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 brightest mode of the MOS scale word with step signature ''a'''''x'''(''b'' + ''c'')'''X''' when treating '''x''' as larger than '''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 ≤ ''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 ''a'''''x'''(''b'''''y'''''c'''''z''')". If ''f'' is the ''k''th brightest mode, this particular circular word is denoted subst ''a'''''x'''(''b'''''y'''''c'''''z''' (''b'' + ''c'' - ''k'')|(''k'' - 1)) (using [[simplified UDP]] for the mode of ''f'').

Suppose ''a'', ''b'', and ''c'' are positive integers. Suppose that the noncircular binary word ''t''('''x''', '''X''') is the brightest mode of the MOS scale word with step signature ''a'''''x'''(''b'' + ''c'')'''X''' when treating '''x''' as larger than '''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 ≤ ''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 ''a'''''x'''(''b'''''y'''''c'''''z''')".

== Original derivation ==

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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 brightest mode of the MOS scale word with step signature ''a'''''x'''(''b'' + ''c'')'''X''' when treating '''x''' as larger than '''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''')". If ''f'' is the ''k''th brightest mode, this particular circular word is denoted subst&nbsp;''a'''''x'''(''b'''''y'''''c'''''z''' (''b'' + ''c'' - ''k'')|(''k'' - 1)) (using [[simplified UDP]] for the mode of ''f'').
+Suppose ''a'', ''b'', and ''c'' are positive integers. Suppose that the noncircular binary word ''t''('''x''', '''X''') is the brightest mode of the MOS scale word with step signature ''a'''''x'''(''b'' + ''c'')'''X''' when treating '''x''' as larger than '''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''')".
 == Original derivation ==