MOS substitution: Difference between revisions
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* the imperfect generator of the filling MOS corresponds to looping back to ''C''<sub>1</sub> but on the next note of ''C''<sub>1</sub>, so it and the ''q'' − 1 notes thereafter are advanced by 1 note from any predecessor notes in the chains. | * the imperfect generator of the filling MOS corresponds to looping back to ''C''<sub>1</sub> but on the next note of ''C''<sub>1</sub>, so it and the ''q'' − 1 notes thereafter are advanced by 1 note from any predecessor notes in the chains. | ||
Hence these particular MOS substitution scales satisfy a property that we call ''parallelogram substring''. An '''e'''-equivalent scale is a ''parallelogram substring'' if there exist integers ''m'' > 0, ''n'' > 0, 0 ≤ ''a'' < ''n'', 0 ≤ ''b'' < ''n'', a vector '''a''', and two linearly independent vectors '''v''' and '''w''' such that the set of notes in the scale as a subset of the lattice of '''e'''-equivalent pitches is | Hence these particular MOS substitution scales satisfy a property that we call ''[[parallelogram substring scale|parallelogram substring]]''. An '''e'''-equivalent scale is a ''parallelogram substring'' if there exist integers ''m'' > 0, ''n'' > 0, 0 ≤ ''a'' < ''n'', 0 ≤ ''b'' < ''n'', a vector '''a''', and two linearly independent vectors '''v''' and '''w''' such that the set of notes in the scale as a subset of the lattice of '''e'''-equivalent pitches is | ||
<math> | <math> | ||