# Function- and Rhythm-Aware Melody Harmonization

Based on Tree-Structured Parsing

and Split-Merge Sampling of Chord Sequences

#### â€”Submitted to ISMIR 2017

### Abstract

##### This paper presents an automatic harmonization method that generates a musically-meaningful chord sequence for a given melody (sequence of musical notes). A standard way is to use hidden Markov models (HMMs) that represent chord transitions on a regular time grid (e.g., bar or beat grid). This approach, however, cannot handle the rhythms, harmonic functions (e.g., tonic, dominant, and subdominant), and hierarchical repetitive structures of chords, which are all important for melody harmonization. To overcome this limitation, we formulate a hierarchical generative model of melodies that consists of (1) a probabilistic context-free grammar (PCFG) for a chord sequence with functions, (2) a metrical Markov model describing chord rhythms, and (3) a Markov model that generates a melody from a chord sequence. To estimate a chord sequence with a variable length and rhythm for a given melody, we iteratively refine the latent tree structure and the labels and durations of chords by using a Metropolis-Hastings sampler with split-merge operations. Experimental results showed that the proposed method outperformed the HMM-based harmonizer in terms of predictive ability and musical appropriateness.

### Experimental Results