Re: How to get irrational tuplets inside a regular meter like 9/8

[Hans Åberg]

> On 8 Nov 2016, at 08:28, mclaren <address@hidden> wrote:
> 
> An alternative method involves simply adding in the required rests, rather
> than squishing or stretching the entire measure with a large tuplet. Since
> this method is easy to calculate exactly because you're just adding and
> subtracting various integer fractions, it always produces guaranteed
> results. With very large tuplets, there seem to sometimes be floating point
> inaccuracies in the calculations done inside Lilypond, so sometimes the
> large tuplet method doesn't work exactly and barlines don't precisely add
> up. 

I gave an example of a true irrational time signature [1]. The code is actually 
written in 12/8, with a MIDI approximation in 19/8. Such meter approximations 
can be obtained using continued fractions convergents [2]. For the rendering, 
it suffices with an approximation that separates and orders the notes that 
occur at different times. For the MIDI it suffices to be within its accuracy, 
or alternatively, what performers might do.

1. https://lists.gnu.org/archive/html/lilypond-user/2014-06/msg00237.html
2. https://en.wikipedia.org/wiki/Continued_fraction