HAEMONY IN MUSIC. 65 



With the exception of the organ, all musical instru- 

 ments, however diverse the methods in which their sounds 

 are produced, have their limit of depth at about the same 

 point in the scale as the piano ; not because it would be 

 impossible to produce slower impulses of the air of suffi- 

 cient power, but because the ear refuses its office, and 

 hears slower impulses separately, without gathering them 

 up into single tones. 



The often repeated assertion of the French physicist 

 Savart, that he heard tones of eight vibrations in a 

 second, upon a peculiarly constructed instrument, seems 

 due to an error. 



Ascending the scale from the contra-C, pianofortes 

 usually have a compass of seven octaves, up to the so- 

 called five-accented c, which has 4,224 vibrations in a 

 second. Among orchestral instruments it is only the 

 piccolo flute which can reach as high, and this will give 

 even one tone higher. The violin usually mounts no 

 higher than the e below, which has 2,640 vibrations — of 

 course we except the gymnastics of heaven-scaling virtuosi, 

 who are ever striving to excruciate their audience by 

 some new impossibility. Such performers may aspire 

 to three whole octaves lying above the five-accented c, 

 and very painful to the ear, for their existence has been 

 established by Despretz, who, by exciting small tuning- 

 forks with a violin bow, obtained and heard the eight- 

 accented c, having 32,770 vibrations in a second. Here 

 the sensation of tone seemed to have reached its upper 

 limit, and the intervals were really undistinguishable in 

 the later octaves. 



The musical pitch of a tone depends entirely on the 

 number cf vibrations of the air in a second, and not at 

 all upon the mode in which they are produced. It is 

 quite indifferent whether they are generated by the 

 vibrating strings of a piano or violin, the vocal chords of 



