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. | ||
In other words, there exist non-negative integers ''m'', ''n'', ''a'' < ''n'', ''b'' < ''n'', and vectors '''a''', '''v''' and '''w''' in the lattice such that the set of notes in the scale is | In other words, there exist non-negative integers ''m'', ''n'', 0 < ''a'' < ''n'', 0 < ''b'' < ''n'', and vectors '''a''', '''v''' and '''w''' in the lattice such that the set of notes in the scale is | ||
<math>\{\mathbf{a} + i\mathbf{v}\}_{i=a}^{n-1} \cup \{\mathbf{a} + i\mathbf{v} + j\mathbf{w}\}_{(i,j) \in [n]_0 \times [m-1]_1} \cup \{\mathbf{a} + i\mathbf{v} + m\mathbf{w}\}_{i=0}^{b}.</math> | <math>\{\mathbf{a} + i\mathbf{v}\}_{i=a}^{n-1} \cup \{\mathbf{a} + i\mathbf{v} + j\mathbf{w}\}_{(i,j) \in [n]_0 \times [m-1]_1} \cup \{\mathbf{a} + i\mathbf{v} + m\mathbf{w}\}_{i=0}^{b}.</math> | ||