# [sdiy] Tap tempo question

chris chris at chrismusic.de
Tue Feb 2 22:43:24 CET 2021

```Could it be that you're all confusing "setting a tempo dial by tapping"
(which was the original question) with "beat-exact synchronization
through a given song"?

Chris

On Tue, 2 Feb 2021 22:30:51 +0100 Mattias Rickardsson <mr at analogue.org>
wrote:

> On Tue, 2 Feb 2021 at 07:12, Brian Willoughby <brianw at audiobanshee.com>
> wrote:
>
> > On Feb 1, 2021, at 16:31, Didier Leplae wrote:
> > >... I tap multiple times with the assumption that the multiple taps are
> > averaged.
>
>
> Averaging might seem like a good idea to find the tempo, but if you just
> average a number of periods between consecutive pairs of taps, the end
> result only depends on the timing of the first and the last tap. The
> timings of all intermediate taps get thrown away in the calculation since
> they are first added (as one end of a period) and then subtracted (as the
> other end of next period).
>
> (If taps occur at times A, B, C, D, E
> then the measured periods are B-A, C-B, D-C, E-D.
> The average of these periods are (B-A + C-B + D-C + E-D) / 4
> which equals (E-A) / 4
> meaning the total time between the first and last taps, divided by the
> number of periods tapped in between.)
>
> While this would converge over time to a better and better measurement of
> the tempo, it converges very slowly and does so only because the total time
> increases. If the first tap is badly timed, it will always follow you in
> the summing even if later taps are becoming better and better. Sure, it
> would have less and less impact along the way, but the only way of getting
> rid of the first tap being off-beat is to end the tapping session with a
> tap that is exactly equally off-beat. And the other taps don't matter.
> Something smells wrong here. Among all imaginable solutions to the problem
> - and especially from a practical perspective where a tireless tempo tapper
> gets better and better and stops tapping when the timing feels good - this
> must be the least good solution.
>
> education way back in time, and a clever trick was introduced in order to
> make this type of calculation much more sensible, using all the taps in the
> details... very annoying! Does anybody know what kind of solution I'm
> after? I won't be able to sleep until this is cleared up. :-)
>
> You can also weight the average so the most recent pair of taps affects the
> > average a lot more than older information.
>
>
> Yes, weighting more recently tapped periods does have a good chance of
> giving a better result and a faster convergence.
>
> Another detail that has already been touched upon in the discussion is the
> concept of phase (or absolute timing). The tempo isn't the only thing that
> can be determined from the tap-tempo button, but the timing of the repeated
> taps is often also important. In the example above where only the first and
> last tap would be significant when calculating the average period (i.e.,
> tempo) and the other taps thrown away, the situation isn't all that bad for
> the absolute timing calculation. Here all the taps actually count, and
> keeping a steady tapping pace pays off. I'm guessing that some "adaptive"
> version of weighting, that both gives a good tempo calculation and
> gradually corrects the absolute timing of the LFO/delay (etc) to match the
> tapping and the music, is what people almost always would want.
>
> Interesting with tap-tempo mechanisms... similarly to chromatic tuner
> functionality in the way that it's a seemingly small and simple task, easy
> to describe loosely, easy to have a gut feeling of what one would expect
> the behaviour to be, but complex to implement without making something far
> worse than those expectations. :-)
>
> /mr

```