Re: Writing notes in Pythagorean tuning in microlily

[Hans Åberg]

> On 24 Nov 2019, at 19:05, Graham Breed <address@hidden> wrote:
> 
> 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 was not able to understand what this system does from this, despite trying 
several times. Perhaps you can give a more compact description.

If one takes multiples of accidentals represented by rational numbers, they 
will meet, which will not happen if they are independent as in a higher rank 
system. So you probably do not consider such higher multiples. For example, if 
one takes a double comma accidental in E53, as for Persian or Arabic music, 
then two of them in succession will be the same as a sharp lowered by a comma 
and notated as such in LilyPond. Then one can separate them by more complicated 
rational numbers, but not eliminate the phenomenon.