Continued fractions, best measurements, and musical scales and intervals

DOI10.1080/17459730601137799zbMath1139.00005OpenAlexW2077469011MaRDI QIDQ3516388

Jack Douthett, Richard Krantz

Publication date: 5 August 2008

Published in: Journal of Mathematics and Music (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17459730601137799

zbMATH Keywords

Continued fractionsEqual-tempered scalesFitting functionsMyhill's propertyPythagorean commaWell-formed scales

Mathematics Subject Classification ID

Other designs, configurations (05B30) Continued fractions (11A55) General applied mathematics (00A69) Continued fractions; complex-analytic aspects (30B70) Distribution modulo one (11J71)

Related Items (9)

On the joint subword complexity of automatic sequences ⋮ Scalar context in musical models ⋮ Algorithmic and computational approaches to pure-tone approximations of equal-tempered musical scales ⋮ On the Euler scale and theμEuclidean integer relation algorithm ⋮ LR property of non-well-formed scales ⋮ On the construction, comparison, and exchangeability of tuning systems ⋮ An alternative approach to generalized Pythagorean scales. Generation and properties derived in the frequency domain ⋮ Musical pitch quantization as an eigenvalue problem ⋮ Tempered monoids of real numbers, the golden fractal monoid, and the well-tempered harmonic semigroup

Cites Work

• Pianos and Continued Fractions
• Musical Scales and the Generalized Circle of Fifths
• Some Musico-Mathematical Curiosities

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