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\subsection{Pitch Classes} Class}  Though the chromatic scale contains 12 notes, there are an infinite 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.