多八度音阶的结构特性

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2022-11-08 DOI:10.1080/17459737.2022.2128450

Emmet Crowley, Francisco Gómez-Martín

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引用次数: 0

摘要

虽然没有广泛扩展，但非八度重复音阶存在于各种音乐设置中，但在现有文献中却很少受到关注。本文提供了一个简要的历史背景，然后根据与西方音乐中最广泛使用的音阶的共同属性，重点介绍了一组特定的双八度音阶。在用数学术语描述它们之后，提供了这些音阶的详尽列表，这是任何给定特征的非八度重复音阶的第一个详尽列表。本文首次提出了全音阶理论领域中具有全音阶集合结构性质的音阶，如良构性、Myhill性质、最大均匀性或全音阶。

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Structural properties of multi-octave scales

Whilst not widely extended, non-octave-repeating scales are present in a variety of musical settings, yet have received scarce attention in the existing literature. This paper provides a brief general historical contextualization before focusing on a specific group of two-octave scales based on properties in common with the most widely used scales in Western music. After characterizing them in mathematical terms, an exhaustive list of such scales is provided, being the first exhaustive list of non-octave-repeating scales of any given characteristics. A scale endowed with structural properties attributed to the diatonic collection in the field of diatonic theory – such as well-formed, Myhill property, maximally even or diatonic – is singled out for the first time in this paper.

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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.