MOS substitution: Difference between revisions

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 == Formal definition ==
-Suppose ''a'', ''b'', and ''c'' are positive integers. Suppose that the noncircular binary word ''t''('''x''', '''X''') is the lexicographically first mode of the MOS scale word with step signature ''a'''''x'''(''b'' + ''c'')'''X''' under the ordering '''x''' < '''X''', and that the noncircular binary word ''f''('''y''', '''z''') is one rotation of the MOS scale word with step signature ''b'''''y'''''c'''''z'''. Then the result of replacing the ''i''th occurrence of '''X''' in ''t'' replaced with the ''i''th letter of ''f'' for 0 &le; ''i'' < |''f''|, treated as a circular word, is said to be a ''MOS substitution scale word'' with ''template MOS'' ''a'''''x'''(''b'' + ''c'')'''X''' and ''filling MOS'' ''b'''''y'''''c'''''z''', or in shorthand, a "subst&nbsp;''a'''''x'''(''b'''''y'''''c'''''z''')".
+A ternary necklace ''w''('''x'''<sub>1</sub>, '''x'''<sub>2</sub>, '''x'''<sub>3</sub>) is a ''MOS substitution'' scale 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
+* deleting '''x'''<sub>π(3)</sub> (called the ''slot letter'') results in a MOS (called the ''filling MOS'').
 == Original derivation ==