Expressive timing analysis in classical piano performance by mathematical model selection.
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Given a piece of music, the timing of each beat varies from performer to performer. The study of these small differences is known as expressive timing analysis. Research into expressive timing helps us to understand human perception of music and the production of enjoyable music. Classical piano music is one music style where it is possible to measure expressive timing and hence provides a promising candidate for expressive timing analysis. Various techniques have been used for expressive timing analysis, such as the Self-Organising Map (SOM), parabolic regression and Bayesian models. However, there has been little investigation into whether these methods are in fact suitable for expressive timing analysis and how the parameters in these methods should be selected. For example, there is a lack of formal demonstration that whether the expressive timing within a phrase can be clustered and how many clusters are there for expressive timing in performed music. In this thesis, we use a model selection approach to demonstrate that clustering analysis, hierarchical structure analysis and temporal analysis are suitable for expressive timing analysis. Firstly in this thesis, we will introduce some common methods for model selection such as Akaike's Information Criterion, Bayesian Information Criterion and cross-validation. Next we use these methods to demonstrate the best model for clustering expressive timing in piano performances. We propose a number of pre-processing methods and Gaussian Mixture Models with different settings for covariance matrices. The candidate models are compared with three pieces of music, including Balakirev's Islamey and two Chopin Mazurkas. The results of our model comparison recommend particular models for clustering expressive timing from the candidate models. Hierarchical analysis, or multi-layer analysis, is a popular concept in expressive timing analysis. To compare different hierarchical structures for expressive timing analysis, we propose a new model that suggests music structure boundaries according to expressive timing information and hierarchical structure analysis. We propose a set of hierarchical structures and we compare the resulting models by showing the probability of observing the boundaries of music structure and showing the similarity of the same-performer renderings. Our analysis supports the proposition that hierarchical structure improves the performance of modelling over non-hierarchical models for the performances that we considered. Researchers have also suggested that expressive timing is in influenced by music structure and temporal features. In order to investigate this, we consider four Bayesian graphical models that model dependencies between a position in a music score and the expressive timing changes in the previous phrase, on expressive timing in the current phrase. Using our model selection criterion, we find that the position of a phrase in music scores is only shown to effect expressive timing in the current phrase when the previous phrase is also considered. The results in this thesis indicate that model selection is useful in the analysis of expressive timing. The model selection methods we use here could potentially be applied to a wide range of applications, such as predicting human perception of expressive timing in music, providing expressive timing information for music synthesis and performance identification.
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