Originally Posted by
calebprime
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I have to understand why this is. Otherwise I'm just chasing my tail.
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It's an opportunity to move the non-matching part of the self-similarity to the end of the series, where it's least audible. (?)
But, to my surprise, each result is different, not merely a rotation of the other results. (?!)
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