> On 26 May 2018, at 08:35, metachromatic <metachroma...@gmail.com> 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) _______________________________________________ lilypond-devel mailing list lilypond-devel@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-devel
