A three-dimensional timbre model via Peano curves

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2022-04-13 DOI:10.1080/17459737.2022.2058636

Daniele Ghisi, Carmine-Emanuele Cella

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.

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通过皮亚诺曲线的三维音色模型

创建音色的正式模型是音乐研究中最引人注目的开放问题之一。与传统的以感知为导向的方法(通常以声音分析为目的)相比，我们引入了一个专门为声音合成设计的音色三维几何模型。所提出的模型依赖于空间填充曲线的特性进行多维缩放，并通过三个参数表示带有附加噪声分量的正弦偏导数的任何静态组合。我们详细介绍了模型的构建及其特性，并讨论了未来对音乐研究的影响。

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.