740 SPECIAL SENSES. 



quality. Duration depends simply upon the length of time during which 

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

 tude of the vibrations, and it has no relation whatsoever to pitch. Pitch de- 

 pends absolutely upon the rapidity of the regular vibrations, and quality, 

 upon the combinations of different notes in harmony, the character of the 

 harmonics of fundamental tones and the form of the vibrations. 



Pitch of Musical Sounds. Pitch depends upon the number of vibrations. 

 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 com- 

 bination 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 absolutely equal rates of vibration. ' Notes equal in 

 pitch are said to be in unison. An educated ear can distinguish slight differ- 

 ences in pitch in ordinary musical notes ; but this power of appreciation of 

 pitch is restricted within well defined limits, which vary slightly in different 

 individuals. According to Helmholtz, the range of sounds that can be legit- 

 imately employed in music is between 40 and 4,000 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 4,752 vibrations. In grand organs there is a 

 pipe which 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 painfully sharp, and their pitch can not be exactly appreciated by the 

 ear. 



Musical Scale. A knowledge of the relations of different notes to each 

 other lies at the foundation of the science of music ; and without a clear 

 idea of certain of the fundamental laws of music, it is impossible to thor- 

 oughly comprehend the mechanism of audition. 



It requires very little cultivation of the ear to enable one to comprehend 

 the fact that the successions and combinations of notes must obey certain 

 fixed laws ; and long before these laws were subjects of mathematical demon- 

 stration, the relations of the different notes of the scale were established, 

 merely because certain successions and combinations were agreeable to the 

 ear, while others were discordant and apparently unnatural. 



The most convenient sounds for study are those produced by vibrating 

 strings, and the phenomena here observed are essentially the same for all 

 musical sounds ; for it is by means of vibrations communicated to the air 

 that the waves of sound find their way to the auditory apparatus. Take, to 

 begin with, a string vibrating 48 times in a second. If this string be divided 

 into two equal parts, each part will vibrate 96 times in a second. The note 

 thus produced is the octave, or the 8th of the primary note, called the 8th, 

 because the natural scale contains eight notes, of which the first is the low- 



