> On 8 Nov 2016, at 21:00, Alexander Kobel <a-ko...@a-kobel.de> wrote: > > On 2016-11-08 18:15, Hans Åberg wrote: >> 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. > > Seriously: I'm a half-mathematician by training (probably a lesser one than > Hans, but still), and work all day in computer algebra; I share the > admiration for the elegance of CF approximations. But for this purpose, I > really think you should use dyadic fractions, say, 2^-20. ... > On a side note, CF approximations are optimal in the sense that they give the > best approximation with numerator and denominator that do not exceed any > given bound. But they are /not/ better than dyadic approximations if your > measure is the asymptotic growth of the worst-case bitlength of numerator and > denominator that is required to achieve a certain approximation quality.
The user does not see the rational approximation, so just use whatever does the job. (Guile has some functions for that, I think.) And a reason of writing a complex time signature might be to make it impossible for the performer to follow it: In Balkan music, one plays by ear, and the variation is greater than the irrational time signature examples I gave. A Western musician when seeing 12/8, 12 = 3+2+2+3+2 with quadruplets on them, might try to play it as exactly as possible, but that is not how it should be performed. Check out the metric time bends indicated here: https://en.wikipedia.org/wiki/Leventikos Otherwise, if one really wants it to be played exactly, a sequencer track would be necessary. _______________________________________________ lilypond-user mailing list lilypond-user@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-user
