DISSONANCE AND CONSONANCE 93 



half steps and able to name the two tones in each, 

 although we may be able to perceive and name all 

 intervals from primes to elevenths and able to define 

 tjiem as pure, major, minor, augmented and dimin- 

 ished, double-augmented and double-diminished, yet 

 at the same time we may have no perception and may 

 be completely ignorant of the one thing essential to 

 our intelligent and true appreciation of a step and an 

 interval, namely, the inherent harmony of each of the 

 two tones that form a step and interval. For exam- 

 ple. Besides hearing that the two tones in the first 

 of the above cadences are ti and do and that the step 

 is a half step and an upward resolution, you should 

 hear that you are stepping from the third of one har- 

 mony (Dominant) to the root of another harmony 

 (Tonic). The perception of these harmonic and 

 inter-harmonic relations is imperative. Far from in- 

 veighing against the customary study and practice of 

 intervals, I consider the working out of intervals from 

 each tone in the octave both a necessary discipline 

 and an essential part of every student's mental equip- 

 ment and technique. But students are warned to dis- 

 criminate with care between interval-numbers which 

 indicate the distance from one tone to another and 

 harmonic numbers which indicate the harmonic rela- 

 tion of each individual tone to its root. 



There being no melody apart from mode each 

 tone in a melody is a mode-tone. There are three 

 groups of mode-tones : 1. Diatonics. 2. Chromatics. 

 3. Enharmonics. We have seen that tone connotes 

 harmonic form and harmonic relation, and that a 

 specific form is due to a specific relation. There- 



