DISSONANCE AND CONSONANCE 87 



Here the syllables indicate the mode-tones; the 

 notes, the pitch or key of the mode-tones; the upper 

 row of numbers, the inherent harmonic relations ; the 

 lower row of numbers, the scale-order from the first 

 to the eighth tone. Scale-numbers are outside, not 

 inside numbers. Street-door numbers tell us nothing 

 of what is going on inside of a house ; no more do scale- 

 numbers tell us what is going on inside of a tone ; that 

 is, they give us no intelligence whatever of the inherent 

 harmonic relations of tones. To be sure the scale- 

 numbers 1, 3, 5 happen to correspond with the har- 

 monic numbers over do^ mi and sol, but the fact that 

 we know that re, /a, la and ti are respectively the 

 second, fourth, sixth and seventh tones of the scale 

 by no means implies the slightest knowledge of the one 

 thing we should know, namely, the inherent harmonic 

 relations of the tones. We have seen that during the 

 regnancy of the Tonic, re is 5, fa is 7, la is 3, <i is 3 ; 

 that during the regnancy of the Dominant, the rela- 

 tions of these tones are the same except in the case of 

 /a, which is a ninth. There are no harmonic percepts 

 answering to the scale-numbers 2, 4 and 6. The habit 

 of orientation by means of scale-numbers is so fixed 

 that when students begin the study of one-voice har- 

 mony they are very apt to confuse the scale-numbers 

 with the harmonic numbers and vice versa. Scale- 

 numbers serve a useful purpose, but that purpose 

 should be defined. We will define all the above sym- 

 bols and so avoid the confusion which would otherwise 

 be inevitable. 



1. A note with and without modifying sharp, flat or 

 natural, is the sign and index of the relative pitch of a 



