Autocorrelation and meter

Douglas Eck

University of Montreal, Canada

Autocorrelation is a simple, fast-to-compute method that has long been used as a tool for analyzing metrical structure in music. Because autocorrelation can be performed online and works on a variety of inputs including filtered and rectified digital audio, it is an interesting method for exploring non-stationary effects such as acceleration and deceleration in performed music. However autocorrelation has a severe limitation: while it provides information about the magnitude of signal energy at different periods, it discards all information about phase. I will 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. Additionally the phase information in the matrix can be used to align a candidate meter with music, making it possible to perform beat induction with an autocorrelation-based model. I believe the autocorrelation phase matrix is a good, relatively efficient representation of temporal structure that is useful for a variety of applications. I will 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. If I'm feeling brave I might even relate this work to the ongoing RPPW ‘clocks’ versus ‘oscillators’ debate.