Ternary parallelogram scales are MOS substitution: Difference between revisions
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=== MOS substitution scale === | === MOS substitution scale === | ||
A ternary scale word ''w''('''x'''<sub>1</sub>, '''x'''<sub>2</sub>, '''x'''<sub>3</sub>) is a ''MOS substitution'' scale word if there exists a permutation <math>\pi \in S_3</math> such that the following holds: | |||
* identifying '''x'''<sub>π(1)</sub> and '''x'''<sub>π(2)</sub> results in a [[MOS]] scale word (called the ''template MOS'') and | |||
* deleting all instances of '''x'''<sub>π(3)</sub> (called the ''slot letter'') results in a MOS (called the ''filling MOS''). | |||
== Proof == | == Proof == | ||
=== Step 1: Get a surjective homomorphism <math>\varphi:\mathbb{Z}^2 \to \mathbb{Z}/mn\mathbb{Z}</math> === | === Step 1: Get a surjective homomorphism <math>\varphi:\mathbb{Z}^2 \to \mathbb{Z}/mn\mathbb{Z}</math> === | ||