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Old 9th October 2013, 06:44 AM   #121
aggle-rithm
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Originally Posted by calebprime View Post
https://app.box.com/s/2i418x7kpiew4d3467io

New piece, approximately 9 minutes.

called Pianos and Regrets.
Reminiscent of Pink Floyd.

ETA: Just the beginning, actually. The piece evolves as you listen to it.
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Old 9th October 2013, 07:40 AM   #122
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Originally Posted by calebprime View Post

It's surprising how consonant a chord like C#0-D#2-F4-D5 sounds, even after many years of thinking about such chords.
I think dissonance works best with widely-space intervals, especially if the timbre is kind of fuzzy.

Cluster chords are fine with some instruments, like piano or trumpet, but in choral music...blech. Sounds like wrong notes.
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Old 24th January 2014, 05:34 AM   #123
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Scale design explanation, post 1

I want to try to describe a process of designing the scale/tuning I'm currently practicing, using screen-shots from Lil' Miss Scale Oven.

eta: If anyone wants audible examples, ask for something specific. I'll post a link.

Every composer or performer seems to have different tastes and different premises. Here are mine:

--Scale repeats at the octave (2:1 frequency ratio)

--Standard off-the-shelf gear is assumed, so standard keyboards of -- sadly -- no more than 88 keys are being used. With two keyboards, and assuming at least a desired two octaves of range, this means one can have up to 43 pitches per octave, resulting in a total of 4 octaves of range.

--Within the home key (1/1), the scale should be able to do everything that a 12-tone scale can do, and a lot more.

--The home key can be changed by pitch-bending the whole thing ("modulation"). This means that some pitches can be omitted in the home key, but reached through pitch-bend. (Instruments are set to pitch-bend range +-12 semitones.)

--The scale should have ratios with primes up to 13 ("13-Limit JI") but it's not necessary to have every product of every generating number. This is a tonal scale, with important pillars at 1/1, 3/2, 4/3, 9/8, 5/4. These important tones can/should have a wider space ("interval") around them. So we can eliminate near-duplicate pitches by choosing the more important pitches, or "tempering out" near duplicates -- splitting the difference, so to speak.


Here we go.


We can use the "waffle iron" feature to make a JI tonality diamond with overtones 8,9,10,11,12,13,14,15 on fundamentals ("undertones") /8,/9,/10,/11,/12,/13,/14,/15.


(Click on this to see a larger size, or use a magnifying glass.)

(more to follow)
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Old 24th January 2014, 06:21 AM   #124
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LMSO will calculate the scale, displaying it in different formats. Already, we have 49 tones, which is too many. But there are several tones which are almost the same, so we can eliminate some. Already, there are some things that the JI scale doesn't do as well as a 12-tone scale, even without considering the big advantage of an equal-tempered scale: That it can work equally well from all starting-points, all "keys".

Here's what we have so far.

Ratio from 1/1: 1/1, 16/15, 15/14, 14/13, 13/12, 12/11, 11/10, 10/9, 9/8, 8/7, 15/13, 7/6, 13/11, 6/5, 11/9, 16/13, 5/4, 14/11, 9/7, 13/10, 4/3, 15/11, 11/8, 18/13, 7/5, 10/7, 13/9, 16/11, 22/15, 3/2, 20/13, 14/9, 11/7, 8/5, 13/8, 18/11, 5/3, 22/13, 12/7, 26/15, 7/4, 16/9, 9/5, 20/11, 11/6, 24/13, 13/7, 28/15, 15/8


Cents from 1/1: 0., 111.731, 119.443, 128.298, 138.573, 150.637, 165.004, 182.404, 203.91, 231.174, 247.741, 266.871, 289.21, 315.641, 347.408, 359.472, 386.314, 417.508, 435.084, 454.214, 498.045, 536.951, 551.318, 563.382, 582.512, 617.488, 636.618, 648.682, 663.049, 701.955, 745.786, 764.916, 782.492, 813.686, 840.528, 852.592, 884.359, 910.789, 933.129, 952.259, 968.826, 996.09, 1017.596, 1034.996, 1049.363, 1061.427, 1071.702, 1080.557, 1088.269


Cents difference: 111.731, 7.712, 8.855, 10.275, 12.064, 14.367, 17.4, 21.506, 27.264, 16.567, 19.13, 22.339, 26.431, 31.767, 12.064, 26.842, 31.194, 17.576, 19.13, 43.831, 38.906, 14.367, 12.064, 19.13, 34.976, 19.13, 12.064, 14.367, 38.906, 43.831, 19.13, 17.576, 31.194, 26.842, 12.064, 31.767, 26.43, 22.34, 19.13, 16.567, 27.264, 21.506, 17.4, 14.367, 12.064, 10.275, 8.855, 7.712, 111.731


Anywhere we see a "cents difference" number of less than, say, 15 cents, it might be an opportunity to eliminate a pitch or to average the two numbers.

From experience, the biggest flaw of this scale so far is that there is no good 4/3 (standard term: "4th") over 16/15, and no good 3/2 (standard term: "5th") over 15/8. That would be 45/32.

Also, there's no 3/2 over 9/8: That would be 27/16. (standard term: "Pythagorean major 6th".)

We might try to add these pitch-relations into our waffle iron generator, and see what happens:



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Old 24th January 2014, 06:31 AM   #125
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Now we have 68 tones, and even more tiny intervals between pitches that are nearly the same, so we have to try to pare down even more:

1/1, 81/80, 45/44, 27/26, 16/15, 15/14, 14/13, 13/12, 12/11, 11/10, 10/9, 9/8, 8/7, 15/13, 7/6, 13/11, 32/27, 6/5, 11/9, 27/22, 16/13, 5/4, 81/64, 14/11, 9/7, 13/10, 4/3, 27/20, 15/11, 11/8, 18/13, 7/5, 45/32, 64/45, 10/7, 13/9, 81/56, 16/11, 22/15, 3/2, 32/21, 20/13, 14/9, 81/52, 11/7, 8/5, 45/28, 13/8, 18/11, 64/39, 5/3, 27/16, 22/13, 12/7, 45/26, 26/15, 7/4, 16/9, 9/5, 20/11, 11/6, 81/44, 24/13, 13/7, 28/15, 15/8, 27/14, 64/33

Cents differences:

21.506, 17.4, 26.431, 46.394, 7.712, 8.855, 10.275, 12.064, 14.367, 17.4, 21.506, 27.264, 16.567, 19.13, 22.339, 4.925, 21.506, 31.767, 7.139, 4.925, 26.842, 21.506, 9.688, 17.576, 19.13, 43.831, 21.506, 17.4, 14.367, 12.064, 19.13, 7.712, 19.552, 7.712, 19.13, 2.376, 9.688, 14.367, 38.906, 27.264, 16.567, 19.13, 2.376, 15.2, 31.194, 7.712, 19.13, 12.064, 4.925, 26.842, 21.506, 4.925, 22.339, 16.567, 2.563, 16.567, 27.264, 21.506, 17.4, 14.367, 7.139, 4.925, 10.275, 8.855, 7.712, 48.77, 9.688, 53.273


The smallest difference is the 2.4 cent difference between 636.6 cents and 639 cents, or the difference between 13/9 and 81/56. We can eliminate one of these pitches, or split the difference.

The ultimate goal is to find an equal-tempered division of the octave ("EDO") that nearly matches our target collection of JI ratios. If we find the right one, it will do a good job of splitting the difference, or "tempering out" these tiny unwanted intervals.
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Old 24th January 2014, 06:40 AM   #126
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Now there's a longish process of paring down so that we preserve the tones we really need all at once, and eliminate the ones we don't need.

One consideration -- opposed to the basic JI generating process -- is that whenever possible, we want any relationship that is a bad approximation of a 3/2 ratio to be corrected to give us a viable approximation of a 3/2. The longer the chains of 3/2's ("Pythagorean chains"), the more flexible our scale/tuning will be.

Here's what I came up with, after a lot of teeth gnashing. LMSO has forgotten most the original ratios, but preserved the absolute cent values and differences:

256/243, 16/15, 13/12, 150.63533, 165.0025, 182.40198, 203.90827, 231.17236, 266.86917, 294.13327, 315.63956, 347.40621, 359.46888, 386.31196, 407.81825, 435.08234, 454.21219, 498.04324, 551.31618, 563.38058, 590.22196, 609.77277, 636.61585, 648.68025, 701.95319, 745.78424, 14/9, 11/7, 8/5, 13/8, 18/11, 5/3, 27/16, 12/7, 7/4, 16/9, 9/5, 20/11, 11/6, 24/13, 15/8, 243/128, 2/1*

differences:

90.225, 21.506, 26.842, 12.062, 14.368, 17.399, 21.506, 27.264, 35.697, 27.264, 21.507, 31.766, 12.063, 26.843, 21.506, 27.264, 19.13, 43.831, 53.273, 12.065, 26.841, 19.551, 26.843, 12.064, 53.273, 43.831, 19.132, 17.576, 31.194, 26.842, 12.064, 31.767, 21.506, 27.264, 35.697, 27.264, 21.506, 17.4, 14.367, 12.064, 26.842, 21.506, 90.225

The smallest interval is a little over 12 cents.

There are a number of bad 3/2's ("5ths") that we hope to improve when we choose an EDO (equal division of the octave).



---------------------
*My keyboard has labels which I added to memorize this. These cent values closely correspond to:

1/1, 256/243, 16/15, 14/13, 12/11, 11/10, 10/9, 9/8, 8/7, 7/6, 32/27, 6/5, 11/9, 16/13, 5/4, 14/11, 9/7, 13/10, 4/3, 18/13, 7/5, 10/7, 13/9, 16/11, 3/2, 20/13, 14/9, 11/7, 8/5, 13/8, 18/11, 5/3, 22/13, 12/7, 7/4, 16/9, 9/5, 20/11, 11/6, 24/13, 15/8, 243/128, 2/1
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Last edited by calebprime; 24th January 2014 at 08:07 AM. Reason: 256/243 was omitted
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Old 24th January 2014, 06:55 AM   #127
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tempering out:

Some tones will have to do double duty. So, for example, 22/13 (910.8 cents) and 27/16 (905.9 cents) will have to be represented by the same pitch.

More principles:

--A little detuning actually sounds better (to me) than absolutely accurate JI, for most purposes.

--Pitch-relations have a zone of acceptability. Outside the zone, they sound bad or like a different relation. The size of the zone varies -- according to taste, purpose, the relative delicacy of the relationship.

Now I can use the Quantize feature of LMSO to find an EDO that will approximate my target set of 43 pitches. I can literally dial up through them using the mouse.

This is the button selected here called "X srutis with less than _N_ cents mean deviation":

LMSO cleverly lets you enter different expressions in the boxes, so I like to enter the "cents mean deviation" as a number over 99, to find all the possibilities.

Dialing up, LMSO gives us the following sequence:

53, 72, 77, 87, 94, 118, 130, (171), 183, 217, 224, 270, 388, 400 (EDO).
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Old 24th January 2014, 07:12 AM   #128
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Originally Posted by calebprime View Post
tempering out:

...
This is the button selected here called "X srutis with less than _N_ cents mean deviation":http://www.internationalskeptics.com...27118e6995.png

...
Dialing up, LMSO gives us the following sequence:

53, 72, 77, 87, 94, 118, 130, (171), 183, 217, 224, 270, 388, 400 (EDO).
These numbers have a history.

53 is the highest EDO considered by Harry Partch in _Genesis of a Music_.

72 is the EDO favored by the Boston Microtonal Society folks: Maneri, Sims, et al.

77 is the lowest EDO that almost works for my purposes.

The sweet spot is 77, 87, 94, 118, 130, 171.

87 has 3/2 approximations that are a little too wide to make a long chain.

77, iirc, fudges the distinction between 20/11 and 11/6.

77, 87, 94, 118, 130, 171.

171 is damn good, but has more pitches than we want.

---------------------------------------------
The bottom line

43 tones of JI, with a 13-limit, tempered to 94, 118, or 130 EDO.

===========
Another bottom line:

With a non-standard (or "generalized") MIDI keyboard, we don't need to be restricted to 43 pitches, so we can do a lot more.

Problem is, if a generalized keyboard -- made by a small company -- breaks, or the company goes out of business, you end up with an expensive paper weight. This sort of thing has happened to me before, which is why I stick to off-the-shelf standard gear.

The xenharmonic folks have developed the knowledge base to an amazing degree. I only understand about one-tenth of what they talk about, but that's enough.

94EDO:https://xenharmonic.wikispaces.com/94edo

118EDO:https://xenharmonic.wikispaces.com/118edo

130EDO:https://xenharmonic.wikispaces.com/130edo
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Old 24th January 2014, 07:39 AM   #129
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One final refinement as part of the process.

The site is down, but I've used an applet called a modular multiplier

http://pages.central.edu/emp/LintonT...Multiples.html

to check my chains of 3/2 approximations.

The idea is that, in a given EDO, an approximate 3/2 will be n many srutis, so this applet makes it easier to check the chains.



[/url]

Here, in 130EDO, I'm checking to see if my chain goes: 76,22,98,44,120,66,12,88,34,110. (It does.)

If there's a near miss, perhaps the pitch should be adjusted.

And, the same process on the 4/3 side, or inversion of 3/2.

At some point, (at 9/5 and 5/3) the chain will end. That's JI without tempering out the 81/80 comma.

Over time, I've been favoring longer 3/2 chains over more accurate higher-limit JI. With 43 tones, there are acceptable compromises.

Here's a Scala format list of my scale, tempered to 94EDO. If you have a program that reads Scala format, you can just plug it in.


!
43T94edo
43
!
89.36170
114.89362
140.42553
153.19149
165.95745
178.72340
204.25532
229.78723
268.08511
293.61702
319.14894
344.68085
357.44681
382.97872
408.51064
434.04255
459.57447
497.87234
548.93617
561.70213
587.23404
612.76596
638.29787
651.06383
702.12766
740.42553
765.95745
778.72340
817.02128
842.55319
855.31915
880.85106
906.38298
931.91489
970.21277
995.74468
1021.27660
1034.04255
1046.80851
1059.57447
1085.10638
1110.63830
1200.00000

and here's a slightly adjusted (tweaked) version of the same scale, tempered to 130EDO:



!
43T130edo tweak
43
!
92.30769
110.76923
138.46154
147.69231
166.15385
184.61538
203.07692
230.76923
267.69231
295.38462
313.84615
350.76923
360.00000
387.69231
406.15385
433.84615
452.30769
498.46154
553.84615
563.07692
590.76923
609.23077
636.92308
646.15385
701.53846
747.69231
766.15385
793.84615
812.30769
840.00000
849.23077
886.15385
904.61538
932.30769
969.23077
996.92308
1015.38462
1033.84615
1052.30769
1061.53846
1089.23077
1107.69231
1200.00000


Under most circumstances, I don't hear the differences between 72 through 171EDO. It's only on certain intervals, with certain instruments, at an adequate volume level.
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Old 24th January 2014, 08:46 AM   #130
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Originally Posted by calebprime View Post
...
The sweet spot is 77, 87, 94, 118, 130, 171.

...
---------------------------------------------
The bottom line

43 tones of JI, with a 13-limit, tempered to 94, 118, or 130 EDO.

...
94EDO:https://xenharmonic.wikispaces.com/94edo

118EDO:https://xenharmonic.wikispaces.com/118edo

130EDO:https://xenharmonic.wikispaces.com/130edo


Another possibility to try is 106EDO (2x53).

We should treat the numbers generated by LMSO with a grain of salt, and consider some other obvious possibilities. But there won't be that many more possibilities -- given my starting assumptions.

http://xenharmonic.wikispaces.com/106edo

At a glance, I notice that 106 doesn't do all that well with 8/7, 7/6, 7/4: the 7-limit intervals I want. But my ear may disagree.


!
43T106edo
43
!
90.56604
113.20755
135.84906
147.16981
169.81132
181.13208
203.77358
226.41509
271.69811
294.33962
316.98113
350.94340
362.26415
384.90566
407.54717
430.18868
452.83019
498.11321
554.71698
566.03774
588.67925
611.32075
633.96226
645.28302
701.88679
747.16981
769.81132
781.13208
815.09434
837.73585
849.05660
883.01887
905.66038
928.30189
973.58491
996.22642
1018.86792
1030.18868
1052.83019
1064.15094
1086.79245
1109.43396
1200.00000


And, if I'm willing to go to 106 or 130, I might consider going to 3x53=159EDO, which is Ozan Yarman territory. Mr. Yarman has already forgotten more about tuning today than I'll every know my entire life:

http://xenharmonic.wikispaces.com/159edo
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Old 25th January 2014, 06:39 AM   #131
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Originally Posted by calebprime View Post
...

77 is the lowest EDO that almost works for my purposes.

...
77, iirc, fudges the distinction between 20/11 and 11/6.

...
Checking that it's true that 77 "fudges" the difference between 20/11 and 11/6.

20/11 = 1035 cents
11/6 = 1049.36 cents

difference is 14.36 cents, is ratio of 1.0083291572750366 to 1, or 121:120.

This comma (121:120) doesn't have a name, that I know of.

http://www.mindspring.com/~alanh/fracs.html

77EDO has pitches at: 1028.6 cents, and 1044.15 cents, and 1059.74 cents.

20/11 will be quantized down by 6.4 cents, and 11/6 will be q'd down by 5.2 cents.

16/11 @ 648.68 cents will be quantized up 5.86 cents to 654.54 cents

The total error of 20/11 over 16/11 (which ideally should be 5:4) is in 77edo now around -12.26 cents (too narrow.) That's too far.

We also see in the microtonal wiki, that "77et tempers out 32805/32768 in the 5-limit, 126/125, 1029/1024 and 6144/6125 in the 7-limit, 121/120, ..."

So I think that's confirmation of what bothers me about 77edo for my purposes.

Now, mostly you wouldn't hear that. But if we're trying to design an elegant system that works as well as it can given our limitations, that's a flaw.

The reason I found this is that I was practicing my scale tempered to 77edo and the interval between what was supposed to be 20/11 to 16/11 sounded wrong. So it was a matter of something hearable. I just didn't know exactly why until now.
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Old 27th January 2014, 05:24 PM   #132
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Up until now, the scales I've composed in have been either overtone series scales or the more-or-less familiar gamut of 5-limit scales -- the familiar modes, Lydian b7 (a mode of melodic minor), and the modes of harmonic minor, the 6-note scales, and the diminished or octotonic 8-note scales.

This has begun to feel too limited. Why do microtones if you're going to limit yourself to familiar-sounding scales? And, the overtone series -- to my ear -- stubbornly resists being inverted, or made into modes. That is, higher prime harmonics (7, 11, 13) in these scales tend to sound out of tune if you use them in too low a register. So overtone series scales seem to resist being used modally. They seem a little inflexible. They're perfect and they just want to sit there, being perfect.

I intend, therefore, to start trying to compose with hybrid scales that are neither overtone series nor traditional scales, but -- more or less -- have "half flat" intervals, as in Arabic or Turkish maqam.

However, to avoid imitating the sound of that music, I hope to avoid the other features of Arabic music. I don't want to sound like I'm going for exoticism, trying to evoke the Middle East or something.

By using non-Arabic instrumentation and composition, maybe I can use similar scales without sounding like I'm trying to charm snakes, or something. But it would be silly not at least to learn a little about what these scales are, because they are in a sense tried and true.

Bayati, Rast, Sabba, Siga. Some names and some tradition to start with.

The tuning is really more subtle than quarter-tones, but this article gives the gist: http://en.wikipedia.org/wiki/Quarter_tone

I intend this post to remind me of approximately when I started thinking seriously about this stuff.
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Old 28th January 2014, 03:06 PM   #133
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A little piece just over 4 minutes.

Called to first stagger chorale

The thing I like about this are the shifts to different blocks in different registers. Kind of a punky late-Stravinsky-does-science-doc effect. And the emotional reserve of it.

77edo, but conventional scales. Self-similar thing again.

https://app.box.com/s/hndecii3fygwtc54npqe
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Old 1st February 2014, 06:37 AM   #134
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Another list of links to pieces.

Three early-middle period pieces, when I was trying harder:


Clay's Way, for Violin and Tape
https://app.box.com/s/q9dknyphurezkxy7z5bj

Pay No Attention to That Man (tape-only version)
https://app.box.com/s/i1sl2xch8xhfl7zfx3eb

Widening Gyre (tape-only version)
https://app.box.com/s/qhy4trmm4utar3ibu1nk

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

A recent piece that some people have liked:

Opening the Window
https://www.box.com/s/48wc435slumb9ano9cc9 (aif version)

https://www.box.com/s/oo4tlpee811uj5j7a7g9 (mp3 version)

About 12 1/2 minutes. Has a little of everything I know.

----------------------------------------------------------------
Other fairly recent pieces that also combine self-similarity, microtonal, and serial techniques:

Chords with Figuration
https://app.box.com/s/daf63fb69db30e7d2cb0

Starting and Stopping
https://app.box.com/s/9pst9o65y6nx67w6lj3u

Fugazzi
https://app.box.com/s/au4esop559vae2353i4n

Elusive Mr. Moy
https://app.box.com/s/0ac8fd057b0c8e44c66a

BEADS (lighten up, Dave)
https://app.box.com/s/10s67yjq1sam01o49gc4

(see here, beginning of this thread, for more info)
http://www.internationalskeptics.com...d.php?t=235850

--------------------------------------------------------
Some dreamy -- or perhaps logy -- piano pieces that apply the self-similar 12-tone idea:

(from: You're Not There )

#1 --
https://app.box.com/s/j9l6i4crj879so3osy6n

#2 --
https://app.box.com/s/chtzh22eubqd4qug3sx3

#3 --
https://app.box.com/s/4ydcshb2ltwv9san0j3d

#4 --
https://app.box.com/s/at7297ejlobphgpexsm6

#8 --
https://app.box.com/s/gi33uqpfmx1476hul47s

---------------------------------------------------------
Long "found sound" collages -- made partly from recordings I made outdoors:


Brighton 10
https://app.box.com/s/ktcxgt617iv94dbmv6yy


Only The Searing Incomprehensible
https://app.box.com/s/pbw2co34gcdagvt0easj

Commons March (Local protest against US military action, etc.)
https://app.box.com/s/h8t3wfr4qimx2r7jc7pm

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

Some middle-period pieces that combine composition, sampling, collage:

(from: Five Sample-Based Pieces)
entire folder: https://app.box.com/shared/vdrhregp02

The Aswang (Voice of Lynda Barry)
https://app.box.com/s/2dtjt9ue9jmzfhqwnykn

Wife and Garden (based on BBC interview with Peter Maxwell Davies, etc.)
https://app.box.com/s/11ibkzjq0c6uh5xpbfvi
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Last edited by calebprime; 1st February 2014 at 06:51 AM.
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Old 25th February 2014, 07:15 AM   #135
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Originally Posted by calebprime View Post
Up until now, the scales I've composed in have been either overtone series scales or the more-or-less familiar gamut of 5-limit scales -- the familiar modes, Lydian b7 (a mode of melodic minor), and the modes of harmonic minor, the 6-note scales, and the diminished or octotonic 8-note scales.

This has begun to feel too limited. Why do microtones if you're going to limit yourself to familiar-sounding scales? And, the overtone series -- to my ear -- stubbornly resists being inverted, or made into modes. That is, higher prime harmonics (7, 11, 13) in these scales tend to sound out of tune if you use them in too low a register. So overtone series scales seem to resist being used modally. They seem a little inflexible. They're perfect and they just want to sit there, being perfect.

I intend, therefore, to start trying to compose with hybrid scales that are neither overtone series nor traditional scales, but -- more or less -- have "half flat" intervals, as in Arabic or Turkish maqam.

However, to avoid imitating the sound of that music, I hope to avoid the other features of Arabic music. I don't want to sound like I'm going for exoticism, trying to evoke the Middle East or something.

By using non-Arabic instrumentation and composition, maybe I can use similar scales without sounding like I'm trying to charm snakes, or something. But it would be silly not at least to learn a little about what these scales are, because they are in a sense tried and true.

Bayati, Rast, Sabba, Siga. Some names and some tradition to start with.

The tuning is really more subtle than quarter-tones, but this article gives the gist: http://en.wikipedia.org/wiki/Quarter_tone

I intend this post to remind me of approximately when I started thinking seriously about this stuff.
I've been practicing scales from many starting-points (in many "keys"). This is a first step to learning more exotic scales. Learning the location of the pitches in a 43-note layout is challenging, especially at my age.

It took me something like 5 years of daily practice to learn an easier tuning (or layout) of 36 pitches per octave. Eventually I got fluent to the point that it was as easy to think with 36 pitches as it is with 12. It's a little like learning a second language, but also different.

Someone might find this list of the standard scales useful. To practice in a variety of keys, I randomize: I roll a 12-sided die.

The "keys" or starting-points I have least facility with currently are: 16/15, 10/7, 15/8. Plus the more exotic 8/7, 16/13, and 16/11. So I try to dwell on those.

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

Standard Scale List: (If anyone is curious or wants an explanation, I'd be happy to discuss this a little more.) The names of the altered modes are somewhat consistent, but not entirely.

Lydian
Ionian
Mixolydian
Dorian
Aeolian
Phrygian
Locrian

Lydian #5
Lydian b7
Ionian b3
Mixo b6
Dor. b2
Aeol b5
Locr. b4

Lydian #2 #5
Lydian b3
Ion. b6 or Har. major
Mixo. b2
Dor. b5
Phryg. b4
Locr. bb7

Lyd. #2
Dor. #4
Aeol. mj7 (N7) Har minor
Phryg. b4
Locr. mj6 (N6)
Ion. #5
Locr. b4 bb7

whole-tone

hex -- minor third
hex -- half-step

Oct. -- dim
Oct. -- dom.


There are also the basic overtone scales to practice in this layout. For example:

8/5, 9/5, 2/1, 11/10, 6/5, 13/10, 7/5, 3/2, (or 8:9:10:11:12:13:14:15:16 repeat at octave)

After working on this basic stuff, the fun begins.

Here are some scales with "half flats" that sound pretty good:

4/3, 13/9, 11/7, 16/9, 1/1, 14/13, 32/27

and a variation on Lydian:

1/1, 9/8, 11/9, 7/5, 3/2, 27/16, 11/6, 2/1

The ratios are approximate.

These scales are easy to come up with, and immediately sound good to me. The resistance I encounter to learning them comes from their newness: I can't yet fit them into the same kind of systematic framework that I can -- and many others have done -- with the "standard" scales.
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Last edited by calebprime; 25th February 2014 at 07:23 AM.
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Old 11th March 2014, 06:23 AM   #136
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Based on recent work, thanks to W. D. Clinger, I was able to put together a more comprehensive list of scales to practice.

(generating rules here: http://www.internationalskeptics.com...86#post9883286)

Of course, they can be varied according to exact tuning.

In the 43-pitch JI scale I'm currently practicing (often tempered to 118EDO, but it doesn't really matter), some of the required quarter-tones aren't available starting from 1/1. This is one reason to practice in many keys. (I can't practice in all 43 keys.)

A reasonable approximation of all these scales -- without the slight problem outlined above -- can be performed in 24edo (Quarter-tone tuning.) This tuning is -- for not very good reasons -- one of the less popular "xenharmonic" tunings. Possibly because it is obvious, well-known, and not "magical" in itself. But it sounds good if used with purposeful choices.

Some of the "quarter-tone" scales outlined below sound even better when slightly altered to include 13-limit intervals. For example the ratio 13/8 is 840.5 cents, or 9.5 cents off from an exact quarter-tone.

The list, um, comprises:

> 65 7-note scales with quarter-tones, in 10 groups
> rotations of maqam Saba, not part of the computer-generated list

> 5-and-6 note "no wolf" sets in 5 groups
> two additions

> All the possible standard scales that conform to the "no 012" rule -- with only modal names given. (ask)
> two more sets of scales/maqams that have one or more 012's.

A minus sign (-) means the pitch is 50 cents, or a "quarter-tone" lower.

65 7-note Scales with at least 1 quarter-tone, in 10 groups. Grouped by interval content, and -- below the line -- by inversion.

Order of groups is somewhat arbitrary. But groupings themselves are not.

Names of some corresponding maqams are given to right of pitch-collection.

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



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



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



A,B,C#,D#-,E,F#,G#
A,B,C#,D,E,F#,G#- Jiharkah/Ajam
A,B,C,D,E,F#-,G
------------------------
A,B,C#-,D,E,F#,G Rast
A,B-,C,D,E,F,G



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



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



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



A,B,C#,D#-,E,F#,G#-
A,B,C#-,D,E,F#,G#- Rast (Wiki)
A,B-,C#-,D#-,E,F#-,G#- Sikah/Nahawand
A,B,C#-,D,E,F#-,G Bayati
-----------------------
A,B-,C,D,E,F#-,G



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



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

=====================
A maqam and its rotations not included in above list, because of the spacing rule. (See link.)

Saba rotations
A Bb C# D E F# G#- 2,6,2,4,4,3,3
A C C# D# F G- G#- 6,2,4,4,3,3,2
A B C# D#- E F G# 4,4,3,3,2,6,2
A B C#- D Eb F# G 4,3,3,2,6,2,4
A B- C C# E F G 3,3,2,6,2,4,4


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

No-"Wolf" 5-and-6-note Lists. These have no intervals of 650 or 750 cents (near-5ths) between any pitches.

In 5 groups, with two additions. Because I'm a liberal.



A, D, E, F#-, G#: 10,4,3,5,2
A, B-, C#, D, G: 3,5,2,10,4
A, Bb, D#, F, G-: 2,10,4,3,5
A, C-, C#-,F#-, G#-: 5,2,10,4,3
A, B, C#-,D#, E: 4,3,5,2,10
=================================
A, D, D#, F#-, G: 10,2,5,3,4
A, C-, C#, D#, G#: 5,3,4,10,2
A, B, E, F, G#-: 4,10,2,5,3
A, B-, C#-,F#-, G-; 3,4,10,2,5
A, Bb, C#-,D, E: 2,5,3,4,10


A, C-, D, D#, F#-, G#: 5,5,2,5,5,2
A, C-, C#-,D#, F#-,G-: 5,2,5,5,2,5
A, Bb, C#-,D#, E, G-: 2,5,5,2,5,5


A, B, F, F#, G#-: 4,12,2,3,3
A, Bb, C-, C#, D#: 2,3,3,4,12
===============================
A, B-, C-, F#-, G#-: 3,2,12,4,3


A, B, E, F#, G#-: 4,10,4,3,3
A, D, E, F#-, G: 10,4,3,3,4
A, B-, C#-,F#-, G#-: 3,4,10,4,3
A, B-, C, D, G: 3,3,4,10,4
A, B, C#-,D, E: 4,3,3,4,10



A, C#-,E, F#-, G#-: 7,7,3,4,3
A, B, C#-,E, G#-: 4,3,7,7,3
A, B-, D, F#-, G: 3,7,7,3,4
A, C#-,D, E, F#-: 7,3,4,3,7
A, B-, C#-,D, F#-: 3,4,3,7,7


A, Bb, C-, C#-, D#, G-: 2,3,2,5,7,5 (against "rules")
A, Bb, C-, D, D#: 2,3,5,2,12


============================================
Standard Modes, with two maqam-rotations not having quarter-tones. The maqams have 012's. That is, two adjacent semitones. The second group of maqams have two sets of 012's. This makes them problematic for easy generation of harmony. Otherwise, they sound good, of course.


Lydian
Ionian
Mixolydian
Dorian
Aeolian
Phrygian
Locrian

Lydian #5
Lydian b7
Ionian b3
Mixo b6
Dor. b2
Aeol b5
Locr. b4

Lydian #2 #5
Lydian b3
Ion. b6 or Har. major
Mixo. b2
Dor. b5
Phryg. b4
Locr. bb7

Lyd. #2
Dor. #4
Aeol. mj7 (N7) Har minor
Phryg. b4
Locr. mj6 (N6)
Ion. #5
Locr. b4 bb7

whole-tone

hex -- minor third
hex -- half-step

Oct. -- dim
Oct. -- dom.

Nawa Athar (No quarter-tones)
A B C D# E F G# 4,2,6,2,2,6,2
A Bb C# D Eb F# G 2,6,2,2,6,2,4,
A B# C# D E# F# G# 6,2,2,6,2,4,2,
A Bb C# D E F G# 2,6,2,4,2,6,2,
A B# C# D# E G G# 6,2,4,2,6,2,2,
A Bb C Db E F Gb 2,4,2,6,2,2,6


Athar Kurd (double 012)
A Bb C D# E F G#
A B D Eb E G G#
A C Db D F F# G
A Bb B D Eb E F#
A Bb C# D Eb F G#
A C Db D E G G#
A Bb B C# E F F#




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Last edited by calebprime; 11th March 2014 at 06:30 AM.
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Old 7th April 2014, 06:28 AM   #137
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Sort of quarter-tone scales by left-most pack to right-most
(Darkest to lightest, generally, kinda)

A,Bb,C,C#,D#,E,g- close to "A oct"
A,Bb,C,Db,Eb,F,g- like Bbhar. min.

A,Bb,C,D-,Eb,F,Gb like Bb har. maj/min.
A,Bb,C,D-,Eb,F,g- like Bb Ion.
A,Bb,C,D-,Eb,F,G like Bb Ion.
A,Bb,C,D,Eb,F,g- like Bbhar. maj.
A,Bb,C,D,Eb,F#-,G like G har. min.

A,Bb,C,D-,E,F,G like F har. maj.
A,Bb,C,D,E,F#-,G like Bb Lyd., like E mel. min. up

A,Bb,C#-,D,E,F,G like D har. min.
A,Bb,C#-,D,E,F#-,G like G Dor. (sort of)
A,Bb,C#-,D,E,F#,G like D har. maj.
A,Bb,C#-,D#,E,F#,G close to "A oct"

A,Bb,C#,D,E,F#-,G Hijaz like D harmonic maj/min.

A,B-,C,D,Eb,F,G like Eb Lyd., like C mel. min. up
A,B-,C,D,Eb,F#-,G (fingering: Am7b5 & Dm)
A,B-,C,D,Eb,F#,G like G har. maj/min.

A,B-,C,D,E,F,G like C Ion.
A,B-,C,D,E,F#-,G
A,B-,C,D,E,F#,G like G Ion.

A B-,C#-,D-,E,F#-,G#- (finger: Am6 & Bm)
A,B-,C#-,D,E,F#-,G
A,B-,C#-,D,E,F#-,G#- (finger: Am7 & Bm triad)

A,B-,C#-,D#-,E,F#-,G#- Sikah/Nahawand
(finger above: a,c,e,g#,b,d#,f#)

A,B-,C#,D,E,F,G mustaar like D har. min.
A,B-,C#,D,E,F#-,G like D Ion
A,B-,C#,D,E,F#,G like C#har. maj.

A,B,C,D,Eb,F#-,G like G har. maj.
A,B,C,D,Eb,F#-,G# close to "D oct"

A,B,C,D,E,F,G#- like A har. min. 1,2,b3,4,5,b6,#-7,
A,B,C,D,E,F#-,G like G Ion.
A,B,C,D,E,F#,G#- like C Lyd., like A mel. min. up
A,B,C,D,E,F#-,G# like A har. min. 1,2,b3,4,5,#-6,#7

A,B,C,D#-,E,F#,G like E har. min.
A,B,C,D#-,E,F#,G#- (finger: 046B on A & B triad)
A,B,C,D#-,E,F#,G# like E har. maj.
A,B,C,D#-,F,F#,G# close to "D oct"

A,B,C,D#,E,F#,G#- like E harmonic maj/min.

A,B,C#-,D,E,F,G like F Lyd., like D mel. min. up
A,B,C#-,D,E,F,G#- (f: A7 & 027 on B)
A,B,C#-,D,E,F,G# like A harmonic maj/min.
A,B,C#-,D,E,F#-,G Bayati (finger: a7, bm7b5)
A,B,C#-,D,E,F#-,G#- (finger: A7 & Bm triad)
A,B,C#-,D,E,F#-,G# like A Ion.
A,B,C#-,D,E,F#,G Rast like D Ion.
A,B,C#-,D,E,F#,G#- Rast (Wiki) (finger: B triad over A7)
(on 1/1, 4/3, 3/2, 9/8, 8/5)
A,B,C#-,D,E,F#,G# like A Ion.

A,B,C#-,D#-,E,F#-,G#-(finger: Amaj7 & Bm triad)
A,B,C#-,D#-,E,F#,G#- (finger: Amaj7 & B triad)

A,B,C#-,D#,E,F#,G like E har. min.
A,B,C#-,D#,E,F#,G#- like E Ion.
A,B,C#-,D#,E,F#,G# like E har. maj.

A,B,C#,D,E,F,G#- like A har. maj.
A,B,C#,D,E,F#-,G like D Ion.
A,B,C#,D,E,F#-,G# like A har. maj.
A,B,C#,D,E,F#,G#- Jiharkah/Ajam like A Ion.

A,B,C#,D#-,E,F#,G like G Lyd., like E mel. min. up
A,B,C#,D#-,E,F#,G#- like E Ion. (f: A, C# triad, B triad)
A,B,C#,D#-,E,F#,G# like E Ion.
A,B,C#,D#-,F,F#,G# like F#har. min.

A,B,C#,D#,E,F#,G#- like E Ion.

A,c-,C#-,D#-,E,F#-,G#- (on 4/3, )
A,c-,C#,D#,E,F#,G# (4/3) like C#har. min.
A,c-,C#,D#,F,F#,G# (4/3,) like C#har. maj. 4,5,b6,#-7,1,2,3
A,c-,D,Eb,F,F#,G# (on 4/3,) close to "D oct"


I sorted the 65 7-note quarter-tone scales listed above in a different way -- by left-most packing to right-most packing. Mostly this is darkest-sounding to lightest, but not always.

The advantage of this way of organizing them is that you can see how one note is altered by a quarter-tone. One quarter-tone difference between each scale.

Both ways of grouping them are useful. If I were smarter, I wouldn't need this at all. These groupings are aids to learning.

Now, I find myself feeling fatigued and bored and distracted when trying to tackle this stuff. This is a sign that I should shift gears and try a different approach. Maybe switch to composing with them. Or maybe see a doctor about type 2 diabetes. I'm not sure. I do know that my doctor made me feel like a piece of meat on my last visit, and she was hopeless when it comes to psychology or empathy, and terse when it comes questions of żevidence? Apparently, what she cannot speak of she passes over in silence. Because being treated like an object is disheartening, and I'm vulnerable to such treatment, I can predict that this will make me feel worse for a long time.

So a little analysis of this project is in order.

Persistence is necessary. But if I persist on the wrong tack, I will have wasted my remaining time. I'm 55, there isn't all that much time left.

I'm trying to learn a 43-pitch non-tempered geography, and also trying to learn 24-pitch-equal geography -- much, much easier, but not easy.

With the quarter-tone scales, it's not hard to sit on one and jam with it. But I'm mystified about how to connect one scale with a different scale, so far.

Maybe: It's not as strange as you think: Just do it.

As Peachy Carnahan says, "We've got to brass it out, Danny. Brass it out."

or as they say in AA: Fake it 'til you make it.

I need the "joy and fierceness" of an Arnold in Pumping Iron. He set absurd goals for himself and somehow attained them.

How to shut off the inner captious critic -- that niggling, nattering, nabob of negativism.

How to not be scared by the inner Professor Terguson:

"I hold music theory sacred. Sacred like a farmer holds the soil. So why don't we dive right in, and tackle one of the easiest forms of microtonality -- the quarter-tone."

http://www.youtube.com/watch?v=QKBfT--rwmc

It's possible to be too committed.
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Old 16th April 2014, 09:13 AM   #138
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The answer to the above is, unsurprisingly, an adjustment to practice habits and expectations.

But surprisingly, there's also a technical fix. This would be to practice something very close to the 43-note fingering, but with exact quarter-tones, and with all possible quarter-tones available. That way, the strain on your elderly canine brain is reduced: You're not trying to practice two entirely different kinds of fingerings.

This can be accomplished by taking a 43EDO scale and quantizing it to 48EDO to get the exact quarter-tones, then adjusting just a few pitches.

Scala file here:

!
43TflatsoT48edo2
43
!
25.00000
50.00000
75.00000
100.00000
150.00000
175.00000
200.00000
225.00000
250.00000
275.00000
300.00000
350.00000
375.00000
400.00000
425.00000
450.00000
475.00000
500.00000
525.00000
550.00000
600.00000
625.00000
650.00000
675.00000
700.00000
725.00000
750.00000
775.00000
800.00000
850.00000
875.00000
900.00000
925.00000
950.00000
975.00000
1000.00000
1025.00000
1050.00000
1100.00000
1125.00000
1150.00000
1175.00000
1200.00000
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Old 11th June 2014, 04:05 AM   #139
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Death of Lee Hyla, composer

Lee was the chairman of the Composition Department at NEC when I was an adjunct prof there.

He was a good composer and a straight shooter.



http://www.bostonglobe.com/metro/obi...vFJ/story.html

I like this quote -- especially this first line that I bolded -- from the obit:

Quote:
“When you’re composing, you’re alone all the time and there is a tremendous struggle to understand your materials,” he told the Globe in 2007.

“Most of the time it’s not a good feeling because it’s just so frustrating to put a piece together. But the moment when things actually crystallize is one of the most transforming moments I’ve had as a human being. When you can hold the whole piece in your hand, so to speak, and you understand all the levels and layers, there’s a way in which you feel like you’re communicating with the music that’s been done before you, and music that’s still to come. It is a very illuminating moment, a very beautiful moment, actually. You’re a couple of feet off the ground.”
Yes. Those brief moments -- there's nothing else that compares.
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Old 26th June 2014, 01:30 AM   #140
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Originally Posted by calebprime View Post
we get to this:

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

and this. observe embedding:

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


by this process:


user row: 0 2 3 5 7 8 10 11 1 4 6 9 #1 complete orbit
grid row: 9 10 11 0 1 2 3 4 5 6 7 8
orbit: 9 0 5 1 7 6 4 11 3 10 2 8


0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 #1 c.o. perm table
5, 7, 8, 10, 11, 1, 4, 6, 9, 0, 2, 3 entry for FRF,
1, 6, 9, 2, 3, 7, 11, 4, 0, 5, 8, 10
7, 4, 0, 8, 10, 6, 3, 11, 5, 1, 9, 2
6, 11, 5, 9, 2, 4, 10, 3, 1, 7, 0, 8
4, 3, 1, 0, 8, 11, 2, 10, 7, 6, 5, 9
11, 10, 7, 5, 9, 3, 8, 2, 6, 4, 1, 0
3, 2, 6, 1, 0, 10, 9, 8, 4, 11, 7, 5
10, 8, 4, 7, 5, 2, 0, 9, 11, 3, 6, 1
2, 9, 11, 6, 1, 8, 5, 0, 3, 10, 4, 7
8, 0, 3, 4, 7, 9, 1, 5, 10, 2, 11, 6
9, 5, 10, 11, 6, 0, 7, 1, 2, 8, 3, 4

P) permutation: 5,7,8,10,11,1,4,6,9,0,2,3
C) center interval of self-similarity: 1
O) minimum number of occurrences of center: 2
D) maximum deviation from center: 1
S) maximum sum of all deviations: 20
F) fixed-position notes: 0:0
E) excluded cells within range:
R) excluded intervals within range:
A) filter original solution: on

enter choice: 1
working...
0 2 9 7 5 1 4 3 10 11 8 6 - 12 0 0
C,D,A,G,F,C#,E,Eb,Bb,B,Ab,Gb
intervals: 2,7,10,10,8,3,11,7,1,9,10,6

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

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

like Mall.

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


which has a tune close enough to a song that it's, um, actionable.

https://app.box.com/s/b70b56cwmutzmbkkn2vk

(15 minutes of spacy, moody music with lots of filter-whooshes)

From this series, I had the computer find this:


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

which is spread out over 15 minutes...




Made a good bed from this. I'm going to try to add more, maybe change a lot. But as this stands, it could be good video-game music, or something. The tuning is slightly different from 12-tone, so that gives some of the chords a different resonance, but it's really 5-limit music -- meaning it doesn't sound that unusual.

The filtering gives it all that chugging rhythm.
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Old 29th June 2014, 09:13 AM   #141
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Originally Posted by calebprime View Post
https://app.box.com/s/b70b56cwmutzmbkkn2vk

(15 minutes of spacy, moody music with lots of filter-whooshes)

From this series, I had the computer find this:


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

which is spread out over 15 minutes...




Made a good bed from this. I'm going to try to add more, maybe change a lot. But as this stands, it could be good video-game music, or something. The tuning is slightly different from 12-tone, so that gives some of the chords a different resonance, but it's really 5-limit music -- meaning it doesn't sound that unusual.

The filtering gives it all that chugging rhythm.
https://app.box.com/s/4pky8bwrr6t9wtxvn91b

This started to seem awfully fatiguing, like jogging through glue, so I cut some and eq'd some of the mids out.

This is better, but still not all that good.

As they say: Life sucks, then you die.
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Old 29th June 2014, 04:53 PM   #142
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https://app.box.com/s/5ff55ygoa55f336vwqwy

More effects, more filtering.

One technique that ended up working just as I'd hoped was convolving a version of this with a classical piece (had to tune the classical piece up 50 cents) using the convolution in SoundHack.

This is as good as this idea is going to get.

My wife is a good critic. She says that this fails to hold her interest and doesn't give her that sense of telling a story. She's never wrong about this kind of thing.

So, not one of my greatest hits.

But it has some production tricks new to me, so that's something.

Another dystopian landscape piece, another false start.

Next.
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Old 23rd July 2014, 07:29 AM   #143
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https://app.box.com/s/g492do0y32vk97z50s15

the piece in the folder here called 2,3,4,5,6, git for bell bet.aif

is -- at this stage in the process -- just an accretion of different speeds, each assigned to a different instrument. But it makes for a very pleasing, serene texture, with ominous looming chords. About 3/12 minutes.

Future work will add more layers, then remove, sculpt, and shape.
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Old 23rd July 2014, 12:01 PM   #144
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Originally Posted by calebprime View Post
https://app.box.com/s/g492do0y32vk97z50s15

the piece in the folder here called 2,3,4,5,6, git for bell bet.aif

is -- at this stage in the process -- just an accretion of different speeds, each assigned to a different instrument. But it makes for a very pleasing, serene texture, with ominous looming chords. About 3/12 minutes.

Future work will add more layers, then remove, sculpt, and shape.

Ominous but not unsettling. I liked that calebprime, a lot.
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Old 24th July 2014, 04:32 AM   #145
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I agree; that was very nice. In the foreground arpeggios, the quarter-tones (or are they eighth-tones? moving from 12 semitones to 48 then truncating 5... never mind; that's what i get for cutting class) don't sound strange at all, more like fragile bridges between familiar pitches; while the harmonies with the background do sound strange, slightly ominous but without overwhelming the foreground serenity, like listening to the sounds of a storm that has passed (that might return, or might not); the addition of the metronomic zillWP notes between 2,3,4,5,6 ruf and 2,3,4,5,6 bell bet give it a balancing 'calm on the horizon' feel. Looking forward to future work (& works) along these lines.
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Old 30th July 2014, 09:16 AM   #146
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Thanks for the nice comments, both a' yuh.

And yes, the "zill" was the late addition -- it sounds calm and metronomic, just as you say. I worried that it is too metronomic. Very perceptive comments as usual, Blobru-san.

I'm going to leave this piece as is, but do another piece in a similar (self-similar) vein.

One thing I've been struggling with, or at least testing, is whether altered tunings work with self-similar generation technique. They tend to be funky, because -- unlike music based on other techniques than self-sim -- every note gets combined with every other note in the tuning. That's the way this self-sim technique works out.

If every note of a just-intonation major scale gets combined with every other note, sooner or later you'll hit a "wolf".

JI tuning of C major scale: (Note: It's conventional to use fractions to denote ratios. They're the same thing, here. That is, 9/8 means 9:8 here.)

1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8 (C,D,E,F,G,A,B)

The wolf, or bad interval, here is the 5/3 against 9/8.

Hearing this, one substitutes 27/16 for 5/3. But then that's out of tune with 5/4. So one grimaces and substitutes 81/64 for 5/4. But that's out of tune with 15/8.

So one ends up with a Pythagorean tuning for a major scale. In this kind of self-similar texture, one might as well use good ol' 12-tone equal temperament tuning for a major scale.

Or one can learn to tolerate a wolf or two, or some equivocation between different versions of a pitch.

In the piece linked to above, there's some subtle funkiness and a few discrepancies that I didn't fix.

The moral is that self-sim technique and simple JI tuning don't play that well together. They can co-exist, but with little advantage and some strain.
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Old 30th July 2014, 09:30 AM   #147
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Random notes -- some things I've been saving up.

I recently heard Not Lilacs by composer and theorist Robert Morris.

http://www.mp3olimp.net/robert-morris-not-lilacs/

To my surprise, this sounds jazzier than it does self-similar or 12-tonish.

Other so-called Third Stream pieces tend to err on one side or another -- either they don't swing (Babbitt, and for different reasons, Schuller) or they don't have much in the way of 12-tone rigor.

Having heard this, I felt freer to pursue my own exploration of self-similar techniques, because I'm hearing that this piece doesn't seem that interested in making self-similarity audible. But it was rather fresh and pretty hip, especially compared to Babbitt -- an entirely different kind of composer.

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

I volunteer at the library perpetual book-sale, so I get first dibs on the CD's and music books that the library is culling.

It's slightly sad to see Pierre Boulez' _Notes of an Apprenticeship_ being culled, along with his recordings.

He was (and is) a giant, but even here in the Athens of America, no one is reading him or listening to him.

Except me.

I find the atmosphere of high intellectualism and historical awareness a little stimulating, but mostly oppressive.

It's hard to feel inspired by someone who would certainly think I was an ignorant hick.

Hard to enjoy banging out a pretty chord when Pierre is talking about historical necessity.

Thing is, for all that brilliance and knowledge, I don't find his music (Repons, etc.) all that compelling or interesting.

He relies a lot on massive twittering textures -- slightly angry birds.
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Old 30th July 2014, 11:43 AM   #148
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Originally Posted by calebprime View Post
...
It's slightly sad to see Pierre Boulez' _Notes of an Apprenticeship_ being culled, along with his recordings.

...
ahem.

Too late to edit, but that should be: Boulez's
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Old 22nd August 2014, 11:14 AM   #149
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This is just the generators -- not the finished piece -- but it makes a nice minimalist piece in itself. Very happy with this.

Having trouble linking to file, but the folder is here.

https://app.box.com/s/2ue7l0ujnsnj61dqtzrr

The piece is titled wrong here: It's called 3 ^n mod 17 skel2, but it really should be 11 ^ n mod 17 skel2
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Old 24th August 2014, 05:01 PM   #150
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now titled Intelligent Pacman. I added a next layer to the first 4 minutes.

Sythesis sounds a little cheesy.

Folder:

https://app.box.com/s/g492do0y32vk97z50s15
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Old 31st August 2014, 06:09 AM   #151
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Some notes before my next piece -- to clarify my thinking, and to come back to later to see how they worked out.

-- The little innovation that makes this different from previous self-sim pieces is that the series will be only gradually explicitly stated; mostly, at first, it will be rests -- with the total result being a combination of series within the master-cycle.

-- 12 tone et.

-- 17-beat cycle (which is a given with a 16-note series, if you want to have all self-similar speeds available.)

-- series mapped to mostly 7-note scales. This is a mapping that works well, for a bunch of reasons.

Series is a permutation of indices of 3 ^ n mod 17. Like all such series, this is self-identical at every other note from the second note, every third note from the third note, every nth note from the nth note.

Table of "master cycle", here:


Base: 3 Mod: 17


9, 7, 10, 5, 14, 8, 4, 3, 11, 12, 0, 6, 13, 2, 15, 1
7, 5, 8, 3, 12, 6, 2, 1, 9, 10, 14, 4, 11, 0, 13, 15
5, 3, 6, 1, 10, 4, 0, 15, 7, 8, 12, 2, 9, 14, 11, 13
3, 1, 4, 15, 8, 2, 14, 13, 5, 6, 10, 0, 7, 12, 9, 11
1, 15, 2, 13, 6, 0, 12, 11, 3, 4, 8, 14, 5, 10, 7, 9
15, 13, 0, 11, 4, 14, 10, 9, 1, 2, 6, 12, 3, 8, 5, 7
13, 11, 14, 9, 2, 12, 8, 7, 15, 0, 4, 10, 1, 6, 3, 5
11, 9, 12, 7, 0, 10, 6, 5, 13, 14, 2, 8, 15, 4, 1, 3

8, 6, 9, 4, 13, 7, 3, 2, 10, 11, 15, 5, 12, 1, 14, 0
6, 4, 7, 2, 11, 5, 1, 0, 8, 9, 13, 3, 10, 15, 12, 14
4, 2, 5, 0, 9, 3, 15, 14, 6, 7, 11, 1, 8, 13, 10, 12
2, 0, 3, 14, 7, 1, 13, 12, 4, 5, 9, 15, 6, 11, 8, 10
0, 14, 1, 12, 5, 15, 11, 10, 2, 3, 7, 13, 4, 9, 6, 8
14, 12, 15, 10, 3, 13, 9, 8, 0, 1, 5, 11, 2, 7, 4, 6
12, 10, 13, 8, 1, 11, 7, 6, 14, 15, 3, 9, 0, 5, 2, 4
10, 8, 11, 6, 15, 9, 5, 4, 12, 13, 1, 7, 14, 3, 0, 2


This is a fairly well-known series, fwiw.
http://www.google.com/search?q=%220%...bv=2&oq=&gs_l=


And the other thought -- or resolution -- that I have going in is that I have to be inhumanly patient -- to not get excited or discouraged by what I'm hearing until the overall design is complete.

That's hard, because it's always an exciting thing that a bunch of numbers seems to acquire a character, a life, of its own.

Think about what a monster of toughness, of stick-to-itness, Beethoven was! He didn't say: "Oh, this sounds pretty good, I'll just go with this sketch." He re-wrote and re-wrote and re-wrote.
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Old 10th September 2014, 07:41 AM   #152
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https://app.box.com/s/g492do0y32vk97z50s15 folder

File name: generators137

This is the minimalist piece resulting from only taking the two original generators, as described in the recipe below.

The chord changes don't start until about a minute in.

Recipe:

9, 7, 10, 5, 14, 8, 4, 3, 11, 12, 0, 6, 13, 2, 15, 1
This is treated as a contour which is applied to mostly 7-note scales ( a lot of modes of melodic minor (or Lydian b7 or Altered, etc. -- all the same thing.)

That creates the fast sequencer lines -- to which I added some effects, just for this version.

It's also used to derive this 12-tone row: p/0/0:..............|A..F..Bb.C#.Eb.G..B..C..D..Ab.E.. F#

Which is combined with versions of itself to make this array:

p/5/5:...............C..E..F..G..C#.A..B.|D..Bb.Eb.F#. Ab
ri/11/8:.............E..G..C..Ab|B..C#.A..Eb.F..F#.Bb.D
p/0/0:..............|A..F..Bb.C#.Eb.G..B..C..D..Ab.E.. F#
ri/6/3:..............Bb.C..C#.F..A..B..D..G..Eb|F#.Ab.E


Which is slowly arpeggiated to create harmonic fields, which merge into each other. This is played through three or four times with variations over the course of 12 minutes. I improvised this a little faster, but slowed it down by a factor of 1.4.

The best-fit chord-scales are chosen, so the fast sequencer-burble changes chords, with mostly a downward trend.

The fastest resultant rhythm is a 16th-note at quarter=137.

When the piece is done, there will be all manner of polyrhythms derived from taking every 2cnd, 3rd, 4th, 5th....16th note of this 16th-note generator.

The score of the arpeggios and chord-scale changes:

2 1 1 E3 F Harmonic Major
2 4 3 A2
2 9 1 C4
2 16 3 Bb1

3 11 3 E4

4 14 3 F2
5 14 1 C2
6 8 1 G3

7 10 1 Db2
7 17 1 F4 (+ E4)
8 6 3 C4
9 6 1 Bb2
10 10 3 Db3
10 14 1 F2
10 17 3 Ab3 F Harmonic Minor
11 3 3 G4

13 12 1 C4
13 15 1 E4
14 1 3 F4
14 5 1 G4

14 13 3 F2
14 13 3 Db3
14 16 1 Ab3
15 2 1 Db4

15 11 1 Ab3 F Altered (Locrian b4), B Lyd. b7
15 13 1 B3
15 16 1 Eb3
16 1 3 A2

16 16 1 A4 A Lyd. b7, B Mixo. b6
17 2 1 Db4
17 5 3 G3
17 10 1 B1

18 12 1 B4 G Lyd. b7, A Mixo. b6
18 15 3 A3
19 2 1 B2
19 5 1 D1

19 13 3 D4 F Lyd. b7, G Mixo. b6
20 2 1 Eb3
20 6 1 C3
20 9 1 G1

21 4 1 Bb3 Bb Mixo.
21 8 1 F3
21 12 1 D3
22 2 1 Eb1

22 10 3 Eb4 Bb Mixo. b6
22 13 3 Gb3
23 1 3 Ab2
23 5 3 Gb1

24 1 3 Gb4 E Lyd. b7
24 5 3 Bb3
24 14 1 E3
25 1 3 Ab1
25 11 1 E1
25 16 1 Gb2
26 3 3 D3
26 7 1 Ab3

28 17 1 C4 E Mixo. b6/D Lyd. b7
29 3 3 E3
29 7 1 A2

30 8 1 E1 F Har. Maj.
30 13 1 Bb1
31 1 1 C1
31 5 3 Db1

31 17 1 E4
32 3 1 G3
32 6 3 F3
32 10 1 Db1
32 13 3 F1

33 8 3 F4
33 12 1 C4
33 15 3 Bb3
34 4 3 F1
34 8 1 A1

35 10 3 C#4 G Lyd#5
35 13 1 B3
35 16 1 D#3
36 1 3 A1
36 5 1 B1
36 12 3 A3
36 16 1 C#3
37 1 3 G2
37 6 3 B1
37 9 1 D1 G Lyd.

39 1 3 B4
39 5 1 A3
39 8 1 B2

40 3 1 G1 C Mel. Minor C,D,Eb,F,G,A,B
40 6 3 C2

41 1 1 D2
41 4 3 G2
41 10 1 Eb2
41 17 1 D4
42 3 3 Eb3
42 7 3 C3

43 6 1 Eb2 Eb Mel. Minor
43 9 3 Gb1
43 14 3 Bb3
43 17 3 F3
44 4 1 D3
44 9 1 Eb1
44 13 1 Gb1

45 1 1 Eb4
45 4 1 Gb3
45 7 3 Ab2
45 17 1 Ab1

46 6 1 Gb4 E Lyd.b7
46 9 3 Bb3
46 12 3 E3
46 16 1 Ab1
47 3 1 E1
47 7 1 F#2
47 10 1 D3
47 13 3 Ab3
47 17 3 C4 D Lyd.b7/E Mix b6

50 1 3 E3 C Lyd b7
50 12 3 A2
50 16 1 Bb1
51 2 3 C4

53 5 3 C4 F Ion.
53 8 3 E4
53 11 1 E3
53 13 1 G3
53 15 1 A2
53 17 3 F2
54 3 1 Bb1
54 5 3 C2

54 12 3 E3 F Har Min.
54 14 3 G3
54 16 1 C4
55 1 1 Ab3
55 16 3 C4
56 1 3 E4
56 3 3 F4
56 5 3 G4

57 2 3 Bb2
57 7 3 Db2

57 17 3 E3 F Har Min.
58 2 3 G3
58 4 1 C4
58 5 3 Ab3
58 8 1 Db2
58 10 3 Bb2
58 12 3 Ab3
58 15 3 G4

59 8 3 A1 A Lyd. b7
59 10 3 Eb2

60 5 1 B3
60 8 1 C#4

61 4 3 A4
61 7 3 C#4
61 10 1 G2
61 13 3 B1
61 17 1 B2

62 16 3 A3
63 2 1 C#4
63 8 1 B3
63 11 1 A3
63 13 3 B2

63 15 3 D2 B Locr. b4 (Alt) (F Lyd. b7)
64 2 3 D4
64 5 3 Eb3
64 10 3 C3

65 9 3 G2 Eb Lyd.
65 15 3 Eb2
66 3 1 D3
66 5 3 F3
66 8 3 Bb3
66 11 1 Eb4 Eb Mel. Min.
66 14 1 Gb3
66 17 3 Ab2
67 6 1 Gb1

68 11 3 Gb4 C whole-tone
68 15 1 Bb3
69 1 1 E3
69 4 1 Ab2
69 7 3 Ab4
69 10 1 D4
69 13 1 F#3
69 15 3 E2
70 5 1 C5

71 4 3 C4 C Mixo.

71 16 3 E3
72 2 1 A2
72 4 1 Bb1

73 11 1 E3
73 14 3 G3
73 17 1 A2
74 2 3 F2
74 5 3 Bb2

74 11 1 C2 296 C Mixo. b2 (C Phryg. N6) C,Db,E,F,G,A,Bb
74 14 1 Db2
74 17 3 Bb2
75 6 1 C3
75 9 1 F3
75 12 1 G3

76 11 3 G4 C Phryg.
76 16 1 Ab3
77 2 3 Db3
77 7 1 F1 306 8

78 5 1 Db4 310 A Lyd. #5 (!)
78 13 1 B2
78 15 3 Eb2
79 1 1 A1

79 12 3 A4 313 A Lyd. b7
79 17 1 Db4
80 4 1 G2
80 9 1 B1

81 5 1 A1 322 A Mixo. b6 (G Lyd. b7)
81 7 1 B1
81 9 3 D2
81 12 3 G1

82 3 1 A4
82 5 1 C#4
82 7 3 G2
82 10 3 G1

83 11 3 D4 331 9 G Har minor
83 15 3 Eb3
84 5 1 C3
84 11 3 Eb1
85 3 1 F#1 337 9

85 14 1 D4
86 1 1 Eb3
86 5 1 C3
86 9 1 G1
86 13 3 Eb1
87 1 1 F#1 345 1 Ab Lyd. b7
87 6 1 Bb3
87 9 1 F3 347
87 13 1 D3
87 17 1 Ab2
88 4 3 F#3
88 8 3 Eb4

89 1 3 Ab1 353 Ab Mixo. b6
89 7 1 Ab2
89 9 1 E1 354 16

89 16 3 Ab4 356 12 E Lyd. b7
90 2 3 D4 357 7
90 6 3 F#3

90 15 3 E1 360 8 Ab Locr. / A Ion.
91 5 3 G#3
91 9 3 D3 363
91 13 3 F#2
91 17 3 E1

92 9 1 C4 367 C Lyd. b7
92 17 3 E3
93 9 3 Bb1
93 14 3 A2


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Old 12th September 2014, 05:43 PM   #153
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This has the next layer, the 1:2 half-speed layer. It sort of grooves in a nerdish way:

https://app.box.com/s/g492do0y32vk97z50s15

called generators137q3
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Old 18th September 2014, 08:41 AM   #154
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added layers, took out fastest, faded in so harmony moves faster at beginning.

This is quite a catchy combination of cross-rhythms.

called bc 2,3,4,8 layers

Folder:

https://app.box.com/s/g492do0y32vk97z50s15
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Old 20th September 2014, 10:17 AM   #155
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In this somewhat odd process, before I can sculpt, I have to layer more tracks.

There are about 10 layers. When the adding is done, there will be around 18 to 20.

Things in some ways are getting less interesting even as the texture gets richer, so I have to resist the feeling that the piece is getting worse. It's not, just overgrown.

When I'm done adding, I'll start to remove most of what I've put in, using midi volume commands.

In this particular sketch version, the bass is pounding out every 8th beat -- it's mixed way too loud. I tried using a multiband compressor to correct this, but further research is needed, as they say.

https://app.box.com/s/g492do0y32vk97z50s15

Same folder, piece is called bc 10 layers.
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Old 22nd September 2014, 12:34 PM   #156
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from: http://www.logicprohelp.com/forum/viewtopic.php?t=75126

Quote:
EdgarRothermich wrote:
I just tested it with an EXS instrument. The ModWheel value gets reset to 0 every time I hit the play button. Both Reset checkboxes in the Preference window and the "No Reset" checkbox have no effect whatsoever.

Ok, I've verified. The "magic combination" does not work with EXS.

Apparently the reset behavior depends on the instrument, perhaps built-in vs. 3rd-party? So it seems rather hopeless to understand the "logic" behind this concept. But at least it works for me with Kontakt.
my hilight.



Once again, I struggle with Logic Pro 8 only to learn that there is an unfixed bug. There are so many things like this with Logic Pro. The program is so big and complicated that -- clearly -- they haven't tested it thoroughly, or they figured it wouldn't hurt sales that much if there were a few "obscure" bugs.

Like Target. Tons of stuff. Quality mixed.

Thing is, it's taken me years to get comfortable with this program. I don't want some new version that's redesigned. I want something that is exactly the same, except it works the way it's supposed to -- or has some really deep incremental improvements.

Anyway.

The piece now has 12 layers, and quite a few mix fixes.

I expect to start shaping this block in about a week, maybe less.

https://app.box.com/s/g492do0y32vk97z50s15 same folder

version is called bc 12L m2

I'm excited about this -- about the cyber-bluegrass quality, and about the potential for making the self-similar aspect really clear.

There's a way that this generating process creates repetition with slow change. That's interesting, also.
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Last edited by calebprime; 22nd September 2014 at 12:38 PM.
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Old 23rd September 2014, 02:37 PM   #157
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https://app.box.com/s/g492do0y32vk97z50s15

name: bc channel mutes1.aiff

This is the first version of this piece that I'd say is worth hearing for contrasts and textural changes. I'm maybe half-way through the whole process.

Having finished the layers, I did a quick improv (captured with Audio Hijack Pro) by muting and unmuting channels, to build up and to thin out the texture.

Heh. My version of Audio Hijack is a demo, so I can only capture about ten minutes. (Which is quite long enough for this version.)

What's missing is the precision required to make the self-similarity element come through clearly. That will take more work.

And, also, required would be more precision in bringing in the materials, to force the listener to hear certain meters. I myself can't hear this in 5, only in duples or triples.

Perhaps one or two more versions to post, to complete the process. These after a lot of trial and error.
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Old 25th September 2014, 02:04 PM   #158
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Well, a little trial, maybe some error.

https://app.box.com/s/g492do0y32vk97z50s15

version is called: bc 66 fx1

There is, at this stage, a strong temptation to call a piece done. Like the temptation to lie down in the snow and rest for a while. Feel pretty warm, maybe even take off my coat. Such nice, restful snow.

NO! Must. Keep. Going.

If I'm going to do a sort of block piece, this version is adequate.

But if I want to stick to my original idea, then it's a failure.

Today I added some effects, changed a bunch of other things. The effects are for the purpose of introducing slow changes of timbre, of spectrum. With slow changes, the repetitions become less abrasive, less monotonous. The balances are always changing, with different instruments fading in and out, slightly. So the effects help -- they're not just there to make it sound weird.

When I took some classes with Mike Gibbs at Berklee a long time ago, he had a simple but effective approach to arranging. He'd suggest that you ask yourself how you felt about whatever the given material was. Then, how you'd like it to be different. Then, what techniques or instruments would achieve that goal.

Mostly, this worked well. But, once, he played us a horrible arrangement -- what he called "Hollywood Strings" -- of a Satie piano piece that he'd done. Big lush textures. Added notes all over the place. Saccharin and schmaltz.

I asked him, appalled, "Why did you do that?"

He said: "I was bored with it."

He'd made it different, all right. From something exquisite into something...hideous.

But mostly, he was pretty tasteful. Good teacher, too, in a kind of mellow way.
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Old 30th September 2014, 09:18 AM   #159
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https://app.box.com/s/g492do0y32vk97z50s15

For some reason, I can't link to the individual piece, but the folder is here.



A final version, rough mix. Called 3 to the n mod 17.

I'm pretty happy with the way some of this turned out.
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Old 6th October 2014, 06:51 AM   #160
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On to the next. Some theory of generating rows.


An attempt at a quick explanatory sketch.

One tendency that guides my composition is that I simply try to do something different from the last piece.

One pole of difference -- so to speak -- is between starting materials that are nearly perfect and regular, and materials that are irregular -- but which have some attributes that are interesting. Along with the starting materials goes an overall intention, a vaguely-conceived world of sound. This piece is going to be less obviously patterned, less reliant on automatic polyrhythms. Working title: Caleb's Inner Spinach.

The only "perfect" series that I'm aware of are the series made by the indices of power-residues. For example, the indices of 2 ^ n mod 13.

My last piece was based on the series from 3 ^ n mod 17 -- a 16-note series. Because the series was based on this power-residue formula, it easily generated lines that are related to each other, but are going at different speeds, all adding up to one big composite line -- from which each strand "grabs" notes.

This next piece will be based on a less well-known, less familiar generating process. No metronomic ticking this time. Rather, dense jungle. Dense inner jungle. Hence, inner spinach.

One problem with power-residue series is that there are only a few of them. (For example, 2 ^ n mod 13 generates 0,1,4,2,9,5,11,3,8,10,7,6, or C,C#,E,D,A,F,B,Eb,Ab,Bb,G,F#, also known as the Mallalieu series, or all-interval series number 44, using the numbering system of Morris and Starr.) There ain't no other 12-tone series that are perfect in this way, apart from the row-complex based on this series.

But by relaxing or altering some constraints, we can find a wealth of series; a trove; indeed, a vast, rich panoply of series, enough for a lifetime of work -- should one be so inclined.

To generate the series I might use for Inner Spinach, the constraints to be altered are:
1) regular permutation
2) exact self-similarity

so that,

1) The series can have a similar embedded series which skips every 2,3, or 4 pitches
and
2) The similar, embedded series is a transposition of the original series, but + or - 1 semitone.

An additional difference is that now I can look to see whether there are series that are self-similar at some other interval rather than 1 semitone. In the example below, the series is self-similar at 2 semitones, + or - 1 semitone.

To help systemize the search, I made an exhaustive list of all possible "expansion" series.



Appendix 4: 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 (Mallalieu)
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





After a lot of trial and error, of brute-force computer searches, I'm choosing permutation pattern #30: 0 2 4 7 B 3 6 8 A 1 5 9 *** 30.234 223443223443

This makes complete orbits with a chromatic scale (0,1,2,3,4,5,6,7,8,9,10,11) in the following 4 ways, (here written as "user row" and "grid row":



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

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

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

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



Now that I'm assured of finding something, I can plug these numbers into one of my apps:


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

1) perform new full search
2) search within results of last full search
9) quit

enter choice: 1
working...
0 1 8 10 6 3 11 2 7 9 5 4 - 6 1 6
0 2 8 9 5 3 11 1 7 10 6 4 - 6 1 6
0 2 8 11 7 5 1 3 9 10 6 4 - 6 1 6
0 3 8 10 6 5 1 2 9 11 7 4 - 6 1 6
found 4 solutions.



Here I'm eliminating any series whose contiguous notes produce "harmonies", or cells, that I don't want. And, that produce undesired cells in the permutation and the permutation of the permutations as well.

There are only 4 series found. On closer examination, these are really only two distinct series. The first and fourth are the same, and the second and third are the same.

I'm calling the second series "All Permutations 026", or "AP 026", because of its many 026 cells. While I don't usually use series that contain whole-tone scales, maybe I'll make an exception. I've been listening to a little Boulez, and maybe I'm allowing a litle French influence to creep in.

Here's the permutation matrix of the series. The second row is the embedded series found in the first row. The columns produce a regular sequence of 1,2, or 3 semitones -- a fairly tight "family resemblance" between all series.

And no row in the matrix contains the hated 0369 chord -- instant failure -- or the equally hated triad-with-added-6th, or a dominant-seventh chord, or a 2-adjacent-semitone cluster -- 0,1,2.



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


Showing the embedding of the second row in the first:

C..D..G#.A..F..Eb.B..C#.G..Bb.F#.E..(first row cycle)

...D...........Eb..........Bb.......(second row embedding)
C.....G#....F........C#..........E..
.........A........B.....G.....F#....




Working along these lines, I've also come up with five other series. I'm not sure if I'll choose only one, or whether I'll write six separate pieces -- an Inner Spinach Suite, perhaps.
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Last edited by calebprime; 6th October 2014 at 07:14 AM.
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