250 PHYSIOLOGY CHAP. 



Minor 



, , 5 .10 .15 .20 .25 .30 . 35 . 40 . 45 . 50 



Minor Sixth 5 : 8 { . ? 



. .16 .24 .32 , 40 .48 .56 . 64 . 72 . 80 



SeC nd 8:9 ' 9 18 27 36 45 54 63 72 



Seventh 8 : 



{ ' ^ ' ^ - ^ - . 



Certain not inconsiderable objections can be made to Helmholtz' 

 theory of consonance and dissonance. To the idea that consonance 

 results from a continuous and dissonance from an intermittent 

 sensation, C. Stumpf (1898) objected that when the octave and 

 fifth are produced with a tremolo they are converted into inter- 

 mittent but not into dissonant intervals. Consequently there is 

 intermittence without dissonance. On the other hand, there can 

 be dissonance without intermittence. A tuning-fork of 500 

 double vibrations makes a discord with another of 700, or this 

 again with one of 1000, without the slightest perceptible beat. 

 Lastly, Stumpf noted that beats may occur with consonant 

 intervals, which do not therefore become dissonant, and that on 

 varying the height of the intervals the nature of the beats that 

 accompany the same interval varies, though the degree of 

 dissonance is unaltered. The beats may influence the effect and 

 pleasing character of an interval, but the discord does not depend 

 upon them. Neither, according to Stumpf, is the coincidence of 

 the partial tones of two simultaneous sounds of any importance 

 as far as consonance is concerned. If this were admitted, then 

 the degree of consonance of any interval would depend on tinibre, 

 which is contrary to musical experience. 



Stumpf replaces Helmholtz' theory by another, which ignores 

 both beats and coincidence of partial tones, and finds the cause 

 of consonance and dissonance in the greater or lesser fusion of 

 the two fundamental tones in the brain. By fusion Stumpf 

 means the gradually varying and qualitatively uniform character 

 that results from two simultaneous impressions of sound. The 

 same psycho-physical phenomenon is common to other specific 

 sensations. We saw, for instance, that a metallic taste results 

 from the fusion of acid and sweet in certain proportions ; 

 we also saw that it is possible to procure a comparatively new 

 olfactory sensation by the psychical fusion of two or more odours 

 simultaneously applied to the mucous membrane. In audi- 

 tory sensation the psychical fusion of two distinct, simultaneous 

 acoustic impressions is, according to Stumpf, one of the most 



