Originally Posted by
calebprime
Indeed, there are small variations produced by rotating the series when they are n-1 orbits.
After I look at the best ones more closely, I'll choose one. One problem is that they will be mapped to diatonic scales (2 octaves of 7+7 notes), so I can't just look at these numbers and hear what they sound like. What I do know is that I want to avoid something that is really essentially the same as the Mallalieu (or 2 ^ n
mod 13) series, simply because Robert Morris already wrote a piece based on that, and, my work has been about trying to find alternatives. Not because Mall is not a good series, but because I want to know if there is wiggle room. Can the alternatives -- all less than perfect -- also generate equally good pieces?
The best candidate series for my next piece. I've quickly grouped them together by basic likeness, but more work needs to be done.
If they all have a disguised but clear family resemblance to Mall, then today's work will have been in vain. (I will have learned something.)
12 2 0 7 3 9 1 6 8 5 4 13 10 11
1 4 2 9 5 11 3 8 10 7 6 13 12 0
2 5 3 10 6 12 4 9 11 8 7 13 0 1
3 6 4 11 7 0 5 10 12 9 8 13 1 2
6 9 7 1 10 3 8 0 2 12 11 13 4 5 these are just inversions of top group
7 10 8 2 11 4 9 1 3 0 12 13 5 6
9 12 10 4 0 6 11 3 5 2 1 13 7 8
10 0 11 5 1 7 12 4 6 3 2 13 8 9
11 1 12 6 2 8 0 5 7 4 3 13 9 10
0 9 5 3 8 2 1 13 10 11 6 12 4 7
12 8 4 2 7 1 0 13 9 10 5 11 3 6
11 7 3 1 6 0 12 13 8 9 4 10 2 5
6 3 11 5 10 9 13 0 1 7 2 4 8 12
This one is AIS #12 plus a couple notes, which would suit me ok -- it's not Mall.
012 0137584A92B60137584A92B6 MOF count: 7/8*
C,Db,Eb,G,F,Ab,E,Bb,A,D,B,F#,C,Db,Eb,G,F,Ab,E,Bb,A ,D,B,F#
1,2,4,10,3,8,6,11,5,9,7,6,1,2,4,10,3,8,6,11,5,9,7, 6
11,10,8,2,9,4,6,1,7,3,5,6,11,10,8,2,9,4,6,1,7,3,5, 6
5,10,8,2,3,4,6,7,1,9,11,6,5,10,8,2,3,4,6,7,1,9,11, 6
7,2,4,10,9,8,6,5,11,3,1,6,7,2,4,10,9,8,6,5,11,3,1, 6 (perfect 6-note mof: every-other note = every note)
This other group of series is not an all-interval series, and has no resemblance to Mall.
0 9 5 3 8 2 1 13 10 11 6 12 4 7
12 8 4 2 7 1 0 13 9 10 5 11 3 6
11 7 3 1 6 0 12 13 8 9 4 10 2 5
So, now I have two prospects to play around with and get into a little deeper.