HAKMONY IN MUSIC. 63 



awakened in my own mind, by endeavouring to exhibit 

 a few of the results of physical and physiological 

 acoustics. 



The short space of time at my disposal obliges me to con- 

 fine 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 acknow- 

 ledged fact that the numbers of the vibrations of concor- 

 dant tones bear to each other ratios expressible by small 

 whole numbers. But why ? What have the ratios of 

 small whole numbers to do with concord ? This is an old 

 riddle, propounded by Pythagoras, and hitherto unsolved. 

 Let us see whether the means at the command of modern 

 science will furnish the answer. 



First of all, what is a musical tone ? Common expe- 

 rience teaches us that all sounding bodies are in a state 

 of vibration. This vibration can be seen and felt ; and 

 in the case of loud sounds we feel the trembling of the 

 air even without touching the sounding bodies. Physical 

 science has ascertained that any series of impulses which 

 produce a vibration of the air will, if repeated with suffi- 

 cient rapidity, generate sound. 



This sound becomes a musical tone, when such rapid 

 impulses recur with perfect regularity and in precisely 

 equal times. Irregular agitation of the air generates only 

 noise. The pitch of a musical tone depends on the 

 number of impulses which take place in a given time ; 

 the more there are in the same time the higher or sharper 

 is the tone. And, as before remarked, there is found to be 

 a close relationship between the well-known harmonious 

 musical intervals and the number of the vibrations of the 

 air. If twice as many vibrations are performed in the 

 same time for one tone as for another, the first is the 

 octave above the second. If the numbers of vibrations 





