v THE SENSE OF HEARING 251 



ordinary and conspicuous phenomena it happens each time two 

 simultaneous tones are appreciated as a consonance. The greater 

 or lesser degree of consonance in the different musical intervals 

 depends upon their varying capacity for complete fusion. A 

 well-trained musical ear is always capable of analysing consonant 

 intervals into their components ; an unmusical or untrained ear 

 is the less capable of such analysis in proportion as the consonance, 

 that is the mental fusion, of the two component sensations is 

 more perfect. Discords are the musical intervals that cannot be 

 fused into a uniform sonorous perception, so that even an 

 unmusical ear is capable of distinguishing the two simultaneous 

 tones. Consonance is thus exclusively due to psychical fusion 

 of the two component tones, and is, within the range of notes 

 utilised in music, independent of the pitch and intensity of the 

 partial tones that make up the interval. 



The explanation of the fusion or non-fusion of tones, on which 

 their consonance or dissonance depends, is a difficult psycho- 

 physical problem, which has up to the present found no convincing 

 or adequate solution. It may be assumed with Stumpf that 

 when the numerical relation of the vibrations of the two simul- 

 taneous tones is comparatively simple two processes take place 

 in the brain, which are more closely interrelated than when this 

 relation is less simple. In the first case there is a specific relation 

 between the two central processes ; in the second, this relation is 

 imperfect or absent. In the present state of our knowledge, 

 however, it is impossible to define in what the supposed 

 " specific relation " essentially consists. 



Zambiasi (1903-1905) has recently formulated a new theory of 

 consonance and dissonance which resembles that of Helmholtz in 

 so far as it holds these phenomena to be' dependent on physical, 

 objective conditions of tone, independent of any central, psychical 

 process ; on the other hand, he adopted Stumpf s view that these 

 phenomena depend essentially on the greater or lesser fusion of 

 elementary sensations into a compound sensation of sound. For 

 Zambiasi as for Stumpf consonance corresponds with complete, 

 dissonance with incomplete fusion of several tones, but this fusion, 

 according to Zambiasi, depends not on mental processes, but on 

 a peripheral physical phenomenon, which consists in a new period, 

 resulting from the combination of the vibrations of the two tones. 



Just as the simple sensation of the pitch of the different 

 elementary tones depends on the duration of the rhythmical 

 vibrations, so the complex sensation that results from the com- 

 bination of two simultaneous tones depends on the different 

 duration of a new periodicity distinct from that of the simple 

 vibrations formed in consequence of this combination. This is 

 clear if we consider the physical significance of the relation 

 between the number of vibrations of the two tones. When, e.g., 



