v THE SENSE OF HEARING 253 



tion of the periods of these intervals it is plain that the shorter the 

 period the greater is the consonance, the longer the period the 

 greater is the dissonance. Unison is not really a musical interval, 

 because the two component tones, since they have the same 

 number of vibrations, do not produce any new periodicity different 

 from that of the simple tones. Consonant intervals appear as 

 such in consciousness, because their period is so short that they 

 fuse into a single uniform sensation. Dissonant intervals, on the 

 contrary, have periods as long as those of the tones which lie near 

 the lower threshold of auditory perception. They cannot, there- 

 fore, fuse into a uniform and continuous impression, and they 

 produce a discontinuous and intermittent sensation in con- 

 sciousness, which makes the two component tones more easily 

 recognisable. Zarnbiasi holds that the lower threshold of audition, 

 both for simple sounds and for intervals, depends on the physio- 

 logical time-constant of the ear, and that no continuous sensation 

 of the same is possible unless the duration of their period is 

 shorter than that of the sensation. 



When we consider that the time required to produce an 

 auditory sensation is about ^Vth second we can understand that 

 at least 20 vibrations per second are necessary to cause a uniform 

 sensation, so that when the elementary sensation of a vibration 

 ceases the sensation of the next vibration should begin without 

 a pause. Beyond this minimum of vibrations per second the 

 threshold of auditory sensation is passed. 



Zambiasi shows by a number of experiments that the new 

 periodicity and the new sensation which arise from the coincidence 

 of two tones forming definite intervals come under the same 

 limitations and the same laws that regulate the sensation of 

 simple tones. In order that the interval may produce a continu- 

 ous uniform sensation the periods must not be so long as to occur 

 less often than 20 to the second, which number is, as we have 

 seen, the threshold of auditory perception. Above this threshold, 

 up to 100 and more periods per second, there are two superposed 

 sensations, one of a continuous sensation of sound, the other of 

 simple a-phonic vibrations. The major third, for example, is 

 hardly perceptible when the lowest tone contains 80 vibrations. 

 This phenomenon is easily explained if we remember that the 

 duration of its period is four times as great as that of the lowest 

 tone, so that in this case the interval of the third has 20 periods, 

 per second, which is the physiological minimum for the percep- 

 tion of tones. 



In polyphonic vocal and instrumental music it is not merely a 

 question of sounding two instruments together, but of producing 

 three or more tones simultaneously, which is commonly known as 

 a chord. Chords, again, like simple intervals, may be consonant 

 or dissonant, according as more or less fused and more or less 



