Am 01.12.2015 um 10:10 schrieb N.
Andrew Walsh:
Hi List,
this is a somewhat specialist request, and more of a
long-term project, but I'm hoping you nice people can help me
with something I'd like to do with Lily someday.
If you've been watching the OpenLilyLib repository, you'll
see that Urs has been working on a set of tools for rendering
music in just intonation. He (quite modestly) says that it
isn't ready for production,
Well, it isn't ...
but there are already some impressive things it can do: for
one, the interface allows to input a fraction and get back a
nearest-semitone pitch with a deviation in cents
*automatically*, which is something the commercial programs
don't offer in any way (every composer I know who works with
JI just inputs text entries manually for every note, with no
change in, for example, MIDI output for ability to handle
transpositions).
Yes, I also find this exciting prospects, and I don't expect the
limitations there are so far to be really problematic. But basically
you can now use the functionality to produce individual notes, in a
monophonic context.
Probably it will be more clear once the second and third part of my
latest blog post are out.
There's something I'd very much like to do with this,
largely out of my own (admittedly rather opinionated) view on
the best means of producing accidentals for just intonation.
I'm going to assume some familiarity with just intonation
concepts, but (in short) it works like this: the relationship
between two pitches is defined in terms of the frequency
relationship, given usually as a fraction. For example, the
interval of a perfect fifth may be rendered as 3/2: that is,
if I play notes with base frequencies of 200 and 300Hz, we
hear them as a (very purely tuned) fifth. The equal-tempered
one you have on a piano (ie, 7 semitones) is about two 1/100th
of a semitone (called "cents" logically enough) too narrow to
be pure (ie, a 3/2 fifth is about 702 cents).
Here's my thing: I believe that the most appropriate type
of accidental for such a system is one that reflects the
harmonic ratio, not the number of steps on a scale. Flats and
sharps tell us whether a pitch is lowered or raised from its
"natural" position in the scale, and just intonation doesn't
have those positions. So, I designed accidentals that
graphically reflect the harmonic ratio between a note and the
tonic.
That's not exactly what I meant. I was rather thinking of the \path
command on
http://lilypond.org/doc/v2.19/Documentation/notation/graphic and
have LilyPond *generate* the paths on-the-fly. This will make the
modularity of your accidentals pretty straightforward to achieve.
But I don't have significant experience with paths (although I'd be
very interested in learning), others have done more on the topic,
and I think there are quite some helper tools and functionality
already availabe that I can't point you to.
There are some potential complicating factors here. First,
the accidentals I use change depending on the prime
factorization of the ratio involved: for example, the ratio
9/8 (a type of whole tone) would comprise two of the symbol
for 3 (because "9/8" is really "(3*3)/8" ), which means that
Urs' interface for JI ratios would need an add-on to do prime
factorization of the ratios (which is also computationally
intensive, even for relatively simple numbers) or a means to
encode ratios as lists of primes that are then calculated to
return the value in cents (that is, do the process in reverse,
starting from "(3*3)/8" and getting 9/8, which might be easier
to do).
The advantage here, though, would be this: one of the
interesting things about just intonation is that there is no
theoretical limit to what kinds of ratios you use. You could
theoretically have unique signs for all the primes you want,
and then the draw function could build them on the fly. The
accidentals become modular, scaling to whatever level of
complexity the composer wants. Harry Partch writes music that
tops out at the 13th overtone, but La Monte Young has pieces
with primes in the upper 300s.
So, List: this is, as I said, a somewhat long-term project,
but would any of you be willing to help me learn/do the
programming necessary to develop a system like this? I also
have in mind a more general add-on to the OLL just-intonation
library: I'd like to see a set of different .ily files, each
with different sets of accidentals, which a composer could
\include into the score as needed. For example, I could write
the ratios using my system, or use a system that shows
accidentals approximated to the nearest 12th-tone, with cents
deviation for more exact tuning (which might be of more
relevance to keyed instruments).
I think this will also become clearer after the third part of the
post-series.
I can send a few hand-drawn mock-ups of the accidentals to
show what I mean; I've been doing them by hand, but I'd really
like to see them engraved.
This would be extremely useful because I'm pretty sure noone has a
clear idea what you are talking about yet.
Urs
Thanks for the help.
Cheers,
A
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