Rank-3 scale: Difference between revisions

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 Rank-3 scales are introduced from here, as generalizations of MOS scales.
+The following table summarizes properties of MOS scales, and the classes of scale that generalize them into rank-3 (not an exhaustive list).
+{| class="wikitable"
+|+Generalizations of MOS scale properties into rank-3.
+!Property
+!Rank-3 scale class
+|-
+|Maximum Variety 2
+|[[MV3]] scales
+|-
+|Distributional Evenness
++ can tessellate the entire lattice of pitch classes that it lives in
+|Pairwise DE/MOS scales = rank-3 Fokker blocks
+(subset of MV3 scales, superset of PWF scales and of Alternating Generator scales)
+|-
+|Generated
+|[[Generator-offset property|Generator Offset]] scales
+|-
+|Myhill's property
+|Trivalent scales (subset of MV3 scales)
+|-
+|Well-formed (includes Myhill's property)
+|Pairwise well-formed scales (intersection of trivalent scales and Pairwise DE scales)
+|-
+|Uniquely defined by step signature and mapping
++ mirror symmetric
+|3-SN scales (rank-3 [[step-nested scales]])
+|-
+|Uniquely defined by mapping and cardinality
++ comprises least complex intervals in temperament defined by the mapping
+|rank-3 [[Hobbit|Hobbit scales]]
+|}
 ==[[User:Inthar/MV3|MV3 scales]]==
 Maximum variety 3, or MV3 scales are a generalization of MOS scales (the scales of MV2) into rank-3.