Although the foregoing would be the best division of the musical scale, if our sole object were to render the harmony of its concords as nearly equal as possible, yet the two other considerations, stated at the beginning of the essay, must by no means be neglected, as has been done by Dr. Smith. It seems to be universally admitted, that the sum of the temperaments may be increased to a certain extent, in order to equalize the harmony of the concords; otherwise the natural scale of major and minor tones, which makes the sum of the temperaments of the Vths, IIIds, and 3ds but 2 commas, ought to be left unaltered. Yet how far this principle ought to be carried, may be a matter of doubt. If we make the IIIds perfect, and flatten the Vths and 3ds each ¼ _c_, according to the old system of mean tones, we shall have the smallest aggregate of temperaments which admits of the different concords of the same name being rendered equally imperfect; but this amounts to 2½ commas. Thus far, however, it seems evidently proper to proceed. If we go still farther, and endeavour to equalize the harmony of the concords of _different_ names, it may be questioned whether nearly as much is not lost as gained; for the aggregate temperaments are increased, in Dr. Smith's scale, to 2⅔ _c_, and in that of the above proposition to 2-5/7 _c_. The system of mean tones, although more unequal in its harmony when but two notes are struck at once, yet when the chords are played full, as they generally are on the organ, never offends the ear by a transition from a better to a worse harmony. For every _triad_ is equally harmonious; being composed of a perfect IIId, and a Vth and 3d, tempered each ¼ _c_, or of their complements to, or compounds with octaves, which, in their kinds, are equally harmonious.