Marc Chemillier

Periodic musical sequences and Lyndon words

When one enumerates periodic musical structures, the computation is done up to a cyclic shift. This means that two solutions which are cyclic shifts of one another are considered the same. Lyndon words provide a powerful way to do so. We illustrate this by two examples taken from African traditional music.

Toward a formal study of jazz chord sequences generated by Steedman’s grammar

This paper shows how to generate jazz chord sequences incrementally using Steedman’s grammar by taking advantage of some formal properties. We point out the specific role played by particular chord sequences called “cadential sequences”. By precompiling them, one could improve the implementation of Steedman’s grammar in a real-time improvisation system, and make it more reactive to the inputs of the user.