An alternative approach to generalized Pythagorean scales: generation and properties derived in the frequency domain
Visualitza/Obre
10.1080/17459737.2020.1726690
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/330498
Tipus de documentArticle
Data publicació2020-03-05
Condicions d'accésAccés obert
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Abstract
Abstract scales are formalized as a cyclic group of classes of projection functions related to iterations of the scale generator. Their representatives in the frequency domain are used to built cyclic sequences of tone iterates satisfying the closure condition. The refinement of cyclic sequences with regard to the best closure provides a constructive algorithm that allows to determine cyclic scales avoiding continued fractions. New proofs of the main properties are obtained as a consequence of the generating procedure. When the scale tones are generated from the two elementary factors associated with the generic widths of the step intervals we get the partition of the octave leading to the fundamental Bézout’s identity relating several characteristic scale indices. This relationship is generalized to prove a new relationship expressing the partition that the frequency ratios associated with the two sizes composing the different step-intervals induce to a specific set of octaves.
Descripció
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of mathematics and music on march 2020, available online at: http://www.tandfonline.com/10.1080/17459737.2020.1726690.
CitacióCubarsi, R. An alternative approach to generalized Pythagorean scales: generation and properties derived in the frequency domain. "JOURNAL OF MATHEMATICS AND MUSIC", 5 Març 2020, vol. 14, núm. 3, p. 266-291.
ISSN1745-9745
Versió de l'editorhttps://www.tandfonline.com/doi/full/10.1080/17459737.2020.1726690
Col·leccions
Fitxers | Descripció | Mida | Format | Visualitza |
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generalized_pythagorean_upc.pdf | Article principal abans de les proves d'imprempta | 633,4Kb | Visualitza/Obre |