MECHANICS OF THE INNER EAR 



6l 



Third law of 

 difference tones 



octave. In these cases three difference 

 tones are often easily noticeable, one cor- 

 responding to the direct difference of 

 the vibration rates {h — /) ; one correspond- 

 ing to the difference between the lat- 

 ter number (h — /) and the vibration rate/ of the lower 

 primary tone, that is, (2/ — h) ; and one corresponding 

 to the difference between the just mentioned differences (h — /) 

 and (2/ — h), that is (2h — 3/). It is to be noticed, however, that 

 a difference tone is rarely audible which corresponds to 

 a difference larger than the subtrahend; for example, the 

 primary tones 9 and 5 produce the difference tones 4 and 1, 

 but not 3 = 4 — 1, or at least not an easily noticeable tone 3, three 

 being larger than one. The following table contains a few ex- 

 amples of this class: 



The fourth class are the ratios made up of comparatively 



small numbers, representing intervals larger than an octave. 



The first fact to be noticed here is the lack 



of an easily observable difference tone 



corresponding to the direct difference 



of the two vibration rates. Such a tone, if 



audible, would lie between the primary 



tones. As a rule, only one difference tone is easily noticeable 



in these cases, which can be found according to the following 



Fourth law of 

 difference tones 



