User:Inthar/MV3: Difference between revisions
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=== Lemma 2: Sizes of chunks of any fixed letter form a MOS (except in the case "XYZYX") === | === Lemma 2: Sizes of chunks of any fixed letter form a MOS (except in the case "XYZYX") === | ||
TODO: account for case XYZYX. | |||
WOLOG consider chunks of X. Use Q for both Y and Z. | WOLOG consider chunks of X. Use Q for both Y and Z. | ||
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''To be continued...'' | ''To be continued...'' | ||
=== Finishing the proof === | |||
We now prove that except in the case XYXZXYX, if the scale is pairwise well-formed, the scale is generated by alternating generators. | |||
== MV3 Theorem 2 == | == MV3 Theorem 2 == | ||
''Once you have chosen a rank-3 temperament and a specific generator interval, there is a mechanical procedure to generate all max-variety-3 scales of a certain size (of which there are, however, infinitely many).'' | ''Once you have chosen a rank-3 temperament and a specific generator interval, there is a mechanical procedure to generate all max-variety-3 scales of a certain size (of which there are, however, infinitely many).'' | ||