Abstract:

The enumeration of musical objects has received heightened attention in the last twenty five years, and whilst such phenomena as tone rows, polyphonic mosaics, and scales have been explored, there has not been prior investigation of the enumeration of chord sequences. In part, analysts may have disregarded the situation as having a trivial solution, namely the number of chord types at each step raised to the power of the number of steps. However, there are more subtle and interesting situations where there are constraints, such as rotational and transpositional equivalence of sequences. Enumeration of such chord sequences is explored through the application of Burnside’s lemma for counting equivalence classes under a group action, and computer generation of lists of representative chord sequences outlined. Potential extensions to ‘McCartney’s Chord Sequence Problem’ for the enumeration of cyclic (looping) chord sequences are further discussed