THE USEFULNESS OF THE FIFTH IN MUSIC. 
235 
Now we may write the notes with the number of sharps 
belonging to them underneath, and get this order : — 
(Notes) C, G, D, A, E, B, #F, #G. 
(Sharps) 0, 1, 2, 3, 4, 5, 6, 7. 
It is evident that here we at once can see how many sharps 
any of these notes requires ; and if we see a piece of music 
with several sharps or flats at the beginning we can tell easily, 
from this set of notes, which key it is written in. As, for ex- 
ample, a piece with 4 sharps as its signature is written in the 
key of E, the 4th sharp above C. More than 7 sharps are not 
needed generally, as they would then be more easily expressed 
otherwise in a way we need not now go into. 
Or the piece could be transposed into a key having a smaller 
number of sharps. 
IX. But, further, we might want to know which notes in 
the signature of any key having sharps are to be so marked , 
and in what order they come after each other. Series II. 
gives a rule for this also. 
For it is found on trial that the notes requiring to be 
sharpened are as follows : 
The key of 
v » 
77 77 
77 77 
77 77 
77 77 
77 77 
(Series VII.) 
C has 0 sharp. 
G has 1 sharp, which is F. 
D has 2 sharps, which are F, C. 
A 
has 
3 
F, 
c, 
G. 
E 
has 
4 
F, 
c, 
a, 
D. 
B 
has 
5 
F, 
o, 
G, 
D, 
A. 
SF 
has 
6 
F, 
0, 
G, 
B, 
A, 
E. 
#0 
has 
7 
V 
F, 
0, 
G, 
B, 
A, 
B, E. 
Now here we see that the notes to be marked sharp follow 
each other in a Series (VII.) which is just similar to Series II., 
with the addition of one F at the beginning ; being the first 
fifth below C. 
The notes to be marked sharp are thus themselves a series 
of fifths , but beginning 2 fifths below the key note they 
signify. 
Series II. therefore gives both the succession of sharp keys, 
and also of the notes to be marked sharp in their signatures. 
X. Let us take now some examples of these uses of Series 
II. and VII. If I see a piece of music marked with 5 sharps, 
and want to know what key it is in, I at once run over in my 
mind these notes of Series II., 
C,G,D, A, E, B,#F,#C, 
0, 1, 2, 3, 4, 5, 6, 7, 
and see it is B that has that number of sharps — standing, as it 
does, 5 fifths above C. 
