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VI. §73.] ANALYSING POWER OF THE EAR. 149
which it has analysed the composite vibration originally presented to it. The ear being deaf to differences of phase in partial-tones (p. 144), perceives no difference between such modes of vibration as those exhibited on p. 146, but merely resolves them into the same single pair of partial-tones. Since, however, only one such resolution of a given vibration-mode is possible, the ear can never vary in the group of partial-tones into which it resolves an assigned clang.
The power possessed by the ear of thus singling out the constituent tones of a clang and assigning to them their relative intensities is unlike any corresponding capacity of the eye. Take for instance the two curves shown in Figs. 51 and 52, and try to determine, by the eye alone, what simple waves, present with what amplitudes, must be superposed in order to reproduce those forms. The eye will be found absolutely to break down in the attempt.
We have seen that the loudness of a composite sound depends on extent of vibration, and its pitch on rate of vibration. There remains only one variable element, viz. mode of vibration, to account for the quality of the sound. From this consideration it follows that some connexion must exist between the quality of a sound and the mode of aerial vibration to which the sound is due. Up to the time of Helm-