170 Proceedings of the Royal Society of Edinburgh. [Sess. 
Diagram VII. 
The Extended Scale. 
The numbers give the pitch of each note in 600ths of an octave, 
as from centre (C). 
G# 
D| 
E# 
B# 
Fx 
Cx 
G x 
Dx 
Ax 
375 
126 
477 
228 
579 
330 
681 
432 
183 
534 
E 
B 
V\ 
'fa 
1 
c# 
G# 
D# 
Af 
Ef 
B# 
Fx ! 
182 
533 
284 
35 
386 
137 
1 
. 488 
239 
590 
341 
C 
G 
\ 
D 1 
1 
A 
E 
B 
n 
6# 
G# 
D| 
589 
340 
91 
442 
193 
544 
295 
46 
397 
148 
Ab 
Eb 
Bb 
F 
C 
G 
D 
A 
E 
B 
396 
147 
498 
249 
0 
351 
102 
453 
204 
555 
Fb 
Cb 
Gb 
Db 
Ab 
Eb 
Bb 
F 
C 
G 
203 
554 
305 
56 
407 
158 
509 
260 
11 
362 
Dbb 
Abb 
Ebb 
BM> 
Fb 
Cb 
1 Gb 
Db 
Ab 
Eb 
10 
361 
112 
463 
214 
565 
316 
67 
418 
169 
Bbbb 
Fi>b 
Cbb 
Gbb 
Dbb 
Abb 
Ebb 
Bbb 
Fb 
Cb. 
417 
168 
519 j 
270 
121 
372 1 
123 
474 
225 
576 
Showing part of the unlimited musical scale, extending in fifths and 
thirds from the central nucleus, and comprising thirty-five tonal systems. 
Every note represented is different in pitch, and all lie within the 
compass of one octave. Those marked (') are flatter and ( ') sharper by 
one “comma” (one-fifth of a semitone) than the notes of corresponding 
name in the centre. (See note above diagram.) 
The diagram indicates the relationship of all keys in general use, and 
shows at a glance the true notes of each chromatic scale. 
Tonality. 
We have said that the scale-diagram is an index of tonality, and we 
must now explain this, but we shall not discuss the subject any further 
than that purpose requires. 
Tonality may be defined as that predominating relationship (of notes, 
chords, and keys) to the tonal centre which gives coherence and stability 
