Generating equivalent rhythmic notations based on rhythm tree languages.

We propose a compact presentation of languages of preferred rhythm notations as formal grammars. It is based on a standard structure of rhythm trees capturing a wide range of rhythms in Western notation. As an application, we then describe a dynamic programming algorithm for the lazy enumeration of equivalent rhythm notations (i.e. notations defining the same durations), from the simplest to the most complex. This procedure, based on the notion of rhythm grammars has been implemented and may be useful in the context of automated music transcription and computer-assistance to composition.