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Computationally comparing chord progressions and approximating subjective human notions of similarity is a difficult task. Influential or unique chord progressions are frequently discussed in cultural contexts \cite{ogihara2008n}. Looking for local similarities between chord progressions has proved effective\cite{hanna2009alignment} and seems to match human intuition. When songs are said to be similar it does not mean that both songs' progressions are similar globally, or throughout the entire song, but rather that there are identical or near-identical local sections of similarity. For instance, The Beatles song \textit{Let It Be} has a progression of $I - V - vi - IV$ occurring at the beginning and frequently during the song. The chorus starts with a different progression but \textit{Let It Be} is still classed with songs of the progression $I - V - vi - IV$ and is included on Wikipedia's "List of songs containing the I–V–vi–IV progression," which at the time of writing includes 189 songs\cite{wikiprog1}. Another famous progression, $vi-IV-I-V$ (which is a cyclic shift of the previous progression), has even been dubbed the "Sensitive Female Chord Progression" for its use in countless pop songs\cite{hirsh2008}.  Chord progression identity is a salient factor in harmonically understanding a song, and preserving notions of local similarity is essential. The following sections detail algorithms that can be used to compare chord progressions, their advantages and disadvantages, and basic experimental results, if any. The following notation will be used:  \begin{align*}  {c1}\text{ and }{c2} & \text{The chord progressions of two songs, respectively} \\  {c_i} & \text{The }i\text{th element of chord progression }c \\  {n1}\text{ and }{n2} & \text{The length of }{c1}\text{ and }{c2}\text{, respectively} \\  C_d & \text{A chord distance function taking as argument two chords and returning a value. Higher scores indicate stronger similarity} \\  t_s & \text{A transposition function that takes a chord as an argument and transposes it }s\text{ semitones} \\  \end{align*}  \subsection{Simple Global Comparison}