6533b858fe1ef96bd12b6256
RESEARCH PRODUCT
On the construction, comparison, and exchangeability of tuning systems
Vicente Liernsubject
Pythagorean tuningComputational MathematicsInterval (music)Similarity (geometry)Applied MathematicsModeling and SimulationOctaveMathematical propertiesMusical tuningAlgorithmMusicMathematicsJust intonationdescription
The aim of this article is to describe mathematically different tuning systems, to study their mathematical properties, and to propose a construction allowing their comparison. In order to reach these goals, we introduce a concept of similarity between tuning systems and then we provide two sufficient conditions for the particular case in which a tuning system generated by an interval and a circulating temperament are compared. Finally, we show by means of an example that, for two tuning systems to be exchangeable, some well-known results determining the suitable number of notes per octave are not enough.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-08-04 | Journal of Mathematics and Music |