Ternary parallelogram scales are MOS substitution: Difference between revisions
| Line 19: | Line 19: | ||
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: | 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 | * 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''). | * deleting all instances of '''x'''<sub>π(3)</sub> (called the ''slot letter'') results in a MOS scale word (called the ''filling MOS''). | ||
== Proof == | == Proof == | ||