67 
be as in Fig. mm. Comparing Fig. Il. 
Fig. 11. with Fig. 1. it will be 
seen that the shaded spaces of 
Fig. 1. are symmetrical with 
respect to AOA’, as those of 
Fig. 1. were with respect to 
DOD’; hence A is the second 
note of the new scale, in other 
words the key-note is G. For it 
will be observed that Fig. It. 
represents a scale of precisely the same kind as Fig. 1: in 
each case the shaded portions occupy one side of a diameter, 
leaving one semicircular space wholly unshaded, and containing 
between them an unshaded section of 120°. The eye will in 
fact at once perceive that if we start from G in Fig. 11. and pass 
round the circumference of the circle in the sense of the motion 
of the hands of a clock, we shall come to exactly the same 
succession of tones and semitones as we should in Fig. 1. if we 
started from C. 
G OG’, then, has now become the tonic line; but this line, 
regarded merely as to its direction, (I mean, GOG’ being re- 
garded as the same line as G’OG,) is removed only one division, 
or 30° degrees, from the original tonic line. Hence it may be 
said, that the effect of sharpening the subdominant is to turn the 
tonic line through one semitonal angular space, or through 30°; 
and as the sharpening of the subdominant of the key of C has 
brought us to the key of G, and turned the tonic line into the 
position GOG", so the sharpening of the subdominant of the key 
of G will turn the tonic line through another angle of 30° into the 
next position DOD’, or will bring us to the key of D, and so on. 
Hence if we drop the accents, the figures above drawn will 
give us, by looking at the extremities of the successive radii, the 
key-notes of the consecutive major scales, namely, 
CGP DASH yas: 
