. You can't freely combine the notes to make chords. It's a collection of melody notes. Neither concordant nor complete. The pitches have more difference of function within the collection than in a scale proper.

My friend Berklee piano-teacher Josh would look at me funny if I said this to him. Because, for him, this is a distinction without an important difference.

The difference between his approach and mine is the difference between using theory simply as a way of talking to other musicians, or using theory as a way of generating new material. Players tend to use the first approach. Composers tend to use the second.

I don't think in terms of tetrachords, because they aren't wholes.

So, with this in mind I've eliminated almost all of the quarter-tone scales on the xenharmonic list with 8 pitches or more.

As an example of why, consider the following case. I'm going to invent a "Super Melodic" scale, which consists of Lydian ascending, and Phrygian descending.

C,D,E,F#,G,A,B ascending

C,Bb,Ab,G,F,Eb,Db descending

and, adding up all the pitches, I'm going to try to claim that this is a 12-tone scale:

C,Db,D,Eb,E,F,F#,G,Ab,A,Bb,B

No.



The remaining work to be done to complete the practice-list is in modifying what are called whole-tone, hexatonic, and octotonic scales (these have specific meanings not implied in the names) by quarter-tones, and testing them by ear to see if they have a pleasing suchness.

A little more winnowing, but I'm mostly done with that.

The twice-winnowed xenharmonic list, with a stub for the next task:

Code:
Scales / Modes

5-note

2 8 3 6 5  Anchihoye: Ethiopia   A,Bb,D,E-,G-  0,2,10, | 1,7
Has 650-cent "5th"

5 5 4 5 5  Quasi-equal Pentatonic              0,5,10, | 2,7   

5 5 5 5 4  Hába's Pentatonic -                 0,5,10, | 3,8 

------------------------------------------------------------------
7-note

3 3 4 3 3 4 4 Ouchairan-Hussaini, Bayatan,  0,3,6,10, |1,4,8   Has 650-cent "5th"

3 4 3 3 4 4 3 Dastgah-e Sehgah,  0,3,7,10,|1,5,9   Has 650-cent "5th"

4 3 3 4 4 3 3 Rast,              0,4,7,10,|2,6,9   same as above

3 3 4 4 3 3 4 Hussaini, Ushaq,   0,3,6,10,|2,5,8   same as above

3 4 4 3 3 4 3 Sikah (Segah),     0,3,7,11,|2,5,9,  same as above

4 4 3 3 4 3 3

4 3 3 4 3 3 4 Miha'il Musaqa: Egypt  0,4,7,10,|2,5,8  called Bayati

3 4 3 3 4 3 4
 
4 3 3 4 3 4 3
 
3 3 4 3 4 3 4
 
3 4 3 4 3 4 3 Sikah Baladi 

4 3 4 3 4 3 3
 
3 4 3 4 3 3 4
 
4 3 4 3 3 4 3
 
3 5 2 4 3 5 2 Dastgah-e Chahargah

4 2 4 4 3 3 4 Dastgah-e Nava, Maqam Ushaq Masri

3 3 4 4 2 4 4 Maqam 'Ushshaq Turki, Urfa, Isfahan, Dastgah-e Shur

3 3 4 4 4 2 4 Maqam Nahfat

3 3 2 6 2 4 4 Maqam Saba

3 3 2 6 2 6 2 Maqam Sabr Jadid

4 3 3 4 2 6 2 Maqam Suznak (Soznak)

4 3 3 4 4 4 2 Maqam Mahur

3 3 4 2 6 2 4 Maqam Qarjighar, Bayati Shuri               0,3,6,10,|0,6,8

3 4 2 6 2 4 3 Maqam Hizam (Huzam, El Houzam), Rahat al Arouah

2 4 4 4 3 3 4 Maqam Nawa

2 5 3 4 2 5 3 Maqam Higaz-kar

3 4 4 2 4 4 3 Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari

4 4 2 4 4 3 3 Maqam Jahargah (Jiharkah), Naghmeh Bayat-e Tork, Naghmeh Dashti

3 5 2 4 2 4 4 Dastgah-e Homayun

4 2 4 4 3 5 2 Naghmeh Esfahan

3 6 1 5 2 6 1 Maqam 'Awg 'ara (Aug-ara)  0,3,9,10, ||3,5,11

4 1 5 4 2 6 2 Maqam Buselik

4 2 6 2 2 5 3 Maqam Neuter

------------------------------------------------------------------
7-note with 1 alternate scale-degree:

2 6 2 4 2 1 3 4  Maqam Hijaz         0,2,8,10, | 2,[4,5,]8
This is only a quarter-tone scale if
it's  0,2,8,10, | 2,5,8

3 3 2 2 4 3 3 4  Maqam Mansuri       0,3,6,[8,10,]|2,5,8   
A, B-, C,[D, Eb,]| E, F#-, G

3 3 2 6 2 4 2 2  Maqam Saba          0,3,6,8,|2,4,[8,10]
A, B-, C, D, |E, F, [G, G#]

3 3 4 4 2 1 3 4  Maqam Bayati        0,3,6,10, | 2,[4,5,]8

3 4 4 2 1 3 4 3  Maqam Musta'ar      0,3,7,11,| [1,2,] 5,9

4 3 1 2 4 4 2 4  Maqam Suzidil 'ara  0,4,[7,8,],10,|2,6,8

4 3 3 4 4 2 1 3  Maqam Rast,         0,4,7,10,|2,6,[8,9]
Dilkashidah, Dilnishin



------------------------------------------------------------------

NOT YET FILLED IN:


6-note: 

Quarter-tone alterations of "whole-tone" and 
"hexatonic" (1,3 or 3,1 semitone) scales.

starting with:
A,B,C#,D#,F,G

starting with:
A,Bb,C#,D,F,F#

starting with:
A,C,C#,E,F,G#
------------------------------------------------------------------
8-note:

3 3 3 3 3 3 3 3  8-equal   

8-note:  Quarter-tone alterations of "diminished" or "octotonic"
Scales, that is, starting with A,Bb,C,Db,Eb,E,F#,G and progressively
lowering (or raising?) pitches by a quarter-tone.

starting with:
A,Bb,C,Db,Eb,E,F#,G

starting with:
A,B,C,D,Eb,F,F#,G#
------------------------------------------------------------------


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Old 16th February 2016, 06:29 AM   #199
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...

I must be losing my mind.

Such a lovely brain, it was, too:

http://enzoloechel.com/wp-content/up...rainguyweb.jpg
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Old 17th February 2016, 04:09 AM   #200
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[quote=calebprime;11128431]...

The remaining work to be done to complete the practice-list is in modifying what are called whole-tone, hexatonic, and octotonic scales (these have specific meanings not implied in the names) by quarter-tones, and testing them by ear to see if they have a pleasing suchness.

A little more winnowing, but I'm mostly done with that.

...
6-note:

Quarter-tone alterations of "whole-tone" and
"hexatonic" (1,3 or 3,1 semitone) scales.

starting with:
A,B,C#,D#,F,G


starting with:
A,Bb,C#,D,F,F#

starting with:
A,C,C#,E,F,G#
------------------------------------------------------------------
8-note:

3 3 3 3 3 3 3 3 8-equal

8-note: Quarter-tone alterations of "diminished" or "octotonic"
Scales, that is, starting with A,Bb,C,Db,Eb,E,F#,G and progressively
lowering (or raising?) pitches by a quarter-tone.

starting with:
A,Bb,C,Db,Eb,E,F#,G

starting with:
A,B,C,D,Eb,F,F#,G#
------------------------------------------------------------------



This little task turns out, through the math of permutation, not to be so little.

With my somewhat restricted tastes, I'm allowing for the following alterations:

Code:
A   B-   C#-   D#-  F    G-
    B    C#    D#   F+   G 
    B+   C#+             G+
That is, A doesn't change. (It's the starting-point: no need.)

B, C#, and G can be in three states.
D# and F can be in two.

Each slot goes from low to high, resetting when the next slot on the left moves.

Having done this by hand this morning, I'm pretty sure I've made a mistake, but I don't see it.

This is perhaps too much, and it would be only one of five such lists.

Ah, my misspent youth. I wish I had learned to code. Computers don't haz a sad when they do boring things like this.

Code:
A,  B-,  C#-,  D#-, F,   G-
A,  B-,  C#-,  D#-, F,   G
A,  B-,  C#-,  D#-, F,   G+
A,  B-,  C#-,  D#-, F+,  G-
A,  B-,  C#-,  D#-, F+,  G
A,  B-,  C#-,  D#-, F+,  G+
A,  B-,  C#-,  D#,  F,   G-
A,  B-,  C#-,  D#,  F,   G
A,  B-,  C#-,  D#,  F,   G+

A,  B-,  C#,   D#,  F,   G-
A,  B-,  C#,   D#,  F,   G
A,  B-,  C#,   D#,  F,   G+

A,  B-,  C#+,  D#-, F,   G-
A,  B-,  C#+,  D#-, F,   G
A,  B-,  C#+,  D#-, F,   G+

A,  B-,  C#+,  D#-, F+,  G-
A,  B-,  C#+,  D#-, F+,  G
A,  B-,  C#+,  D#-, F+,  G+

A,  B-,  C#+,  D#,  F,   G-
A,  B-,  C#+,  D#,  F,   G
A,  B-,  C#+,  D#,  F,   G+

A,  B,   C#-,  D#-, F,   G-
A,  B,   C#-,  D#-, F,   G
A,  B,   C#-,  D#-, F,   G+

A,  B,   C#-,  D#-, F+,  G-
A,  B,   C#-,  D#-, F+,  G
A,  B,   C#-,  D#-, F+,  G+

A,  B,   C#-,  D#,  F,   G-
A,  B,   C#-,  D#,  F,   G
A,  B,   C#-,  D#,  F,   G+

A,  B,   C#-,  D#,  F+,  G-
A,  B,   C#-,  D#,  F+,  G
A,  B,   C#-,  D#,  F+,  G+

A,  B,   C#,   D#-, F,   G-
A,  B,   C#,   D#-, F,   G
A,  B,   C#,   D#-, F,   G+

A,  B,   C#,   D#-, F+,  G-
A,  B,   C#,   D#-, F+,  G
A,  B,   C#,   D#-, F+,  G+

A,  B,   C#,   D#,  F,   G-
A,  B,   C#,   D#,  F,   G+

A,  B,   C#,   D#,  F+,  G-
A,  B,   C#,   D#,  F+,  G
A,  B,   C#,   D#,  F+,  G+

A,  B,   C#+,  D#-, F,   G-
A,  B,   C#+,  D#-, F,   G
A,  B,   C#+,  D#-, F,   G+

A,  B,   C#+,  D#-, F+,  G-
A,  B,   C#+,  D#-, F+,  G
A,  B,   C#+,  D#-, F+,  G+

A,  B+,  C#-,  D#-, F,   G-
A,  B+,  C#-,  D#-, F,   G
A,  B+,  C#-,  D#-, F,   G+

A,  B+,  C#-,  D#-, F+,  G-
A,  B+,  C#-,  D#-, F+,  G
A,  B+,  C#-,  D#-, F+,  G+

A,  B+,  C#-,  D#,  F,   G-
A,  B+,  C#-,  D#,  F,   G
A,  B+,  C#-,  D#,  F,   G+

A,  B+,  C#,   D#-, F,   G-
A,  B+,  C#,   D#-, F,   G
A,  B+,  C#,   D#-, F,   G+

A,  B+,  C#,   D#-, F+,  G-
A,  B+,  C#,   D#-, F+,  G
A,  B+,  C#,   D#-, F+,  G+

A,  B+,  C#+,  D#-, F,   G-
A,  B+,  C#+,  D#-, F,   G
A,  B+,  C#+,  D#-, F,   G+

A,  B+,  C#+,  D#-, F+,  G-
A,  B+,  C#+,  D#-, F+,  G
A,  B+,  C#+,  D#-, F+,  G+

A,  B+,  C#+,  D#,  F,   G-
A,  B+,  C#+,  D#,  F,   G
A,  B+,  C#+,  D#,  F,   G+

A,  B+,  C#+,  D#,  F+,  G-
A,  B+,  C#+,  D#,  F+,  G
A,  B+,  C#+,  D#,  F+,  G+

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Last edited by calebprime; 17th February 2016 at 04:12 AM.
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