> On 14 Dec 2015, at 20:28, Graham Breed <gbr...@gmail.com> wrote: > >> From: "N. Andrew Walsh"<n.andrew.wa...@gmail.com> > >> Converting cents to ratios only makes even a bit of sense if you have some >> preexisting music in some temperament, which you then want to approximate >> in just intonation. But even that isn't really something that would be >> served by calculation from cents and not simply determining yourself what >> ratios you want (because, at base, deciding which ratio you want to have is >> entirely arbitrary). Now, if you have some closed scale, it's simply a >> matter of figuring out the cents values for the notes in the scale, and >> then rounding your preexisting notes to the nearest one. > > It makes sense because at the point you choose the accidental, the deviation > from the unaltered pitch is the only information you have — unless you have > some other mechanism for passing it along. But what some of the discussion > implies is that you could keep a global hash table of the alteration (which > happens to be rational and so unique and hashable) chosen for a given ratio > input. That would work as long as the input is always JI, and that's a > perfectly reasonable assumption. Transposition would still have some > wrinkles, though. > > Using an equal temperament to set the accidentals is problematic even if you > allow Sagittal-style wraparound. Sometimes errors will accumulate so that > the correct spelling doesn't match the nearest approximation of a complex > ratio to the equal temperament.
If one wants to preserve some algebraic properties, like two syntonic commas is the same as a double syntonic comma, and so on for some other algebraically independent intervals, then it is not possible to use an ET to describe that. - I made a search up to tens of thousands. What happens is that when one goes up in ET, it becomes harder for these multiples to become preserved. The code I wrote [1] would do it correctly. 1. http://lists.gnu.org/archive/html/lilypond-devel/2014-12/msg00075.html _______________________________________________ lilypond-user mailing list lilypond-user@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-user
