232 
POPULAR SCIENCE REVIEW. 
tones with a circumflex, we get this order for a major scale 
of C— 
C, D, E, F, G, A, B, C, 
1, 2, 3, 4, 5, G, 7, 8; 
where the semitones must occur between the 3rd and 4th, and 
between the 7th and 8th, notes of the scale. This is the case 
for any of the other notes, if made the starting or key note of 
a piece of music. But in the case of any other key note except 
C the semitones will therefore need rearranging, which is done 
by adding sharps or flats to the notes of the scale until the 
right succession of tones and semitones is got. If we take G 
for instance as the key note, and rise to an octave above it, the 
first semitone between its 3rd and 4th note happens to coin- 
cide with one already there in the scale of C, but the 2nd 
semitone, to be between the 7th and 8th notes, requires to be 
made by sharpening the 7th note, F. We thus have the right 
succession of tones and semitones for the scale of G by making 
one note sharp. This mark of F sharp is put once for all at 
the beginning of any piece of music written in the scale of G, 
and such mark is called the signature of the key. 
In a similar way we must alter by sharps or flats the notes 
of the scale, for any key note we need to write music in, until 
we have got the right arrangement for the major scale of that 
particular note. At present minor scales, which have a different 
arrangement of the tones and semitones, are not considered. 
III. The musical interval called a fifth consists of three 
whole tones and one semitone. For instance, between C and G 
there is a fifth, G being the 5th note above C, counting each 
of them : — 
C, D, E, F, G. 
1, 2, 3, 4, 5. 
In this case the natural arrangement of tones and semitones 
is right. But, if needed, the notes would have to be altered 
by sharps or flats to make the interval perfect. 
Now we may go to work with this interval, and see what we 
can get out of it in various ways. 
IV. If we write the natural scale of C several times over in 
succession, and rise from the starting note by jumps of a fifth 
each, we get a series such as the following : — 
CDEFGABCDEFGABCDEFGABCDEFGABC 
Here G is the first fifth above C ; D the next above G ; and 
so on, till we come to another C, at the 7th fifth above the G 
we started from. 
