Recursive structure of MOS scales: Difference between revisions
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first proof was incomplete, adding a sketch idea for now |
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=== Proof === | === Proof === | ||
Suppose we had three chunks L...s with n, n+1 and n+2 'L's. Then we have a length n+2 subword that's only 'L's, one that has one s at the end and one that has two 's's on either side, which means that the original scale was not MOS. | Suppose we had three chunks L...s with n, n+1 and n+2 'L's. Then we have a length n+2 subword that's only 'L's, one that has one s at the end and one that has two 's's on either side, which means that the original scale was not MOS. Therefore the reduced word has two step sizes. | ||
[to be continued: proving MOS. idea: Each step of the reduced scale can be associated with, not necessarily the whole chunk, but the interval that spans the length of the shortest chunk. These chunks and multiples thereof are max variety 2 in the original scale, and we can maybe lift that to the reduced scale directly] | |||
== Finding the MOS pattern from nLms == | == Finding the MOS pattern from nLms == | ||