Re: Writing notes in Pythagorean tuning in microlily

[Hans Åberg]

> On 24 Nov 2019, at 00:58, kupirijo <address@hidden> wrote:
> 
> I think I found it here 
> https://lists.gnu.org/archive/html/lilypond-devel/2018-10/msg00129.html

Adam has worked quite a but on it since then, so get the latest.

> Yes it seems to have both AEU notation and some other notation that is new 
> (it cannot be HE as HE is for just notation) I will try it out anyway.

It is Helmoltz-Ellis, because in E53 they are the same, and in addition AEU is 
not transposable, so it makes sense to use when transposing, which was one 
motivation, but others, such as it is easy to read. The interval difference is 
small, and may only be significant in harmony, simultaneous pitches, in which 
case it is Just Intonation one should use anyway.

> By the way, what is a generator?

One has a finite set of pitches and add transposition to that, then it is what 
is called in mathematics a finitely generated torsion free Abelian group, and 
such is a product of number of copies of the set of integers, and the number of 
those opcies is the rank.

> Is it related to meantone temperament?

An extended meantone temperament has two generators, which traditionally is the 
octave and the the fufth, 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.

> Also in the new turkish_makam.ly, why is the Holdrian comma 1/10 of a whole 
> 12-TET tone i.e. 200/10 = 20 cents? The HC is approx. 22.64 cents (i.e. very 
> close to a 1/9 of a 12-TET whole tone)

Adam will have to come along and say exactly what he has done. But if one does 
not want to use the file regular.ly as it is not in the current LilyPond 
distribution, then E72 or E60 are alternatives one can use.