Academic Journal
Choosing the representative tones of an abstract Pythagorean scale with regard to just intonation
| Τίτλος: | Choosing the representative tones of an abstract Pythagorean scale with regard to just intonation |
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| Συγγραφείς: | Cubarsí Morera, Rafael |
| Πηγή: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Στοιχεία εκδότη: | Informa UK Limited, 2025. |
| Έτος έκδοσης: | 2025 |
| Θεματικοί όροι: | Scale temperament, Just intonation, Pythagorean comma, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica, Syntonic comma, Generated scale, Pythagorean tuning |
| Περιγραφή: | Hellegouarch [1999a. “Gammes naturelles.” Gazette des Matematiciens 81:25–39.] relies on a remark that Euler made to state that the way of choosing the representatives of an abstract Pythagorean scale should be based on the fact that the sense of hearing tends to identify with a single ratio all the ratios which are only slightly different from it. For this reason, the representatives were chosen as the simpler ratios among the possible tones of the Pythagorean scale. However, this could be a misinterpretation of Euler's remark, since there may be single ratios much simpler in the vicinity of the Pythagorean ratios. This paper is only a brief contribution on the discussion about how to select these representatives and shows that if Pythagorean tuning is to emulate or replace syntonic just tuning, it is better to adapt the scale to the key. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| ISSN: | 1745-9745 1745-9737 |
| DOI: | 10.1080/17459737.2025.2450315 |
| Rights: | CC BY NC ND |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....39eb046133d6fd8fc078939a19e53cad |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 17459745 17459737 |
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| DOI: | 10.1080/17459737.2025.2450315 |