Let me give another example of what I mean, just so you have an idea. I'm
in a singing ensemble that performs music in just intonation. We have a
soprano who is *terrifyingly* good at it. One of the things she does is
sing a scale comprising the following harmonic ratios relative to the
tonic: 14/8, 16/9, 18/10, 20/11, 22/12, 24/13, 26/14, 28/15, 30/16. The
first and last pitches reduce to 7/4 and 15/8, respectively: a minor and
major seventh. So, she can sing a total of *nine* pitches within the space
of a semitone and, because she can hear the harmonic ratios they each
represent, tune them all correctly. She can do this without accompaniment
(like I said, she's scary!).
Now, you *could* just give those pitches as flats and sharps, with their
respective deviations in cents, but it would be much harder to tune by ear.
Even then, it would be guesswork. The last two pitches are less than 8
cents apart; it would be extremely difficult to get them both tuned
accurately, even with feedback from a tuner. Knowing the ratios, though,
makes it possible to hear, and thus to perform.
But, as I said, whether that's a music that others might find æsthetically
interesting is an entirely different discussion. My question is: if I were
to use such a system, how would I engrave it?
Cheers,
A
On Tue, Dec 1, 2015 at 11:01 AM, Urs Liska <u...@openlilylib.org> wrote:
>
>
> 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 <n.andrew.wa...@gmail.com>
> *To:* lilypond-user <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
>
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