Rank 3 scale: Difference between revisions
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Maximum variety 3, or MV3 scales are a generalization of MOS scales (the scales of MV2) into rank 3. | Maximum variety 3, or MV3 scales are a generalization of MOS scales (the scales of MV2) into rank 3. | ||
For all odd-cardinality MV3 scales apart from the scales abacaba, and its repetitions abacabaabacaba etc., at least two of the three steps must occur the same number of times. Moreover, excluding the scales abacaba, abcba, and their repetitions, and na nb nc scales, there always exists a generator for a MV3 scale such that the scale can be expressed as two parallel chains of this generator whose lengths are equal, or differ by 1. | For all odd-cardinality MV3 scales apart from the scales abacaba, and its repetitions abacabaabacaba etc., at least two of the three steps must occur the same number of times. Moreover, excluding the scales abacaba, abcba, and their repetitions, and na nb nc scales, there always exists a generator for a MV3 scale such that the scale can be expressed as two parallel chains of this generator whose lengths are equal, or differ by 1. This is the [[AG]] property. | ||
All [[AG]] scales of odd cardinality are MV3. The only AG scale of even cardinality is abac. | All [[AG]] scales of odd cardinality are MV3. The only AG scale of even cardinality is abac. | ||