Tap along with the music and the intervals between your taps become a tempo. The measurement is your counting, which is the point: it records the pulse you hear rather than the one a correlation finds.
Averaging window
Every tap adds an interval, and the tempo is the mean of the last few. How many is the trade.
A window of 4 follows a tempo that moves, which is what you want on a live recording or a DJ set where the tempo drifts. The whole run is more precise on a programmed track, because averaging more intervals cancels more of your own timing error.
Switching the window does not throw taps away, so you can tap sixteen times and compare both readings.
Spread
The spread is the standard deviation of the intervals in the window, and it is the honest part of the reading.
A tempo of 128.0 BPM with a spread of 4 ms is a measurement. The same 128.0 with a spread of 60 ms is a coincidence, and the next four taps will produce a different number. Averaging longer does not fix a wide spread, because the error is in the tapping, not in the sample size.
The plot shows the same thing per tap. A run that wanders up and down around the dashed average is normal human timing. A run that slopes in one direction means the track is speeding up or you are.
Tapping on bars
At 174 BPM, tapping quarter notes means nearly three taps a second, and hand timing gets worse the faster you go.
Set each tap to a bar of 4/4 instead and you tap once every 1.4 seconds. The tempo is multiplied back up, and the spread drops because the error is now spread across four beats instead of one. Same technique for half notes on anything above about 140 BPM.
Note lengths
The table converts the beat into the numbers other tools take.
At 120 BPM a beat is 500 ms. A 1/8 delay is 250 ms, a dotted 1/8 is 375 ms, and an 1/8 triplet is 166.7 ms. The dotted setting is the one that gives repeats landing between the beats, which is where most rhythmic delay comes from.
The Hz column is the same figure as a rate. A tremolo at 2 Hz is one cycle per beat at 120 BPM, and 4 Hz is one per eighth note.
Where tapping is the wrong tool
Tapping cannot measure something you cannot count: a rubato piano piece, an ambient track with no pulse, or a recording that changes tempo halfway through.
It is also worse than analysis on a file you already have, where the BPM detector reads the onsets directly and reports a confidence figure with them. Tapping earns its place on audio you cannot load: a stream, a rehearsal room, a record playing across the shop.