In jazz, a contrafact is a new melody composed over an existing, but often reharmonized chord progression. Because reharmonization can introduce a wide range of variations, detecting contrafacts is a challenging task. This paper develops a novel vector-space model to represent chord progressions, and uses it for contrafact detection. The process applies principles from music theory to reduce the dimensionality of chord space, determine a common key signature representation, and compute a chordal co-occurrence matrix. The rows of the matrix form a basis for the vector space in which chord progressions are represented as piecewise linear functions, and harmonic similarity is evaluated by computing the membrane area, a novel distance metric. To illustrate our method's effectiveness, we apply it to the Impro-Visor corpus of 2,612 chord progressions, and present examples demonstrating its ability to account for reharmonizations and find contrafacts.
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