Re: Irrational time signature and tuplets

[Hans Aberg]

On 13 Jun 2014, at 01:26, Mark Stephen Mrotek <address@hidden> wrote:

> Thank you for your detailed and informative response. I shall take time to
> study it and the references that you provide.

You are welcome.

In short, one can use any mathematically irrational number and work it back to 
rational approximations using continued fractions. Continued fractions are also 
useful when computing equal temperament approximations of intervals. For 
example, for the perfect 5th rational interval 3/2, one takes the continued 
fractions of log_2(3/2). The convergents, then, are 7/12, 24/41, 31/53, ..., 
where the denominators are the equal temperaments 12, 41, 53, ..., and the 
numerators 7, 24, 31, ..., the approximations of the perfect fifth in these 
temperaments.