Meter and Autocorrelation *

This paper introduces a novel way to detect metrical structure in music. We introduce a way to compute autocorrelation such that the distribution of energy in phase space is preserved in a matrix. The resulting autocorrelation phase matrix is useful for several tasks involving metrical structure. First we can use the matrix to enhance standard autocorrelation by calculating the Shannon entropy at each lag. This approach yields improved results for autocorrelation-based tempo induction. Second, we can efficiently search the matrix for combinations of lags that suggest particular metrical hierarchies. This approach yields a good model for predicting the meter of a piece of music. Finally we can use the phase information in the matrix to align a candidate meter with music, making it possible to perform beat induction with an autocorrelation-based model. We argue that the autocorrelation phase matrix is a good, relatively efficient representation of temporal structure that is useful for a variety of applications. We present results for several relatively large meter prediction and tempo induction datasets, demonstrating that the approach is competitive with models designed specifically for these tasks. We also present preliminary beat induction results on a small set of artificial patterns. ∗Presented at Rhythm Perception Production Workshop (RPPW) 2005. Draft. Do Not Cite.