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Pattern matching in polyphonic music as a weighted geometric translation problem
 In Proc. 5th International Conference on Music Information Retrieval
, 2004
"... We consider the music pattern matching problem—to find occurrences of a small fragment of music called the “pattern” in a larger body of music called the “score”—as a problem of translating a set of horizontal line segments in the plane to find the best match in a larger set of horizontal line segme ..."
Abstract

Cited by 18 (1 self)
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We consider the music pattern matching problem—to find occurrences of a small fragment of music called the “pattern” in a larger body of music called the “score”—as a problem of translating a set of horizontal line segments in the plane to find the best match in a larger set of horizontal line segments. Our contribution is that we use fairly general weight functions to measure the quality of a match, thus enabling approximate pattern matching. We give an algorithm with running time O(nm log m), where n is the size of the score and m is the size of the pattern. We show that the problem, in this geometric formulation, is unlikely to have a significantly faster algorithm because it is at least as hard as a basic problem called 3SUM that is conjectured to have no subquadratic algorithm. We present some examples to show the potential of this method for finding minor variations of a theme, and for finding polyphonic musical patterns in a polyphonic score. 1.