Modal union: Difference between revisions
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== Properties == | == Properties == | ||
For any [[MOS scale]] with a ''n''L 1s step pattern | For any [[MOS scale]] with a ''n''L 1s step pattern in any non-[[basic]] tuning, the modal union is a child MOS scale with either an (''n''+1)L ''n''s or an ''n''L (''n''+1)s step pattern. The archeotonic example above shows that the modal union of [[6L 1s]] is [[6L 7s]] for a hard tuning, while it would be [[7L 6s]] for a soft tuning. | ||
For any ''n''-tone MOS scale tuned as a subset of an [[equal tuning]] with fewer than 2''n''−1 tones per period, the modal union is the tuning itself. The case of the 12edo diatonic scale mentioned above is an example of that property. It could also be generalized to non-MOS scales with a different restriction on the number of tones for the tuning. | For any ''n''-tone MOS scale tuned as a subset of an [[equal tuning]] with fewer than 2''n''−1 tones per period, the modal union is the tuning itself. The case of the 12edo diatonic scale mentioned above is an example of that property. It could also be generalized to non-MOS scales with a different restriction on the number of tones for the tuning. | ||