Re: improving our contributing tools and workflow

[Hans Aberg]

On 26 Sep 2013, at 17:16, Phil Holmes <address@hidden> wrote:

>> On 26/09/13 16:37, Trevor Daniels wrote:
>>> Almost exactly what I was about to reply, but Phil beat me to it!  In fact I
>>> think I remember helping you add the Contemporary music headings some
>>> time ago, or was it someone else?
>> 
>> The section originates with me but I got diverted into trying to create a 
>> more elegant solution for how to rewrite accidentals in transposed music. It 
>> was all related to the need for an effective chromatic transposition 
>> solution that also worked well with arbitrary microtonal accidentals.
>> 
>> I was also rather discouraged by the fact that the quarter-tone arrow 
>> notation issue didn't find a solution -- see:
>> https://code.google.com/p/lilypond/issues/detail?id=1278
> 
> I think it's waiting for someone to propose how it could be represented in 
> LilyPond.  If _someone_ were to do that, it might progress - it was only a 
> few months ago it was last looked at.

It is easily solved by not using E24, as it does not sound good anyway. :-)

But the problem is similar to that of enharmonic equivalences in E12: the staff 
system is not designed to express that. So first engrave as though they are 
different, end apply enharmonic equivalences at the end according to taste.

In mathematical terms, the staff system is generated by an (abstract) minor 
second m and a major second M, all formal combinations r*m + s*M, where r, s 
runs through all integers: a free abelian group of rank 2. The degree d = 
deg(r*m + s*M) is the staff position. Each staff position has a note also of 
this form: subtract it, and what remains is a note of of degree d = 0. A sharp 
raises with M - m, and a flat lowers with the same amount. If d = 0, then r + s 
= 0, then so if s > 0, add s sharps, and if r > 0, add r flats.

Now, this works also with microtonality: just add neutrals n = n_0, n_1, ..., 
n_k, which will result in a rank 2 + (k + 1) free abelian group of the pitches 
r*m + s*M + t*n + ... + t_k*n_k. Engrave the same way: compute degree d = 
deg(r*m + s*M + t*n + ... + t_k*n_k) := r + s + t + ... + t_k, which is the 
staff position, subtract the staff note, and what remains is a note of degree 
0. It can be expressed by a suitable combinations of accidentals, where those 
that involve a neutral n_i are microtonal.

Now, if you add a "quarter-note", that is, a neutral n that when assigning 
pitches should have the value n = (m + M)/2. However, there is no way to 
express that in the staff system, just as it is not possible to express that 
2*m = M.

So in the staff system, the accidental going from m to n, the raising 
"quarter-tone", will always be different from the one going from M to n, the 
lowering "quarter-tone".

Summarizing: E12 and E24 are tuning systems, which the staff system does not 
express. If one wants them to be properly expressed, invent a new notation 
system.

Hans