Bayesian Melody Harmonization Based on a Tree-Structured Generative Model of Chord Sequences and Melodies
Bayesian Melody Harmonization Based on a Tree-Structured Generative Model of Chord Sequences and Melodies
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DOI：
10.1109/taslp.2020.2996088
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发表时间：
2020-05
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通讯作者：
Hiroaki Tsushima;Eita Nakamura;Kazuyoshi Yoshii
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文献类型：
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作者：
Hiroaki Tsushima;Eita Nakamura;Kazuyoshi Yoshii
本文描述了一种旋律协调方法，该方法为给定的旋律（音符序列）生成和弦序列（符号和起始位置）。旋律协调的典型方法是使用隐马尔可夫模型（HMM），该模型将和弦和音符分别表示为潜在变量和观测变量。然而，这种方法没有考虑语法功能（例如，主音、属音和下属音）和和弦的层次结构，在传统的和声理论中起着至关重要的作用。在本文中，我们提出了一个统一的层次生成模型，由概率上下文无关语法（PCFG）模型生成的和弦符号与句法功能，一个度量马尔可夫模型生成和弦开始位置，和马尔可夫模型生成的旋律和弦序列的条件。为了估计音乐上自然的树结构，通过使用具有树结构注释的和弦序列以半监督的方式训练PCFG。给定旋律，可以通过使用马尔可夫链蒙特卡罗方法来估计可变数量的和弦的序列，该方法根据和弦序列的后验分布部分地和迭代地更新和弦的符号、起始位置和树结构。实验结果表明，该方法的预测能力优于基于HMM的方法和传统的基于规则的方法。
This article describes a melody harmonization method that generates a sequence of chords (symbols and onset positions) for a given melody (a sequence of musical notes). A typical approach to melody harmonization is to use a hidden Markov model (HMM) that represents chords and notes as latent and observed variables, respectively. This approach, however, does not consider the syntactic functions (e.g., tonic, dominant, and subdominant) and hierarchical structure of chords that play vital roles in traditional harmony theories. In this paper, we propose a unified hierarchical generative model consisting of a probabilistic context-free grammar (PCFG) model generating chord symbols associated with syntactic functions, a metrical Markov model generating chord onset positions, and a Markov model generating a melody conditioned by a chord sequence. To estimate a musically natural tree structure, the PCFG is trained in a semi-supervised manner by using chord sequences with tree structure annotations. Given a melody, a sequence of a variable number of chords can be estimated by using a Markov chain Monte Carlo method that partially and iteratively updates the symbols, onset positions, and tree structure of chords according to the posterior distribution of chord sequences. Experimental results show that the proposed method outperformed the HMM-based method and a conventional rule-based method in terms of predictive abilities.