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Another measure to normalize the Smith-Waterman score is  \[ SW_{norm}(c1,c2)=\frac{SW(c1,c2)}{\max [SW(c1,c1), SW(c2,c2)]} \]  which involves running the Smith-Waterman algorithm over chord progressions against themselves. This returns the score of identity in the distance metric multiplied by the length of the sequence being tested, which has a direct linear correlation with sequence length. Essentially, this is linearly equivalent to a normalization by dividing by the maximal length of the sequences being tested and returns values from 0.0 to 1.0.  The only normalization measures considered in this paper are \textit{raw score} and this measure I call \textit{SW_{norm}}.  % % C, F, C, *, G, F, C, G, Dm, C  % % | | ins | | | del | |  % % F, C, Dm, G, F, C, *, Dm, C, F  % \item Localized comparison, dynamic programming, find minimum number of required "transformations" and optimal localized slice. Dynamic programming  % \item Works well with inexact data, can deal with common pitfalls of chord extraction.  % \item Isolates similar substructures.  % \item Does not penalize closely related chords, i.e. Em7 and Gmaj  % \item Difficulty in extracting multiple "best" options but good at finding one top contender  % \item Difficulty in comparing scores  % \subsection{Example Smith-Waterman Algorithm}  % The following example shows how the Smith-Waterman algorithm could be applied to the alphabet of musical chord symbols:  % This example assumes the following costs:  % If the chord begins on the same root, then add 3 \\  % Otherwise, subtract 4 \\