Let, for example, the length of the line a b be any definite duration of time, and let the curves above this line denote the condensations (+), and the curves below this line the rarefactions (-); then every ordinate erected at the extremity of an abscissa gives us the strength of the condensation in consequence of which the drum-skin vibrates, at the moment indicated by the position of the foot of the ordinate.
Anything more than that which is exhibited in this way or by similar curves our ear cannot in the least perceive, and this is sufficient to bring to our consciousness each single tone and each given combination of tones. For, if several tones are produced at the same time, the sound-conducting medium is put under the influence of several simultaneously acting forces which are subject to the laws of mechanics.
If all the forces operate in the same sense, then the magnitude of the motion is proportional to the sum of the forces. If the forces act in opposite directions, the magnitude of the motion is proportional to the difference between the opposing forces.
Consequently it is possible out of the condensation-curves of several simultaneously-occurring tones to compound, by the foregoing principles, a condensation-curve which exactly expresses that which our ear experiences on the reception of these simultaneously-acting tones. The objection ordinarily made to this, that a musician, or even any one, is able to hear separately the single tones of which this combined curve is built and constructed, cannot be admitted as a proof to the contrary; for one expert in the science of colour will, for example, in the same way discern in green a mixture of yellow and blue in their various shades: and the one phenomenon equally with the other may be referred back to this; that, to the person concerned, the factors which make up the product of that which reaches his consciousness are well known.
According to that which has been already explained, it is easy to construct the condensation-curves of various tones, chords, &c., and for the sake of clearness some examples follow:—
[Fig. 1, Plate I.],[25] shows a combination curve of three tones, in which all the proportions of the components recur successively.
[Fig. 2] shows such a curve of more than three tones, in which the proportions in the drawing can no longer so evidently be given; yet the practised musician would here recognise them, even although in practice it might be difficult for him to single out, in such chords, the separate tones.
This method of exhibiting the action of tones upon the human ear offers the advantage of a very clear perception of the process; and that which is exhibited ([Fig. 3]) shows also why a discord must affect our ear unpleasantly.
This apparent digression from the aim set forth was necessary in order to indicate that as soon as it is possible for us to create anywhere, and in any manner whatever, vibrations whose curves and magnitudes are similar to the vibrations of any given tone, or of any given combination of tones, we shall have the same impression as this original tone or this original combination of tones would have produced upon us.