Rank-3 scale: Difference between revisions
→MV3 scales: This part is falsified by the 14-note SV3 LLLMLLLsLLMLLs: "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." |
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All GO scales of odd cardinality are MV3. The only GO scale of even cardinality is ''abac''. | All GO scales of odd cardinality are MV3. The only GO scale of even cardinality is ''abac''. | ||
'''Conjecture:''' The only mirror-symmetric MV3 scales are abacaba (and its repetitions) and the scales of the form '' | '''Conjecture:''' The only mirror-symmetric MV3 scales are abacaba (and its repetitions) and the scales of the form ''a…ba…c'' (and their repetitions). Therefore the only MV3 scales that are mirror-symmetric are the only MV3 scales that are also 3-[[SN scales]] (introduced below). | ||
== Trivalent scales == | == Trivalent scales == | ||
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== List of named rank-3 scales == | == List of named rank-3 scales == | ||
The following is a list of (temperament-agnostic) names that have been given to 3-step scales. | The following is a list of (temperament-agnostic) names that have been given to 3-step scales. | ||
*[[diasem]] (5L 2M 2S) | * [[diasem]] (5L 2M 2S) | ||
*[[blackdye]] (5L 2M 3S) | * [[blackdye]] (5L 2M 3S) | ||
*[[onyxwood]] (5L 3M 2S) | * [[onyxwood]] (5L 3M 2S) | ||
*blackville / antiwood? (2L 5M 3S) | * [[blackville]] / antiwood? (2L 5M 3S) | ||
[[Category:Rank-3 scales| ]] <!--main article--> | [[Category:Rank-3 scales| ]] <!--main article--> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||