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Posted by Caleb Morgan 147 01857B92A43601857B92A436 (Also, x-swap of 5p (every 5th note) = 5M) (mof: 7/5) This is a series that Mead calls "remarkable" in his Lempel-Golomb Costas log 1-2^n mod 13: 2^n mod 13: 2,4,8,3,6,12,11,9,5,10,7,1 1-2, 1-4, 1-8, 1-3, 1-6, etc. mod 13: 12,10,6,11,8,2,3,5,9,4,7,(0) log of this: 6,10,5,7,3,1,4,9,8,2,11,(0) pc's: f#,a#,f,g,d#,c#,e,a,g#,d,b,(c) intervals: 4,7,2,8,10,3,5,11,6,9,1,6 (all-interval series) ---------------------------------------------- And, here's a Multiple-Order (or self-similar) series I really like that has a 5-note motive reproduced in 11 different places in the main matrix! Plus it's got all kinds of tonal associations! 1. start with limited-interval series: 2.2.3.3.5.2.3.3.2.5.3.3 2. transpose up a minor third, so start on Eb. 3. Do cyclical perm with chromatic scale: 0 1 2 3 4 5 6 7 8 9 A B 0 3 A 9 4 1 5 6 8 2 7 B then do "X-swap" or index swap: 3 5 7 A 1 6 8 B 2 4 9 0 B 4 8 0 9 1 5 2 6 A 3 7 rotate and transpose to C starting note: final result: C, Eb, Db, Ab, G, E, F, Bb, D, F#, A, B intervals: 3 10 7 11 9 1 5 4 4 3 2 1 (good variety) The 5-note motif c-eb-db-ab-g is present in eleven different places (if you skip up to 5 notes and wrap around) in the main matrix. Think Spinal Tap. Eleven! p/11/2: C,G,F#,D#,E,A,C#,F,Ab,Bb,B,D p/6/9: C,Eb,F,F#,A,G,D,C#,A#,B,E,Ab r/2/4: C,G,F#,A,Bb,Eb,F,D,C#,B,Ab,E r/4/8: C,F,G,E,Eb,C#,A#,F#,D,A,Ab,B r/9/10: C,A,Ab,F#,Eb,B,G,D,C#,E,F,Bb i/1/2: C,F,F#,A,G#,D#,B,G,E,D,C#,Bb i/7/4: C,Eb,D,A,F,C#,Bb,Ab,G,E,F#,B i/6/9: C,A,G,F#,Eb,F,Bb,B,D,C#,G#,E i/11/11: C,B,Ab,Bb,Eb,E,G,F#,C#,A,F,D ri/9/1: C,Eb,G,B,E,F,D,C#,G#,F#,A,Bb ri/3/10: C,Eb,E,F#,A,C#,F,Bb,B,G#,G,D I've looked at a lot of these MOFS, and eleven is one of the highest counts I've seen. This limited-interval cycle (2.2.3.3.5.2.3.3.2.5.3.3) seems to produce many good MOFS with lots of triads (which I like), good harmonic fields, and good interval variety. -CM
on 10/17/2006, 6:13 am
68.166.233.235
Here's the famous all-interval series #147: (using Morris
numbering)
C,Db,Ab,F,G,B,A,D,Bb,E,Eb,F#,C,Db,Ab,F,G,B,A,D,Bb,E,Eb,F#
1,7,9,2,4,10,5,8,6,11,3,6,1,7,9,2,4,10,5,8,6,11,3,6
11,5,3,10,8,2,7,4,6,1,9,6,11,5,3,10,8,2,7,4,6,1,9,6
7,1,3,2,4,10,11,8,6,5,9,6,7,1,3,2,4,10,11,8,6,5,9,6
5,11,9,10,8,2,1,4,6,7,3,6,5,11,9,10,8,2,1,4,6,7,3,6,
"Isomorphism" articles.
Construction:
or: C,D,E,G,Bb,Eb,F,Ab,B,C#,F#,A
3 5 7 A 1 6 8 B 2 4 9 0
0 1 2 3 4 5 6 7 8 9 A B
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