An approach to melodic segmentation and classification based on filtering with the Haar wavelet

We present a novel method of classification and segmentation of melodies in symbolic representation. The method is based on filtering pitch as a signal over time with the Haar-wavelet, and we evaluate it on two tasks. The filtered signal corresponds to a single-scale signal ws from the continuous Haar wavelet transform. The melodies are first segmented using local maxima or zero-crossings of ws. The segments of ws are then classified using the k–nearest neighbour algorithm with Euclidian and city-block distances. The method proves more effective than using unfiltered pitch signals and Gestalt-based segmentation when used to recognize the parent works of segments from Bach’s Two-Part Inventions (BWV 772–786). When used to classify 360 Dutch folk tunes into 26 tune families, the performance of the method is comparable to the use of pitch signals, but not as good as that of string-matching methods based on multiple features

Generation of folk song melodies using Bayes transforms

The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models

Information dynamics: patterns of expectation and surprise in the perception of music

This is a postprint of an article submitted for consideration in Connection Science © 2009 [copyright Taylor & Francis]; Connection Science is available online at:http://www.tandfonline.com/openurl?genre=article&issn=0954-0091&volume=21&issue=2-3&spage=8

Variational Hilbert space truncation approach to quantum Heisenberg antiferromagnets on frustrated clusters

We study the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a series of finite-size clusters with features inspired by the fullerenes. Frustration due to the presence of pentagonal rings makes such structures challenging in the context of quantum Monte-Carlo methods. We use an exact diagonalization approach combined with a truncation method in which only the most important basis states of the Hilbert space are retained. We describe an efficient variational method for finding an optimal truncation of a given size which minimizes the error in the ground state energy. Ground state energies and spin-spin correlations are obtained for clusters with up to thirty-two sites without the need to restrict the symmetry of the structures. The results are compared to full-space calculations and to unfrustrated structures based on the honeycomb lattice.Comment: 22 pages and 12 Postscript figure

Cognitive and affective judgements of syncopated musical themes

This study investigated cognitive and emotional effects of syncopation, a feature of musical rhythm that produces expectancy violations in the listener by emphasising weak temporal locations and de-emphasising strong locations in metric structure. Stimuli consisting of pairs of unsyncopated and syncopated musical phrases were rated by 35 musicians for perceived complexity, enjoyment, happiness, arousal, and tension. Overall, syncopated patterns were more enjoyed, and rated as happier, than unsyncopated patterns, while differences in perceived tension were unreliable. Complexity and arousal ratings were asymmetric by serial order, increasing when patterns moved from unsyncopated to syncopated, but not significantly changing when order was reversed. These results suggest that syncopation influences emotional valence (positively), and that while syncopated rhythms are objectively more complex than unsyncopated rhythms, this difference is more salient when complexity increases than when it decreases. It is proposed that composers and improvisers may exploit this asymmetry in perceived complexity by favoring formal structures that progress from rhythmically simple to complex, as can be observed in the initial sections of musical forms such as theme and variations