Computational Tonality Estimation: Signal Processing and Hidden Markov Models

Abstract

This thesis investigates computational musical tonality estimation from an audio signal. We present a hidden Markov model (HMM) in which relationships between chords and keys are expressed as probabilities of emitting observable chords from a hidden key sequence. The model is tested first using symbolic chord annotations as observations, and gives excellent global key recognition rates on a set of Beatles songs. The initial model is extended for audio input by using an existing chord recognition algorithm, which allows it to be tested on a much larger database. We show that a simple model of the upper partials in the signal improves percentage scores. We also present a variant of the HMM which has a continuous observation probability density, but show that the discrete version gives better performance. Then follows a detailed analysis of the effects on key estimation and computation time of changing the low level signal processing parameters. We find that much of the high frequency information can be omitted without loss of accuracy, and significant computational savings can be made by applying a threshold to the transform kernels. Results show that there is no single ideal set of parameters for all music, but that tuning the parameters can make a difference to accuracy. We discuss methods of evaluating more complex tonal changes than a single global key, and compare a metric that measures similarity to a ground truth to metrics that are rooted in music retrieval. We show that the two measures give different results, and so recommend that the choice of evaluation metric is determined by the intended application. Finally we draw together our conclusions and use them to suggest areas for continuation of this research, in the areas of tonality model development, feature extraction, evaluation methodology, and applications of computational tonality estimation.