8o C. M. BROOMALL : 



ginal vibration. By the relative number and intensity of these 

 is the quality of the note determined. 



Another phenomenon to be referred to is that of " beats." 

 If two notes of different pitch are sounded together the waves 

 of one continually gain upon the other, producing alternate 

 reenforcement and weakening of the sound. If these beats 

 become rapid enough, a new note, called a " resultant tone," 

 is produced, which is faintly heard together with the two 

 primaries. Without going into the theory of beats we may 

 note that there are always theoretically two sets of beats and 

 that it may be possible to have two resultant tones. These 

 resultant tones in turn may form beats with other resultant 

 tones or with the primaries and so on, theoretically, ad iyifin- 

 itum. Practically, however, the resultants soon become too 

 weak to be heard. The rule for calculating the number of 

 beats is as follows : The lower vibration number is divided 

 into the higher the nearest number of whole times and the 

 remainder gives the number of beats. There are two sets of 

 beats depending upon whether this remainder is counted from 

 the next highest or next lowest multiple of the low note. 



With an apology for this reference to elementary princi- 

 ples let us turn to the question of the evolution of the modern 

 scale. The adoption of the present scale may be briefly 

 stated to have been brought about by a process of uncon- 

 scious selection on the part of the musician. The presence of 

 beats being extremely unpleasant even to the untrained ear, it 

 has been the effort to avoid this which has led to the uncon- 

 scious evolution of the modern scale. There has thus resulted 

 a scale which, when used in harmonical composition, will pro- 

 duce on one hand the fewest instances of and weakest beats, 

 and on the other hand the greatest number of resultant tones 

 in consonance with primaries and harmonics. No matter 

 what the original melodic scale might have been, harmony 

 required its evolution into the modern form. 



An analysis of the ordinary major chord will serve as a 

 good example of what we have tried to illustrate. We will 



