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- Cardinality_equals_variety abstract "The musical operation of scalar transposition shifts every note in a melody by the same number of scale steps. The musical operation of chromatic transposition shifts every note in a melody by the same distance in pitch class space. In general, for a given scale S, the scalar transpositions of a line L can be grouped into categories, or transpositional set classes, whose members are related by chromatic transposition. In diatonic set theory cardinality equals variety when, for any melodic line L in a particular scale S, the number of these classes is equal to the number of distinct pitch classes in the line L.For example, the melodic line C-D-E has three distinct pitch classes. When transposed diatonically to all scale degrees in the C major scale, we obtain 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 degreesMelodic lines in the C major scale with n distinct pitch classes always generate n distinct patterns.The property was first described by John Clough and Gerald Myerson in "Variety and Multiplicity in Diatonic Systems" (1985) (Johnson 2003, p.68, 151). Cardinality equals variety in the diatonic collection and the pentatonic scale, and, more generally, what Carey and Clampitt (1989) call "nondegenerate well-formed scales." "Nondegenerate well-formed scales" are those that possess Myhill's property.".
- Cardinality_equals_variety thumbnail Cardinality_equals_variety_CDE.PNG?width=300.
- Cardinality_equals_variety wikiPageID "1439664".
- Cardinality_equals_variety wikiPageLength "2321".
- Cardinality_equals_variety wikiPageOutDegree "13".
- Cardinality_equals_variety wikiPageRevisionID "514135248".
- Cardinality_equals_variety wikiPageWikiLink Category:Diatonic_set_theory.
- Cardinality_equals_variety wikiPageWikiLink Degree_(music).
- Cardinality_equals_variety wikiPageWikiLink Diatonic_collection.
- Cardinality_equals_variety wikiPageWikiLink Diatonic_scale.
- Cardinality_equals_variety wikiPageWikiLink Diatonic_set_theory.
- Cardinality_equals_variety wikiPageWikiLink Gerald_Myerson.
- Cardinality_equals_variety wikiPageWikiLink John_Clough.
- Cardinality_equals_variety wikiPageWikiLink Myhills_property.
- Cardinality_equals_variety wikiPageWikiLink Pentatonic_scale.
- Cardinality_equals_variety wikiPageWikiLink Pitch_class.
- Cardinality_equals_variety wikiPageWikiLink Scale_degree.
- Cardinality_equals_variety wikiPageWikiLink Set_theory_(music).
- Cardinality_equals_variety wikiPageWikiLink Transposition_(music).
- Cardinality_equals_variety wikiPageWikiLink File:Cardinality_equals_variety_CDE.PNG.
- Cardinality_equals_variety wikiPageWikiLinkText "Cardinality equals variety".
- Cardinality_equals_variety wikiPageWikiLinkText "cardinality equals variety".
- Cardinality_equals_variety hasPhotoCollection Cardinality_equals_variety.
- Cardinality_equals_variety wikiPageUsesTemplate Template:Set_theory_(music).
- Cardinality_equals_variety subject Category:Diatonic_set_theory.
- Cardinality_equals_variety comment "The musical operation of scalar transposition shifts every note in a melody by the same number of scale steps. The musical operation of chromatic transposition shifts every note in a melody by the same distance in pitch class space. In general, for a given scale S, the scalar transpositions of a line L can be grouped into categories, or transpositional set classes, whose members are related by chromatic transposition.".
- Cardinality_equals_variety label "Cardinality equals variety".
- Cardinality_equals_variety sameAs m.051qc1.
- Cardinality_equals_variety sameAs Q5038646.
- Cardinality_equals_variety sameAs Q5038646.
- Cardinality_equals_variety wasDerivedFrom Cardinality_equals_variety?oldid=514135248.
- Cardinality_equals_variety depiction Cardinality_equals_variety_CDE.PNG.
- Cardinality_equals_variety isPrimaryTopicOf Cardinality_equals_variety.