Re: improving our contributing tools and workflow

[Hans Aberg]

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

>> 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.  

For one microtonal accidental, one needs, in addition to the minor/major 
seconds m and M, a neutral second n. For a pitch x = r*m + s*M + t*n, compute 
its degree deg(x) := r + s + t, which is its staff position, and subtract the 
staff pitch.

There remains a new pitch, which I also call x, but now with r + s + t = 0. As 
sharps/flats alter with a multiple of r - s, reduce using them so that only one 
of r, s is non-zero.

Assume first that t = 1, i.e., one n. Then it must be either n - M or n - m.

We have six microtonal symbols, sharp/natural/flat with up/down arrows, but it 
will, as we shall see, suffice with four. One way to make a choice is to 
conceptualize n as below or above (m + M)/2: if it is a small or large neutral. 
This choice is purely formal at this point, but will be of importance when 
plugging in values.

If one thinks of n as between m and M, which is possible with actual values by 
reducing using sharps and flats, then n' := (m + M) - n (the minor third m3 
complement) is also a neutral between m and M. If n is small, then n' is large, 
and vice versa.

Returning to the situation above, assume n to be small. The up/down arrows will 
be thought of as changing with a small amount: n - m.

There are two possibilities: n - m, and n - M. In the first case, n - m 
represents a small positive amount, so it is the natural with up arrow. In the 
second case, it is a large negative amount, so it is the flat with up arrow.

Assume now that t = -1, so the two cases are m - n and M - n. The first case 
lowers with the small amount n - m, so it is a natural with a down arrow. And M 
- n raises with a large amount, so it must be a sharp with a down arrow. 

If the absolute value |t| of t is larger than 1, then one needs as many arrows 
as |t|: up if t is positive, and down if t is negative.

Two symbols where not used: sharp with up arrow and flat with down arrow. But 
they conceptually fall without the region of raising a sharp M - m or lowering 
with a flat -(M - m), and can in fact be reduced using a natural with up/down 
arrow plus a sharp/flat. So here, one would need notation simplification 
algorithm.

Hans