Pitch questions

[Rune Zedeler]

I am looking into splitting pitch into pitchclass and pitch.
Therefore I need to understand what is going on in the pitch class.
Some questions (inserted as c++-comments):

void
Pitch::normalize ()
{
  Rational pitch = tone_pitch ();
  while (notename_ >= (int) scale_->step_tones_.size ())
    {
      notename_ -= scale_->step_tones_.size ();
      octave_++;
      // why? isn't this always 0? -rz
      alteration_ -= tone_pitch () - pitch;
    }
  while (notename_ < 0)
    {
      notename_ += scale_->step_tones_.size ();
      octave_--;
      // do -rz
      alteration_ -= tone_pitch () - pitch;
    }

  while (alteration_ > Rational (1))
    {
      // code duplication. Remove this and move the two above 
while-loops below this one: -rz
      if (notename_ == int (scale_->step_tones_.size ()))
        {
          notename_ = 0;
          octave_++;
        }
      else
        notename_++;

      // isn't this the same as alteration_ = pitch - tone_pitch() -rz
      alteration_ = Rational (0);
      alteration_ -= tone_pitch () - pitch;
    }
  while (alteration_ < Rational (-1))
    {
      // do -rz
      if (notename_ == 0)
        {
          notename_ = scale_->step_tones_.size ();
          octave_--;
        }
      else
        notename_--;

      // do -rz
      alteration_ = 0;
      alteration_ -= tone_pitch () - pitch;
    }
}

And something a bit more serious:

void
Pitch::transpose (Pitch delta)
{
  Rational new_alter = tone_pitch () + delta.tone_pitch ();

  octave_ += delta.octave_;
  notename_ += delta.notename_;
  alteration_ += new_alter - tone_pitch ();

  normalize ();
}

This looks very ineffecient.

  Rational new_alter = tone_pitch () + delta.tone_pitch ();
  alteration_ += new_alter - tone_pitch ();

is equivalent to

alteration_ += delta.tone_pitch ();

So if we transpose a huge distance then we add a lot to the alteration. 
(A simple transpose c, c'' will add 18 to the alteration)
And the normalize () function is linear in the size of the alteration. 
So transposing time-usage is linear in the distance we transpose.
Afaics.

-Rune