Musical improvisation - Lycée Emmanuel d'Alzon (Nîmes)

How many tunes can one compose from 7 notes ? As much as we want, since the tune C-C-C-...-C can be made as long as necessary. Now we make the problem more tricky by giving some constraints: how many tunes can one compose, forbidding any repetition of a 2 note-long pattern (for instance ...-E-C-...-E-C-..., is forbidden) or forbidding any direct repetition of a single note (for instance ...-D-D-... is forbidden). The article tackles these problems and some related problems, such as the evaluation of the number of tunes of a given length, using graph theory.