Bob Draper writes:

>Each octave is divided in twelve because this is the smallest frequency
>variation that can be detected by the average human ear.

Not so.  Average listeners can detecte much smaller pitch variances than a
semitone.  The even tempered scale (which divides the octave into 12 steps)
is an almost magical compromise that makes it possible to modulate into
remote keys without too radically mistuning the important intervals of the
diatonic scale.

len.