Re: JI notation (was: converting svg glyph to path data for use in scheme)

[Hans Åberg]

> On 14 Dec 2015, at 20:28, Graham Breed <address@hidden> wrote:
> 
>> From: "N. Andrew Walsh"<address@hidden>
> 
>> 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