Re: irrational meters

[Hans Åberg]

> On 18 Jan 2023, at 01:46, H. S. Teoh via LilyPond user discussion 
> <lilypond-user@gnu.org> wrote:
> 
> … it would be interesting if somebody composed a
> piece with an actually irrational meter, like π/4 or 3/π.  

I gave an example [1] where the numerator is an irrational number, 8+2√5.

If one wants to typeset them in LilyPond, one can apply continued fraction 
convergents to a suitable degree of accuracy.

> Only thing
> is, it would be impossible for human performers to play correctly, since
> there isn't any way to count the beats correctly (counting beats implies
> a rational fraction, since by definition it's impossible to count up to
> an irrational ratio by counting finite parts).

The example [1] is based on a popular Macedonian meter 12=3+2+2+3+2 [2], which 
in performance has heavy metric time bends [3].

A musical motivation writing such a meter might be to make performers to avoid 
trying to play an exact 3+2+2+3+2.


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