Pattern Matching in Polyphonic Music as a Weighted Geometric Translation Problem

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 3-SUM 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.

• Type: Conference
• Year: 2004
• Where: ISMIR
• Authors: Anna Lubiw, Luke Tanur
• Keywords: Horizontal Line Segments, ISMIR 2004, Pattern Matching, Pattern Matching Problem—to