A model for tonal progressions of seventh chords

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2021-06-02 DOI:10.1080/17459737.2021.1928311

Luka Marohnić

引用次数: 0

Abstract

In this paper, we propose a model for idealized diatonic and chromatic voice leadings between seventh chords and study its computational aspects. The model provides a mathematical formalization of the concept of tonal seventh chord realizations including augmented sixth chords. Certain contrapuntal aspects, such as preparation and resolution of certain dissonant intervals, are taken into account. Possible applications of the model are discussed using a graph-theoretic approach. In particular, we present an algorithm for generating concrete voicings from sequences of seventh-chord symbols.

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七和弦的调性进展模型

在本文中，我们提出了一个理想化的全音阶和七和弦之间的半音音阶的模型，并研究了它的计算方面。该模型提供了包括增音六和弦在内的调性七和弦实现概念的数学形式化。某些对位方面，如某些不和谐音程的准备和解决，都要考虑在内。用图论的方法讨论了该模型的可能应用。特别地，我们提出了一种从七和弦符号序列生成具体语音的算法。

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.