Section: New Results

Representation of Rhythm and Quantization

Participants : Florent Jacquemard, Adrien Ycart, Pierre Donat-Bouillud.

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 structures, which were originally used in natural language processing. We are particularly interested in two well established formalisms with solid theoretical foundations: weighted automata for trees and dags and term rewriting.

Our 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 5.2. 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. In collaboration with Jean Bresson (Ircam) and Slawek Staworko (LINKS), we are developing 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 [22], [23].

Moreover, in collaboration with Prof. Masahiko Sakai (Nagoya University), we are working on symbolic processing of music notation, based on the above models. We proposed a structural theory (equational system on rhythm trees) defining equivalence on rhythm notations [42], [51], and use this approach, for instance, to generate, by transformation, different possible notations of the same rhythm, with the ability to select either alternative notation in accordance with certain constraints, e.g. in the context of transcription.

Related results on the property of confluence of term rewriting systems were presented in [19] (invited talk), and other work on data tree processing, in collaboration with Luc Segoufin and Jeremie Dimino, have published in [16].