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\chapter{Initial Results} \chapter{Results}  \section{Variables Used and Notation}  This section details a number of experiments run on the data. To compare chord progressions, only the Smith-Waterman algorithm ($SW$) is used, with normalization measures \textit{raw score} and ${SW}_{norm}$ being tested. Gap costs (${gap}_{open}$ and ${gap}_{ext}$) are allowed to vary from 0 through 128 (maximum range of an 8-bit integer). The Harte distance metric ($Harte$) and Tonal Pitch Space ($TPS$) are used to evaluate chord distances. Lastly, multiplication and subtraction factors $m_x$ and $m_s$ are used to round the chord distance metrics to integers with an expected value below 0. A full summary of the variables and their tested ranges is as follows:  \begin{align*}  \textbf{Variables} & \hspace{1cm} & \textbf{Values} \\  \text{Normalization } (norm) && \{\textit{raw score},{SW}_{norm}\} \\  \text{Gap open cost } ({gap}_{open}) && [0-128] \\  \text{Gap extension cost } ({gap}_{ext}) && [0-128] \\  \text{Chord Distance Metric } (C_d) && \{Harte, TPS\} \\  \text{Chord Distance Multiplier } (m_x) && \{1, 30\} \\  \text{Chord Distance Subtraction Factor } (m_s) && \{0, 30\} \\  \end{align*}  \subsection{Smith-Waterman Normalization}  \subsection{Smith-Waterman Gap Costs}  \subsection{Chord Distance Function}  \subsection{Pairwise distance computation}  \subsection{Clustering}  \subsection{Visualization}  \subsection{Ranking Fully Connected Pairwise Comparisons}  \subsection{Ranking Random N-Gram Search}  \subsection{Key-Finding Accuracy}  \section{Smith-Waterman Results}