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
>
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