Representation of pitches and scales

[Rune Zedeler]

Wondering how to solve the absolute pitch-compare-problem I mentioned in 
the ambitus bug report, I took a look into how pitches and scales are 
represented in lily.
I see that the diatonic scale is represented as

(ly:make-scale #(0 1 2 5/2 7/2 9/2 11/2)

thereby effectively hardcoding a semitone to be exactly half a whole 
tone - which is rather inadequate because it makes it impossible to 
distinguish e.g. cis from des.
I didn't look deeply into the code - it seems like it could use some 
cleanup - in scale.cc The comment to ly:make-scale says that the 
function takes an int-vector as argument even though it takes a rational 
vector. The vector is also named "semitones" even though it counts whole 
tones (?!?!).
In tone_pitch it seems like it is hardcoded that an octave consists of 
exactly 6 whole notes.

Another question:
Pitch::rounded_semitone_pitch () const
{
  return int (double (tone_pitch () * Rational (2)));
}
Converting a double to an int always rounds down. Isn't it wrong not to 
call round() on the double before casting it to int?

Well, having tone_pitch returning the pitch in 1/6-octaves is pure 
messy. I have never heard of that scale before.

I would propose using the cents-scale, that is sortof a standard. A cent 
is 1/1200 of an octave.
Having tone_pitch returning a number of cents - and having the scale 
defined as a list of cents relative to base-tone- would IMO be the right 
thing to do.
This would also make it easier to type in alternative scales, because 
scales are always reported in cents.

I also think that the Scale object should contain information about the 
size of an alteration (that is, how many cents a quartertone takes).

We could add some nifty scheme functions to calculate a scale given a 
fifth-size in cents, or a whole-tone-size in cents.

Please comment.

-Rune