Tapping response to sudden tempo changes

This webpage describes an experiment where the tapping response is measured for a set of audio clicks which randomly switch between two tempos. Two cases were examined: (1) response when the time of the tempo change was unpredictable, and (2) response when the time of the tempo change was predictable.

For the first case, the tempo changed at a random beat. Each tempo region was between 8 and 16 beats long. So, the number of beats in a fixed tempo can be anywhere between 8 and 16 beats before a new tempo region starts. The two tempos chosen were 80 MM (750 ms) and 112 MM (536 ms). These two tempos were chosen since they have no common rhythmic divisors: 536 * sqrt(2) is approximately 750.

For the second case, each tempo region consisted of 8 beats. After every 8 beats, the tempo changed abruptly to the other tempo. In this case the location of the tempo change was predictable.

These two tests measure the effect of memory on adjusting to sudden tempo changes. The first experiment measuring unpredictable tempo changes is how a tapper would respond to an unknown selection of music which contains a sudden change in tempo. The second experiment measuring the predictable tempo changes shows the best expected following response to a known (i.e., memorized) tempo change.

Unpredictable sudden tempo change

In the plot below, the horizontal axis is time, the blue lines are the times of clicks in the audio input, the thick orange regions in the middle of the plot are the ~200 individual tap responses for that particular beat, the thin orange line at the bottom is the average tapping position of all taps for the beat, and the dashed line indicates where the clicks would be located if they continued in a constant tempo.

Here is a similar plot where the tempo suddenly slows down rather than speeding up:

Here are plots of the tempo for each beat, showing the same information as in the above two plots:

Predictable sudden tempo change

In this test, the audio clicks were generated in a regular fashion: 8 clicks in a tempo of 80 MM alternating with 8 clicks in a tempo of 112 MM. In this case notice that there is no misalignment at the tempo transitions.

Again, here is the plot of the same data in terms of tempo versus beat. Compare the plots for the unpredictable data above with these plots.