Section: New Results

Representation of Rhythm and Quantization

Rhythmic data are commonly represented by tree structures (rhythms trees) in assisted music composition environments, such as OpenMusic, due to the theoretical proximity of such structures with traditional musical notation. We are studying the application in this context of techniques and tools for processing tree structure, which were originally developed for other areas such as natural language processing, automatic deduction, Web data ... We are particularly interested in two well established formalisms with solid theoretical foundations: term rewriting and tree automata.

The problem of rhythm transcription, or quantization, is to generate, from a timed sequence of notes (e.g. a file in MIDI format), a score in traditional music notation. The input events can come from an interpretation on a MIDI keyboard or be the result of a computation in OpenMusic. This problem arises immediately as insoluble unequivocally: we shall calibrate the system to fit the musical context, balancing constraints of precision, or of simplicity / readability of the generated scores. For this purpose, we are developing in collaboration with Slawek Staworko (LINKS, currently on leave at University of Edinburgh) for algorithms searching optimums in large sets of weighted trees (tree series), representing possible solutions to a problem quantification. A prototype has been developed and is under evaluation on real case studies. For the construction of appropriate tree series, we turn to semi-supervised systems, where the composer's interactions are predominant in the smooth process. These work have been presented in an invited talk in the workshop of the IFIP working group on term rewriting.

With Prof. Masahiko Sakai (Nagoya University, a specialist in term rewriting), we conduct a complementary work [14] on the representation of rhythmic notation. The goal is to define a structural theory as equations on trees rhythms. This approach can be used for example to generate, by transformation, different notations possible the same rate, with the ability to select in accordance with certain constraints.