Re: Lilypond's internal pitch representation and microtonal notation

[Hans Aberg]

On 20 Sep 2010, at 18:00, Wols Lists wrote:

> > > As a related issue, have you considered how (different kinds of)
> > > transposition would be handled in your pitch scheme?
> >
> >
> > This is much simpler: the linear combinations are vectors that you
> > just add. For example, if a, b, c, ... are represented by 0, M, m+M,
> > ..., and you want to transpose from b to c, just add m. A sharp is  
> > M-m
> > and a flat m-M. If you want transpose from a note x to a note y, just
> > add y - x.
> What you've missed (and I need to address) is "what is x?".
>
> Let's say I want to transpose up three semitones. That's probably  
> easy,
> it's a minor third, but it could be an augmented second. So, trying to
> remember the pitch class, is it (0,2,sharp) or (0,3,flat)?

The staff system always distinguishes between those, because they have  
different degrees, which are put in different positions. A minor third  
m3 = m + M has deg(m + M) = deg m + deg M = 2; an augmented second M +  
(M - m) = 2M - m has degree 1 as an accidental does not change the  
degree. The first one will move the notes two steps, and the second  
one step.

> And, for your
> example of that, I've currently got a modified chord engraver on the
> frogs list that's added a guitar capo property. All the engraver is  
> told
> is how many semitones to transpose, and it's got to sort out all the  
> keys!

Then with this system, you will have to add E12 enharmonic  
equivalences afterwards. It is not difficult: add or subtract M - 2m.  
But the degree of M - 2m is -1, so the position on the staff will  
change, like for example F# <-> Gb.