168 Prof. Barton and Miss Browning on the Resonance 



of say one vibration in a thousand, or about the fortieth of an 

 equal- tempered semitone. 



4. The range of audition is limited at both ends, each limit 

 varying with the individual, but about eleven octaves are 

 usually audible. 



5. Before either limit of audition is absolutely reached, the 

 note is recognized to be very high or very low, but the power 

 of distinct location of pitch is lost, only about seven octaves 

 being musically audible. 



6. A musical shake of about ten notes per second on a 

 tone of frequency a hundred and ten per second is heard 

 quite distinctly. 



Variables of Responding System. — If a set of vibrating 

 responders is provisionally postulated as existing in the ear, 

 and if in order to test the validity of the postulate we are to 

 make a working model on this principle, it is evident that 

 many variables are at our disposal, and probably the success 

 of the model in accounting for the actual facts of audition, 

 should that prove possible, will depend somewhat upon the 

 right choice of these variables. 



The chief variables in question may be stated as follows : — 



(a) The total range of responders. 



(6) The musical intervals between adjacent responders. 



(c) The damping natural to these responders. 



(d) The constancy or otherwise of the intervals and of the 



clamping throughout the range. 

 We must also suppose that 



(e) a certain order of discrimination of relative amplitudes 



of vibrations of different responders is possible by 

 means of the nerves attached to them. 



Obviously these variables must be chosen so as to accord 

 as far as possible with the facts of audition previously 

 enumerated. Thus the facts under headings 1, 2, and 3 

 - give some clue to the smallness of the interval between 

 adjacent responders and also show that the damping must 

 not be too large., Otherwise the sharpness of resonance 

 would not be great enough to facilitate location of pitch. 



The facts of limited range of audition and loss of exact 

 sense of pitch near ends (headings 4 and 5) show that the 

 range of responders should extend to about seven octaves. 



From the sixth fact as to the clearness of a shake, 

 Helmholtz concluded that the expiring tone is reduced to 

 one tenth of its orioinal amount in the fifth of a second. If 

 therefore the ear has vibrational responders, their natural 

 damping at this pitch must correspond to a logarithmic 

 decrement of the order \ = 0"06. This shows that the 

 damping must not be too small. 



