PHYSIOLOGICAL ACOUSTICS 297 



view, be held to be almost verbal, were it not that Young's 

 theory fails to give an explanation of combination-tones other 

 than the first difference-tone. 



96. Influence of Combination-Tones on Musical In- 

 tervals. 



A brief indication of the way in which combination-tones 

 may assist in defining the consonant intervals is all that can be 

 attempted here. Take first the case of (primarily) pure tones. 

 In the case of a slightly mistuned Octave, say ^ = 100, 

 N 9 = 201, we have N z N 1 = 101, which gives a difference-tone 

 making 1 beat per second with N l9 



For the Fifth, let N, = 200, N 2 =301. We have 



giving combination-tones with 2 beats per second. 

 For the Fourth, let ^ = 300, N 2 = 401. Then 



2^-^=199, 2^-2^ 



and the corresponding tones make 3 beats per second. 



For the Major Third, let ^=400, JV 2 = 501. We have 

 2^-2^ = 202, 3^-2^=198, giving 4 beats per second. 



We might proceed further in the list, but it will already 

 have been remarked that combination-tones of increasingly 

 high order are being invoked. This is quite in conformity 

 with the observed fact that the beats are, in all cases after the 

 octave, very faint unless the primaries be especially vigorous. 



A more effective part is played by the combination-tones 

 when the notes concerned have one or two overtones, but not a 

 sufficient range of them to account for the definition on the 

 principles of 93. Take for instance the case of the Fifth, 

 when each note has a first harmonic in addition to the 

 fundamental. If the interval be slightly mistuned, we have say 

 the primary tones: 200, 400; 301, 602. These give the two 

 difference-tones 301 - 200 = 101, 400 - 301 = 99, which inter- 

 fere with one another. 



The combination- tones have an influence again, in the case 



