THE USEFULNESS OF THE FIFTH IN MUSIC. 
237 
below C, we can gather from it what keys require 1 or more 
fiats to mark them at the beginning of a piece of music. 
For it is found on trial that 
The key of 
n n 
n n 
n if 
ii ii 
ii ii 
ii ii 
ii ii 
C has no flats. 
F 
yy 
1 
flat. 
bB 
yy 
2 
flats. 
bE 
yy 
3 
flats. 
b A 
yy 
4 
fiats. 
bD 
yy 
5 
flats. 
bG 
yy 
6 
flats. 
bG 
)) 
7 
flats. 
Each note in the Series V. has therefore 1 flat more than 
the note before it. 
Writing the notes and their flats under them — thus, 
C, F, bB, b E, bA, bD, bG, bC, 
0 ) 1 > 2, 3, 4, 5, b, 7, 
we see at a glance what number of flats is needed for each 
note. 
More than 7 flats need not practically be taken. 
XIV. Further, if we want to know which are the notes that 
in the signature of these flat keys are to he marked flat, and 
in what order they come, we take the descending series of fifths, 
and find by trial that 
The key of C needs 0 flat. 
(Sekies VIII.) 
F 
bB 
bE 
bA 
bD 
bG 
bC 
1 flat, which is B. 
2 flats, which are B, E. 
B, E, A. 
B, E, A, D. 
B, E, A, D, G. 
B, E, A, D, G, C. 
B, E, A, D, G, C, F. 
Hence we see that the notes themselves to be marked flat in 
signatures are also a series of Fifths , and they are the same 
notes read baclcwards as the notes of Series VII. for sharps. 
From this succession we can at once allot the right number 
of flats, and place them on their proper places. 
If, for example, a piece of music is written in 5 flats, and 
I want to know what key it is in, I run over the series of fifths 
descending from C, and take the 5th one, b D ; or, if I was told 
to write a piece in the key of bD, I see at once from the 
series that 5 flats must he marked in the signature, and that 
these notes are the first 5 of Series VIII. So in like manner 
for any other number of flats. 
XV. A useful rule for knowing at sight, by inspection of the 
flats, what key a piece is written in, is also got from Series VIII. 
There it can be seen that the key note is a fourth below the 
