hearing, must be different likewise, and afford the mind a sufficient foundation for distinguishing sounds in respect of strength and feebleness.
Secondly, the gravity and acuteness of sounds arise from the slowness or frequency of the vibrations. Now, as the vibrating of the membrana tympani are synchronous to those of the air, they may either excite synchronous ones in the particles of the auditory nerves, and thus be distinguished from each other in respect of frequency by the mind; or if every pulse of the air, and oscillation of the membrana tympani, excite innumerable infinitesimal vibrations in the auditory nerves, the renewal of these at different intervals according to the different gravity or acuteness of the sound will, however, afford a like criterion.
It may be remarked, that grave sounds are in general strong, acute ones feeble. For the bodies which yield grave sounds are in general large, and consequently will make an impression upon the air by a large number of trembling particles.
Thirdly, all very loud noises are disagreeable. Now it is easy to conceive, that very violent agitations of the membrana tympani may produce the solution of continuity in the small medullary particles of the auditory nerve. An inflammation in the small vessels of the auditory nerve may render it so susceptible of violent vibrations, as to be hurt by gentle sounds, as sometimes happens in distempers; and to produce that acuteness in the sense of hearing, which answers to the nyctalopia in the eye.
Fourthly, Single musical, i.e. uniform sounds, whether vocal or instrumental, are pleasant in proportion to their loudness, provided this be not excessive. We must therefore suppose here, that the repeated impulses of the air, at equal distances, make the vibrations approach to the solution of continuity; yet still so as to fall short of it.
Fifthly, Two musical notes sounded together, suppose upon an organ or violin, afford a greater original pleasure than one, provided the ratios of their vibrations be sufficiently simple. Thus any note sounded with its eighth, fifth, fourth, third major or minor, sixth major or minor, affords pleasure, the ratios being here, respectively, those of 1 to 2, 2 to 3, 3 to 4, 4 to 5, 5 to 6, 3 to 5, and 5 to 8, which are all very simple ones. But a note with its flat or sharp, second, or seventh, or flat fifth, is originally disagreeable. It may be observed also, that concords seem to be originally pleasant in proportion to the simplicity of the ratios by which they are expressed, i.e. in the order above set down. Hence we may perhaps suspect, that even the concords were originally unpleasant to the ear of the child, from the irregularity of the vibrations which they impress upon the membrana tympani, and consequent solution of continuity; and that they fell at last within the limits of pleasure, as many other pains do, by repetition. For thus those concords in which the ratios are simplest would become pleasant first, and the others would continue to
