Rank-3 scale: Difference between revisions
→Rank-2 scales: Added reference to Erv's original MOS definition |
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PWF scales can only have odd numbers of notes. | PWF scales can only have odd numbers of notes. | ||
==Pairwise DE/MOS scales== | ==Pairwise DE/MOS scales== | ||
A similar generalization, a larger subset of product words, and a superset of PWF scales are ''pairwise-DE scales'', defined for rank-3 scales such that equating any pair of steps (tempering out their difference, if we involve mappings), leads to 3 DE scales, or equivalently, MOS scales. We may also call these pairwise MOS scales. | A similar generalization, a larger subset of product words, and a superset of PWF scales are ''pairwise-DE scales'', defined for rank-3 scales such that equating any pair of steps (tempering out their difference, if we involve mappings), leads to 3-DE scales, or equivalently, MOS scales. We may also call these pairwise MOS scales. | ||
Pairwise-DE scales have MV3. Pairwise-DE scales that are not PWF are not trivalent; and one of the DE scales / MOS scales found by equating a pair of steps of such scales is a Multi-MOS, which is DE / MV2, but does not demonstrate Myhill's property. | Pairwise-DE scales have MV3. Pairwise-DE scales that are not PWF are not trivalent; and one of the DE scales / MOS scales found by equating a pair of steps of such scales is a Multi-MOS, which is DE / MV2, but does not demonstrate Myhill's property. | ||