deletions | additions       diff --git a/CImplementation.tex b/CImplementation.tex  index aa8e5e2..058f1e0 100644  --- a/CImplementation.tex  +++ b/CImplementation.tex 
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\end{cases}  \]  Extracting features from an integer $i$ representing a chord is then a simple task that can be represented in psuedocode as follows:  \begin{verbatim}  function  ExtractFeatures(i) if (i = 0)  return NoChord  else 
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return (Bass, Root, Harmony)  \end{verbatim}  \subsection{Bitwise representation of harmonies} harmony}  Chord quality can be represented as a 12-bit integer in which each bit corresponds to whether a certain interval is included. This compact representation provides a means for quick computation and allows chord distance computations to be represented  , a 12-bit integer can represent harmony in which each bit corresponds to whether a certain interval is included in the chord or not. Since leading 0's are excluded, the representation can start with 1 in the first binary position (right-to-left) to represent the root of the chord. Thus, a concise 12-bit integer representation of harmony consists of a 1 in the first binary position with the following $i$th From right-to-left, the $i$th bit represents whether the interval $i - 1$ (where 0 is the root note) is included in the chord or not (see figure~\ref{fig:qualitytable}). All harmonies used in the program and associated intervals can be seen in figure~\ref{fig:qualitybitstable}.  For quick computation \begin{figure}[h!]  \begin{center}  \begin{tabular}{lll}  \toprule  Chord Quality & Shorthand & Binary Representation & Base 10 Representation \\  \midrule  Major & & 10010001 & 145 \\  Major 6th & 6 & 10001001 & 137 \\  Major 7th & maj7 & 1001001 & 73 \\  Minor & m & 100010001 & 273 \\  Minor 6th & m6 & 100010010001 & 2193 \\  Minor 7th & m7 & 10010001001 & 1161 \\  Dominant 7th & 7 & 10010010001 & 1169 \\  Augmented & aug & 1001001001 & 585 \\  Diminished & dim & 10001001001 & 1097 \\  Diminished 7th & dim7 & 1010010001 & 657 \\  Half-diminished 7th & m7b5 & 1010001001 & 649 \\  \bottomrule  \end{tabular}  \caption{Binary Representation  of chord distances based on pitch classes, a 11-bit integer can represent harmony, where the $i$th bit represents whether the interval $i+1$ is included in the chord or not (see figure~\ref{fig:qualitytable}). Chords}  \label{fig:qualitytable}  \end{center}  \end{figure}  \item Cleverness with representing chords and harmonies as integers and allowing simple bitwise operations and bitmasks