DISSONANCE AND CONSONANCE 65 



tones re and la cadence up and down into do-mi-sol, 

 the regnant harmony. Ascend or descend on this 

 pentatonic scale in every conceivable rhythm, yet the 

 harmonic relations remain unchanged. However, the ^ 

 analysis of a scale has little purpose, for a scale is but a 

 record of tones in use during a certain period of his- 

 tory; briefly, scales are so many tone-systems of his- 

 tory. What is of essential importance is the analysis 

 of the melodies which are responsible for these tone- 

 systems the progressive development of which has 

 resulted in our present complex system. Thus far we 

 have accounted for and exemplified but one regnant 

 harmony, the Major Tonic. How a second and a 

 third regnant harmony were generated are subjects 

 presently to be considered. Here an important fact^ 

 to which we shall revert later on may be mentioned. I 

 It is this : During the regnancy of the Major Tonic- I 

 harmony la always reports itself as third of /a, while I 

 the remaining tones of the germs dissonance during | 

 this regnancy of the Tonic always report themselves 

 in their ^^Tii^^-relations, ti as third, re as fifth, fa as 

 seventh of sol, the Dominant. La reports itself as 

 ninth only during the regnancy of the Dominant- 

 harmony, which is the genus dissonance. The tone la, 

 as we shall see, plays a leading and significant part in 

 the development of harmony and tonality. 



The above explanations of the genesis of the four 

 cadence-tones and the order of sequence in which 

 they arose are further supported by deduction and by 

 induction ; by deduction from the principles of causa- 

 tion and harmonic genesis set forth in these pages, 

 by induction through data derived from exact analysis 



