Sistemas de afinación en música desde el punto de vista de las matemáticas
- María Aguado Yáñez
- Ángel Rivas Vargas
ISSN: 0210-3680
Year of publication: 2023
Issue Title: 1º y 2º trimestre 2023
Volume: 54
Issue: 1-2
Pages: 23-29
Type: Article
More publications in: Revista de acústica
Abstract
Within the area of musical acoustics, the evolution of Western tuning systems can be studied through the perspective of mathematical models, since a tuning system isa set of mathematical relations imposed on frequencies. In this document, the Pythagorean and mesotonic tunings, as well as the equal temperament, are analyzed. Firstly, a historical analysis of these systems will be performed. Secondly, the systems will be modelled using geometric curves. Lastly, two quantitative methods will be applied to make a numerical description which exploits their symmetries. The results show that complexity decreases the more modern the systems are, which partly explains their historical evolution. Moreover, these models can be extended for further new systems, and are meant to be intuitive and visual for both scientists and musicians to understand the advantages and disadvantages of each system.