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.
