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Re: JI notation (was: converting svg glyph to path data for use in schem
From: |
Hans Åberg |
Subject: |
Re: JI notation (was: converting svg glyph to path data for use in scheme) |
Date: |
Mon, 14 Dec 2015 22:40:08 +0100 |
> 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