Re: Writing notes in Pythagorean tuning in microlily

[Graham Breed]

On 24/11/2019, Hans Åberg <address@hidden> wrote:
>
>> On 24 Nov 2019, at 11:57, Graham Breed <address@hidden> wrote:
>>
>> 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 Sagittal JI and Extended
>> Helmholtz-Ellis.
>
> Whatever rational numbers assigned to the accidentals and how many, one only
> gets one generator, unless there has been an extension lately. Perhaps you
> expect not transposing too far?

I had tripod notation working in 2009.  This is a rank 3 system, so
two octave-equivalent generators.  Here's the lilypond-book document I
made:

http://x31eq.com/magic/tripod.pdf

I initially had problems with transposition because there are 9
nominals to the octave, so there's a missing staff position.  I fixed
this using the chromatic staff support.  Now it transposes fine, and
I've even used LilyPond's transposition with tone rows.  Eventually,
the transposition will break because it runs out of symbols.  It'll do
that with common practice notation as well.  There's no special
problem with higher ranks.

There does have to be a linear chain of accidentals, so it has to be
quantized to an equal temperament at some level.  With tripod
notation, this means "inches" have to be reconciled to "semitoes" or
the spellings become very restricted.  Because the pitch system uses
rationals, an implicit equal temperament is inevitable anyway — unless
you use Scheme expressions to choose the accidentals, like with the
Extended Helmholtz-Ellis support.


                           Graham