Generator-offset property: Difference between revisions
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=== Theorem 4 (Classification of PWF scales) === | === Theorem 4 (Classification of PWF scales) === | ||
Let ''S'' be a | Let ''S''(a, b, c) be a scale word in three '''Z'''-linearly independent step sizes a, b, c. Suppose ''S'' is PWF. Then ''S'' is SV3 and has an odd number of notes. Moreover, ''S'' is either GO or equivalent to the scale word abacaba. | ||
==== Proof ==== | ==== Proof ==== | ||
===== If the generator of a projection of ''S'' is a ''k''-step, the word of stacked ''k''-steps in ''S'' is PWF ===== | ===== If the generator of a projection of ''S'' is a ''k''-step, the word of stacked ''k''-steps in ''S'' is PWF ===== | ||