Estimating the Error Distribution of a Single Tap Sequence without Ground Truth

Detecting beats, estimating tempo, aligning scores to audio, and detecting onsets are all interesting problems in the field of music information retrieval. In much of this research, it is convenient to think of beats as occuring at precise time points. However, anyone who has attempted to label beats by hand soon realizes that precise annotation of music audio is not possible. A common method of beat annotation is simply to tap along with audio and record the tap times. This raises the question: How accurate are the taps? It may seem that an answer to this question would require knowledge of “true” beat times. However, tap times can be characterized as a random distribution around true beat times. Multiple independent taps can be used to estimate not only the location of the true beat time, but also the statistical distribution of measured tap times around the true beat time. Thus, without knowledge of true beat times, and without even requiring the existence of precise beat times, we can estimate the uncertainty of tap times. This characterization of tapping can be useful for estimating tempo variation and evaluating alternative annotation methods.