In a Just musical scale, the frequency of each semitone
is related to the
root (tonic) frequency by a small, wholenumber ratio.
For example, a musical fifth is
3/2 of the root frequency while a musical fourth is 4/3 of the root.
In other words, the 11 semitones above the root have no rational relationship to any of the other semitones, only to the
root. If you try to play in a key that starts on a note other
than the root, several of the note's semitones will be significantly
off the Just ratios and the shifted scale will sound noticeably out of tune.
It's interesting to note that when you play a chord in a Just scale,
heterodyning
produces frequencies that are already present in or suggested by the
chord, with pleasing results.
For example, a 440 Hz root beating with a 220 Hz suboctave generates a
difference frequency of 220 Hz (already present) and a sum frequency of
660 Hz, which is a musical 5th (3/2 of 440).
Of course, the disadvantage of a Just scale is that it only plays in
tune in one key.
