TEMPERAMENT, in music, is defined by Rousseau to be an operation, which, by means of a slight alteration in the intervals, causes the difference between two contiguous sounds to disappear, makes each of these sounds seem identical with the other, which, without offending the ear, may still preserve their respective intervals or distances one from the other. By this operation, the scale is rendered more simple, and the number of sounds which would otherwise be necessary retrenched. Had not the scale been thus modified, instead of twelve sounds alone which are contained in the octave, more than 60 would be indispensably required to form what we properly call modulation in every tone.
It is proved by computation, that upon the organ, the harpsichord, and every other instrument with keys, there is not, and there scarcely can be, any chords properly in tune, save the octave alone. The cause is this, that though three thirds major, or four thirds minor, ought to form a just octave, those are found to surpass, and these not to reach it.