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dc.contributor.authorSmethurst, Reilly
dc.date.accessioned2020-03-17T06:30:56Z
dc.date.available2020-03-17T06:30:56Z
dc.date.issued2018
dc.identifier.issn0343-6993
dc.identifier.doi10.1007/s00283-018-9800-z
dc.identifier.urihttp://hdl.handle.net/10072/392406
dc.description.abstractThanks to free software synthesisers that support custom tuning files, it is now possible for a massive number of people to experiment with alternatives to semitones and quartertones. Indeed, contemporary musicians are not forced to choose 12-tone equal temperament or 24-tone equal temperament. I begin this article with a critique of 24-tone equal temperament. I then present a variation on the well-known whole-tone scale plus new symmetrical modes inspired by the French composer Olivier Messiaen. Finally, I show how one can map a little-known, non-octave scale by the German physicist Heinz Bohlen to a conventional, Halberstadt keyboard. Since one can only make symmetrical modes (modes à transpositions limitées) with an equal temperament, most of the musical intervals discussed in this article are approximations of frequency-ratios; they are not pure frequency-ratios.
dc.description.peerreviewedYes
dc.languageEnglish
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofpagefrom37
dc.relation.ispartofpageto42
dc.relation.ispartofissue3
dc.relation.ispartofjournalThe Mathematical Intelligencer
dc.relation.ispartofvolume40
dc.subject.fieldofresearchMathematical sciences
dc.subject.fieldofresearchPhysical sciences
dc.subject.fieldofresearchcode49
dc.subject.fieldofresearchcode51
dc.subject.keywordsScience & Technology
dc.subject.keywordsMathematics
dc.subject.keywords13 TONE STEPS
dc.titleAlternatives to Semitones and Quartertones: Music-Theoretical Suggestions
dc.typeJournal article
dc.type.descriptionC1 - Articles
dcterms.bibliographicCitationSmethurst, R, Alternatives to Semitones and Quartertones: Music-Theoretical Suggestions, The Mathematical Intelligencer, 2018, 40 (3), pp. 37-42
dc.date.updated2020-03-17T04:59:45Z
gro.hasfulltextNo Full Text
gro.griffith.authorSmethurst, Reilly K.


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