transposition

[Ady Ecker]

I was facing a problem with the transposition functionality. Suppose I write a 
whole tone scale:

\header{
  title = "A whole tone scale in LilyPond"
}

\relative{
\time 2/4
  c16 d e fis gis ais c8
\transpose c dis
\relative
{
  c16 d e fis gis ais c8
}
}

While mathematically the transposition is correct, in practice it is 
unreadable due to the double sharps.
I suggest the following rule: if a note after transposition gets a double 
sharp (or double flat), and the one tone higher (or lower) is not modified by 
the key signature, display the note a tone higher (or lower). 

A more delicate point to consider is what should be done when there was an 
accidental on the tone higher/lower note previously in the bar, but not in the 
key signature. In my opinion, this accidental should be canceled by a natural 
sign. That is, if the tone-higher/lower is not modified by the key signature, 
double sharp/flats should be eliminated, even if natural signs and maybe other 
accidentals will be introduced later in that bar.

Note that for transitions of a semitone, like e-f and b-c, this means adding a 
sharp/flat instead of double sharp/flat. In the example above, it would be 
much more readable if the second last note be c-sharp instead of b-double 
sharp. That also means that if c is modified by the key signature to c-sharp, 
the program should convert b-sharp-sharp to c (which gets its sharp from the 
key signature).