The Mathematical Intelligencer

, Volume 40, Issue 3, pp 37–42 | Cite as

Alternatives to Semitones and Quartertones: Music-Theoretical Suggestions

  • Reilly SmethurstEmail author

Thanks 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.1

The field of software synthesisers often changes, so there is little point in discussing current options. Instead, I...

Supplementary material

Supplementary material 1 (MOV 1903 kb)

Supplementary material 2 (MOV 2450 kb)

Supplementary material 3 (MOV 7989 kb)


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.BrisbaneAustralia

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