62 ON THE PHYSIOLOGICAL CAUSES OF 



sight as if those were still in the right who reject all 

 ' anatomisation of pleasurable sensations.' This art, bor- 

 rowing no part of its material from the experience of our 

 senses ; not attempting to describe, and only exceptionally 

 to imitate the outer world, necessarily withdraws 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 wonderful and peculiarly inte- 

 resting 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 mathematics should prove preeminently fer- 

 tile. Thorough bass is a kind of applied mathematics. 

 In considering musical intervals, divisions of time, and 

 so forth, numerical fractions, and sometimes even loga- 

 rithms, 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 physiolo- 

 gical 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 



