Developing the Art of Music 



to the human ear, have a rapidity which ranges from i6 to 

 36,500 per second. As a matter of comparison of some of 

 the different vibrations, heat vibrations begin at 134 trillion 

 per second, while light vibrations, visible to the naked eye, 

 begin at 483 trillion per second. Many others are so great 

 that they are beyond our sense perception. It can thus be 

 readily seen that sound vibrations are the slowest of all. 



A demonstration of the process of vibration may be 

 made with a piece of string or wire. When it is tightly 

 stretched and undisturbed, it represents a straight line. When 

 it is plucked or scratched, it is bent out of its course and 

 forms a curved line or segment, and its elasticity causes it 

 to return to its former position. This is a single vibration. 

 But because of the momentum it has acquired by being dis- 

 turbed, it does not stop when it reaches its former straight 

 position but it goes in the opposite direction, thus forming 

 another curve, the same as the first curve produced but in 

 the opposite direction. This makes a double vibration. The 

 vibrations thus produced are isochronous; that is they 

 occupy exactly the same length of time. By shortening or 

 lengthening the strings, we get vibrations of different veloci- 

 ties, thus determining the pitches of the vibrations. The 

 same acoustical results may be produced with pipes or wind 

 instruments of varying lengths. All the qualities of music 

 depend upon the rapidity of the vibrations. 



It is demonstrated that these vibrations are governed by 

 mathematical laws ; that the number of vibrations of strings 

 is inversely proportional to their length; that they are in 

 inverse ratio to their diameter; that they are inversely pro- 



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