Generator-offset property: Difference between revisions
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=== Theorem 5 (Classification of MV3 scales) === | === Theorem 5 (Classification of MV3 scales) === | ||
# A single-period MV3 is either PWF, equivalent to XYZYX, or a "twisted" word constructed as follows: | # A single-period MV3 is either PWF, equivalent to XYZYX, or a "twisted" word constructed as follows: | ||
## Start with a power of a multimos word ''w''(X, Z) = aX bZ such that each period of ''w'' has an even number of | ## Start with a power of a multimos word ''w''(X, Z) = aX bZ such that each period of ''w'' has an even number of X's and is of the form X''P''(X, Z)Z where ''P''(X, Z) is a palindrome, | ||
## Interchange some of the Z's and X's at some (possibly none) of the borders of these copies of the mos word ''w''. | ## Interchange some of the Z's and X's at some (possibly none) of the borders of these copies of the mos word ''w''. | ||
## Replace every other X with Y in ''w''. | ## Replace every other X with Y in ''w''. | ||