Generator-offset property: Difference between revisions
Tags: Mobile edit Mobile web edit |
|||
| Line 224: | Line 224: | ||
=== 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) = | ## Start with a power of a multimos word ''w''(X, Z) = ''ka''X ''kb''Z such that each ''a''X ''b''Z subword 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''. | ||