通过最长递增子序列发现复调音乐中扭曲的重复模式

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2021-04-05 DOI:10.1080/17459737.2021.1896811

A. Laaksonen, Kjell Lemström

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引用次数: 2

摘要

研究了复调符号音乐在换位和时空不变性下的重复识别问题。使用一种新颖的起始时间对表示，我们将重复模式发现问题简化为寻找最长递增子序列的经典问题的实例。结果算法适用于时间，其中n是音乐作品中的音符数。我们还研究了问题的窗口变体，其中音符之间的启动时间差异受到限制，并表明它们也可以使用该算法及时解决。

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Discovering distorted repeating patterns in polyphonic music through longest increasing subsequences

We study the problem of identifying repetitions under transposition and time-warp invariances in polyphonic symbolic music. Using a novel onset-time-pair representation, we reduce the repeating pattern discovery problem to instances of the classical problem of finding the longest increasing subsequences. The resulting algorithm works in time where n is the number of notes in a musical work. We also study windowed variants of the problem where onset-time differences between notes are restricted, and show that they can also be solved in time using the algorithm.

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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.