Ternary scale theorems: Difference between revisions
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## Interchange some of the Z's and X's at some of the borders of these copies of the mos word ''w''. | ## Interchange some of the Z's and X's at some 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) are always SV3, and those of type ( | # Single-period MV3 scales not of type (3) are always SV3, and those of type (4) are SV3 with the exception of the n/2-step (n = scale length) which is variety 2. | ||
# Single-period MV3 scales not of type (4) and not of the form XYZYX are ''balanced'': for any ''k'', any pair of k-steps has a difference that contains +1, -1, or 0 of each step size. | # Single-period MV3 scales not of type (4) and not of the form XYZYX are ''balanced'': for any ''k'', any pair of k-steps has a difference that contains +1, -1, or 0 of each step size. | ||
=== Proof === | === Proof === | ||