The Musical Scale. 
163 
1919-20.] 
Take now the interval of the major third above and below each of 
these four notes, that is, the ratios 5/4, 4/5, and we get the complete 
chromatic scale (or tonal system), as follows : — 
Diagram II. 
Chromatic Scale of C. 
A 
E 
B 
F# 
F 
c 
G 
D 
Db 
Ab 
i 
Bb 
Tonal system measured symmetrically by fifths horizontally and thirds 
vertically from central interval. 
Diagram II is of great importance, and will repay careful study, for 
it represents in simple and graphic form all the principal facts of scale- 
structure associated with the tonic C and its dominant G. 
It shows the symmetrical derivation both of the chromatic and diatonic 
scales ; it discloses the true harmonic order of the chromatic scale ; it is an 
index of tonality, and (in its extended form, given below) it explains the 
phenomena of the relative major and minor keys. 
For the present we will confine our attention to the diatonic major 
and minor scales. 
Let it be observed that the major scale consists of the four funda- 
mentals or their octaves (F, C, G, D), together with the three upward 
measured thirds or their octaves (A, E, B) ; whilst the minor scale consists 
of the same fundamentals in association with the three downward measured 
thirds (Ab, Eb, Bb). 
Now observe the position of these scale-notes in relation to the tonal 
centre (C G), according to the measurements shown in Diagram II, and it 
will be seen that the two scales are perfectly symmetrical, and that the 
minor scale is therefore the exact mathematical inversion of the major, 
its natural form being downward from the dominant, just as that of the 
major scale is upward from the tonic. 
