Burnside’s lemma can be used to compute the number of orbits when a group acts on a set.  Musically, this is equivalent to counting the number of set classes of d-note collections within a chromatic universe of size c.  This calculation can be very time consuming.  However, by allowing the dihedral group of order 2d to act on the set of scale vectors of d-note collections (within a c-note chromatic universe), the counting process may become drastically easier.  Given c and d, the number of set-classes can be considered a form of complexity.  How does the complexity change as we adjust the variable c and d, and what does it mean musically?  This talk will serve as a progress report of the current research.