THE MUSICAL SCALE 



283 



@ 



The intervals of F and A are not strictly | and f , but are 

 nearly so; if F made 341.3 vibrations per second instead of 

 341; and if A made 426.6 instead of 427, then the intervals 

 would be exactly f and |. Since the real difference is so slight, 

 we can assume the simpler ratios without appreciable error. 



Any eight notes whose frequencies are in the ratio of |, f , 

 etc., will when played in succession give the familiar musical 

 scale; for example, the deepest bass voice starts a musical 

 scale whose notes have the frequencies 80, 90, 100, 107, 120, 

 133, 150, 1 60, but the intervals here are identical with those 

 of a higher scale ; the interval between C and D, 80 and 90, 

 is f, just as it was before when the frequencies were much 

 greater; that is, 256 and 288. In singing "Home, Sweet 

 Home," for ex- 

 ample, a bass voice i ^ j- ^ J. 4. A &. 



may start with a ' * \\ ri * f \ v *\ m _~^~~ i i 



., . , /r>? Jl F r I I I f r Ir-P rl ^=J A 

 note vibrating only 



132 times a second ; 



while a tenor may 



start at a higher 



pitch, with a note 



vibrating 198 times 



per second, and a 



soprano would 



probably take a 



much higher range 



still, with an initial 



frequency of 528 



vibrations per second. But no matter where the voices start, 



the periods are always identical. The air as sung by the 



bass voice would be represented by A. The air as sung by 



the tenor voice would be represented by B. The air as sung 



by the soprano voice would be represented by C. 



P 



132 vibrations 



' i If If 



if 



iqs 



.bra.t,ons 



f 



ii 



3F 



sHffffl f 



* ^ 



5Z8 vibrations 



FIG. 178. A song as sung by three voices of 

 different pitch. 



