An alternative approach to generalized Pythagorean scales. Generation and properties derived in the frequency domain
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Publication:4993924
DOI10.1080/17459737.2020.1726690zbMath1466.00013OpenAlexW3010100139WikidataQ114098042 ScholiaQ114098042MaRDI QIDQ4993924
Publication date: 11 June 2021
Published in: Journal of Mathematics and Music (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/2117/330498
continued fractionsBézout's identitywell-formed scalesequal temperamentPythagorean tuningPythagorean comma
Metric spaces, metrizability (54E35) Distance in graphs (05C12) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Mathematics and music (00A65)
Cites Work
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- Sturmian words, Lyndon words and trees
- On continued fractions and finite automata
- The Mathematics of Musical Instruments
- Recounting the Rationals
- On the construction, comparison, and exchangeability of tuning systems
- Amazing and Aesthetic Aspects of Analysis
- Generalized Tonnetz and Well-Formed GTS: A Scale Theory Inspired by the Neo-Riemannians
- Triads as Modes within Scales as Modes
- Pseudo-diatonic Scales
- Generalized diatonic scales
- Continued fractions, best measurements, and musical scales and intervals
- Musical intervals and special linear transformations
- Well-formedness in two dimensions: a generalization of Carey and Clampitt's theorem
- On Hellegouarch's definition of musical scales
- Musical Scales and the Generalized Circle of Fifths
- Addendum to “Two theorems concerning rational approximations”
- Algorithmic and computational approaches to pure-tone approximations of equal-tempered musical scales
- Two theorems concerning rational approximations
- FUNCTIONAL PEARL: Enumerating the rationals
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