Actually, coverting between the ratios and semitones has alread been done, as there's a simple set of log and mround functions that do it. Have a look in the OLL repository under notation-tools and you should find the .ily files.
Cheers, A On Sun, Dec 13, 2015 at 7:51 AM, <msk...@ansuz.sooke.bc.ca> wrote: > On Sat, 12 Dec 2015, N. Andrew Walsh wrote: > > accidentals as needed. I suppose, rather than having Lily/Scheme > calculate > > prime factors on the fly at runtime, it would be easier to have a lookup > > table of the prime factorization for each integer up to a certain limit > (but > > that would end up being very high, so maybe not). That's a computational > > problem for further down the road, though. > > For numbers of 32 bits or so, doing prime factorization by simple-minded > trial and error on a present-day computer is cheaper than most people > realize. It's a tight loop that fits in cache; the arithmetic may > actually be faster than a lookup table in main memory, and it's at least > unlikely to be prohibitively slow. > > I think a trickier computational problem may be converting between > LilyPond's "rational number of semitones" and just-intonation's "rational > ratio of frequencies" ways to express pitch. Because of the log function > in between, in general any number that has a representation on one of > those scales will have no exact representation on the other, and you're > forced to do some kind of rounding, or maybe abandon LilyPond's pitch > scheme for something else. Have you decided how you want to deal with > this issue yet? > > -- > Matthew Skala > msk...@ansuz.sooke.bc.ca People before principles. > http://ansuz.sooke.bc.ca/ >
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