Let the line a, b, indicate any given length of time, and the curve above the line a condensation (+), the curve below the line a rarefaction (-), then every ordinate erected at the end of an abscissa will give [according to the height of it], at a moment indicated by the position of the foot of the ordinate, the strength of the condensation that is causing the drum-skin to vibrate.
Our ear can perceive absolutely nothing more than is capable of being represented by similar curves, and this method is completely sufficient to bring before our clear consciousness every tone and every combination of tones.
If several tones are produced at the same time, then the medium that conducts sound is placed under the influence of several simultaneous forces; and the two following laws hold good:—
If all the forces operate in the same sense, the resultant motion is proportional in magnitude to the sum of the forces.
If the forces operate in opposite senses, the resultant motion is proportional in magnitude to the difference of the opposing forces.
Let us exhibit the condensation-curves for three tones—each singly (Table I.)[16]: then, by adding together the ordinates corresponding to equal abscissæ, we can determine new ordinates and develop a new curve which we may call the combination-curve [or resultant curve]. Now this gives us just exactly what our ear perceives from the three simultaneous tones. It ought to cause us as little wonder that a musician can recognize the three tones, as that (as is the fact) a person conversant with the science of colour, can recognize in green, blue and yellow tints. The combination-curves of table I. present, however, very little difficulty, since in them all the proportions of the component curves recur successively. In chords consisting of more than three tones (Table II.), the proportions of the components are no longer so easy to recognize in the drawing. But it is also difficult to an accomplished musician, in such chords to recognize the individual notes.
Table III. shows us a discord. Why discords affect us so unpleasantly I leave provisionally to the contemplation of the gentle reader, as I may perhaps return to this point in another memoir.
It follows from the preceding that:—
(1.) Every tone and every combination of tones evokes in our ear, if it enters it, vibrations of the drum-skin, the motions of which may be represented by a curve.[17]
(2.) The motions of these vibrations evoke in us the perception (sensation) of the tone: and every change in the motion must change the sensation.