Theory of Audition subjected to Experiments, 169 



We have thus obtained some light on (a), (b), and (c), but 

 not upon (d), which would require more refined examination. 



Further, it should be pointed out that these facts of 

 audition do not lead us to any exact determination of the 

 variables at our disposal in the set of responders. On the 

 contrary, they suggest values of a certain order of magnitude, 

 or furnish us with approximate upper and lower limits. Thus 

 it would be sometimes possible to account for the facts of the 

 -case with certain values of the variables or to account for 

 them equally well by changing one variable, some other 

 being adjusted in compensation. For example, the less the 

 damping of the responders, the sharper is the resonance and 

 the easier would it be to locate the pitch of maximum response. 

 But a greater damping of the responders, leading to less sharp- 

 ness of resonance, could be compensated by an enhanced 

 discrimination of relative amplitudes of responding vibrations 

 near the maximum. 



Experimental Arrangements. — No attempt has been 

 made to set up the whole seven octaves of responders 

 postulated, but only a single representative octave, which 

 suffices for experimental tests. In order to have a definite 

 and constant interval between adjacent responders throughout 

 the octave, they were set at distances from one end, and 

 adjusted to lengths, which formed a geometrical progression. 

 And it seemed desirable to make the intervals correspond 

 musically to those of the tempered chromatic scale. Thus 



the ratio of adjacent pendulum lengths was v'2, the ratio 

 of periods being accordingly ^/2. Thus the thirteen res- 

 ponders for the one octave may be referred to by the letters 



T H 



Experimental Arrangement. 



used for the notes of tiie scale with sharps and flats where 

 required. Eight of these are indicated in the figure by 

 0, D, E, F, Gr, A, B, C, the five corresponding to the sharps 

 and flats being left unlettered. 



All these responding pendulums have bobs in the form of 



