# BacHMMachine: An Interpretable and Scalable Model for Algorithmic Harmonization for Four-part Baroque Chorales

arXiv: https://arxiv.org/abs/2109.07623 · HTML: https://mlsanity.com/paper/2109.07623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 25 references that are in the map.
- First posted on arXiv 15 Sep 2021.

## Builds on (most cited first, 2 of 2)

- [DeepBach: a Steerable Model for Bach Chorales Generation](https://mlsanity.com/paper/1612.01010/) (2016)
- [Counterpoint by Convolution](https://mlsanity.com/paper/1903.07227/) (2019)

## Abstract (arXiv)

Algorithmic harmonization - the automated harmonization of a musical piece given its melodic line - is a challenging problem that has garnered much interest from both music theorists and computer scientists. One genre of particular interest is the four-part Baroque chorales of J.S. Bach. Methods for algorithmic chorale harmonization typically adopt a black-box, "data-driven" approach: they do not explicitly integrate principles from music theory but rely on a complex learning model trained with a large amount of chorale data. We propose instead a new harmonization model, called BacHMMachine, which employs a "theory-driven" framework guided by music composition principles, along with a "data-driven" model for learning compositional features within this framework. As its name suggests, BacHMMachine uses a novel Hidden Markov Model based on key and chord transitions, providing a probabilistic framework for learning key modulations and chordal progressions from a given melodic line. This allows for the generation of creative, yet musically coherent chorale harmonizations; integrating compositional principles allows for a much simpler model that results in vast decreases in computational burden and greater interpretability compared to state-of-the-art algorithmic harmonization methods, at no penalty to quality of harmonization or musicality. We demonstrate this improvement via comprehensive experiments and Turing tests comparing BacHMMachine to existing methods.