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23rd January 2018, 02:51 AM
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#81 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Today's row of the day is Renuzit, named after the air freshener brand.
The orbit at the minor third is not quite complete, but the family of series it finds that are nearly complete is very close -- 10 notes are perfect and the other 2 are off by only 1 semitone. Code:
Db,A,Eb,E,F#,B,Ab,C,G,D,F,Bb
********* 8,6,1,2,5,9,4,7,7,3,5,3 [1,2,3,4,5,6,7,8,9] = 9 intervals
Renuzit
Db, A, Eb, E, F#, B, Ab, C, G, D, F, Bb
A, E, B, C, D, Bb, Db, Eb, F#, Ab, G, F
E, C, Bb, Eb, Ab, F, A, B, D, Db, F#, G
C, Eb, F, B, Db, G, E, Bb, Ab, A, D, F#
Eb, B, G, Bb, A, F#, C, F, Db, E, Ab, D
B, Bb, F#, F, E, D, Eb, G, A, C, Db, Ab
Bb, F, D, G, C, Ab, B, F#, E, Eb, A, Db
F, G, Ab, F#, Eb, Db, Bb, D, C, B, E, A
G, F#, Db, D, B, A, F, Ab, Eb, Bb, C, E
F#, D, A, Ab, Bb, E, G, Db, B, F, Eb, C
D, Ab, E, Db, F, C, F#, A, Bb, G, B, Eb
Ab, Db, C, A, G, Eb, D, E, F, F#, Bb, B
8,7,8,3,8,11,7,2,11,8,6,5
Db, A, Eb, E, F#, B, Ab, C, G, D, F, Bb
F, Db, G, Ab, Bb, Eb, C, E, B, F#, A, D
B, G, Db, D, E, A, F#, Bb, F, C, Eb, Ab
Bb, F#, C, Db, Eb, Ab, F, A, E, B, D, G
Ab, E, Bb, B, Db, F#, Eb, G, D, A, C, F
Eb, B, F, F#, Ab, Db, Bb, D, A, E, G, C
F#, D, Ab, A, B, E, Db, F, C, G, Bb, Eb
D, Bb, E, F, G, C, A, Db, Ab, Eb, F#, B
G, Eb, A, Bb, C, F, D, F#, Db, Ab, B, E
C, Ab, D, Eb, F, Bb, G, B, F#, Db, E, A
A, F, B, C, D, G, E, Ab, Eb, Bb, Db, F#
E, C, F#, G, A, D, B, Eb, Bb, F, Ab, Db
p/0/0:...............C# A Eb E F# B Ab C G D F Bb
11 0 1 2 3 4 5 6 7 8 9 10
p/3/11:..............C# E C F# G A D B Eb Bb F Ab
.....................c#.............a........eb............
........................e.....f#..........b...........ab...
...........................c.....g.....d........F..Bb
11,4,7,0,2,6,10,1,3,5,8,9
enter choice: 2
working...
0 1 7 8 4 9 11 10 5 6 2 3 - 10 1 2
0 1 7 9 4 8 11 10 5 6 2 3 - 10 1 2
0 1 7 9 4 8 11 10 6 5 2 3 - 10 1 2
0 1 7 9 4 8 11 10 6 5 3 2 - 10 1 2
0 2 8 9 5 10 1 11 6 7 3 4 - 10 1 2
0 2 8 9 5 10 1 11 6 7 4 3 - 10 1 2
0 2 8 9 5 10 1 11 7 6 4 3 - 10 1 2
0 2 8 10 5 9 1 11 7 6 4 3 - 10 1 2
0 4 10 8 7 9 11 1 5 6 2 3 - 10 1 2
0 4 10 9 7 8 11 1 5 6 2 3 - 10 1 2
0 4 10 9 7 8 11 1 6 5 2 3 - 10 1 2
0 4 10 9 7 8 11 1 6 5 3 2 - 10 1 2
0 5 11 9 8 10 1 2 6 7 3 4 - 10 1 2
0 5 11 9 8 10 1 2 6 7 4 3 - 10 1 2
0 5 11 9 8 10 1 2 7 6 4 3 - 10 1 2
0 5 11 10 8 9 1 2 7 6 4 3 - 10 1 2
0 7 1 8 10 9 11 4 5 6 2 3 - 10 1 2
0 7 1 9 10 8 11 4 5 6 2 3 - 10 1 2
0 7 1 9 10 8 11 4 6 5 2 3 - 10 1 2
0 7 1 9 10 8 11 4 6 5 3 2 - 10 1 2
0 8 2 9 11 10 1 5 6 7 3 4 - 10 1 2
0 8 2 9 11 10 1 5 6 7 4 3 - 10 1 2
0 8 2 9 11 10 1 5 7 6 4 3 - 10 1 2
0 8 2 10 11 9 1 5 7 6 4 3 - 10 1 2
0 10 4 8 1 9 11 7 5 6 2 3 - 10 1 2
0 10 4 9 1 8 11 7 5 6 2 3 - 10 1 2
0 10 4 9 1 8 11 7 6 5 2 3 - 10 1 2
0 10 4 9 1 8 11 7 6 5 3 2 - 10 1 2
0 11 5 9 2 10 1 8 6 7 3 4 - 10 1 2
0 11 5 9 2 10 1 8 6 7 4 3 - 10 1 2
0 11 5 9 2 10 1 8 7 6 4 3 - 10 1 2
0 11 5 10 2 9 1 8 7 6 4 3 - 10 1 2
found 32 solutions.
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23rd January 2018, 03:38 AM
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#82 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Renuzit is deemed distinct and gets a wristband -- that is, admission to the posh club.
Code:
number of rows found: 23 removing near-duplicates...done number of rows remaining: 23 mallalieu (0 1 7 2 10 8 4 3 6 11 5 9) (0 2 3 9 10 6 7 1 5 8 4 11) (0 1 4 2 9 5 11 3 8 10 7 6) (0 2 5 4 10 7 11 6 9 1 3 8) (0 2 8 4 5 10 1 6 3 7 9 11) (0 3 7 6 4 10 8 9 2 11 5 1) (0 3 10 7 8 1 4 2 6 11 9 5) (0 4 6 10 7 3 11 1 8 2 5 9) (0 4 7 8 1 11 9 3 10 5 6 2) (0 5 4 10 1 9 7 3 8 6 11 2) (0 5 8 10 4 1 11 3 7 9 2 6) (0 7 2 1 4 9 5 8 6 10 3 11) (0 7 4 2 11 1 6 10 9 5 3 8) (0 7 9 11 4 2 5 10 8 6 1 3) (0 8 2 3 5 10 7 11 6 1 4 9) (0 8 5 3 6 1 7 11 10 2 4 9) (0 8 7 4 9 5 3 10 11 1 2 6) (0 9 1 6 11 10 5 3 2 8 4 7) (0 9 2 6 1 11 7 3 4 10 5 8) (0 9 4 3 6 11 10 8 2 7 1 5) (0 10 2 3 6 7 4 1 9 11 5 8) (0 10 2 7 11 9 4 3 1 8 5 6) (0 10 4 8 7 3 1 6 11 5 9 2) |
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24th January 2018, 10:38 AM
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#83 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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much work on the database of rows, so things are delayed.
Here's a dump of that database as it currently exists. Up to 25 series now. |
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24th January 2018, 02:11 PM
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#84 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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I may have permanently confused myself about the spelling of Billy Childs. If I've confused anyone else I apologize.
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25th January 2018, 10:27 AM
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#85 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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All the work on the row database found exactly one hidden connection.
It happened to be a series that I didn't seem to have a title for, so no problem there deciding which title to lose. Here's the current database, with 24 approved series. That is, each series passed some quick tests for uniqueness in the collection. |
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26th January 2018, 04:18 AM
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#86 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Today's applicant to the club, Melvin-Lieben.
0 1 9 2 4 10 8 3 6 5 7 11 Code:
C,C#,A,D,E,Bb,Ab,Eb,F#,F,G,B 1,8,5,2,6,10,7,3,11,2,4,1 C, C#, A, D, E, Bb, Ab, Eb, F#, F, G, B C#, D, Bb, Eb, F, B, C, A, E, Ab, F#, G D, Eb, B, A, Ab, G, C#, Bb, F, C, E, F# Eb, A, G, Bb, C, F#, D, B, Ab, C#, F, E A, Bb, F#, B, C#, E, Eb, G, C, D, Ab, F Bb, B, E, G, D, F, A, F#, C#, Eb, C, Ab B, G, F, F#, Eb, Ab, Bb, E, D, A, C#, C G, F#, Ab, E, A, C, B, F, Eb, Bb, D, C# F#, E, C, F, Bb, C#, G, Ab, A, B, Eb, D E, F, C#, Ab, B, D, F#, C, Bb, G, A, Eb F, Ab, D, C, G, Eb, E, C#, B, F#, Bb, A Ab, C, Eb, C#, F#, A, F, D, G, E, B, Bb 1,1,1,6,1,1,8,11,10,1,3,4 Upon return, Gy-Rah will Judge the new series. |
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26th January 2018, 06:32 AM
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#87 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Melvin-Lieben is distinct, and must now undergo ordeals in the desert before full approval.
Melvin-Lieben comes close to ok complete orbits but never does better than 10 matches out of 12. The options are many but all imperfect. |
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27th January 2018, 04:13 AM
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#88 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Steer Gazing
B,F,G,C#,C,Eb,A,Ab,E,F#,D,Bb Code:
B, F, G, C#, C, Eb, A, Ab, E, F#, D, Bb
F, C#, Eb, Ab, F#, Bb, B, G, C, A, E, D
C#, Ab, Bb, G, A, D, F, Eb, F#, B, C, E
Ab, G, D, Eb, B, E, C#, Bb, A, F, F#, C
G, Eb, E, Bb, F, C, Ab, D, B, C#, A, F#
Eb, Bb, C, D, C#, F#, G, E, F, Ab, B, A
Bb, D, F#, E, Ab, A, Eb, C, C#, G, F, B
D, E, A, C, G, B, Bb, F#, Ab, Eb, C#, F
E, C, B, F#, Eb, F, D, A, G, Bb, Ab, C#
C, F#, F, A, Bb, C#, E, B, Eb, D, G, Ab
F#, A, C#, B, D, Ab, C, F, Bb, E, Eb, G
A, B, Ab, F, E, G, F#, C#, D, C, Bb, Eb
6,8,7,11,8,7,4,2,8,6,3,2
8 9 10 11 0 1 2 3 4 5 6 7
p/7/8:...............B C# A F F# C D Ab G Bb E Eb
.....................b........f..............g............
........................c#..........c.................eb..
...........................a..............ab.......e......
.................................f#....d........bb........
8,11,4,9,1,7,10,3,6,0,2,5
0 6 4 10 11 8 2 3 7 5 9 1 - 12 0 0
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28th January 2018, 03:06 AM
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#89 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Steer Gazing sounds like it could be cheap gay porn.
My old favorite, Mof3, is rotated to a beginning that looks a little like a power-res series. Eb,C,F,Ab,G,D,B,E,Bb,Gb,A,Db Discussion of how inexact or bad a power-residue self-resemblance can be. > Best case, there is perfect self-sim, as in Mallalieu series >First six notes vs. every-other-from-second is most important, followed by every-third. >The resemblance from every-other series may be inexact if there is some accident that produces interesting relations that could be exploited. But that is rare as far as I know. >A complete permutation pattern that is fairly compact is a plus, and might compensate for loose self-sim of the first 6 notes. > Usually the range of how exact the self-sim is: best is mallalieu or complete compact perm systems, but the typical power-res series has only "half" self-sim. Usually, it's clear if the self-sim is adequate or not, and rarely an inadequate self-sim accidently produces some good tonal exchanges that makes up for the looseness. |
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28th January 2018, 06:11 AM
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#90 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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It occurs to me how far-fetched are ideas of reference about this crazy poem from a crazy scene from a crazy book, and the source of the craziness is too much sensitivity, too much defensiveness, about artifice/contrivance/construction/formalism in composition.
Some of this prickliness comes from hearing people say dumb things when they should know better -- superficial misunderstandings about the craft of serial composition. Some of the prickliness comes from the fact that the critics are at least partly right. Serialism without cheating tends to sound artificial. Not like roots music. Hard to depict innocent joy in 12-tone idiom. As far-fetched as the analogy of the itchy precious poet that I imagine are all the things that people have said -- people including composers -- about serialism. That it's like soduku or a crossword puzzle. That the row determines the piece. That you have to do x or y. That it has to be atonal. That tonal and atonal hearing are somehow different. That consonance and dissonance mean something like expected and unexpected. That...blah blah. There are ranges of responses to an open situation such as this -- the best ones are ones that aim toward mastery but don't fake it before some real understanding is achieved. I mean that the master isn't concerned with rules, only with what result she wants to achieve within this form. She is as powerful as her technique allows her to be in this world. If someone has a good reason to repeat a note or whatever, she can. Nor is it (or ought it to be) showing off. It's not competition. However, there is joy in mastery just as there is joy in natural motion, in anything well-conceived and finished. The complexity and rightness of a line by Bach or Mozart isn't about them, it's the very joy of music. Serial music was invented by a very tense man in a tense time with intense intentions -- Arnie, that is. But it need not be so. The range is from the screaming-skull-from-hell to more like an artificial mellow rictus of you're-with-stupid-now. From abattoirs o' death to sort of attenuated anxious wan pleasures. Anhedonic but coping white knuckle style. Fun stuff! |
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29th January 2018, 03:24 AM
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#91 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Today's series (One and One and One) is an all-interval series with self-sim at 1, but it's different enough from Mallalieu, I think. Further research needed to see whether it's different enough from recent series Melven-Lieben.
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29th January 2018, 04:25 AM
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#92 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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No problems with distinctness with either series at this stage.
Code:
number of rows remaining: 28
(0 1 9 2 4 10 8 3 6 5 7 11) (0 8 7 4 9 5 3 10 11 1 2 6) (0 2 3 9 10 6 7 1 5 8 4 11)
(0 8 2 3 5 10 7 11 6 1 4 9) (0 2 8 4 5 10 1 6 3 7 9 11) mallalieu
(0 1 4 2 9 5 11 3 8 10 7 6)
(0 10 2 3 6 7 4 1 9 11 5 8) (0 3 7 6 4 10 8 9 2 11 5 1) (0 4 7 8 1 11 9 3 10 5 6 2)
(0 3 10 7 8 1 4 2 6 11 9 5) (0 1 7 2 4 8 6 3 11 5 10 9) (0 9 2 6 1 11 7 3 4 10 5 8)
(0 1 7 2 10 8 4 3 6 11 5 9) (0 10 2 7 11 9 4 3 1 8 5 6) (0 7 2 1 4 9 5 8 6 10 3 11)
(0 7 9 11 4 2 5 10 8 6 1 3) (0 2 5 4 10 7 11 6 9 1 3 8) (0 4 6 10 7 3 11 1 8 2 5 9)
(0 8 5 3 6 1 7 11 10 2 4 9) (0 5 8 10 4 1 11 3 7 9 2 6) (0 7 4 2 11 1 6 10 9 5 3 8)
row 1* mof3 (0 5 4 10 1 9 7 3 8 6 11 2)
(0 3 8 10 7 11 5 1 4 2 9 6) (0 9 2 5 4 11 8 1 7 3 6 10)
(0 7 3 2 5 10 6 9 1 8 11 4) (0 9 1 6 11 10 5 3 2 8 4 7) (0 9 4 3 6 11 10 8 2 7 1 5)
(0 10 4 8 7 3 1 6 11 5 9 2)
or, sorted in common-sense order....
number of rows remaining: 28
mallalieu (0 1 7 2 4 8 6 3 11 5 10 9) (0 1 7 2 10 8 4 3 6 11 5 9)
(0 1 4 2 9 5 11 3 8 10 7 6)
(0 1 9 2 4 10 8 3 6 5 7 11) (0 2 3 9 10 6 7 1 5 8 4 11) (0 2 5 4 10 7 11 6 9 1 3 8)
(0 2 8 4 5 10 1 6 3 7 9 11) (0 3 7 6 4 10 8 9 2 11 5 1) row 1*
(0 3 8 10 7 11 5 1 4 2 9 6)
(0 3 10 7 8 1 4 2 6 11 9 5) (0 4 6 10 7 3 11 1 8 2 5 9) (0 4 7 8 1 11 9 3 10 5 6 2)
(0 5 4 10 1 9 7 3 8 6 11 2) (0 5 8 10 4 1 11 3 7 9 2 6) (0 7 2 1 4 9 5 8 6 10 3 11)
(0 7 3 2 5 10 6 9 1 8 11 4) (0 7 4 2 11 1 6 10 9 5 3 8) (0 7 9 11 4 2 5 10 8 6 1 3)
(0 8 2 3 5 10 7 11 6 1 4 9) (0 8 5 3 6 1 7 11 10 2 4 9) (0 8 7 4 9 5 3 10 11 1 2 6)
(0 9 1 6 11 10 5 3 2 8 4 7) mof3 (0 9 2 6 1 11 7 3 4 10 5 8)
(0 9 2 5 4 11 8 1 7 3 6 10)
(0 9 4 3 6 11 10 8 2 7 1 5) (0 10 2 3 6 7 4 1 9 11 5 8) (0 10 2 7 11 9 4 3 1 8 5 6)
(0 10 4 8 7 3 1 6 11 5 9 2)
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29th January 2018, 05:01 AM
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#93 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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what about this all-interval series? It looks a lot like it might be a 5m of one of those three series.
Code:
C, F, B, Bb, Ab, E, F#, Eb, G, Db, D, A series intervals: 5,6,11,10,8,2,9,4,6,1,7,3 F, Bb, E, Eb, Db, A, C, B, Ab, F#, G, D 5.5.5.5.5.5.6.7.1.5.5.5 Bb, Eb, A, B, F#, D, F, E, Db, C, Ab, G Eb, B, D, E, C, G, Bb, A, F#, F, Db, Ab B, E, G, A, F, Ab, Eb, D, C, Bb, F#, Db E, A, Ab, D, Bb, Db, B, G, F, Eb, C, F# A, D, Db, G, Eb, F#, E, Ab, Bb, B, F, C D, G, F#, Ab, B, C, A, Db, Eb, E, Bb, F G, Ab, C, Db, E, F, D, F#, B, A, Eb, Bb Ab, Db, F, F#, A, Bb, G, C, E, D, B, Eb Db, F#, Bb, C, D, Eb, Ab, F, A, G, E, B F#, C, Eb, F, G, B, Db, Bb, D, Ab, A, E 5,5,5,8,5,5,5,5,1,5,7,6 |
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29th January 2018, 06:40 AM
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#94 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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It passes the first hurdle, it's not obviously like any of the others:
Code:
near-duplicate tolerance: 4
finding rows....done
number of rows found: 29
removing near-duplicates...done
number of rows remaining: 29
mallalieu (0 1 7 2 4 8 6 3 11 5 10 9) (0 1 7 2 10 8 4 3 6 11 5 9)
(0 1 4 2 9 5 11 3 8 10 7 6)
(0 1 9 2 4 10 8 3 6 5 7 11) (0 2 3 9 10 6 7 1 5 8 4 11) (0 2 5 4 10 7 11 6 9 1 3 8)
(0 2 8 4 5 10 1 6 3 7 9 11) (0 3 7 6 4 10 8 9 2 11 5 1) row 1*
(0 3 8 10 7 11 5 1 4 2 9 6)
(0 3 10 7 8 1 4 2 6 11 9 5) (0 4 6 10 7 3 11 1 8 2 5 9) (0 4 7 8 1 11 9 3 10 5 6 2)
(0 5 4 10 1 9 7 3 8 6 11 2) (0 5 8 10 4 1 11 3 7 9 2 6) (0 5 11 10 8 4 6 3 7 1 2 9)
(0 7 2 1 4 9 5 8 6 10 3 11) (0 7 3 2 5 10 6 9 1 8 11 4) (0 7 4 2 11 1 6 10 9 5 3 8)
(0 7 9 11 4 2 5 10 8 6 1 3) (0 8 2 3 5 10 7 11 6 1 4 9) (0 8 5 3 6 1 7 11 10 2 4 9)
(0 8 7 4 9 5 3 10 11 1 2 6) (0 9 1 6 11 10 5 3 2 8 4 7) mof3
(0 9 2 5 4 11 8 1 7 3 6 10)
(0 9 2 6 1 11 7 3 4 10 5 8) (0 9 4 3 6 11 10 8 2 7 1 5) (0 10 2 3 6 7 4 1 9 11 5 8)
(0 10 2 7 11 9 4 3 1 8 5 6) (0 10 4 8 7 3 1 6 11 5 9 2)
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30th January 2018, 02:15 AM
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#95 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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There is a huge perm group at the retrograde inversion (backwards upside down.)
I decided to filter it aggressively until there were only 58 solutions, by omitting any series that has an 012 per 5 notes, wrapping, or an 036 per 3 notes. Chromatic crunches and the diminished chord are removed, but this setting is my preference, could be different. E) excluded cells within range: 0,3,6,9:4 0,3,6:3 0,1,2:5 Code:
C,Eb,D,Gb,E,F,Bb,A,B,G,Db,Ab
intervals:3,11,4,10,1,5,11,2,8,6,7,4 [1,2,3,4,5,6,7,8,10,11] = 10 intervals
Woah Nellie
C, Eb, D, Gb, E, F, Bb, A, B, G, Db, Ab
Eb, Gb, F, A, G, Ab, C, D, E, Bb, B, Db 3.3.3.3.3.3.2.5.3.10.5
Gb, A, Ab, D, Bb, Db, Eb, F, G, C, E, B
A, D, Db, F, C, B, Gb, Ab, Bb, Eb, G, E
D, F, B, Ab, Eb, E, A, Db, C, Gb, Bb, G 2.2.9.2.11.11.11.4.1.11.9.11
F, Ab, E, Db, Gb, G, D, B, Eb, A, C, Bb 5.5.2.5.2.2.4.2.4.2.11.2
Ab, Db, G, B, A, Bb, F, E, Gb, D, Eb, C
Db, B, Bb, E, D, C, Ab, G, A, F, Gb, Eb
B, E, C, G, F, Eb, Db, Bb, D, Ab, A, Gb
E, G, Eb, Bb, Ab, Gb, B, C, F, Db, D, A
G, Bb, Gb, C, Db, A, E, Eb, Ab, B, F, D
Bb, C, A, Eb, B, D, G, Gb, Db, E, Ab, F
3,3,3,5,3,3,5,10,5,3,3,2
p/0/0:...............C Eb D F# E F Bb A B G C# Ab
p/9/1:...............C B Eb C# D G F# Ab E Bb F A
.....................c.....eb....d.....f#....e.....f......
................................................bb....a...
........................b.....C# G.....ab...
p/6/3:...............C Bb B E Eb F C# G D F# A Ab
.....................c...........eb..........d..f#.........
..............................e.....f..............A
..................... Bb.b..............g
p/8/4:...............C C# F# F G Eb A E Ab B Bb D
.....................c..............eb................d...
..........................f#..............e...............
..............................f....................bb.....
.......................................a........b.........
........................C# G...........ab
r/4/0:...............C F B Eb C# D A Ab Bb F# G E
.....................c........eb....d...........f#....e...
........................f..............A.....Bb...........
...........................b.......................g......
.................................c#.......ab..............
r/11/1:..............C F# Bb Ab A E Eb F C# D B G
.....................c.................eb.......d.........
........................f#..........e.....f...............
...........................bb....a.................b..g...
..............................Ab C#...........
i/4/4:...............C B F# G F A Eb Ab E C# D Bb
.....................c.................eb..........d.......
...........................f#................e.............
.................................f....................bb...
....................................a......................
........................b.....g...........Ab C#.........
0 11 10 9 8 7 6 5 4 3 2 1
ri/0/11:.............C E B F C# Eb D G Ab F# Bb A
.....................c..............eb.d........f#.......
........................e.....f....................bb.a..
...........................b..............g..............
.................................c#..........ab..........
0,7,6,3,11,9,2,1,10,5,8,4,
enter choice: e
E) excluded cells within range: 0,1,2:4 0,3,6,9:4 0,3,6:3
enter new value: 0,3,6,9:4 0,3,6:3 0,1,2:5
M) modulus: 12
P) permutation: 0,7,6,3,11,9,2,1,10,5,8,4
C) center interval of self-similarity: 0
I) invert test (use sums instead of differences): on
O) minimum number of occurrences of center: 12
D) maximum deviation from center: 1
S) maximum sum of all deviations: 30
F) fixed-position notes: 0:0
E) excluded cells within range: 0,3,6,9:4 0,3,6:3 0,1,2:5
R) excluded intervals within range:
A) filter original solution: on
B) filter permuted solution: off
X) permutation depth: 2
N) number of solutions to print: 7000
W) wrap: on
1) perform new full search
2) search within results of last full search
9) quit
enter choice: 2
working...
0 1 8 6 9 2 4 11 5 10 7 3 - 12 0 0
0 1 8 6 9 2 4 11 7 10 5 3 - 12 0 0
0 1 9 6 7 2 3 11 8 10 4 5 - 12 0 0
0 1 9 6 8 2 3 11 7 10 5 4 - 12 0 0
0 1 10 6 4 7 2 11 9 5 3 8 - 12 0 0
0 1 10 6 4 9 2 11 7 3 5 8 - 12 0 0
0 1 10 6 7 4 2 11 9 8 3 5 - 12 0 0
0 1 10 6 8 3 2 11 7 9 5 4 - 12 0 0
0 1 10 6 9 4 2 11 7 8 5 3 - 12 0 0
0 2 9 6 5 1 3 10 8 11 4 7 - 12 0 0
0 2 9 6 7 1 3 10 8 11 4 5 - 12 0 0
0 2 9 6 8 1 3 10 5 11 7 4 - 12 0 0
0 2 9 6 8 1 3 10 7 11 5 4 - 12 0 0
0 2 11 6 3 8 1 10 5 4 7 9 - 12 0 0
0 2 11 6 4 9 1 10 5 3 7 8 - 12 0 0
0 2 11 6 5 8 1 10 3 4 9 7 - 12 0 0
0 2 11 6 8 3 1 10 5 9 7 4 - 12 0 0
0 2 11 6 8 5 1 10 3 7 9 4 - 12 0 0
0 3 8 6 2 11 4 9 7 1 5 10 - 12 0 0
0 3 8 6 11 2 4 9 7 10 5 1 - 12 0 0
0 3 10 6 7 11 2 9 4 1 8 5 - 12 0 0
0 3 10 6 8 1 2 9 5 11 7 4 - 12 0 0
0 4 9 6 2 11 3 8 7 1 5 10 - 12 0 0
0 4 9 6 11 2 3 8 7 10 5 1 - 12 0 0
0 4 11 6 9 2 1 8 5 10 7 3 - 12 0 0
0 5 8 6 2 11 4 7 9 1 3 10 - 12 0 0
0 5 8 6 11 2 4 7 9 10 3 1 - 12 0 0
0 5 9 6 10 1 3 7 8 11 4 2 - 12 0 0
0 5 10 6 9 1 2 7 4 11 8 3 - 12 0 0
0 7 2 6 3 11 10 5 8 1 4 9 - 12 0 0
0 7 3 6 2 11 9 5 4 1 8 10 - 12 0 0
0 7 4 6 1 10 8 5 3 2 9 11 - 12 0 0
0 7 4 6 10 1 8 5 3 11 9 2 - 12 0 0
0 8 1 6 3 10 11 4 7 2 5 9 - 12 0 0
0 8 3 6 1 10 9 4 5 2 7 11 - 12 0 0
0 8 3 6 10 1 9 4 5 11 7 2 - 12 0 0
0 9 2 6 4 11 10 3 7 1 5 8 - 12 0 0
0 9 2 6 5 1 10 3 8 11 4 7 - 12 0 0
0 9 4 6 1 10 8 3 5 2 7 11 - 12 0 0
0 9 4 6 10 1 8 3 5 11 7 2 - 12 0 0
0 10 1 6 4 7 11 2 9 5 3 8 - 12 0 0
0 10 1 6 4 9 11 2 7 3 5 8 - 12 0 0
0 10 1 6 7 4 11 2 9 8 3 5 - 12 0 0
0 10 1 6 8 3 11 2 7 9 5 4 - 12 0 0
0 10 1 6 9 4 11 2 7 8 5 3 - 12 0 0
0 10 3 6 4 11 9 2 5 1 7 8 - 12 0 0
0 10 3 6 4 11 9 2 7 1 5 8 - 12 0 0
0 10 3 6 5 11 9 2 4 1 8 7 - 12 0 0
0 10 3 6 7 11 9 2 4 1 8 5 - 12 0 0
0 11 2 6 3 8 10 1 5 4 7 9 - 12 0 0
0 11 2 6 4 9 10 1 5 3 7 8 - 12 0 0
0 11 2 6 5 8 10 1 3 4 9 7 - 12 0 0
0 11 2 6 8 3 10 1 5 9 7 4 - 12 0 0
0 11 2 6 8 5 10 1 3 7 9 4 - 12 0 0
0 11 3 6 4 10 9 1 5 2 7 8 - 12 0 0
0 11 3 6 5 10 9 1 4 2 8 7 - 12 0 0
0 11 4 6 3 10 8 1 5 2 7 9 - 12 0 0
0 11 4 6 3 10 8 1 7 2 5 9 - 12 0 0
found 58 solutions.
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30th January 2018, 02:35 AM
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#96 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Woah Nellie is distinct enough to get in the door. With this and the last few series, I have to test more to see if there are hidden connections.
Code:
number of rows found: 30
removing near-duplicates...done
number of rows remaining: 30
mallalieu (0 1 7 2 4 8 6 3 11 5 10 9) (0 1 7 2 10 8 4 3 6 11 5 9)
(0 1 4 2 9 5 11 3 8 10 7 6)
(0 1 9 2 4 10 8 3 6 5 7 11) (0 2 3 9 10 6 7 1 5 8 4 11) (0 2 5 4 10 7 11 6 9 1 3 8)
(0 2 8 4 5 10 1 6 3 7 9 11) (0 3 2 6 4 5 10 9 11 7 1 8) (0 3 7 6 4 10 8 9 2 11 5 1)
row 1* (0 3 10 7 8 1 4 2 6 11 9 5) (0 4 6 10 7 3 11 1 8 2 5 9)
(0 3 8 10 7 11 5 1 4 2 9 6)
(0 4 7 8 1 11 9 3 10 5 6 2) (0 5 4 10 1 9 7 3 8 6 11 2) (0 5 8 10 4 1 11 3 7 9 2 6)
(0 5 11 10 8 4 6 3 7 1 2 9) (0 7 2 1 4 9 5 8 6 10 3 11) (0 7 3 2 5 10 6 9 1 8 11 4)
(0 7 4 2 11 1 6 10 9 5 3 8) (0 7 9 11 4 2 5 10 8 6 1 3) (0 8 2 3 5 10 7 11 6 1 4 9)
(0 8 5 3 6 1 7 11 10 2 4 9) (0 8 7 4 9 5 3 10 11 1 2 6) (0 9 1 6 11 10 5 3 2 8 4 7)
mof3 (0 9 2 6 1 11 7 3 4 10 5 8) (0 9 4 3 6 11 10 8 2 7 1 5)
(0 9 2 5 4 11 8 1 7 3 6 10)
(0 10 2 3 6 7 4 1 9 11 5 8) (0 10 2 7 11 9 4 3 1 8 5 6) (0 10 4 8 7 3 1 6 11 5 9 2)
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30th January 2018, 05:54 AM
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#97 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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theoretical nugget and some comments --
The end is in sight for candidates for dual-property rows. There are probably dozens rather than hundreds at this point. After that is exhausted, there is another pool of series which will be better permutation-shapes, but which won't have the power-residue property. Theoretical nugget for the day. Using the permutation square to create expansions of self-similar series, to see if we like any of the expansions. There are a bunch of ways to "expand" a self-similar series we like, usually at some loss of perfection, the exception being the perfect expanion five times, or 5m, and the related 7 (and 11, for inversion.) Today's way is to enter the series for expansion as the row and enter the expansion series derived from 2 ^ n mod 13 as the column. Translated into pitches, and using the perfect Mallalieu as starting-point: Code:
row: C,Db,E,D,A,F,B,Eb,Ab,Bb,G,F# col: C,Db,Eb,G,D,F,B,Bb,Ab,E,A,F#, dhv: C, Db, E, D, A, F, B, Eb, Ab, Bb, G, F# mallalieu original Db, Eb, A, F, F#, B, Bb, G, E, Ab, D, C 2x Eb, G, F#, B, C, Bb, Ab, D, A, E, F, Db 4x G, D, C, Bb, Db, Ab, E, F, F#, A, B, Eb 8x D, F, Db, Ab, Eb, E, A, B, C, F#, Bb, G 3x F, B, Eb, E, G, A, F#, Bb, Db, C, Ab, D 6x B, Bb, G, A, D, F#, C, Ab, Eb, Db, E, F Bb, Ab, D, F#, F, C, Db, E, G, Eb, A, B Ab, E, F, C, B, Db, Eb, A, D, G, F#, Bb E, A, B, Db, Bb, Eb, G, F#, F, D, C, Ab A, F#, Bb, Eb, Ab, G, D, C, B, F, Db, E F#, C, Ab, G, E, D, F, Db, Bb, B, Eb, A all columns are c,db,eb,g,d,f,b,bb,ab,e,a,f# rotations |
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31st January 2018, 04:39 AM
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#98 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Artists should only be middling smart -- like actresses or farmers. That way they can stay delighted with their paltry rags, their little toys.
Today's nuggets are two. -- Presumably you can always work backwards from the column results of an every-other square to produce the top line, the series. You can easily make well-formed patterns rather than relying on the results from other generation techniqes. Here's an example that I just made up. -- A different kind of self-similarity was called by Robert Morris "saturation". It's possible to set the harmonic filters to require rows that are highly saturated with certain cells that you specify. It will be possible to combine this kind of self-sim with the other kinds -- power-res pattern, mof, etc. Here, it turns out there are only 3 distinct series fully saturated with 014 and 015 cells: bad cells: ((3 0 3 6) (4 0 1 2)) maximum number of bad cells: 0 good cells: ((5 0 1 4) (5 0 3 4) (5 0 1 5) (5 0 4 5)) minimum number of good cells: 37 removing near-duplicates...done number of rows remaining: 3 (0 1 3 4 9 11 7 6 2 10 8 5) (0 1 5 8 4 9 11 6 7 2 10 3) (0 1 8 6 11 3 10 2 7 5 9 4) |
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31st January 2018, 06:19 AM
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#99 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Originally Posted by calebprime
The attentive reader will perceive that our task is now to generate all the models for columns, from bands of 3 intervals, then bands of 4 intervals, as in 1,2,3 and 2,3,4 and 3,4,5 etc., and 1,2,3,4, and 2,3,4,5, etc. This was trivially easy and lightening fast with microtonal scales. intervals 1,2,3: (0 1 3 4 6 7 9 11 2 5 8 10) (0 1 3 4 6 7 10 11 2 5 8 9) (0 1 3 4 6 8 9 11 2 5 7 10) (0 1 3 4 6 8 10 11 2 5 7 9) (0 1 3 4 7 8 10 11 2 5 6 9) (0 1 3 5 6 8 10 11 2 4 7 9) (0 1 3 5 7 9 11 2 4 6 8 10) (0 1 3 5 7 10 11 2 4 6 8 9) (0 1 3 5 8 9 11 2 4 6 7 10) (0 1 3 6 7 10 11 2 4 5 8 9) (0 1 3 6 8 9 11 2 4 5 7 10) intervals 2,3,4: (0 2 4 6 8 11 3 7 10 1 5 9) (0 2 4 6 9 11 3 7 10 1 5 8) (0 2 4 7 9 11 3 6 10 1 5 8) (0 2 4 7 10 1 5 8 11 3 6 9) (0 2 4 7 10 1 5 9 11 3 6 8) (0 2 4 7 11 3 6 8 10 1 5 9) (0 2 5 7 10 1 4 8 11 3 6 9) (0 2 5 8 10 1 4 7 11 3 6 9) etc. So now the task is to generate the corresponding series, then compile them into a searchable list. Generating the corr. series is just a fixed re-ordering of each column, I think, the reordering is I suppose technically derived from 2 ^ n mod 13 series, or something, but it's just working backwards. That is, take each new column number in order, and put it in the slot corresponding to this series: C,Db,Eb,G,D,F,B,Bb,Ab,E,A,F#, which is to say, put pitch 0,1,2,3,4,5,6,7,8,9,10,11 in slot 0,1,3,7,2,5,11,10,8,4,9,6, and Bob's your uncle. eta: this is a perverse way to notate it, using pitches for order-numbers, then 0 as the first number. works, though. |
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31st January 2018, 07:32 AM
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#100 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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rather than do every possibility, I'll do one or two of each, and then a handful of the last kind.
columns to be converted to self-similar series: number of rows remaining: 2 (0 1 3 4 6 8 9 11 2 5 7 10) (0 1 3 5 8 10 11 2 4 6 7 9) (0 2 4 6 9 11 3 7 10 1 5 8) (0 2 5 9 11 3 7 10 1 4 6 8) (0 3 6 10 1 5 9 2 7 11 4 8) (0 4 8 1 7 11 5 10 3 9 2 6) (0 5 10 3 8 1 7 2 9 4 11 6) (0 6 1 8 2 9 5 11 7 3 10 4) (0 7 2 10 5 1 9 6 3 11 8 4) (0 8 4 1 10 6 3 11 9 7 5 2) (0 8 4 1 10 7 5 3 11 9 6 2) (0 9 6 4 1 11 10 8 7 5 3 2) (0 9 7 5 4 2 11 10 8 6 3 1) have 7,8,9,10: number of rows remaining: 10 (0 7 2 9 5 1 10 6 4 11 8 3) (0 7 2 9 5 1 11 8 3 10 6 4) (0 7 2 10 5 1 8 4 11 9 6 3) (0 7 3 1 10 8 6 4 11 9 5 2) (0 7 3 10 8 5 1 11 9 6 4 2) (0 7 3 11 8 6 1 10 5 2 9 4) (0 7 4 1 11 9 5 3 10 8 6 2) (0 8 4 1 11 9 7 5 3 10 6 2) (0 8 4 11 9 6 3 1 10 7 5 2) (0 8 6 2 11 9 4 1 10 7 5 3) eta: This is working really well! Results to be posted soonish. |
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31st January 2018, 10:05 AM
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#101 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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As a generating technique, this is quick and flawless. I can't believe I didn't see this sooner.
However, the rows produced by these parameters so far seem less appealing than previous, so I don't regret finding those other series first. I'm going to look for ways to vary the formula so that the results seem better. Code:
c,db,f#,eb,f,g#,bb,e,d,g,b,a (0 1 3 4 6 8 9 11 2 5 7 10) c, db, f#, eb, f, g#, bb, e, d, g, b, a db, eb, g#, e, g, a, c, f#, f, bb, d, b eb, e, a, f#, bb, b, db, g#, g, c, f, d e, f#, b, g#, c, d, eb, a, bb, db, g, f f#, g#, d, a, db, f, e, b, c, eb, bb, g g#, a, f, b, eb, g, f#, d, db, e, c, bb a, b, g, d, e, bb, g#, f, eb, f#, db, c b, d, bb, f, f#, c, a, g, e, g#, eb, db d, f, c, g, g#, db, b, bb, f#, a, e, eb f, g, db, bb, a, eb, d, c, g#, b, f#, e g, bb, eb, c, b, e, f, db, a, d, g#, f# bb, c, e, db, d, f#, g, eb, b, f, a, g# C, Db, Ab, Eb, F#, Bb, A, F, E, G, D, B Db, Eb, Bb, F, G, B, C, Ab, F#, A, E, D Eb, F, B, Ab, A, D, Db, Bb, G, C, F#, E F, Ab, D, Bb, C, E, Eb, B, A, Db, G, F# Ab, Bb, E, B, Db, F#, F, D, C, Eb, A, G Bb, B, F#, D, Eb, G, Ab, E, Db, F, C, A B, D, G, E, F, A, Bb, F#, Eb, Ab, Db, C D, E, A, F#, Ab, C, B, G, F, Bb, Eb, Db E, F#, C, G, Bb, Db, D, A, Ab, B, F, Eb F#, G, Db, A, B, Eb, E, C, Bb, D, Ab, F G, A, Eb, C, D, F, F#, Db, B, E, Bb, Ab A, C, F, Db, E, Ab, G, Eb, D, F#, B, Bb (0 2 4 6 9 11 3 7 10 1 5 8) C, D, A, E, Db, B, Ab, F#, Bb, F, G, Eb D, E, B, F#, F, Eb, C, A, Db, Ab, Bb, G E, F#, Eb, A, Ab, G, D, B, F, C, Db, Bb F#, A, G, B, C, Bb, E, Eb, Ab, D, F, Db A, B, Bb, Eb, D, Db, F#, G, C, E, Ab, F B, Eb, Db, G, E, F, A, Bb, D, F#, C, Ab Eb, G, F, Bb, F#, Ab, B, Db, E, A, D, C G, Bb, Ab, Db, A, C, Eb, F, F#, B, E, D Bb, Db, C, F, B, D, G, Ab, A, Eb, F#, E Db, F, D, Ab, Eb, E, Bb, C, B, G, A, F# F, Ab, E, C, G, F#, Db, D, Eb, Bb, B, A Ab, C, F#, D, Bb, A, F, E, G, Db, Eb, B C, D, B, F, E, Eb, Ab, A, Db, Gb, Bb, G D, F, Eb, A, Gb, G, C, B, E, Ab, Db, Bb F, A, G, B, Ab, Bb, D, Eb, Gb, C, E, Db A, B, Bb, Eb, C, Db, F, G, Ab, D, Gb, E B, Eb, Db, G, D, E, A, Bb, C, F, Ab, Gb Eb, G, E, Bb, F, Gb, B, Db, D, A, C, Ab G, Bb, Gb, Db, A, Ab, Eb, E, F, B, D, C Bb, Db, Ab, E, B, C, G, Gb, A, Eb, F, D Db, E, C, Gb, Eb, D, Bb, Ab, B, G, A, F E, Gb, D, Ab, G, F, Db, C, Eb, Bb, B, A Gb, Ab, F, C, Bb, A, E, D, G, Db, Eb, B Ab, C, A, D, Db, B, Gb, F, Bb, E, G, Eb C, Eb, Db, F#, B, F, Ab, Bb, G, E, D, A Eb, F#, F, Bb, E, A, C, Db, B, Ab, G, D F#, Bb, A, Db, Ab, D, Eb, F, E, C, B, G Bb, Db, D, F, C, G, F#, A, Ab, Eb, E, B Db, F, G, A, Eb, B, Bb, D, C, F#, Ab, E F, A, B, D, F#, E, Db, G, Eb, Bb, C, Ab A, D, E, G, Bb, Ab, F, B, F#, Db, Eb, C D, G, Ab, B, Db, C, A, E, Bb, F, F#, Eb G, B, C, E, F, Eb, D, Ab, Db, A, Bb, F# B, E, Eb, Ab, A, F#, G, C, F, D, Db, Bb E, Ab, F#, C, D, Bb, B, Eb, A, G, F, Db Ab, C, Bb, Eb, G, Db, E, F#, D, B, A, F C, E, G, Ab, A, B, F#, Db, Eb, D, Bb, F E, Ab, B, Db, D, F, C, G, A, F#, Eb, Bb Ab, Db, F, G, F#, Bb, E, B, D, C, A, Eb Db, G, Bb, B, C, Eb, Ab, F, F#, E, D, A G, B, Eb, F, E, A, Db, Bb, C, Ab, F#, D B, F, A, Bb, Ab, D, G, Eb, E, Db, C, F# F, Bb, D, Eb, Db, F#, B, A, Ab, G, E, C Bb, Eb, F#, A, G, C, F, D, Db, B, Ab, E Eb, A, C, D, B, E, Bb, F#, G, F, Db, Ab A, D, E, F#, F, Ab, Eb, C, B, Bb, G, Db D, F#, Ab, C, Bb, Db, A, E, F, Eb, B, G F#, C, Db, E, Eb, G, D, Ab, Bb, A, F, B C, F, Ab, Bb, E, Db, Gb, Eb, A, B, D, G 5,3,2,6,9,5,9,6,2,3,5,5 F, Bb, Db, Eb, B, G, C, Ab, E, Gb, A, D Bb, Eb, G, Ab, Gb, D, F, Db, B, C, E, A 5,4,1,10,8,3,8,10,1,4,5,1 Eb, Ab, D, Db, C, A, Bb, G, Gb, F, B, E Ab, Db, A, G, F, E, Eb, D, C, Bb, Gb, B Db, G, E, D, Bb, B, Ab, A, F, Eb, C, Gb G, D, B, A, Eb, Gb, Db, E, Bb, Ab, F, C D, A, Gb, E, Ab, C, G, B, Eb, Db, Bb, F A, E, C, B, Db, F, D, Gb, Ab, G, Eb, Bb E, B, F, Gb, G, Bb, A, C, Db, D, Ab, Eb B, Gb, Bb, C, D, Eb, E, F, G, A, Db, Ab Gb, C, Eb, F, A, Ab, B, Bb, D, E, G, Db 5,5,5,5,5,6,7,7,7,7,7,6 C, F#, D, C#, D#, A, E, G#, G, Bb, B, F F#, C#, A, G#, Bb, F, C, D, D#, E, G, B C#, G#, F, D, E, B, F#, A, Bb, C, D#, G G#, D, B, A, C, G, C#, F, E, F#, Bb, D# D, A, G, F, F#, D#, G#, B, C, C#, E, Bb A, F, D#, B, C#, Bb, D, G, F#, G#, C, E F, B, Bb, G, G#, E, A, D#, C#, D, F#, C B, G, E, D#, D, C, F, Bb, G#, A, C#, F# G, D#, C, Bb, A, F#, B, E, D, F, G#, C# D#, Bb, F#, E, F, C#, G, C, A, B, D, G# Bb, E, C#, C, B, G#, D#, F#, F, G, A, D E, C, G#, F#, G, D, Bb, C#, B, D#, F, A C, G, F, D, B, Db, E, Bb, Eb, Ab, F#, A G, D, Db, Bb, Ab, A, C, F, B, E, Eb, F# D, Bb, A, F, E, F#, G, Db, Ab, C, B, Eb Bb, F, F#, Db, C, Eb, D, A, E, G, Ab, B F, Db, Eb, A, G, B, Bb, F#, C, D, E, Ab Db, A, B, F#, D, Ab, F, Eb, G, Bb, C, E A, F#, Ab, Eb, Bb, E, Db, B, D, F, G, C F#, Eb, E, B, F, C, A, Ab, Bb, Db, D, G Eb, B, C, Ab, Db, G, F#, E, F, A, Bb, D B, Ab, G, E, A, D, Eb, C, Db, F#, F, Bb Ab, E, D, C, F#, Bb, B, G, A, Eb, Db, F E, C, Bb, G, Eb, F, Ab, D, F#, B, A, Db C, Ab, Bb, E, G, F#, D, Db, A, F, B, Eb Ab, E, F#, Db, F, Eb, C, Bb, G, D, A, B E, Db, Eb, Bb, D, B, Ab, F#, F, C, G, A Db, Bb, B, F#, C, A, E, Eb, D, Ab, F, G Bb, F#, A, Eb, Ab, G, Db, B, C, E, D, F F#, Eb, G, B, E, F, Bb, A, Ab, Db, C, D Eb, B, F, A, Db, D, F#, G, E, Bb, Ab, C B, A, D, G, Bb, C, Eb, F, Db, F#, E, Ab A, G, C, F, F#, Ab, B, D, Bb, Eb, Db, E G, F, Ab, D, Eb, E, A, C, F#, B, Bb, Db F, D, E, C, B, Db, G, Ab, Eb, A, F#, Bb D, C, Db, Ab, A, Bb, F, E, B, G, Eb, F# C, Ab, Bb, E, A, G, D, Db, B, F#, Eb, F Ab, E, G, Db, F#, F, C, Bb, A, D, B, Eb E, Db, F, Bb, D, Eb, Ab, G, F#, C, A, B Db, Bb, Eb, G, C, B, E, F, D, Ab, F#, A Bb, G, B, F, Ab, A, Db, Eb, C, E, D, F# G, F, A, Eb, E, F#, Bb, B, Ab, Db, C, D F, Eb, F#, B, Db, D, G, A, E, Bb, Ab, C Eb, B, D, A, Bb, C, F, F#, Db, G, E, Ab B, A, C, F#, G, Ab, Eb, D, Bb, F, Db, E A, F#, Ab, D, F, E, B, C, G, Eb, Bb, Db F#, D, E, C, Eb, Db, A, Ab, F, B, G, Bb D, C, Db, Ab, B, Bb, F#, E, Eb, A, F, G C, A, E, G, Gb, D, Db, F, Ab, Eb, Bb, B A, G, D, F, Eb, B, C, E, Gb, Db, Ab, Bb G, F, B, E, Db, Bb, A, D, Eb, C, Gb, Ab F, E, Bb, D, C, Ab, G, B, Db, A, Eb, Gb E, D, Ab, B, A, Gb, F, Bb, C, G, Db, Eb D, B, Gb, Bb, G, Eb, E, Ab, A, F, C, Db B, Bb, Eb, Ab, F, Db, D, Gb, G, E, A, C Bb, Ab, Db, Gb, E, C, B, Eb, F, D, G, A Ab, Gb, C, Eb, D, A, Bb, Db, E, B, F, G Gb, Eb, A, Db, B, G, Ab, C, D, Bb, E, F Eb, Db, G, C, Bb, F, Gb, A, B, Ab, D, E Db, C, F, A, Ab, E, Eb, G, Bb, Gb, B, D C, Ab, B, Gb, G, A, Eb, D, Bb, F, C#, E Ab, Gb, A, D, F, E, C, B, G, Eb, Bb, C# Gb, D, E, B, Eb, C#, Ab, A, F, C, G, Bb D, B, C#, A, C, Bb, Gb, E, Eb, Ab, F, G B, A, Bb, E, Ab, G, D, C#, C, Gb, Eb, F A, E, G, C#, Gb, F, B, Bb, Ab, D, C, Eb E, C#, F, Bb, D, Eb, A, G, Gb, B, Ab, C C#, Bb, Eb, G, B, C, E, F, D, A, Gb, Ab Bb, G, C, F, A, Ab, C#, Eb, B, E, D, Gb G, F, Ab, Eb, E, Gb, Bb, C, A, C#, B, D F, Eb, Gb, C, C#, D, G, Ab, E, Bb, A, B Eb, C, D, Ab, Bb, B, F, Gb, C#, G, E, A |
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1st February 2018, 08:38 AM
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#102 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Thanks to Worm, I was able to convert my columns into top rows without having to do it by hand.
I wanted to share the results of my first search of all this data: The best of the best of the best. number of rows remaining: 4 (0 3 4 6 11 7 9 1 8 2 5 10) (0 1 10 5 3 2 8 9 11 4 7 6) (0 1 8 4 11 3 9 5 10 2 7 6) (0 2 11 4 3 1 7 9 10 5 8 6) When I return, some discussion. First impression: One of these is well-known. The others I don't see why they're so great. And that, actually, is typical for this kind of work, and it's also why I don't regret starting from power-residue series. |
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1st February 2018, 10:50 AM
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#103 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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row of the day:
Code:
(0 3 4 6 11 7 9 1 8 2 5 10) Turn of the Worm C,Eb,E,F#,B,G,A,C#,G#,D,F,Bb C, Eb, E, F#, B, G, A, C#, G#, D, F, Bb 3,1,2,5,8,2,4,7,6,3,5,2 [1,2,3,4,5,6,7,8] Eb, F#, G, C#, D, Bb, C, E, B, A, G#, F 3,1,6,1,8,2,4,7,10,11,9,10 [1,2,3,4,6,7,8,9,10,11] F#, C#, Bb, E, A, F, Eb, G, D, C, B, G# 7,9,6,5,8,10,4,7,10,11,9,10 [4,5,6,7,8,9,10,11] C#, E, F, G, C, G#, F#, Bb, A, Eb, D, B 3,1,2,5,8,10,4,11,6,11,9,2 [1,2,3,4,5,6,8,9,10,11] E, G, G#, Bb, Eb, B, C#, F, C, F#, A, D 3,1,2,5,8,2,4,7,6,3,5,2 [1,2,3,4,5,6,7,8] G, Bb, B, F, F#, D, E, G#, Eb, C#, C, A Bb, F, D, G#, C#, A, G, B, F#, E, Eb, C F, G#, A, B, E, C, Bb, D, C#, G, F#, Eb G#, B, C, D, G, Eb, F, A, E, Bb, C#, F# B, D, Eb, A, Bb, F#, G#, C, G, F, E, C# D, A, F#, C, F, C#, B, Eb, Bb, G#, G, E A, C, C#, Eb, G#, E, D, F#, F, B, Bb, G 3,3,7,3,3,7,3,3,3,7,3 |
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1st February 2018, 11:16 AM
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#104 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Turn of the Worm seems to be distinct.
Code:
number of rows found: 31
removing near-duplicates...done
number of rows remaining: 31
mallalieu (0 1 7 2 4 8 6 3 11 5 10 9) (0 1 7 2 10 8 4 3 6 11 5 9)
(0 1 4 2 9 5 11 3 8 10 7 6)
(0 1 9 2 4 10 8 3 6 5 7 11) (0 2 3 9 10 6 7 1 5 8 4 11) (0 2 5 4 10 7 11 6 9 1 3 8)
(0 2 8 4 5 10 1 6 3 7 9 11) (0 3 2 6 4 5 10 9 11 7 1 8) (0 3 4 6 11 7 9 1 8 2 5 10)
(0 3 7 6 4 10 8 9 2 11 5 1) row 1* (0 3 10 7 8 1 4 2 6 11 9 5)
(0 3 8 10 7 11 5 1 4 2 9 6)
(0 4 6 10 7 3 11 1 8 2 5 9) (0 4 7 8 1 11 9 3 10 5 6 2) (0 5 4 10 1 9 7 3 8 6 11 2)
(0 5 8 10 4 1 11 3 7 9 2 6) (0 5 11 10 8 4 6 3 7 1 2 9) (0 7 2 1 4 9 5 8 6 10 3 11)
(0 7 3 2 5 10 6 9 1 8 11 4) (0 7 4 2 11 1 6 10 9 5 3 8) (0 7 9 11 4 2 5 10 8 6 1 3)
(0 8 2 3 5 10 7 11 6 1 4 9) (0 8 5 3 6 1 7 11 10 2 4 9) (0 8 7 4 9 5 3 10 11 1 2 6)
(0 9 1 6 11 10 5 3 2 8 4 7) mof3 (0 9 2 6 1 11 7 3 4 10 5 8)
(0 9 2 5 4 11 8 1 7 3 6 10)
(0 9 4 3 6 11 10 8 2 7 1 5) (0 10 2 3 6 7 4 1 9 11 5 8) (0 10 2 7 11 9 4 3 1 8 5 6)
(0 10 4 8 7 3 1 6 11 5 9 2)
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1st February 2018, 12:11 PM
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#105 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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For varwoche, we'd love to be able to enter rows as entire strings, like
0 1 7 2 4 8 6 3 11 5 10 9 integers 0 to 11 with spaces and have the program output a string that i can grab with one motion ----- eta: if the program is only re-ordering symbols and doesn't care about values, then it would great to have it be able to re-order any arbitrary symbols, so I can do pitches (c, c#) for my own self |
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1st February 2018, 02:08 PM
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#106 |
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Penultimate Amazing
Join Date: Feb 2004
Location: Puget Sound
Posts: 11,273
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Originally Posted by calebprime
(a b c ...) I can fix that though. add: expectation of parens removed |
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__________________
To survive election season on a skeptics forum, one must understand Hymie-the-Robot.
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2nd February 2018, 04:19 AM
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#107 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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https://docs.google.com/spreadsheets...YRQ/edit#gid=0
This should be a link to varwoche's latest version of the "column-to-row converter". What this convertor does is let you specify a string that is intuitive as a pattern of self-similarity, and converts it to a string that is a self-similar 12-tone row with that pattern of self-similarity. The numbers you specify are some reasonable set of picks-and-skips that pick all 12 tones of the chromatic scale eventually. A classic-and-so-simple-that-it's-stupid-example of picks is 0,1,2,3,4,5,6,7,8,9,10,11. This gives the classic Mallalieu series, in varwoche's converter. Assigning those numbers to pitches, we can type in a chromatic scale and get back out Mallalieu: C C# D D# E F F# G G# A A# B gives back C C# E D A F B D# G# A# G F#. If we pop the new Mallalieu string above into our every-other-square generator (or do it by hand) we get the classic perfect Mallalieu every-other square: Code:
0, 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6 1, 2, 5, 3, 10, 6, 0, 4, 9, 11, 8, 7 2, 3, 6, 4, 11, 7, 1, 5, 10, 0, 9, 8 3, 4, 7, 5, 0, 8, 2, 6, 11, 1, 10, 9 4, 5, 8, 6, 1, 9, 3, 7, 0, 2, 11, 10 5, 6, 9, 7, 2, 10, 4, 8, 1, 3, 0, 11 6, 7, 10, 8, 3, 11, 5, 9, 2, 4, 1, 0 7, 8, 11, 9, 4, 0, 6, 10, 3, 5, 2, 1 8, 9, 0, 10, 5, 1, 7, 11, 4, 6, 3, 2 9, 10, 1, 11, 6, 2, 8, 0, 5, 7, 4, 3 10, 11, 2, 0, 7, 3, 9, 1, 6, 8, 5, 4 11, 0, 3, 1, 8, 4, 10, 2, 7, 9, 6, 5 row: C,C#,E,D,A,F,B,Eb,Ab,Bb,G,F# col: . dhv: C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F# C#, D, F, Eb, Bb, F#, C, E, A, B, Ab, G D, Eb, F#, E, B, G, C#, F, Bb, C, A, Ab Eb, E, G, F, C, Ab, D, F#, B, C#, Bb, A E, F, Ab, F#, C#, A, Eb, G, C, D, B, Bb F, F#, A, G, D, Bb, E, Ab, C#, Eb, C, B F#, G, Bb, Ab, Eb, B, F, A, D, E, C#, C G, Ab, B, A, E, C, F#, Bb, Eb, F, D, C# Ab, A, C, Bb, F, C#, G, B, E, F#, Eb, D A, Bb, C#, B, F#, D, Ab, C, F, G, E, Eb Bb, B, D, C, G, Eb, A, C#, F#, Ab, F, E B, C, Eb, C#, Ab, E, Bb, D, G, A, F#, F |
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2nd February 2018, 04:38 AM
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#108 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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How Every-Other Square-Type Struct. Duz A Cool Trick
Imagine that our series are numbers attached to 12 spokes on a wheel, and we're turning the wheel fast enough that the pitches are going by as fast as we could possibly hear or distinguish or perform them:
C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F#, R, C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F#, R, C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F#, R, C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F#, R, C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F#, R, C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F#, R, C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F#, R, C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F#, R, C, C#, E, D, A, F, B, Eb, Ab, Bb, G, F#, R, Now imagine that instead of each spoke triggering an audible note, we're only hearing every nth spoke of our wheel, say every 7th: B, C, Eb, C#, Ab, E, Bb, etc. What do we hear? We hear our theme, at a rate of speed of 1/7th, and in a certain key. If our wheel is going fast enough, get this: We can specify any arbitary polyrythmic relation between any number of parts, in ratios of, say, 99:97:83:53:32:17:9:5:2 -- any arbitrary monstrosity of a polyrhythm. Any combination of these parts will be the theme, and the whole will be the theme. That is, the combination of the parts always adds up something like the overall 12-tone ostinato-wheel. Next post: a link to a piece of music that does that, so at least there's something concrete here. It's uploading as I type. So, the question of what trick-wheels we can come up with, and to what musical ends, becomes important if we want to hear all this. |
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2nd February 2018, 04:45 AM
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#109 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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https://app.box.com/s/r1y98pl8xsv109y3rqqzuu6z3iermdw3
This should be a piece that generates almost all the pitches with this rapidly-revolving wheel technique. I used a fairly perfect self-similar series derived from 3 ^ n mod 17. The net effect is that there are nice cross-rhythms and hocketing between parts all of which the whole "system" gives the composer for free, so to speak. (Not free, you have to figure this stuff out and enter it in.) Gy-Rah sez: Listen to my works, Ye Missie Lynda Barry, and despair! Here's Spinning Wheel, by BS & T in an astonishing arrangement https://www.youtube.com/watch?v=SFEewD4EVwU Someone is waiting just for you Spinnin' wheel, spinnin' true Drop all your troubles by the riverside Catch a painted pony on the spinning wheel ride |
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3rd February 2018, 04:50 AM
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#110 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Grr lost my post.
The gist was that this little advance adds another tool but doesn't crack the problem. We're still generating a list of likely suspects by indirect means. This latest list has lots of ugly examples. Today's poem, therefore: O'er the wires the electric message came, "He is no better; he is much the same." and today's series: Code:
Prince of Wales C, E, F#, G#, A, B, G, Db, Eb, D, Bb, F ** better E, G#, B, Db, D, F, C, F#, A, G, Eb, Bb G#, Db, F, F#, G, Bb, E, B, D, C, A, Eb Db, F#, Bb, B, C, Eb, G#, F, G, E, D, A F#, B, Eb, F, E, A, Db, Bb, C, G#, G, D B, F, A, Bb, G#, D, F#, Eb, E, Db, C, G F, Bb, D, Eb, Db, G, B, A, G#, F#, E, C Bb, Eb, G, A, F#, C, F, D, Db, B, G#, E Eb, A, C, D, B, E, Bb, G, F#, F, Db, G# A, D, E, G, F, G#, Eb, C, B, Bb, F#, Db D, G, G#, C, Bb, Db, A, E, F, Eb, B, F# G, C, Db, E, Eb, F#, D, G#, Bb, A, F, B 4,4,5,5,5,6,5,5,6,5,5,5 |
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3rd February 2018, 02:10 PM
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#111 |
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Mistral, mistral wind...
Join Date: Aug 2013
Posts: 3,736
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Originally Posted by calebprime
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__________________
I'm tired of the bombs, tired of the bullets, tired of the crazies on TV; I'm the aviator, a dream's a dream whatever it seems Deep Purple- "The Aviator" Life was a short shelf that came with bookends- Stephen King |
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4th February 2018, 03:32 AM
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#112 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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I neglected to give much of description of that piece. I think adequate description by the maker can tell some potential listener whether she should bother listening. It should give length, basic process and intent, basic materials, and maybe some hint of how the maker feels about it.
Without an adequate frame provided by the composer, or by the listener who just happened to know already what to expect, the listener is forced into an unfamiliar and uncongenial role as some kind of critic. I've seen this many many times with my work and with other people's work and it's not very interesting. That is to say, every modernist piece ever written will fail if something entirely different is wanted from the git-go. Anyway, this piece is about 12 minutes, and it's very mechanical, very quantized, and very MIDI sounding. It's not bored, boring, excited or exciting, in my view, nor was it intended to be. It also took a fair amount of work, it realizes the idea pretty well, it has all kinds of payoffs and rewards for a listener who can get them. I'm proud of it. The payoffs are getting the relation of the cross-rhythms, and how the listener is forced to hear all those rhythms grouped in multiples of 4 when they're not in 4 at all, causing him to hear syncopations or staggerings. The roll of cowbell is played by a flanged cymbal sample that pans around. If you get off on hearing rhythmic design and have some patience, this piece has rewards. One of them is hearing the slow changes in the chord-scales in the midst of this busy texture. Another is the cutaway effects where the underlying structures are revealed. There are also strange interactions between the parts later on: There might be an effect there of interest for future compositions. If I had to do it over I'd be more careful not to put tacky timbres like sampled banjo right up front. It's basically a cold and serious piece that should please by its design, not by casualness. Sounds like that mislead the listener about the intent. I've composed thousands of pieces and sold them, so I have a good idea of what people like, how they listen, and where this stands in terms of craft. To me this piece is more successful than just a proof of concept. But oddly enough, the fact that it is one of my more substantial and perfect of pieces has won it few admirers. My circle of critics is tiny but I trust the consensus. This piece is sort of perfect aside from the tacky timbres or two, but it's never going to be a beloved favorite. |
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4th February 2018, 03:48 AM
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#113 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Today's self-similar series: "0137".
Code:
0137 row: C,Db,G,Eb,F#,A,Bb,F,E,Ab,D,B col: . dhv: C, Db, G, Eb, F#, A, Bb, F, E, Ab, D, B Db, Eb, A, F, Ab, B, C, G, F#, Bb, E, D Eb, F, B, G, Bb, D, Db, A, Ab, C, F#, E F, G, D, A, C, E, Eb, B, Bb, Db, Ab, F# G, A, E, B, Db, F#, F, D, C, Eb, Bb, Ab A, B, F#, D, Eb, Ab, G, E, Db, F, C, Bb B, D, Ab, E, F, Bb, A, F#, Eb, G, Db, C D, E, Bb, F#, G, C, B, Ab, F, A, Eb, Db E, F#, C, Ab, A, Db, D, Bb, G, B, F, Eb F#, Ab, Db, Bb, B, Eb, E, C, A, D, G, F Ab, Bb, Eb, C, D, F, F#, Db, B, E, A, G Bb, C, F, Db, E, G, Ab, Eb, D, F#, B, A |
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4th February 2018, 05:19 AM
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#114 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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With no restrictions, there are are around five hundred thousand series that have a complete self-similar orbit in a restricted number of steps -- 2 to 5 spaces.
500k gets boiled down very quickly to a mere dozen if we add some harmonic restrictions, prohibit self-identical series, and require that it be a double MOF, tighten the spacing to be 2 to 4. |
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5th February 2018, 04:28 AM
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#115 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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This search got it down to 3 already-named series, one of which we have in our little collection already.
For today, I think I'll just include the other two in our collection and do the bookkeeping from the last few series, explicitly check for retrogrades. Next post will do that. |
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5th February 2018, 04:41 AM
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#116 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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It's a good thing I'm doing this simple housekeeping, it looks like most recent series are too close to being dupes. The number of series should be 35 if I didn't have some work to do removing redundant series, I guess 3 of them.
Code:
number of rows found: 36
removing near-duplicates...done
number of rows remaining: 32
(0 1 9 2 4 10 8 3 6 5 7 11) (0 8 7 4 9 5 3 10 11 1 2 6) (0 2 3 9 10 6 7 1 5 8 4 11)
(0 3 4 6 11 7 9 1 8 2 5 10) (0 8 2 3 5 10 7 11 6 1 4 9) mof6B*
(0 1 3 9 4 7 11 2 10 5 8 6)
(0 2 8 4 5 10 1 6 3 7 9 11) mallalieu (0 10 2 3 6 7 4 1 9 11 5 8)
(0 1 4 2 9 5 11 3 8 10 7 6)
(0 3 7 6 4 10 8 9 2 11 5 1) (0 4 7 8 1 11 9 3 10 5 6 2) (0 3 2 6 4 5 10 9 11 7 1 8)
(0 3 10 7 8 1 4 2 6 11 9 5) (0 1 7 2 4 8 6 3 11 5 10 9) (0 9 2 6 1 11 7 3 4 10 5 8)
(0 1 7 2 10 8 4 3 6 11 5 9) (0 10 2 7 11 9 4 3 1 8 5 6) (0 7 2 1 4 9 5 8 6 10 3 11)
(0 5 11 10 8 4 6 3 7 1 2 9) (0 7 9 11 4 2 5 10 8 6 1 3) (0 2 5 4 10 7 11 6 9 1 3 8)
(0 4 6 10 7 3 11 1 8 2 5 9) (0 8 5 3 6 1 7 11 10 2 4 9) (0 5 8 10 4 1 11 3 7 9 2 6)
(0 7 4 2 11 1 6 10 9 5 3 8) row 1* mof3
(0 3 8 10 7 11 5 1 4 2 9 6) (0 9 2 5 4 11 8 1 7 3 6 10)
(0 5 4 10 1 9 7 3 8 6 11 2) (0 7 3 2 5 10 6 9 1 8 11 4) (0 9 1 6 11 10 5 3 2 8 4 7)
(0 9 4 3 6 11 10 8 2 7 1 5) (0 10 4 8 7 3 1 6 11 5 9 2)
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5th February 2018, 04:49 AM
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#117 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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The following series are banned from the club as being too much like other series.
(0 1 7 3 6 9 10 5 4 8 2 11) aka "0137" (0 2 6 9 7 10 3 1 8 5 11 4) aka "mof5" (0 4 6 8 9 11 7 1 3 2 10 5) aka "Prince of Wales" |
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6th February 2018, 05:28 AM
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#118 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Today's series are a pair, neither of which have the every-other kind of self-sim that I'm aware.
As a substitute for that, they are both self-identical at every fifth note. Now, you don't hear a series and say wow, that's self-identical at the inversion rotated 6 six degrees at every fifth note. What you might hear is a composed passage in a piece of music in which a series unfolds at 2 or more rates of speed -- there are groups of 5 notes, and then there is a slower line of 1 note every 5 notes that turns out to sound very much like the 5-note groups. The composer must make the connection clear if she wants anyone to care about the property of the row. The property is hidden but very hearable if brought out. If not brought out, there was no reason to select that row -- why, because it had an awesome hidden property?* I'm calling the pair of these 5p/i/7/6 and 5p/i/7/2. The first one is also self-identical in an esoteric 5m (the program calls it 5x) way. * Conclusions like this might be obvious except I've made this very mental mistake in the past -- fetishizing or just being impressed by some abstruse row properties. If you don't use them, they're not worth anything. |
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6th February 2018, 08:01 AM
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#119 |
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Penultimate Amazing
Join Date: Feb 2004
Location: Puget Sound
Posts: 11,273
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Originally Posted by calebprime
* * * What would make the re-order thingy more usable? Please don't be shy to tell me. I want the satisfaction of making it useful. |
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__________________
To survive election season on a skeptics forum, one must understand Hymie-the-Robot.
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7th February 2018, 02:52 AM
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#120 |
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moleman
Join Date: Jul 2006
Posts: 12,158
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Thanks, varwoche, that really means a lot.
As for the re-order thingy. Well, if you insist! Lessee: -- Any re-ordering is possible, user just enters the numbers. (done) -- Will re-order 1-series input iteratively, number of times specified by user, or until the output loops (matches input). It takes the output that was the re-ordered input, and re-orders that, and prints it if it's different from input or other outputs in group. Probably with the current re-ordering, there are only a pair of series, because two re-orderings gets you back to the beginning. -- Will do one re-ordering on a list of series This is really the deluxe version that I can imagine! |
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