Ternary scale theorems: Difference between revisions
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A ''[[arity|ternary]] scale'' is a scale with three (positive) step sizes, with no other constraints such as maximum variety. This page documents known properties of subtypes of ternary scales and their proofs. | A ''[[arity|ternary]] scale'' is a scale with three (positive) step sizes, with no other constraints such as maximum variety. This page documents known properties of subtypes of ternary scales and their proofs. | ||
== Conventions == | == Conventions == | ||
* Bolded Latin variables refer to step vectors | * Bolded Latin variables refer to step vectors (linear combinations of step sizes). | ||
* Indices for all words are 1-indexed. | * Indices for all words are 1-indexed. | ||
** If ''s'' is a circular word and ''i'' < 1 or ''i'' > len(''s''), we first replace ''i'' with ''i'' % len(''s'') + 1 before using it as an argument in ''s''[-]. | ** If ''s'' is a circular word and ''i'' < 1 or ''i'' > len(''s''), we first replace ''i'' with ''i'' % len(''s'') + 1 before using it as an argument in ''s''[-]. | ||