This thesis is based to a large extent on the work of Lindley and Turner-Smith [14]. Their work includes the notion of pitch class as a possibly two-dimensional entity characterized by P5 and M3 relationships. This is similar to the notion of triadic pitch class used in this thesis. Their use of Cayley diagrams to describe these P5 and M3 relationships is instructive. The idea of characterizing tunings by their deviation from just P5 and M3 is used in their work and in this thesis. Their work is one of the few that uses the mil rather than the cent as the unit of logarithmic frequency ratio, although they conflate interval and frequency ratio by identifying a mil as a millioctave, not a millidoubling. Their work makes use of an interval size convention similar to Blackwood's and therefore suffers from similar inability to deal with register. Their use of group theory to describe pitch class relationships is powerful but in general adds unnecessary complexity compared to the simple vector representation of pitch used in this thesis.