Recursive structure of MOS scales: Difference between revisions

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 === Reduced words from chunking are binary and preserve the gcd of the step signature ===
-It now remains to show that reduction and expansion preserve the MOS property.
+We must show that reduction and expansion preserve the MOS property.
 Suppose w(L, s) had three chunks L...s with r, r+1 and r+2 'L's. Then we have a length r+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.