David Kastrup wrote Monday, December 14, 2015 11:32 AM
> Urs Liska <u...@openlilylib.org> writes: > >> Am 13.12.2015 um 14:09 schrieb Graham Breed: >>> On 13/12/15 12:48, N. Andrew Walsh wrote: >>>> Take a look at conversions.ly (sorry; mround is the equivalend >>>> function in >>>> the spreadsheet I use to do the same thing). Those functions will >>>> convert >>>> the input (given as a fraction comprising two integers) into Lily's >>>> semitone values. That should allow you to convert between >>>> just-intonation >>>> ratios an the nearest note name. Urs has some comments in there >>>> explaining >>>> a bit how it works. >>> >>> Converting from ratios to cents is easy. Converting between ratios >>> and cents requires a function from cents to ratios. That's a lot more >>> difficult because information is lost. You got us excited by >>> suggesting that had been solved. >> >> Well, this is because conversion from cent to ratio isn't part of the >> objective currently. > > Guile has > > (rationalize (inexact->exact (atan 0 -1)) #e1e-6) > > so you can try converting irrational numbers to ratios. However, > figuring out the precision to use may be tricky and there is no "prefer > simple ratios" option. All you have to work with is the eps argument. One way to approach this would be via continued fractions. These provide a means to determine the "best" rational approximations to a real number. The continued fractions give a list of rational approximations in which each member is a closer approximation to the real value than the previous members, and each is also closer than any approximation with a smaller or equal denominator. For example, pi = [3;7,15,1,292,1,1,...] as a continued fraction, which gives the successive "best" rational approximations to pi of 3/1, 22/7, 333/106, 355/113, ... Not sure how you'd determine which of the ratios was "correct" when used for conversion from cent to ratio, though. Maybe try a few and see what comes out. Trevor _______________________________________________ lilypond-user mailing list lilypond-user@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-user
