On some combinatorial problems concerning the harmonic structure of musical chord sequences

We present some combinatorial problems which arise in the fields of music representation and music processing, in particular in the context of analysis of the harmonic structure of chord sequences. We are mainly concerned with problems related to chord sequences which exhibit a certain kind of regular harmonic structure, and provide also algorithms to solve some of them. In particular, we present an O(n+m)-time algorithm, based on bit-parallelism, to check whether a given chord progression of length n is regular, where m is the size of the chords in the progression.