Turning the volvelle: Exploring Jack Douthett's voice leading dynamics

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2022-09-02 DOI:10.1080/17459737.2022.2157059

Roger Asensi Arranz, T. Noll

引用次数: 1

Abstract

This paper explores Jack Douthett's model of dynamical voice leading on the level of harmonic states. It investigates global contiguous and stroboscopic dynamical systems on the entire state space and introduces a measure of effectiveness for the trajectories under consideration. Special attention is paid to the harmonic state spaces behind second-order Clough-Myerson scales, such as diatonic triads and seventh chords. Finally, a set of trajectories as a tiling of exemplifies the connection with the Spectral Conjecture.

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翻盘:探索杰克·杜塞特的声音领导动力

本文探讨了杰克·杜特在谐波水平上的动态语音引导模型。它研究了整个状态空间上的全局连续和频闪动力系统，并引入了考虑中的轨迹的有效性度量。特别注意二阶克拉夫-迈尔森音阶后的谐波状态空间，如全音阶三和弦和七和弦。最后，作为平铺图的一组轨迹举例说明了与谱猜想的联系。

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.