Bipentatonic scale: Difference between revisions
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== Abstract dipentatonic scales == | == Abstract dipentatonic scales == | ||
=== Dipentatonic mosses === | === Dipentatonic mosses === | ||
The degenerate case of a dipentatonic mos is 5L 5s, where the interleaved pentatonic is 5edo. The nondegenerate cases are: | |||
* 1L 9s: Lsssssssss (pentatonic 1L 4s) | |||
* 2L 8s: LssssLssss (pentatonic 2L 3s) | |||
* 3L 7s: LssLssLsss (pentatonic 3L 2s) | |||
* 4L 6s: LsLssLsLss (pentatonic 4L 1s) | |||
* 6L 4s: LLsLsLLsLs (pentatonic 1L 4s) | |||
* 7L 3s: LLLsLLsLLs (pentatonic 2L 3s) | |||
* 8L 2s: LLLLsLLLLs (pentatonic 3L 2s) | |||
* 9L 1s: LLLLLLLLLs (pentatonic 4L 1s) | |||
=== Dipentatonic rank-3 scale patterns === | === Dipentatonic rank-3 scale patterns === | ||
A rank-3 dipentatonic scale with step sizes ''5x ay (5-a)z'' has the form ''xYxYxYxYxY'' where the ''Y'''s are the ''y'' and ''z'' arranged in the [[MOS]] pattern ay (5-a)z. The interlocking pentatonics are copies of the mos ''aL (5-a)s'' if ''y > z'' and ''(5-a)L as'' if ''z > y''. The following is a complete list of such abstract patterns, assuming octave equivalence: | A rank-3 dipentatonic scale with step sizes ''5x ay (5-a)z'' has the form ''xYxYxYxYxY'' where the ''Y'''s are the ''y'' and ''z'' arranged in the [[MOS]] pattern ay (5-a)z. The interlocking pentatonics are copies of the mos ''aL (5-a)s'' if ''y > z'' and ''(5-a)L as'' if ''z > y''. The following is a complete list of such abstract patterns, assuming octave equivalence: | ||