MOS substitution: Difference between revisions
→Formal definition: Replace with shorter and more functional definition |
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== Formal definition == | == Formal definition == | ||
A ternary | 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 (called the ''template MOS'') and | * identifying '''x'''<sub>π(1)</sub> and '''x'''<sub>π(2)</sub> results in a MOS (called the ''template MOS'') and | ||
* deleting '''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 (called the ''filling MOS''). | ||
== Original derivation == | == Original derivation == | ||
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</syntaxhighlight> | </syntaxhighlight> | ||
[[Category:Combinatorics on words]] | [[Category:Combinatorics on words]] | ||
[[Category:Scale]] | [[Category:Scale]] | ||