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, 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).
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.
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 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.
Thanks for the help.
Cheers,
A