Generator-offset property: Difference between revisions
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(1) and (2) were proved in the proof of Prop 1. (3) is easy to check using (1). | (1) and (2) were proved in the proof of Prop 1. (3) is easy to check using (1). | ||
=== Theorem 4 (PWF | === Theorem 4 (Classification of PWF scales) === | ||
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. | 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 ==== | ||