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Posted by caleb "quixotic" morgan This is just one of many series that I happen to like. 39 ^ n mod 59: raw values of 1st 12 indices: if we rank these numbers from lowest (0) to highest (11), we get: 11 1 5 3 0 7 4 6 10 2 8 9 transposed, and notated in pitch-classes: C D F# E C# G# F G B Eb A Bb Supposing we align this series with every other note starting on the second note. C D F# E C# G# F G B Eb A Bb And write down the intervals when the these two series are aligned: 2 2 2 3 2 2 7 11 2 2 2 11 there is a strong resemblance between the two series. Supposing we take every 3rd note of 39 ^ n mod 59, starting on the 3rd note: C D F# E C# G# F G B Eb A Bb 6 6 5 6 1 5 2 2 1 1 8 5 again, there is a resemblance, but less explicit. The useful thing about these series is that--in a sense--they generate their own variations of themselves under permutation. The Mac program Serial Composer, written by the brilliant Tuukka Ilomaki, will find self-similar series, but only under strict rules and only with certain patterns. The formula I’m describing above gets around that limitation. For anyone who’s interested, I can e-mail you a custom calculator and an extensive data-base of series that have been organized and cross-referenced to some extent. This is an ongoing, big project. Probably never to be completed.
on 9/27/2006, 6:54 am, in reply to "mallalieu & self-sim series"
68.166.234.51
Here’s one example of the “fuzzy” self-similarity produced by the indices of discrete logarithms.
58 11 28 22 8 39 24 33 56 19 43 50
D E G# G Eb Bb C F# C# F B A
F# g# b a# d c# g a c e f eb
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