Generative statistical models with self-emergent grammar of chord sequences

ABSTRACT

Generative statistical models of chord sequences play crucial roles in music processing. To capture syntactic similarities among certain chords (e.g. in C major key, between G and G7 and between F and Dm), we study hidden Markov models and probabilistic context-free grammar models with latent variables describing syntactic categories of chord symbols and their unsupervised learning techniques for inducing the latent grammar from data. Surprisingly, we find that these models often outperform conventional Markov models in predictive power, and the self-emergent categories often correspond to traditional harmonic functions. This implies the need for chord categories in harmony models from the informatics perspective.

Keywords:

• Statistical music language model
• harmonic (tonal) function
• unsupervised grammar induction
• Bayesian inference
• hidden Markov model
• probabilistic context-free grammar

Notes

1 The number of possible ways to tie transition probabilities is given by the partition number. For example, with 10 symbols, it is 42 for a first-order model and about for a second-order model (with bigram contexts).

2 To make the relation between PCFG models and HMMs explicit, we here do not include the start symbol in .

3 J-Total Music: http://music.j-total.net (Researchers who wish to have access to the J-Pop data should contact the authors.)

4 The dataset was downloaded from the McGill Billboard Project webpage: http://ddmal.music.mcgill.ca/research/billboard (Complete Annotation section).

Additional information

Funding

E. Nakamura is supported by the JSPS Postdoctoral Research Fellowship. This work is in part supported by JSPS KAKENHI [grant number 24220006], [grant number 26280089], [grant number 26700020], [grant number 15K16054], [grant number 16H01744], [grant number 16H02917], [grant number 16K00501], [grant number 16J05486]; JST ACCEL [grant number JPMJAC1602].