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Re: Writing notes in Pythagorean tuning in microlily
From: |
Graham Breed |
Subject: |
Re: Writing notes in Pythagorean tuning in microlily |
Date: |
Sun, 24 Nov 2019 10:57:08 +0000 |
On 24/11/2019, Hans Åberg <address@hidden> wrote:
[amended]
> An extended meantone temperament has two generators, which traditionally is
> the octave and the the fifth, but one can change basis and take any two,
> such as the minor and major second. LilyPond uses the sharp and the major
> second. Two generators is necessary for correct typesetting of the staff
> system. In Turkish, Arabic, and Persian music, one would need three
> generators each, but LilyPond cannot handle that.
LilyPond can easily handle multiple generators with alternative pitch
names. I've had "tripod notation" support with 3 generators for
several years. It does mean alternative pitch names, though, rather
than regular transformations of (any of) the standard names. Or
Scheme code to retune pitches, like I did for Sagital JI and Extended
Helmholtz-Ellis.
Where LilyPond has difficulty is with scales that don't repeat about
the octave. It's possible to get around this with post-processing,
but easier not to. So it's convenient to think of one of the
generators as an octave (or equal division of the octave). In this
case, common practice notation (tuned as either meantone or
Pythagorean) has a single octave-equivalent generator, which could be
a fourth or a fifth. LilyPond, however, goes a step beyond this by
providing half-sharps and half-flats. When you do the algebra, it
turns out that this gives an octave-equivalent generator of a neutral
third (half a perfect fifth).
Graham
- Re: Writing notes in Pythagorean tuning in microlily, (continued)
- Re: Writing notes in Pythagorean tuning in microlily, kupirijo, 2019/11/23
- Re: Writing notes in Pythagorean tuning in microlily, Graham Breed, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, Hans Åberg, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, kupirijo, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, Hans Åberg, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, David Kastrup, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, Hans Åberg, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, David Kastrup, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, Hans Åberg, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, Hans Åberg, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily,
Graham Breed <=
- Re: Writing notes in Pythagorean tuning in microlily, Hans Åberg, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, Graham Breed, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, Hans Åberg, 2019/11/24
- vertical positioning of \mark\markup "blah blah", Mario Bolognani, 2019/11/24
- Re: vertical positioning of \mark\markup "blah blah", Phil Holmes, 2019/11/24
- Re: Writing notes in Pythagorean tuning in microlily, kupirijo, 2019/11/24