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\section{Harte Distance Metric}  The Harte chord distance metric, proposed by Christopher Harte in \cite{harte2010towards}, is a simple and convenient means of calculating a score representing the distance between any two chords. Letting $P_c$ represent the given pitch classes of a chord, we can define Harte's formula as follows:  \[ H(c_1,c_2) = \frac{\left| P_c(c_1) \cap P_c(c_2) \right|}{\left| P_c(c_1) \cup P_c(c_2) \right|} \]