of Consonances of the Form h : 1. 



425 



A. 



Statical Analysis of Disturbance proportional to Square of Displacement 

 showing origin of the combination-tone. Fifth 2 : 3. 



A 



Difference-tone 

 (Tartini), 3-2=1. 



Uniform increase 

 of pressure. 



Summation-tone i 



vibration -number 



3+2=5. 



Resultant of octayei 

 4 and 6. 



I. 



From disturbance proportional to square of displacement subtract simple 

 tone. Amplitude | of disturbance. Period = that of the beat. (Vibra- 

 tion-number = difference of vibration-numbers, 3—2 = 1.) 



II. Subtract ■£ of amplitude of disturbance. 



III. Subtract a simple tone. Amplitude | of that of disturbance. Period = $ 



that of resultant vibration in original beat. (Vibration-number = sum 

 of vibration-numbers of original tones, 3+2 — 5.) 



IV. There remains a succession of beats like" the original beats of the fifth, an 



octave higher, i. e. the combination of the octaves of the original notes. 



B. 



Beat of Fifth, 2:3. Disturbed by term proportional to square of 

 displacement, showing origin of the combination-tone. 



