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 processing... We are particularly interested in two well established formalisms with solid theoretical foundations: tree automata and term rewriting.

Our first main contribution in that context is the development of a new framework for rhythm transcription, the problem of the generation, from a sequence of timestamped notes, e.g. a file in MIDI format, of a score in traditional music notation) – see Section  6.4 . 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. We are developing in collaboration with Jean Bresson (Ircam) and Slawek Staworko (LINKS, currently on leave at University of Edinburgh) an approach based on algorithms for the enumeration of large sets of weighted trees (tree series), representing possible solutions to a problem of transcription. The implementation work is performed by Adrien Ycart, under a research engineer contract with Ircam. This work has been presented in [23] .

Our second contribution, in collaboration with Prof. Masahiko Sakai (Nagoya University), is a proposal of a structural theory (equational system on rhythm trees) defining equivalence on rhythm notations [14] , [16] . 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. We have also conducted related work on the theory of term rewriting [17] .