{"title":"A three-dimensional timbre model via Peano curves","authors":"Daniele Ghisi, Carmine-Emanuele Cella","doi":"10.1080/17459737.2022.2058636","DOIUrl":null,"url":null,"abstract":"Creating a formal model for timbre is one of the most compelling open questions in music research. In contrast to more traditional perceptually-oriented approaches, often aimed at sound analysis, we introduce a three-dimensional geometric model of timbre, specifically designed for sound synthesis. The proposed model relies on the properties of space-filling curves for multidimensional scaling, and represents via three parameters, any static combination of sinusoidal partials with an additional noisiness component. We detail the construction of the model and its properties and discuss future implications for music research.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-04-13","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/10.1080/17459737.2022.2058636","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
Creating a formal model for timbre is one of the most compelling open questions in music research. In contrast to more traditional perceptually-oriented approaches, often aimed at sound analysis, we introduce a three-dimensional geometric model of timbre, specifically designed for sound synthesis. The proposed model relies on the properties of space-filling curves for multidimensional scaling, and represents via three parameters, any static combination of sinusoidal partials with an additional noisiness component. We detail the construction of the model and its properties and discuss future implications for music research.
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.
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