Three-string inharmonic networks

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2022-11-07 DOI:10.1080/17459737.2022.2136776

Saba Goodarzi, W. Sethares

引用次数: 0

Abstract

This paper studies the resonant frequencies of three-string networks by examining the roots of the relevant spectral equation. A collection of scaling laws are established which relate the frequencies to structured changes in the lengths, densities, and tensions of the strings. Asymptotic properties of the system are derived, and several situations where transcritical bifurcations occur are detailed. Numerical optimization is used to solve the inverse problem (where a desired set of frequencies is specified and the parameters of the system are adjusted to best realize the specification). The intrinsic dissonance of the overtones provides an approximate way to measure the inherent inharmonicity of the sound.

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三弦非谐波网络

本文通过考察相关谱方程的根，研究了三弦网络的谐振频率。建立了一系列的标度定律，将频率与弦的长度、密度和张力的结构变化联系起来。导出了系统的渐近性质，并详细讨论了发生跨临界分岔的几种情况。数值优化用于解决反问题(即指定一组期望的频率，并调整系统参数以最好地实现该规格)。泛音的固有不谐音提供了一种近似的方法来测量声音的固有不谐音。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematics and Music 数学-数学跨学科应用

CiteScore

1.90

自引率

18.20%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematics and Music aims to advance the use of mathematical modelling and computation in music theory. The Journal focuses on mathematical approaches to musical structures and processes, including mathematical investigations into music-theoretic or compositional issues as well as mathematically motivated analyses of musical works or performances. In consideration of the deep unsolved ontological and epistemological questions concerning knowledge about music, the Journal is open to a broad array of methodologies and topics, particularly those outside of established research fields such as acoustics, sound engineering, auditory perception, linguistics etc.