In a Just musical scale, semitone frequencies relate to the
fundamental frequency (also called the tonic) by small, whole number
ratios. A musical fifth, for example, vibrates at
3/2 of the tonic while a musical fourth vibrates at 4/3 of the tonic.
This means that, numerically, the semitones aren't evenly spaced. If you
try to move the tonic to a different note of the scale,
the semitones will no longer have just ratios and the scale will sound noticeably out of tune.
The advantage of a Just scale is that chordal beating (heterodyning)
produces harmonic frequencies that are already in or suggested by the original notes, with pleasing results.
A 440Hz tonic, for example, beating with a 220Hz suboctave generates a
difference frequency of 220Hz (already present) and a sum frequency of
660Hz which is a musical 5th (3/2 ratio above 440Hz).
The disadvantage of a Just scale is that it only plays in
tune in one key.
