Periodic scale: Difference between revisions
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=== Modes === | === Modes === | ||
A mode, or "rotation", of a periodic scale is a scale r such that r[''i''] = s[''i'' + ''N''] - s[''N''], where ''N'' is a fixed integer; in other words, it is the same scale pattern, but starting on a different scale degree. Since s[''i'' + ''P''] - s[''P''] = s[''i''], there are only a finite number of rotations, equal to the number of notes of the scale reduced to the range of the interval of equivalence, 0 ≤ s[''i''] < ''s[P]'', which entails 0 ≤ ''i'' < ''P''. | A mode, or "rotation", of a periodic scale is a scale r such that r[''i''] = s[''i'' + ''N''] - s[''N''], where ''N'' is a fixed integer; in other words, it is the same scale pattern, but starting on a different scale degree. Since s[''i'' + ''P''] - s[''P''] = s[''i''], there are only a finite number of rotations, equal to the number of notes of the scale reduced to the range of the interval of equivalence, 0 ≤ s[''i''] < ''s[P]'', which entails 0 ≤ ''i'' < ''P''. | ||
=== Classes === | === Classes === | ||