724 SPECIAL SENSES 



rapid, the sound is excessively sharp, but it is painfully acute and has no 

 pitch that can be accurately determined by the auditory apparatus. Such 

 sounds may be occasionally employed in musical compositions, but in 

 themselves they are not strictly musical. 



Musical sounds have the characters of duration, intensity, pitch and 

 quality. Duration depends on the length of time during which the 

 vibrating body continues in action. Intensity depends on the ampli- 

 tude of the vibrations and has no relation to pitch. Pitch depends on 

 the rapidity of the regular vibrations. Quality depends on combinations 

 of different notes in harmony, the character of the harmonics of funda- 

 mental tones and the form of the vibrations. 



Pitch of Musical Sounds. Pitch depends on the number of vibra- 

 tions. A musical sound may be of greater or less intensity ; it may at 

 first be quite loud and gradually die away ; but the number of vibrations 

 in a definite note is invariable, be it weak or powerful. The rapidity of the 

 conduction of sound does not vary with its intensity or pitch ; and in the 

 harmonious combination of the sounds of different instruments, be they 

 high or low in pitch, intense or feeble, it is always the same in the same 

 conducting medium. Distinct musical notes may present a great variety 

 of qualities, but all notes of the same pitch have equal rates of vibration. 

 Notes equal in pitch are said to be in unison. An educated ear can dis- 

 tinguish slight differences in pitch in ordinary musical notes ; but this 

 power of appreciation of pitch is restricted within well-defined limits 

 that vary slightly in different individuals. According to Helmholtz, the 

 range of sounds that may be legitimately employed in music is between 

 40 and 4000 vibrations in a second, embracing about seven octaves. 

 In an orchestra the double bass gives the lowest note, which has 

 40.25 vibrations in a second, and the highest note, given by the small 

 flute, has 4752 vibrations. In grand organs there is a pipe that gives 

 a note of 16.5 vibrations, and the deepest note of modern pianos has 

 27.5 vibrations; but delicate shades of pitch in these low notes are not 

 appreciable to most persons. Sounds above the limits just indicated are 

 audible but are painfully sharp, and their pitch can not be exactly appre- 

 ciated by the ear. 



The limits of appreciation of musical sounds do not apply to ordi- 

 nary audition ; and the extreme range of hearing is much greater, being 

 about eleven octaves. Shrill sounds, that can not be recognized as musi- 

 cal, still are audible and the number of their vibrations may be measured 

 mechanically. " Galton's whistle " produces sounds that have between 

 30,000 and 40,000 vibrations in a second ; but beyond these limits the 

 vibrations are inaudible. It is possible, however, that vibrations inau- 

 dible to the human subject may be heard by some of the lower animals. 



