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- Structure_implies_multiplicity abstract "In diatonic set theory structure implies multiplicity is a quality of a collection or scale. This is that for the interval series formed by the shortest distance around a diatonic circle of fifths between member of a series indicates the number of unique interval patterns (adjacently, rather than around the circle of fifths) formed by diatonic transpositions of that series. Structure being the intervals in relation to the circle of fifths, multiplicity being the number of times each different (adjacent) interval pattern occurs. The property was first described by John Clough and Gerald Myerson in "Variety and Multiplicity in Diatonic Systems" (1985). (Johnson 2003, p.68, 151)Structure implies multiplicity is true of the diatonic collection and the pentatonic scale, and any subset.For example, cardinality equals variety dictates that a three member diatonic subset of the C major scale, C-D-E transposed to all scale degrees gives three interval patterns: M2-M2, M2-m2, m2-M2.three member diatonic subset of the C major scale, C-D-E transposed to all scale degreesOn the circle of fifths:C G D A E B F (C) 1 2 1 2 1 2 3E and C are three notes apart, C and D are two notes apart, D and E two notes apart. Just as the distance around the circle of fifths between forms the interval pattern 3-2-2, M2-M2 occurs three times, M2-m2 occurs twice, and m2-M2 occurs twice.Cardinality equals variety and structure implies multiplicity are true of all collections with Myhill's property or maximal evenness.".
- Structure_implies_multiplicity thumbnail Cardinality_equals_variety_CDE.PNG?width=300.
- Structure_implies_multiplicity wikiPageID "1444194".
- Structure_implies_multiplicity wikiPageLength "2300".
- Structure_implies_multiplicity wikiPageOutDegree "16".
- Structure_implies_multiplicity wikiPageRevisionID "514135260".
- Structure_implies_multiplicity wikiPageWikiLink Cardinality_equals_variety.
- Structure_implies_multiplicity wikiPageWikiLink Category:Diatonic_set_theory.
- Structure_implies_multiplicity wikiPageWikiLink Circle_of_fifths.
- Structure_implies_multiplicity wikiPageWikiLink Degree_(music).
- Structure_implies_multiplicity wikiPageWikiLink Diatonic_collection.
- Structure_implies_multiplicity wikiPageWikiLink Diatonic_scale.
- Structure_implies_multiplicity wikiPageWikiLink Diatonic_set_theory.
- Structure_implies_multiplicity wikiPageWikiLink Diatonic_transposition.
- Structure_implies_multiplicity wikiPageWikiLink Gerald_Myerson.
- Structure_implies_multiplicity wikiPageWikiLink Interval_(music).
- Structure_implies_multiplicity wikiPageWikiLink John_Clough.
- Structure_implies_multiplicity wikiPageWikiLink Maximal_evenness.
- Structure_implies_multiplicity wikiPageWikiLink Myhills_property.
- Structure_implies_multiplicity wikiPageWikiLink Pentatonic_scale.
- Structure_implies_multiplicity wikiPageWikiLink Scale_(music).
- Structure_implies_multiplicity wikiPageWikiLink Scale_degree.
- Structure_implies_multiplicity wikiPageWikiLink Transposition_(music).
- Structure_implies_multiplicity wikiPageWikiLink File:Cardinality_equals_variety_CDE.PNG.
- Structure_implies_multiplicity wikiPageWikiLinkText "Structure implies multiplicity".
- Structure_implies_multiplicity wikiPageWikiLinkText "structure implies multiplicity".
- Structure_implies_multiplicity hasPhotoCollection Structure_implies_multiplicity.
- Structure_implies_multiplicity wikiPageUsesTemplate Template:Set_theory_(music).
- Structure_implies_multiplicity subject Category:Diatonic_set_theory.
- Structure_implies_multiplicity hypernym Quality.
- Structure_implies_multiplicity type Organisation.
- Structure_implies_multiplicity comment "In diatonic set theory structure implies multiplicity is a quality of a collection or scale. This is that for the interval series formed by the shortest distance around a diatonic circle of fifths between member of a series indicates the number of unique interval patterns (adjacently, rather than around the circle of fifths) formed by diatonic transpositions of that series.".
- Structure_implies_multiplicity label "Structure implies multiplicity".
- Structure_implies_multiplicity sameAs m.0522m7.
- Structure_implies_multiplicity sameAs Q7625101.
- Structure_implies_multiplicity sameAs Q7625101.
- Structure_implies_multiplicity wasDerivedFrom Structure_implies_multiplicity?oldid=514135260.
- Structure_implies_multiplicity depiction Cardinality_equals_variety_CDE.PNG.
- Structure_implies_multiplicity isPrimaryTopicOf Structure_implies_multiplicity.