Rank-3 scale theorems: Difference between revisions
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# (k-1) g1 + (k-1) g2 + g3, | # (k-1) g1 + (k-1) g2 + g3, | ||
if a step is an odd number of generators (since the scale size is odd, we can always ensure this by taking octave complements of all the generators). The first two sizes must occur the same number of times. | if a step is an odd number of generators (since the scale size is odd, we can always ensure this by taking octave complements of all the generators). The first two sizes must occur the same number of times. | ||
(The above holds for any odd n >= 3.) | |||
This proof shows that AG and unconditionally-MV3 scales must have odd size or size 4. | This proof shows that AG and unconditionally-MV3 scales must have odd size or size 4. | ||