In this article, a combination of two novel approaches to the harmonization of chorales in the style of J. S. Bach is proposed, implemented, and profiled. The first is the use of the bass line, as opposed to the melody, as the primary input into a chorale-harmonization algorithm. The second is a compromise between methods guided by music knowledge and by machine-learning techniques, designed to mimic the way a music student learns. Specifically, our approach involves learning harmonic structure through a hidden Markov model, and determining individual voice lines by optimizing a Boltzmann pseudolikelihood function incorporating musical constraints through a weighted linear combination of constraint indicators. Although previous generative models have focused only on codifying musical rules or on machine learning without any rule specification, by using a combination of musicologically sound constraints with weights estimated from chorales composed by Bach, we were able to produce musical output in a style that closely resembles Bach's chorale harmonizations. A group of test subjects was able to distinguish which chorales were computer generated only 51.3% of the time, a rate not significantly different from guessing.

中文翻译：

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巴赫合唱团低音线的自动协调：一种混合方法

在本文中，提出、实施和描述了两种新方法的组合，以协调 JS Bach 风格的合唱团。第一个是使用低音线，而不是旋律，作为合唱协调算法的主要输入。第二个是音乐知识指导的方法和机器学习技术之间的折衷，旨在模仿音乐学生的学习方式。具体来说，我们的方法涉及通过隐马尔可夫模型学习谐波结构，并通过约束指标的加权线性组合优化包含音乐约束的玻尔兹曼伪似然函数来确定单个语音线。尽管以前的生成模型只关注编纂音乐规则或没有任何规则规范的机器学习，通过结合使用音乐学上的声音约束和根据巴赫创作的合唱团估计的权重，我们能够以非常类似于巴赫的合唱团和声的风格产生音乐输出。一组测试对象仅在 51.3% 的时间内能够区分哪些合唱团是由计算机生成的，这一比率与猜测没有显着差异。