THE USEFULNESS OF THE FIFTH IN MUSIC. 
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Now, putting these notes for the fifths in regular order by 
themselves, we get this series : — 
Series I. 
C, G, D, A, E, B, F, C, 
which succession of notes is to do wonders for us. It is a series 
which it is well to learn by heart, to repeat when needed, 
either forwards or backwards. 
But before using it, it needs a little adjustment ; for, like 
many other things, it is not perfect at first. On inspecting the 
position of the semitones in the long succession of notes we 
took it from, we see that the first 5 fifths are right in their 
tones and semitones ; but the sixth would contain 2 semi- 
tones, those between B C, and E F ; therefore we must make 
F sharp to perfect this fifth. But that will derange also the 
next fifth, which will require its last note, C, to be similarly 
sharpened, that the interval may be perfect between F sharp 
and C sharp. 
Series I., when thus corrected in these points, becomes 
Series II. 
C, G, D, A, E, B, ftF, #0, 
0, 1, 2, 3, 4, 5, 6, 7. 
V. Now, if we continued this series of fifths still further 
above this C sharp, we should have 5 more fifths, coming at last 
to one on B sharp. But B sharp is the same as C natural. 
So that at the 12th fifth we return into the same key note 
we started from, and the fifths would only repeat themselves 
again if we went further. The complete series of fifths is 
thus made : — 
Series III. 
C, G, D, A, E, B, ftF, #0, ftG, #1), ft A, ftE, ftB (or C). 
0, 1, 2, 3, 4, 5 , 6, 7, 8, 9, 10, 11, 12. 
VI. We may notice in passing, that in the tuning of a piano- 
forte this high C, got by rising up 12 fifths, does not exactly 
coincide in sound with the C got by rising towards the same 
pitch by octaves from C. The high C got by fifths is a little 
higher than the C got by octaves ; and hence the necessity, in 
the actual tuning of the piano, of flattening all the fifths a 
very little , in order that the two Cs may coincide. 
VII. Leaving now for a little this Series III . of fifths as- 
cending from C, let us examine what would be the order of a 
falling series of fifths descending from C. Taking a similar 
long succession of notes, but reading them backwards from the 
top C, we should get our fifths as before. 
