Re: Lilypond's internal pitch representation and microtonal notation

[Hans Aberg]

On 21 Sep 2010, at 16:52, Carl Sorensen wrote:

> Here are scans from the relevant section of Stone's book.  It  
> explicitly
> *says* that natural+1/4 and sharp-1/4 are enharmonic equivalents,  
> and that
> the notation for those pitches must be chosen with care.

Another interpretation might be slightly sharp/flat, that is, not  
exact E24. Exact quarter-tones look like these, or some variation:
  http://en.wikipedia.org/wiki/Modern_musical_symbols#Quarter-tone_accidentals

Assume it is a small amount, denote the interval of the up (resp.  
down) arrow by n-m (resp. m-n), where n is a neutral second. Then  
sharp + down = (M-m)+(m-n) = M-n, which is an accidental that would be  
needed. And also flat + up = (m-M) + (n-m) = n-M. Call these large up  
and large down.

My algorithm produces the accidental as a combination of these four:  
up, down, large up and large down. But the accidentals can be  
rewritten. Here, I reasoned that it would be simplest first finding  
the smallest amount of accidentals and then rewrite them.

So if one gets a M-n, rewrite it to (M-m)+(m-n), add 1 to the number  
of sharps to typeset, and then select the symbol with the down arrow.  
Similarly, rewrite n-M to (m-M) + (n-m), add 1 to the number flats,  
and then select the symbol with the up arrow.

The implementation would need to just do the rewriting, because the  
selection is done by a map from positive coefficient linear  
combinations of pairs of seconds (which is the internal representation  
of accidentals). In other words, the rewriting is done as to make sure  
one is choosing from the set of existing symbols.