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