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- Maximal_evenness abstract "In diatonic set theory maximal evenness is the quality of a collection or scale which for every generic interval there are either one or two consecutive (adjacent) specific intervals, in other words a scale which is \"spread out as much as possible.\" This property was first described by music theorist John Clough and mathematician Jack Douthett in \"Maximally Even Sets\" (1991). (Johnson 2003, p.27, 150)Myhill's property, that there are two specific intervals for every generic interval, follows from maximally evenness, and both properties are true of the diatonic collection, for instance adjacent notes are separated only by half-tones and whole-tones (1 and 2). The whole-tone scale is also maximally even, for instance adjacent notes are separated only by whole-tones.Second-order maximal evenness is maximal evenness of subcollections with regards to a larger collection which is maximally even. Diatonic triads and seventh chords possess second-order maximal evenness, being maximally even in regard to the maximally even diatonic scale but are not maximally even with regard to the chromatic scale. (ibid, p.115) This nested quality resembles Fred Lerdahl's \"reductional format\" for pitch space from the bottom up:(Lerdahl, 1992)The musical theory of maximal evenness has been used as part of the Ising model in physics to model electron behavior. (Johnson 2003, p.144).In a dynamical approach, spinning concentric circles and iterated maximally even sets have been constructed as an alternate approach to Riemann theory. This approach leads to some interesting connections between diatonic and chromatic theory. (Douthett, 2008)".
- Maximal_evenness thumbnail Maximal_evenness_seconds.png?width=300.
- Maximal_evenness wikiPageID "1447276".
- Maximal_evenness wikiPageLength "3832".
- Maximal_evenness wikiPageOutDegree "24".
- Maximal_evenness wikiPageRevisionID "694930506".
- Maximal_evenness wikiPageWikiLink Category:Diatonic_set_theory.
- Maximal_evenness wikiPageWikiLink Concentric.
- Maximal_evenness wikiPageWikiLink Diatonic_and_chromatic.
- Maximal_evenness wikiPageWikiLink Diatonic_scale.
- Maximal_evenness wikiPageWikiLink Diatonic_set_theory.
- Maximal_evenness wikiPageWikiLink Dynamical_system.
- Maximal_evenness wikiPageWikiLink Electron.
- Maximal_evenness wikiPageWikiLink Fred_Lerdahl.
- Maximal_evenness wikiPageWikiLink Generic_interval.
- Maximal_evenness wikiPageWikiLink Ising_model.
- Maximal_evenness wikiPageWikiLink Jack_Douthett.
- Maximal_evenness wikiPageWikiLink John_Clough_(music_theorist).
- Maximal_evenness wikiPageWikiLink Major_second.
- Maximal_evenness wikiPageWikiLink Mathematician.
- Maximal_evenness wikiPageWikiLink Music_theory.
- Maximal_evenness wikiPageWikiLink Myhills_property.
- Maximal_evenness wikiPageWikiLink Physics.
- Maximal_evenness wikiPageWikiLink Pitch_space.
- Maximal_evenness wikiPageWikiLink Semitone.
- Maximal_evenness wikiPageWikiLink Specific_interval.
- Maximal_evenness wikiPageWikiLink File:Maximal_evenness_seconds.png.
- Maximal_evenness wikiPageWikiLink File:Not_maximal_evenness_seconds.png.
- Maximal_evenness wikiPageWikiLinkText "Maximal evenness".
- Maximal_evenness wikiPageWikiLinkText "Maximal evenness#Distributional evenness".
- Maximal_evenness wikiPageWikiLinkText "maximal evenness".
- Maximal_evenness wikiPageWikiLinkText "maximally even".
- Maximal_evenness wikiPageWikiLinkText "rhythmic evenness".
- Maximal_evenness wikiPageUsesTemplate Template:Anchor.
- Maximal_evenness wikiPageUsesTemplate Template:Set_theory_(music).
- Maximal_evenness wikiPageUsesTemplate Template:Xenharmonic_wiki.
- Maximal_evenness subject Category:Diatonic_set_theory.
- Maximal_evenness hypernym Quality.
- Maximal_evenness type Organisation.
- Maximal_evenness comment "In diatonic set theory maximal evenness is the quality of a collection or scale which for every generic interval there are either one or two consecutive (adjacent) specific intervals, in other words a scale which is \"spread out as much as possible.\" This property was first described by music theorist John Clough and mathematician Jack Douthett in \"Maximally Even Sets\" (1991).".
- Maximal_evenness label "Maximal evenness".
- Maximal_evenness sameAs Q6795638.
- Maximal_evenness sameAs m.0529ml.
- Maximal_evenness sameAs Q6795638.
- Maximal_evenness wasDerivedFrom Maximal_evenness?oldid=694930506.
- Maximal_evenness depiction Maximal_evenness_seconds.png.
- Maximal_evenness isPrimaryTopicOf Maximal_evenness.