EVOLUTION OF THE MUSICAL SCALE. 79 



with this simple form of music. There arose a desire for 

 more complicated music in which the performers made use of 

 other relations than unison and the octave. They began to 

 try various simultaneous combinations of the notes of their 

 scale and harmony began to develop. But along with this the 

 intervals of the scale changed. Unconsciously the musician 

 was changing the intervals of his scale under the domination 

 of scientific laws of which he had no knowledge. After two 

 centuries of slow change and when harmony has reached its 

 full development in the music of to-day, the ratios of the 

 scale are found as follows : — 



I 9:8 5:4 4:3 3:2 5:3 15:8 2 



Its intervals are evidently much simpler than those of the 

 Pythagorean scale. 



This scale is a product of evolution and illustrates the 

 survival of the fittest, or rather the survival of that which is 

 most agreeable and acceptable to the ear of the musician. 

 No matter what form the original scale of melody might have 

 had, no other possible evolution product than the present 

 form could have resulted, now that harmotn' has become the 

 basis of music. 



It is most interesting to study out the reason for this evo- 

 lution. Before doing this it may be well to recall to mind a 

 few of the fundamentals of sound. To begin with, sound 

 has three characteristics, namely, pitch, intensity and quality. 

 The first two are determined by the number and amplitude 

 of the vibrations. The third characteristic, quality, that pro- 

 perty by which we are enabled to distinguish the note of one 

 instrument from another, is determined by the number and 

 intensity of the overtones or harmonics accompanying the 

 fundamental. These harmonics are produced by a secondary 

 vibration of the string or reed or pipe superimposed upon the 

 fundamental. Thus, for instance, a vibrating string, in addi- 

 tion to vibrating as a whole, vibrates faintly in 2, 3, 4, 5, etc., 

 segments, these vibrations V)eing superimposed upon the ori- 



