54 ON THE PHYSIOLOGICAL CAUSES OF 



only exceptionally to imitate the outer world, necessarily with- 

 draws from scientific consideration the chief points of attack 

 which other arts present, and hence seems to be as incompre- 

 hensible and wonderful as it is certainly powerful in its effects. 

 We are, therefore, obliged, and we purpose, to confine ourselves, 

 in the first place, to a consideration of the material of the art, 

 musical sounds or sensations. It always struck me as a wonder- 

 ful and peculiarly interesting mystery, that in the theory of 

 musical sounds, in the physical and technical foundations of 

 music, which above all other arts seems in its action on the 

 mind as the most immaterial, evanescent, and tender creator of 

 incalculable and indescribable states of consciousness, that here 

 in especial the science of purest and strictest thought mathe- 

 matics should prove pre-eminently fertile. Thorough bass is a, 

 kind of applied mathematics. In considering musical intervals,, 

 divisions of time, and so forth, numerical fractions, and some- 

 times even logarithms, play a prominent part. Mathematics 

 and music ! the most glaring possible opposites of human 

 thought! and yet connected, mutually sustained! It is as- 

 if they would demonstrate the hidden consensus of all the 

 actions of our mind, which in the revelations of genius makes 

 us forefeel unconscious utterances of a mysteriously active 

 intelligence. 



When I considered physical acoustics from a physiological 

 point of view, and thus more closely followed up the part which 

 the ear plays in the perception of musical sounds, much became 

 clear of which the connection had not been previously evident. 

 I will attempt to inspire you with some of the interest which 

 these questions have awakened in my own mind, by endeavour- 

 ing to exhibit a few of the results of physical and physiological 

 acoustics. 



The short space of time at my disposal obliges me to confine 

 my attention to one particular point; but I shall select the 

 most important of all, which will best show you the significance 

 and results of scientific investigation in this field ; I mean the 

 foundation of concord. It is an acknowledged fact that the 

 numbers of the vibrations of concordant tones bear to each 



