will be judged as different by a trained observer whose vibration rates differ by but 0.2 vibration in the 1 sec. Measurements of this sort require a delicate apparatus, which has usually taken the form of a series of tuning-forks, whose pitch can be varied at will by the movement of a rider along their prongs, or of a series of reeds, very carefully tuned to minute differences of pitch, sounding under wind pressure.
The psychology of the simple noises is as yet incomplete. There seems to be no doubt that noises show differences of quality or pitch more or less resembling those of tones. The crack of a pistol is 'higher' than the roar of a cannon; the snap of a large soap-bubble is 'deeper' than the snap of a small one. Experiments have been made in which the sound of a tuning-fork is cut off from the observer's ear before the prongs have executed two complete wave-movements; the sound in such a case is not a tone, but a noise. The results seem to indicate that we can distinguish between 500 and 600 simple noises, or that there are about 20 times fewer noise than tone sensations. This statement, however, requires confirmation. It has recently been suggested that there are two ultimate types of simple noise: the snap (electric spark, soap-bubble, curtailed sound of fork) and the hiss; but no classification of hisses by pitch or quality has been attempted.
A word must be said about two striking phenomena of auditory sensation — beats and combination-tones. (1) If two tones whose vibration-rates are slightly different are sounded together, the resulting sound is not smooth, but 'wavy': it fluctuates in intensity, according as a hill of the one curve coincides with a hill or with a valley of the other. Thus two tones of 100 and 101 vibrations in the 1 sec. beat once in the 1 sec.; tones of 100 and 102 beat twice; and so on. Beats can be counted up to about 5 in the 1 sec, and can be heard separately up to about 60; beyond this limit the beating complex merely sounds harsh and rough. In certain cases the two beating tones give rise to a third — intermediate — tone which carries the beats. (2) If two tones are sounded together, various extra-tones are generated, whose vibration-rates stand in definite relations to the vibration-rates of the primary tones. Most important, theoretically, are (a) the first difference-tone and (b) the summation-tone. The pitch-number of the former is equal to the difference between the vibration-rates of the two generators. Thus tones of 300 and 400 vs. produce a first difference-tone whose pitch-number is 100. The pitch-number of the latter is equal to the sum of the vibration-rates of the generators; thus tones of 300 and 400 vs. produce a summation-tone of 700. It is probable that the difference-tone is a beat-tone, and that the summation-tone is due to the presence of over-tones in the primaries. See Clang-tint.
Sensations of sound appear to have developed from general bodily sensations of jar or tremor. (See Static Sense.) The first auditory sensation proper is, probably, the noise; this theory is borne out by facts of genetic psychology as well as by the circumstance that, for our own ears, the physical stimulus of noise is an imperfect tonal stimulus: the sensations are different in kind, but their exciting causes differ only in degree. The ruling theory of audition,
that of Helmholtz (q.v.), maintains that tonal sensations are set up by the vibration of the cross-fibres of a triangular membrane stretched between the bony walls of the cochlea of the internal ear. This 'basilar' membrane repre- sents, in miniature, the arrangement of a harp, or of the backboard of an upright piano; the long strings are tuned to the bass tones, the short strings to the treble tones. The external air-wave strikes the drumskin of the ear, is transmitted inward by the chain of auditory ossicles, and arouses a wave-movement in the endolymph of the internal ear. The motion is taken up by that basilar fibre which is 'tuned' to its particular rate; the motion of the fibre excites the hair of a sensory cell resting upon it; and the nervous impulse passes from this cell along the auditory nerve to the brain. An overlying membrane, the 'tectoria,' acts as dam- per, to bring the vibrating hair to rest again, The details of the theory, as amended by Hen- sen, Exner, and Ebbinghaus, afford a fairly satisfactory explanation of the details of audi- tory sensation. We have seen that there are some 11,000 tonal qualities. It has been found that the basilar membrane consists of 16,000 to 20,000 cross-fibres — more than enough to serve as the basis of these sensations. The qualities of noise we may suppose to be mediated by the simultaneous jarring of a number of adjacent basilar fibres. Beats are accounted for on the hypothesis that the incoming air-wave sets in vibration not only the basilar fibre which is specifically attuned to it, but (in a lesser de- gree) the neighboring fibres as well. If, then, two fibres that lie near together within the membrane are set swinging by two waves of but slightly different rates, the fibres lying be- tween these two will also be affected, and affected by both stimuli. There is, consequently, interference of the two wave-motions in this nar- row intermediate strip of membrane, and the intermediate tone (which carries the beats) is aroused. Combination-tones were explained by Helmholtz as due to asymmetrical vibrations of the conductive apparatus (ossicles and mem- branes). The explanation is, however, unsatis- factory; it divorces the difference-tones from the beats, placing the one in one part of the ear and the other in another; and it offers no- reason for the intensity of the difference-tones. Ebbinghaus has restored these tones to the coch- lea by two simple and natural extensions of Helmholtz's principles. He supposes — (a) that, a simple wave-movement of the endolymph ex- cites a limited number of adjacent fibres, and thus a number of hair-cells; and that the cells are not so sharply differentiated in function but that all alike (though in varying degrees) can mediate the same tonal sensation; and (b) that a given wave-motion excites not only its own particular basilar string, but also (within cer- tain limits) the strings that are attuned to its harmonic undertones. Thus a stimulus of 600 vi- brations in the 1 sec. would, perhaps, excite the strings attuned to .599.6, 599.8, 600, 600.2, 600.4; and the cells lying upon these strings would all alike give the tone 600 in sensation. More- over, the stimulus 600 would excite not only the 600-string, but also the strings that respond directly to stimuli of 300, 200, 150, 120, etc. These assumptions afford an easy explanation of the phenomena in question. We may add that
