MOS substitution: Difference between revisions
| Line 208: | Line 208: | ||
* 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 ''quasi-parallelogram''. An '''e'''-equivalent scale is a ''quasi-parallelogram'' if there exist non-negative integers ''m'', ''n'', 0 | Hence these particular MOS substitution scales satisfy a property that we call ''quasi-parallelogram''. An '''e'''-equivalent scale is a ''quasi-parallelogram'' if there exist non-negative integers ''m'', ''n'', 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> | ||