[sdiy] Tap tempo question

Mattias Rickardsson mr at analogue.org
Wed Feb 3 08:58:11 CET 2021


Den tis 2 feb. 2021 22:44chris <chris at chrismusic.de> skrev:

> 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"?
>

No, I was first discussing the former, then the latter.

(Or does "you're all" mean "you all are"?
If so, I can't speak for everyone.) :-)

/mr



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.
> >
> > I'm sure I've heard about this dilemma during some lecture in some
> > 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
> > result. I've thought about this several times but I cannot remember 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
>
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