88 THE CREATION OF MATTER 



Hence there are thicker strings in instruments for the 

 lower notes and thinner for the higher. The number of 

 vibrations is also inversely proportional to the density of 

 the strings. Combining these two, we have a law that 

 the number of vibrations is inversely proportional to the 

 square root of the weight of the strings. 



Here, as everywhere, all is according to law, measures, 

 and numbers. Strings of the same measures produce in 

 the same kinds of particles the same number of oscillations. 

 The particles aggregated and cohering in the strings exe- 

 cute their motions accurately, according to their length, 

 tension, diameter, and density. The particles of every 

 medium by which sound is carried respond with unfailing 

 accuracy to measured causes, and yield sounds in harmony 

 with those causes. 



Musical instruments differ in the qualities of the notes 

 they yield, in what has been called their timbre or clang- 

 tint. This is due to overtones. A stretched string may 

 be made to vibrate in whole or in parts. It is found 

 impossible in practice to make it vibrate as a whole with- 

 out also vibrating in parts. The higher notes, produced 

 by the parts, are termed the harmonics of the string. It 

 is the union of the harmonics with the fundamental note 

 that gives to each instrument the peculiarities or tint that 

 distinguishes it. If fundamental notes be separated from 

 harmonics, from whatever source they come they cannot 

 be recognised as different. It is therefore a very beauti- 

 ful arrangement that sounding bodies should give birth 

 to overtones in addition to those that are specially sought 

 from them, and that there should thus be produced so 

 great and pleasing a variety of clang-tint. It is an ex- 

 quisite result that the overtones should all be harmonics 

 of the fundamental, should be of such a nature as to blend 

 with it, and with each other, to form one perfectly 



