User:Inthar/MV3: Difference between revisions
| Line 127: | Line 127: | ||
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. QED. | 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. QED. | ||
=== 3-DE implies MV3 === | |||
We prove that 3-DE + not abcba implies PMOS, which is known to imply MV3. | We prove that 3-DE + not abcba implies PMOS, which is known to imply MV3. | ||
=== 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).'' | ||