In a Just musical scale, each semitone frequency is related to the
root (or tonic) frequency by a small, wholenumber ratio.
For example, the musical fifth ratio is
3:2 and the musical fourth ratio is 4:3. The majorthird ratio is
5:4 and the minorthird ratio is 6:5.
This means that none of the instrument's semitone frequencies have any rational relationship to any
of the other semitones, only to the
root.
If you start a musical scale on a note other than the root, several of
the semitones will differ significantly
from the just ratios, The shifted scale will sound noticeably out of tune.
Just Heterodyning
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.
