Am 01.12.2015 um 10:45 schrieb Phil Holmes: > I have quite an interest in intonation, and my degree dissertation was > based on the study of musician's reaction to just and equal tempered > music, and was created using LilyPond. However, I'm not clear why you > believe that accidentals in non-equal temperaments require different > signs (I think that's what you're proposing here).
This is because Andrew is not talking about music that uses a scale of notes that just deviates from the well-tempered scale through a tuning system. Instead he's (and of course a number of composers) conceiving pitches as ratios over fundamental frequencies. So you may have two consecutive notes that are very similar in frequency but stem from completely different contexts: for example a 5/1 ratio (major third flageolet) over b, resulting in a pitch that is 14 cent below d', followed by a pitch that is 2 cent above d' because it is the 3/1 ratio over g. You can notate that as d' -\markup "(-14)" d' -\markup "(-2)" but what Andrew suggests (and does himself by hand so far IIUC) is a notation that indicates the same as (pseudo-code): b,{5:1] g{3:1} Depending on the instrument that will create those pitches different notations may be appropriate. I clarinetist who is bending will prefer the indication of the cent detuning, while when I have to play them as piano flageolets I don't really care about that and have to know the key to press (fundamental note) and the ratio or node of the string - the resulting pitch with its cent deviation will only be there as a courtesy. > It's said that early music was based on one or other form of just > temperament, and used normal accidental signs. To me, they indicate > that the music is altered to the next higher or lower semitone in the > key and temperament being employed: so why are other signs needed? I don't know how Andrew "thinks" as a composer, but music in just intonation (in it's modern conception) is a very different thing from ancient music in different tunings. Urs > > The only extra indication that I would use would be rather like a > tempo sign, but instead a temperament sign: "Quarter comma meantone" > at the top, for example. > > -- > Phil Holmes > > > > ----- Original Message ----- > *From:* N. Andrew Walsh <mailto:n.andrew.wa...@gmail.com> > *To:* lilypond-user <mailto:lilypond-user@gnu.org> > *Sent:* Tuesday, December 01, 2015 9:10 AM > *Subject:* accidentals for just intonation > > 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. > > 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. > > 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 > > ------------------------------------------------------------------------ > _______________________________________________ > lilypond-user mailing list > lilypond-user@gnu.org > https://lists.gnu.org/mailman/listinfo/lilypond-user > > > > _______________________________________________ > lilypond-user mailing list > lilypond-user@gnu.org > https://lists.gnu.org/mailman/listinfo/lilypond-user
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