Performance Measures for Tempo Analysis
William A. Sethares, Robin D. Morris · 2004
This paper builds on a method of tracking the beat in musical performances that preprocesses raw audio into a collection of low level features called “rhythm tracks ” and then combines the information using a Bayesian decision framework to choose a set of parameters that represent the beat. An early version of the method used a set of four rhythm tracks that were based on easily understood measures (energy, phase discontinuities, spectral center and dispersion) that have a clear intuitive relevance to the onset and offset of beats. For certain kinds of music, especially those with a steady pulse such as popular, jazz, and dance styles, these four were often adequate to successfully track the beat. Detailed examination of pieces for which the beat tracking was unsuccessful suggested that the rhythm tracks were failing to provide a clear indicator of the beat times. This paper presents new sets of features (new methods of generating rhythm tracks) and a way of quantifying their relevance to a particular corpus of musical pieces. These measures involve the time waveform, spectral characteristics, the cepstrum, and sub-band decompositions, as well as tests using (empirical) probability density and distribution functions. Each measure is tested with a variety of “distance ” metrics. Results are presented in summary form for all the proposed rhythm tracks, and the best are highlighted and discussed in terms of their “meaning ” in the beat tracking problem.