{"title":"Three-string inharmonic networks","authors":"Saba Goodarzi, W. Sethares","doi":"10.1080/17459737.2022.2136776","DOIUrl":null,"url":null,"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.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics and Music","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/17459737.2022.2136776","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
