One categorization of microtonal scales
General Mathematics
2018-02-02 v1
Abstract
This study considers rational approximations of musical constant , which defines perfect fifth. This constant has been the subject of the numerous studies, and this paper determines quality of rational approximations in regards to absolute error. We analysed convergents and secondary convergents (some of these are the best Huygens approximations). Especially, we determined quality of the secondary convergents which are not the best Huygens approximations - in this paper we called them non-convergents approximations. Some of the microtonal scales have been positioned and determined by using non-convergents approximation of music constant which defines perfect fifth.
Cite
@article{arxiv.1802.00348,
title = {One categorization of microtonal scales},
author = {Luka Milinkovic and Branko Malesevic and Dragana Pavlovic-Sumarac and Bojan Banjac and Miomir Mijic},
journal= {arXiv preprint arXiv:1802.00348},
year = {2018}
}