Generator-offset property: Difference between revisions

Inthar (talk | contribs)
Tags: Mobile edit Mobile web edit
Inthar (talk | contribs)
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) = ''ka''X ''kb''Z such that ''a'' is even and each ''a''X ''b''Z subword of ''w'' is of the form X''P''(X, Z)Z where ''P''(X, Z) is a palindrome,
## Start with a power of a multimos word ''w''(X, Z) = ''ka''X ''kb''Z such that ''a'' is even and each ''a''X ''b''Z subword of ''w'' 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''.