82 C. M. BROOMALL : 



It must be borne in mind that this table represents only a 

 small proportion of the total number of resultants, and that 

 only the resultants of the primaries are of much importance. 



Considering the preceding table it is seen how many are 

 the points of coincidence and how it must result that the 

 major chord is so perfect. It would be impossible to take -any 

 other intervals of approximately the same size which would 

 present so many cases of unison, octaves, etc. Any variation 

 from these intervals would produce utter confusion. 



The table shows another thing, that the chord can be made 

 more perfect by adding to it the lower octave and double 

 octave of the fundamental, as in several cases at least will 

 these reenforce the resultant tones between the primaries. 

 Piano players will recognize how important these tones are in 

 making the major chord agreeable. 



When it is considered that no other intervals than these 

 can produce so many unisons, octaves, etc., we see at once 

 what necessity there is that the modern scale of harmony 

 should be exactly as it is. It is evident how, side by side 

 with the growth of harmony, artists were inevitably pushed 

 toward the adoption of these intervals in their search for 

 agreeable combinations of notes. Of the multitudinous com- 

 binations of ratios that have been tested, those of this scale 

 and this only were able to survive. 



Indeed, the harmony and sweetness of music based upon 

 the major chord only is so perfect as to become often mono- 

 tonous and dull. The musician feels the necessity of intro- 

 ducing an occasionally less perfect chord in order that the 

 contrast thus aiforded may add additional charm to the music. 

 An instance of this is the well known chord of the dominant 

 seventh, which alone is decidedly rough, but which most 

 agreeably resolves itself into the tonic major chord. The 

 minor scale is another instance of the same tendenc}'. 



The musical system is hence perfect as far as theory goes. 

 But the artist has another difficulty to contend with due to the 

 mechanical imperfection of the majority of musical instru- 



