Decoding Tempo and Timing Variations in Music Recordings from Beat Annotations

This paper addresses the problem of determining tempo and timing data from a list of beat annotations. Whilst an approximation to the tempo can be calculated from the inter-beat interval, the annotations also include timing variations due to expressively timed events, phase shifts and errors in the annotation times. These deviations tend to propagate into the tempo graph and so tempo analysis methods tend to average over recent inter-beat intervals. However, whilst this minimises the effect such timing deviations have on the local tempo estimate, it also obscures the expressive timing devices used by the performer. Here we propose a more formal method for calculation of the optimal tempo path through use of an appropriate cost function that incorporates tempo change, phase shift and expressive timing.