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. > > I'd like to be able to put these into Lily, and Urs tells me it can be > done by calling a draw function to draw a path. I can relatively > easily make up some paths with Inkscape and save them as SVGs, but is > there a better way to do this? The NR describes > (here: > http://lilypond.org/doc/v2.19/Documentation/notation/formatting-text#graphic-notation-inside-markup) > the means to include eps files into a markup, which presumably could > be used to replace the accidental. 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 > > > _______________________________________________ > lilypond-user mailing list > lilypond-user@gnu.org > https://lists.gnu.org/mailman/listinfo/lilypond-user
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