| Résumé |
e concept of rhythmic canons, as it has been introduced by mathematician Dan Vuza in the 1990s, is the art of filling the time axis with some finite rhythmic patterns and their translations, without onsets superposition. The musical notion have been linked with some mathematical results, and since then, its mathematical study has always followed a will of picturing every new results in the visual programming language OpenMusic, which enables mathematicians and composers to work together. In this paper we present some new results in an enriched version of rhythmic tiling canons, where some controlled superposition are allowed. This enhanced version of rhythmic tiling canons is presented at the beginning of this article, as well as main constructive results, because it is fairly recent. Then the paper focuses on the presentation of some generative transformations, building canons with the same superposition. The latter is at the heart of the study of canons allowing superposition, because they are the key of linking them back to seminal canons. In order to help composers experiment with these new canons, every constructive method has been implemented in OpenMusic as part of the MathTools environment. |
