"In following out this idea, we find that the chords whose beats we cannot hear are precisely those which the musicians call consonances and that those whose beats are heard are the dissonances, and that when a chord is a dissonance in one octave and a consonance in another, it beats in the one and does not beat in the other. Consequently it is called an imperfect consonance. It is very easy by the principles of M. Sauveur, here established, to ascertain what chords beat and in what octaves, above or below the fixed note. If this hypothesis be correct, it will disclose the true source of the rules of composition, hitherto unknown to science, and given over almost entirely to judgment by the ear. These sorts of natural judgment, marvellous though they may sometimes appear, are not so but have very real causes, the knowledge of which belongs to science, provided it can gain possession thereof."[143] Sauveur thus correctly discerns in beats the cause of the disturbance of consonance, to which all disharmony is "probably" to be referred. It will be seen, however, that according to his view all distant intervals must necessarily be consonances and all near intervals dissonances. He also overlooks the absolute difference in point of principle between his old view, mentioned at the outset, and his new view, rather attempting to obliterate it. R. Smith[144] takes note of the theory of Sauveur and calls attention to the first of the above-mentioned defects. Being himself essentially involved in the old view of Sauveur, which is usually attributed to Euler, he yet approaches in his criticism a brief step nearer to the modern theory, as appears from the following passage.[145] "The truth is, this gentleman confounds the distinction between perfect and imperfect consonances, by comparing imperfect consonances which beat because the succession of their short cycles[146] is periodically confused and interrupted, with perfect ones which cannot beat, because the succession of their short cycles is never confused nor interrupted. "The _fluttering roughness_ above mentioned is perceivable in all other perfect consonances, in a smaller degree in proportion as their cycles are shorter and simpler, and their pitch is higher; and is of a _different kind_ from the _smoother beats_ and undulations of _tempered consonances_; because we can alter the rate of the latter by altering the temperament, but not of the former, the consonance being perfect at a given pitch: And because a judicious ear can often hear, at the same time, both the flutterings and the beats of a tempered consonance; sufficiently distinct from each other.