Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Unsupervised Learning of Harmonic Analysis Based on Neural HSMM with Code Quality Templates

Yui Uehara

TL;DR

The chord quality templates are introduced, which specify the probability of pitch class emissions given a root note and a chord quality, and it is shown how to recognize the tonic without prior knowledge, based on the transition probabilities of the Markov model.

Abstract

This paper presents a method of unsupervised learning of harmonic analysis based on a hidden semi-Markov model (HSMM). We introduce the chord quality templates, which specify the probability of pitch class emissions given a root note and a chord quality. Other probability distributions that comprise the HSMM are automatically learned via unsupervised learning, which has been a challenge in existing research. The results of the harmonic analysis of the proposed model were evaluated using existing labeled data. While our proposed method has yet to perform as well as existing models that used supervised learning and complex rule design, it has the advantage of not requiring expensive labeled data or rule elaboration. Furthermore, we also show how to recognize the tonic without prior knowledge, based on the transition probabilities of the Markov model.

Unsupervised Learning of Harmonic Analysis Based on Neural HSMM with Code Quality Templates

TL;DR

The chord quality templates are introduced, which specify the probability of pitch class emissions given a root note and a chord quality, and it is shown how to recognize the tonic without prior knowledge, based on the transition probabilities of the Markov model.

Abstract

This paper presents a method of unsupervised learning of harmonic analysis based on a hidden semi-Markov model (HSMM). We introduce the chord quality templates, which specify the probability of pitch class emissions given a root note and a chord quality. Other probability distributions that comprise the HSMM are automatically learned via unsupervised learning, which has been a challenge in existing research. The results of the harmonic analysis of the proposed model were evaluated using existing labeled data. While our proposed method has yet to perform as well as existing models that used supervised learning and complex rule design, it has the advantage of not requiring expensive labeled data or rule elaboration. Furthermore, we also show how to recognize the tonic without prior knowledge, based on the transition probabilities of the Markov model.
Paper Structure (20 sections, 22 equations, 5 figures, 6 tables)

This paper contains 20 sections, 22 equations, 5 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Automated harmonic analyses
  4. Rule-based harmonic analysis
  5. Harmonic analyses with supervised learning
  6. Unsupervised harmonic analysis
  7. Deep latent variable models
  8. Methodology
  9. The hidden semi-Markov model for harmonic analysis
  10. Emission distribution with chord quality templates
  11. Hidden state transition distribution
  12. Training
  13. Inference (harmonic analysis)
  14. Experiments
  15. Datasets
  16. ...and 5 more sections

Figures (5)

  • Figure 1: An example of possible paths of hidden states where the number of keys is 2, the number of roots is 2, and the maximum duration is 3. For simplicity, the number of keys, roots, and the maximum duration are less than the actual settings. Thin solid lines represent root transitions, dotted lines represent key transitions (modulations), and bold solid lines represent the consumption of the remaining duration times.
  • Figure 2: Harmonic analysis of BWV269 (Riemenschneider No.1), bars 13 -- 20.
  • Figure 3: Harmonic analysis of BWV40.8 (Riemenschneider No.8), bars 7 -- 10.
  • Figure 4: Result of the stationary distribution of root pitch classes (JSBChorales371, seed=789). The left side is mode $m = 0$, and the right is mode $m = 1$.
  • Figure 5: Result of the pitch class probabilities (JSBChorales371, seed=789). The left side is mode $m = 0$, and the right is mode $m = 1$.