Re: Microrhythm

[Hans Åberg]

> On 26 May 2018, at 08:35, metachromatic <address@hidden> wrote:
> 
> ... let's calculate the
> difference in time twixt a tuplet like 7919/4451 against a tuplet
> 7909/4447 over the course of two minutes and 13 seconds of 4/4 time at
> a tempo of metronome marking 90:
> 
>    The difference is (0.00064839149)*60/90 seconds per quarter note =
> 0.00043226099 seconds per quarter note.  But after only 200 quarter
> notes (that is, 50 measures of 4/4, taking only two minutes and 13
> seconds), that difference in timing has grown to ~ 1/11 second. And I
> guarantee you that you can easily hear whether one melodic line is
> offset from another by 1/11 second, since that equates to a difference
> of slightly less than an eighth note at tempo 90.

The human internal tick time is about 1/60 s, so a piece running time t seconds 
need a resolution of 60*t to not let a one tick error grow to that size, and 
then the numerator needs to be 60*t^2. For 64 bits, this is log_2 t about (64 - 
6)/2 = 29 bits, i.e. 2^29 seconds or about 17 years.

For performing musicians, like in the [1-2] example, the variation is much 
greater than 1/60 s even between measures, and the reason is that performers 
know how to sync.  

For video synchronization, one is using shorter times, and there is a proposal 
for about a nano-second "flick" [3].

1. https://lists.gnu.org/archive/html/lilypond-user/2014-06/msg00237.html
2. https://www.youtube.com/watch?v=vYR_pvRWO_g
3. https://en.wikipedia.org/wiki/Flick_(time)