Estimating Tempo and Metrical Features by Tracking the Whole Metrical Hierarchy

Abstract

Meter is known to play a paramount role in the aesthetic appreciation of music, yet computational modelling remains deficient compared to other dimensions of music analysis. Classical audio-based methods detect the temporal repartition of notes, leading to an onset detection curve that is further analysed, in a second step, for periodicity estimation. Current state of the art in onset detection, based on energy and spectral flux, cannot handle complex but common musical configurations such as dense orchestral textures. Our proposed im-provement of the flux method can detect new notes while ignoring spectral fluctuation produced by vibrato. Concerning periodicity estimation, we demonstrate the limitation of immediately restricting the range of tempi and of filtering out harmonics of periodicities. We show on the contrary how a complete tracking of a broad set of metrical levels offers a detailed description of the hierarchical metrical structure. One metrical level is selected as referential level defining the tempo and its evolution throughout the piece, by comparing the temporal integration of the autocorrelation score for each level. Tempo change is expressed independent-ly from the choice of a metrical level by computing the difference between successive frames of tempo ex-pressed in logarithmic scale. A new notion of dynamic metrical centroid is introduced in order to show how particular metrical levels dominate at particular moments of the music. Similarly, dynamic metrical strength is defined as a summation of beat strength estimated on dominant metrical levels. The model is illustrated and discussed through the analysis of classical music excerpts.