Re: converting svg glyph to path data for use in scheme

[mskala]

On Sun, 13 Dec 2015, Graham Breed wrote:
> 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.

Indeed.  One can pretty easily define a set of ratios that will be allowed
(for instance, by saying "use primes up to this limit, at powers up to
this other limit") and then ask for the nearest ratio in that set, to a
given pitch in cents; it wouldn't be terribly difficult to implement that.
I think it turns into integer programming (an NP-hard problem in general)
but the size of the instances is small enough that the computation would
be easy in practice.  However, I don't have a strong sense of what's
actually a good set of allowed ratios to use for such purposes, and I was
hoping the people working on doing this in OLL had an opinion on that.

Having this kind of algorithm would be interesting for converting pitches
that were *not* originally written as just frequency ratios, for instance
from an EDO scale, into rational approximations to notate them with a
just-intonation notation scheme such as yours or "Saggittal notation."

-- 
Matthew Skala
address@hidden                 People before principles.
http://ansuz.sooke.bc.ca/