Re: Representation of pitches and scales

[Han-Wen Nienhuys]

> 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.

Music notation is idiosyncratic, so any representation will have its
sharp edges. I agree that representing 1/6th of octaves doesn't make
sense from a musical point of view; however, I think that rational
numbers are better than cents for representing microtones. The
microtonal support was requested by Turkish-music players, who use
1/9th tones as their unit. Such divisions can not be represented
exactly using cents. When we're using exact rationals, we might as
well drop the factor 100, which I assume to be an attempt to have a
more exact measure for pitch.  Also, I think there is some logic to
representing a "half tone" as the number 1/2.

In any event, it should not be that hard to write a cent -> tone
conversion function.

> 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.

No, this defines the scale.  If anything, this defines a temperament;
alterations can have their own rational definitions.

> 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 (?!?!).

patches appreciated.

> In tone_pitch it seems like it is hardcoded that an octave consists of
> exactly 6 whole notes.

No, that's an oversight. It should use scale_->step_tones_.size()

> 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?

sure, patch appreciated.

--
Han-Wen Nienhuys - address@hidden - http://www.xs4all.nl/~hanwen