On 13 Jun 2014, at 01:26, Mark Stephen Mrotek <[email protected]> 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. _______________________________________________ lilypond-user mailing list [email protected] https://lists.gnu.org/mailman/listinfo/lilypond-user
