通过拓扑数据分析和人工神经网络实现韩语音乐的机器作曲

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2023-05-03 DOI:10.1080/17459737.2023.2197905

Mai Lan Tran, Dongjin Lee, Jae-Hun Jung

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引用次数: 0

摘要

常见的人工智能作曲算法通过输入一组音乐片段来训练机器。这种方法是一种黑盒优化，即底层的组合算法通常对用户来说是未知的。在本文中，我们提出了一种机器作曲的方法，该方法使用重叠矩阵的概念教机器嵌入音乐中的作曲原则。在(Tran Mai Lan, Changbom Park & Jae-Hun Jung, 2023)《Jeongganbo韩国音乐的拓扑数据分析:一个循环结构》，Journal of Mathematics and music, DOI: 10.1080/17459737.2022.2164626)中，使用拓扑数据分析(TDA)分析了一种称为Dodeuri音乐的韩国音乐类型。为了应用TDA，首先将音乐数据重构为图形。通过构造图上的TDA，找到了唯一的一组环。重叠矩阵让我们直观地看到这些循环在音乐中是如何相互联系的。我们解释了如何使用重叠矩阵进行机器组合。重叠矩阵不仅适用于算法合成，而且为训练人工神经网络提供了种子音乐。

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Machine composition of Korean music via topological data analysis and artificial neural network

Common AI music composition algorithms train a machine by feeding a set of music pieces. This approach is a blackbox optimization, i.e. the underlying composition algorithm is, in general, unknown to users. In this paper, we present a method of machine composition that teaches a machine the compositional principles embedded in the music using the concept of overlap matrix. In (Tran Mai Lan, Changbom Park & Jae-Hun Jung (2023) Topological data analysis of Korean music in Jeongganbo: a cycle structure, Journal of Mathematics and Music, DOI: 10.1080/17459737.2022.2164626), a type of Korean music called Dodeuri music has been analysed using topological data analysis (TDA). To apply TDA, the music data is first reconstructed as a graph. Through TDA on the constructed graph, a unique set of cycles is found. The overlap matrix lets us visualize how those cycles are interconnected in music. We explain how we use the overlap matrix for machine composition. The overlap matrix is suitable for algorithmic composition and also provides seed music to train an artificial neural network.

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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.