THE EAR. 505 



Evidently in harmonics we are not concerned with the 

 absolute number of vibrations but only with the relative. 

 We may select as the number of vibrations of our funda- 

 mental note any desired number, but once having selected 

 this number arbitrarily, the others must bear these definite 

 ratios to it. Thus, the French standard for middle C is 

 about 256; the C of the Italian opera has about 273, while 

 a Musical Congress in 1834 at Stuttgart recommended 264 

 as a standard for middle C. 



Expressed then in physical terms, a harmonious chord on 

 the piano is a combination of those notes which bear simple 

 mathematical ratios. Taking the key of C, such a chord 

 would be composed of C-E-G and C, or C-F-A and C. 

 These are the ordinary combinations. Music begins to be 

 less and less harmonious as the ratios become more com- 

 plex, and when the ratios can no longer be perceived at all 

 we speak of sounds as mere noise. 



SYMPATHETIC VIBRATIONS. 



In order to understand the manner in which sounds in 

 the air finally succeed in stimulating the internal ear, it is 

 necessary to understand those phenomena of vibrating 

 bodies designated as sympathetic vibrations. It is a very 

 general experience, when singing a clear note near some 

 musical instrument, that the musical instrument will catch 

 up that tone and give it out itself. Sometimes it is neces- 

 sary to remove instruments from the room to prevent this 

 interference. Two tuning-forks tuned alike and placed 

 near each other mutually affect each other. If one tuning- 

 fork be sounded the vibrations from that tuning-fork will 

 put the second tuning-fork in vibration, even though it was 

 perfectly silent to begin with, and the second tuning-fork 

 may go on sounding after the first one has been mechanic- 

 ally stopped. In a music store where numbers of instru- 

 ments are found close together the strong sounding of a 

 chord on one piano will usually set similar chords vibrating 

 in the other pianos. These phenomena are produced by 



