Ternary scale theorems: Difference between revisions
| Line 229: | Line 229: | ||
# A single-period MV3 is either (1) pairwise well-formed, (2) equivalent to XYZYX, (3) constructed from ''w''(X, Z)^2 (power of a primitive mos ''w''(X, Z) with #X odd) by replacing every other X with Y, or (4) a "twisted" word constructed as follows: | # A single-period MV3 is either (1) pairwise well-formed, (2) equivalent to XYZYX, (3) constructed from ''w''(X, Z)^2 (power of a primitive mos ''w''(X, Z) with #X odd) by replacing every other X with Y, or (4) 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 ( | ## 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''. | ||
# Single-period MV3 scales not of type (3) or (4) are always SV3. | # Single-period MV3 scales not of type (3) or (4) are always SV3. | ||