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Constructing an optimal circulating temperament based on a set of musical requirements

Farup, Ivar
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2461820
Date
2014
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  • Institutt for datateknologi og informatikk [7453]
  • Publikasjoner fra CRIStin - NTNU [41954]
Original version
Journal of Mathematics and Music - Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance. 2014, 8 (1), 25-39.   10.1080/17459737.2013.847978
Abstract
A novel parametric circulating temperament is presented using a constructive approach. The temperament is optimal with respect to a heuristically chosen set of musical requirements. It is parametric in the sense that the tempering of the narrowest (i.e. closest to pure) major third can be freely chosen. Equal temperament arises as a limiting case. The temperament is optimal in the sense that the tempering of the widest major third and the narrowest fifth is minimized given the size of the least tempered major third. Also, under this constraint, the tempering of the major thirds closest to the least tempered third along the circle of fifths is minimized. The remaining degree of freedom is used to minimize the number of unique intervals. The resulting temperament exhibits various symmetries, and has, in general, two differently sized fifths and five differently sized major thirds. The temperament has no historic relevance as such, but can find good uses within all keyboard music from early baroque till today due to the selection of optimization criteria that closely follow historical requirements for good temperaments. With some exercise it can be tuned by ear.
Publisher
Taylor & Francis
Journal
Journal of Mathematics and Music - Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance

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