Re: accidentals for just intonation

[N. Andrew Walsh]

Well, this is a much longer and different discussion, but in short: I don't intend these for non-equal temperaments, but rather music in an open system of justly-tuned ratios. So, for example, you might certainly wish to define your basic scale that way (a major scale thus being 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2/1), but you could also go *much* further up the harmonic series. How would you describe an 11th? A 13th? Those are primes that have no representation in music of the common practice, and a ratio like 13/9 is on the relatively low end of what's possible (like I said, La Monte Young uses primes up to the low 300s, I think). 

I don't like using symbols from tempered music because they are visually and semiotically confusing: after a while, you have so many very similar looking signs that telling them apart becomes difficult (is the sign for a 13th a sharp sign with an arrow, or with a minus?). If you're using a system with 50 or 60 different pitches to the octave, it very quickly gets difficult to tell the signs apart. They also don't convey the information that is actually important to just intonation: the harmonic ratio. 

Obviously, this is also very much a matter of taste. I tend to think in terms of wanting to convey the essential information of the musical material, and nothing more. Efficiency of visual information comes at the cost of it being based on different principles, and thus being rather unfamiliar, relative to the usual systems. You could very certainly use modified quartertone accidentals for extended meantone temperaments (such as the 24-pitch meantone temperament Johannes Keller is playing in here: https://www.youtube.com/channel/UCFG2Y__ODlxuIwcdzMM5zrQ), and that might even be the appropriate system to use. But for an open system of just intonation, I feel that those accidentals convey too much of the wrong information, and not enough of the important information.

But that's a bit of a different discussion, as I said. There are probably more different systems for notating music in non-standard tunings than there are composers using them, and I certainly don't expect everybody to use *this* system (though it'd be nice to see it get more use). 

Hope that makes sense.

A

On Tue, Dec 1, 2015 at 10:45 AM, Phil Holmes <address@hidden> wrote:

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).  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?

 

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

To: lilypond-user

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

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