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\subsection{Pitch Class}  Though the chromatic scale contains 12 notes, there are an infinite amount of  ways to represent any singular pitch within the octave. For instance, a $C\#$ note can be represented as a $Db$, a $B\#\#$ ("B-double-sharp"), or a $Fbbbb$, among other possibilities. There are notational reasons to represent a pitch in these ways, and outside of \textit{equal temperament}, the tuning system upon which Western music is based, these notes sound different and have different perceptual frequencies. In equal temperament, which is an assumption guiding this paper, all these different notes have identical pitches. A \textit{pitch class} is the collection of all pitches across all octaves. The $C\#$ pitch class, for instance, contains all the $C\#$ pitches over all the octaves, in addition to the $Db$ pitches and any other pitch that represents the same note name.