SOUND. 



rests upon two bridges, one of which is fixed, and the other can 

 be moved with a sliding motion to and fro, so as to vary at 

 pleasure the length of the part of the string included between the 

 two bridges. 



A divided scale is picked under them, so that the length of the 

 vibrating part of the string may be regulated at pleasure. By 

 varying the weight, the tension of the string may be increased or 

 diminished in any desired proportion. This may be accomplished 

 with facility by circular weights which are provided for the pur- 

 pose, and which may be slipped upon the stem of the weight. 

 By means of this apparatus, the relation between the various 

 notes of the musical scale and the rate of vibration by which they 

 are respectively produced have been ascertained. 



19. The rate of vibration of a string such as that of the mono- 

 chord is inversely as its length, other things being the same. 

 Thus, if its length be halved, its rate of vibration is doubled ; if 

 its length be diminished or increased in a threefold proportion, 

 its rate of vibration will be increased or diminished in the same 

 proportion ; and so forth. 



Let the bridges be placed at a distance from each other as 

 great as the apparatus admits, and let the weight which stretches 

 the string be so adjusted, that the note produced by vibrating the 

 string shall correspond with any proposed note of the musical 



scale ; such, for example, as fo , the low c of the treble clef. 



*J -O- 



This being done, let the movable bridge be moved towards the 

 fixed bridge, continually sounding the string until it produces the 

 octave above the note first sounded, that is, until it produces the 



middle c fc^ ^ the treble. 



If the length of the string be now ascertained by reference to 

 the scale of the monochord, it will be found to be precisely one- 

 half its original length 



20. Hence it follows, that the same string will sound an octave 

 higher if the length is halved. But the rate of vibration will be 

 doubled when the length of the string is halved. Hence it 

 follows, that two sounds, one of which is an octave higher than 

 the other, will be produced by vibrations, the rate of which will 

 be in the proportion of 2 to 1 ; and, consequently, the length of 

 the undulation producing the lower note will be double that of 

 the undulation producing the higher note. 



By like experiments it is shown that the more frequent the 

 coincident vibrations are the more perfect is the harmony, and 

 the less frequent they are the more discordant are the notes. 



192 



