Chord Recognition Considering All Interval Relations Using Weight-Sharing Classification Semi-Restricted Boltzmann Machines

Abstract

Recent research in chord recognition has utilized machine learning models. However, few models adequately consider harmonic co-occurrence, a known musical feature. Since the harmonic structure is complex and varies with instrument and pitch, the model itself would need to consider harmonics explicitly, but few such methods exist. We propose the classification semi-restricted Boltzmann machine (CSRBM), a machine learning model that can explicitly consider the co-occurrence of any two pitches. A model parameter learns the co-occurrence function to enable chord recognition with flexible consideration of the harmonic structure. We demonstrate how to incorporate the structure as prior knowledge into the model by setting up a prior distribution of the parameter. We also propose weight-sharing CSRBM (WS-CSRBM), an extension of CSRBM that allows time series to be considered. This model enables the CSRBM to consider time series more efficiently not only by arranging some of the CSRBMs in parallel with the number of frames to be considered but also by sharing some of the parameters. Experimental results show that the recognition accuracies of the proposed methods outperform that of a conventional method that considers the co-occurrence of some harmonics. The effectiveness of the CSRBM's parameter in learning pitch co-occurrence, setting up a prior distribution for the parameter, and sharing some parameters in WS-CSRBM are also confirmed.