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- Generated_collection abstract "In diatonic set theory, a generated collection is a collection or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection or scale is formed. All scales which have the deep scale property may be generated by any interval coprime with (in twelve-tone equal temperament) twelve. (Johnson 2003, p.83)The C major diatonic collection may be generated by adding a cycle of perfect fifths (C7) starting at F: F-C-G-D-A-E-B = C-D-E-F-G-A-B. Using integer notation and modulo 12: 5 + 7 = 0, 0 + 7 = 7, 7 + 7 = 2, 2 + 7 = 9, 9 + 7 = 4, 4 + 7 = 11.The C major scale could also be generated using cycle of perfect fourths (C5), as 12 minus any coprime of twelve is also coprime with twelve: 12 − 7 = 5. B-E-A-D-G-C-F.A generated collection for which a single generic interval corresponds to the single generator or interval cycle used is a MOS (for "moment of symmetry"[1]) or well formed generated collection. For example, the diatonic collection is well formed, for the perfect fifth (the generic interval 4) corresponds to the generator 7. Though not all fifths in the diatonic collection are perfect (B-F is a diminished fifth, tritone, or 6), a well formed generated collection will have only one specific interval between scale members (in this case 6) which corresponds to the generic interval (4, a fifth) but to not the generator (7) and this one differing interval will always be the generator (7) plus or minus one (7 − 1 = 6) if the total number of specific intervals (12) and the generic interval's corresponding specific interval (7) are coprime (12 and 7 are). The pentatonic scale is also well formed. (ibid)The properties of generated and well-formedness were described by Norman Carey and David Clampitt in "Aspects of Well-Formed Scales" (1989), (ibid, p. 151.) In earlier (1975) work, non-academic theoretician Erv Wilson considered the idea, and called such a scale a MOS, an acronym for "Moment of Symmetry". While unpublished, this terminology became widely known and used in the microtonal music community.A degenerate well-formed collection are scales in which the generator and the interval required to complete the circle or return to the initial note are equivalent and include all scales with equal notes, such as the whole-tone scale. (ibid, p.158n14)A bisector is a weaker substitute used to create collections which may not be generated.".
- Generated_collection thumbnail 7-note_segment_of_C5.svg?width=300.
- Generated_collection wikiPageExternalLink mos.PDF.
- Generated_collection wikiPageExternalLink mos.aspx.
- Generated_collection wikiPageID "1446797".
- Generated_collection wikiPageLength "3574".
- Generated_collection wikiPageOutDegree "25".
- Generated_collection wikiPageRevisionID "585872309".
- Generated_collection wikiPageWikiLink Bisector_(music).
- Generated_collection wikiPageWikiLink Category:Diatonic_set_theory.
- Generated_collection wikiPageWikiLink Chromatic_circle.
- Generated_collection wikiPageWikiLink Circle_of_fifths.
- Generated_collection wikiPageWikiLink Coprime.
- Generated_collection wikiPageWikiLink Coprime_integers.
- Generated_collection wikiPageWikiLink David_Clampitt.
- Generated_collection wikiPageWikiLink Deep_scale_property.
- Generated_collection wikiPageWikiLink Diatonic_set_theory.
- Generated_collection wikiPageWikiLink Distance_model.
- Generated_collection wikiPageWikiLink Erv_Wilson.
- Generated_collection wikiPageWikiLink Generic_interval.
- Generated_collection wikiPageWikiLink Integer_notation.
- Generated_collection wikiPageWikiLink Interval_(music).
- Generated_collection wikiPageWikiLink Interval_cycle.
- Generated_collection wikiPageWikiLink Microtonal_music.
- Generated_collection wikiPageWikiLink Norman_Carey.
- Generated_collection wikiPageWikiLink Pentatonic_scale.
- Generated_collection wikiPageWikiLink Perfect_fifth.
- Generated_collection wikiPageWikiLink Perfect_fourth.
- Generated_collection wikiPageWikiLink Pitch_class.
- Generated_collection wikiPageWikiLink Pythagorean_tuning.
- Generated_collection wikiPageWikiLink Scale_(music).
- Generated_collection wikiPageWikiLink Set_(music).
- Generated_collection wikiPageWikiLink Specific_interval.
- Generated_collection wikiPageWikiLink Whole-tone_scale.
- Generated_collection wikiPageWikiLink Whole_tone_scale.
- Generated_collection wikiPageWikiLink File:7-note_segment_of_C5.svg.
- Generated_collection wikiPageWikiLinkText "Degenerate well-formed collection".
- Generated_collection wikiPageWikiLinkText "Generated collection".
- Generated_collection wikiPageWikiLinkText "MOS".
- Generated_collection wikiPageWikiLinkText "Moments of Symmetry".
- Generated_collection wikiPageWikiLinkText "Well formed generated collection".
- Generated_collection wikiPageWikiLinkText "drawn".
- Generated_collection wikiPageWikiLinkText "generated collection".
- Generated_collection wikiPageWikiLinkText "generator".
- Generated_collection hasPhotoCollection Generated_collection.
- Generated_collection wikiPageUsesTemplate Template:Set_theory_(music).
- Generated_collection subject Category:Diatonic_set_theory.
- Generated_collection hypernym Collection.
- Generated_collection type Book.
- Generated_collection comment "In diatonic set theory, a generated collection is a collection or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection or scale is formed. All scales which have the deep scale property may be generated by any interval coprime with (in twelve-tone equal temperament) twelve.".
- Generated_collection label "Generated collection".
- Generated_collection sameAs m.05288z.
- Generated_collection sameAs Q5532550.
- Generated_collection sameAs Q5532550.
- Generated_collection wasDerivedFrom Generated_collection?oldid=585872309.
- Generated_collection depiction 7-note_segment_of_C5.svg.
- Generated_collection isPrimaryTopicOf Generated_collection.