336 DR. kcenig's researches on 



sired number of vibrations within their own limits. Beside this colos- 

 sal master piece, Dr. Kcenig's collection includes several large wave- 

 sirens and innumerable pieces of apparatus in which his ingenious 

 nianometric flames are adapted to acoustical investigation. There also 

 stands his tonometric clock, a timepiece governed, not by a pendulum, 

 but by a standard tuning-fork, the rate of vibration of which it accu- 

 rately records. 



It is not surprising that one who lives amongst the instruments of 

 his own creation and who is familiar with their every detail should 

 discover amongst their properties things which others whose acquaint- 

 ance with them is less intimate have either overlooked or only im- 

 perfectly discerned. If he has in his researches advanced propositions 

 which contradict or seem to contradict the accepted doctrines of the 

 professors of natural philosophy, it is not that he deems himself one 

 whit more able than they to offer mathematical or philosophical expla- 

 nations of them ; it is because, with his unique opportunities of ascer 

 taining the facts by daily observation and usage, he is impelled to state 

 what those facts are and to propound generalized statements of them, 

 even though those facts and generalized statements differ from those at 

 present commonly received and supposed to be true. 



At the very foundations of the physical theory of music stand three 

 questions of vital importance: 



(1) Why is it that the ear is pleased by a succession of sounds be- 

 longing to a certain particular set called a scale ? 



(2) Why is it that, when two (or more) musical sounds are simultane- 

 ously sounded, the ear tinds some combinations agreeable and others 

 disagreeable ? 



(3) Why is it that a note sounded on a musical instrument of one sort 

 is different from and is distinguishable from the same note sounded 

 Avith equal loudness upon an instrument of another sort ? 



These three queries involve the origin of melody, the cause of harmony, 

 and the reason of timbre. 



The theories which have been framed to account for each of these 

 three features of music are based on a double foundation, paitly 

 physical, partly physiological. With the physiological aspect of tliis 

 foundation we have to-night nothing to do, being concerned only with 

 the physical aspect. What, then, are the physical foundations of 

 melody, of harmony, and of timbre? Demonstrable by experiment 

 they must be, in common with all other physical facts; otherwise they 

 can not be accepted as proven. What are the facts and how can they 

 be demonstrated ? 



We are not here, however, to tight over again the battle of the tem- 

 peraments, nor do I purpose to enter upon a discussion of the origin 

 of melody, which, indeed, I believe to be associative rather than phys- 

 ical. I shall confine myself to two matters only, with which the recent 

 researches of Dr. Koenig are concerned : — the cause of harmony, and the 



