Transposition-Invariant Self-Similarity Matrices

Self-similarity matrices have become an important tool for visualizing the repetitive structure of a music recording. Transforming an audio data stream into a feature sequence, one obtains a self-similarity matrix by pairwise comparing all features of the sequence with respect to a local cost measure. The basic idea is that similar audio segments are revealed as paths of low cost along diagonals in the resulting self-similarity matrix. It is often the case, in particular for classical music, that certain musical parts are repeated in another key. In this paper, we introduce the concept of a transposition-invariant self-similarity matrix, which reveals the repetitive structure even in the presence of key transpositions. Furthermore, we introduce an associated transposition index matrix displaying harmonic relations within the music recording. As an application, we sketch how our concept can be used for the task of audio structure analysis.