Discovering translational patterns in symbolic representations of music

Tom Collins http://users.mct.open.ac.uk/tec69

Supervisors Robin Laney

Alistair Willis Paul Garthwaite

Department/Institute Centre for Research in Computing Status Fulltime Probation viva After Starting date October 2008

RESEARCH QUESTION How can current methods for pattern discovery in music be improved and integrated into an automated composition system? The presentation will address the first half of this research question: how can current methods for pattern discovery in music be improved?

INTRA-OPUS PATTERN DISCOVERY Suppose that you wish to get to know a particular piece of music, and that you have a copy of the score of the piece or a MIDI file. (Scores and MIDI files are symbolic representations of music and are the focus of my presentation, as opposed to sound recordings.) Typically, to become familiar with a piece, one listens to the MIDI file or studies/plays through the score, gaining an appreciation of where and how material is repeated, and perhaps also gaining an appreciation of the underlying structure. The literature contains several algorithmic approaches to this task, referred to as ‘intra-opus’ pattern discovery [2, 4, 5]. Given a piece of music in a symbolic representation, the aim is to define and evaluate an algorithm that discovers and returns patterns occurring within the piece. Some potential applications for such an algorithm are as follows:

• A pattern discovery tool to aid music students. • Comparing an algorithm’s discoveries with those of a music expert as a means

of investigating human perception of music. • Stylistic composition (the process of writing in the style of another composer

or period) assisted by using the patterns/structure returned by a pattern discovery algorithm [1, 3].

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TWO IMPROVEMENTS Current methods for pattern discovery in music can be improved in two ways:

1. The way in which the algorithm’s discoveries are displayed for a user can be improved.

2. A new algorithm can be said to improve upon existing algorithms if, according to standard metrics, it is the strongest-performing algorithm on a certain task.

Addressing the first area for improvement, suppose that an algorithm has discovered hundreds of patterns within a piece of music. Now these must be presented to the user, but in what order? Various formulae have been proposed for rating a discovered pattern, based on variables that quantify attributes of that pattern and the piece of music in which it appears [2, 4]. To my knowledge, none have been derived or validated empirically. So I conducted a study in which music undergraduates examined excerpts taken from Chopin’s mazurkas and were instructed to rate already-discovered patterns, giving high ratings to patterns that they thought were noticeable and/or important. A model useful for relating participants’ ratings to the attributes was determined using variable selection and cross-validation. This model leads to a new formula for rating discovered patterns, and the basis for this formula constitutes a methodological improvement. Addressing the second area for improvement, I asked a music analyst to analyse two sonatas by Domenico Scarlatti and two preludes by Johann Sebastian Bach. The brief was similar to the intra-opus discovery task described above: given a piece of music in staff notation, discover translational patterns that occur within the piece. Thus, a benchmark of translational patterns was formed for each piece, the criteria for benchmark membership being left largely to the analyst’s discretion. Three algorithms—SIA [5], COSIATEC [4] and my own, SIACT—were run on the same pieces and their performance was evaluated in terms of recall and precision. If an algorithm discovers x of the y patterns discovered by the analyst then its recall is x/y. If the algorithm also returns z patterns that are not in the analyst’s benchmark then the algorithm’s precision is x/(x + z). It was found that my algorithm, SIACT, out-performs the existing algorithms with regard to recall and, more often than not, precision. My presentation will give the definition of a translational pattern, discuss the improvements outlined above, and demonstrate how these improvements are being brought together in a user interface.

SELECTED REFERENCES 1. Collins, T., R. Laney, A. Willis, and P.H. Garthwaite, ‘Using discovered, polyphonic patterns to filter computer-generated music’, in Proceedings of the International Conference on Computational Creativity, Lisbon (2010), 1-10. 2. Conklin, D., and M. Bergeron, ‘Feature set patterns in music’, in Computer Music Journal 32(1) (2008), 60-70.

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3. Cope, D., Computational models of musical creativity (Cambridge Massachusetts: MIT Press, 2005). 4. Meredith, D., K. Lemström, and G.A. Wiggins, ‘Algorithms for discovering repeated patterns in multidimensional representations of polyphonic music’, in Cambridge Music Processing Colloquium, Cambridge (2003), 11 pages. 5. Meredith, D., K. Lemström, and G.A. Wiggins, ‘Algorithms for discovering repeated patterns in multidimensional representations of polyphonic music’, in Journal of New Music Research 31(4) (2002), 321-345.

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