The Musical Scale. 
171 
1919-20.] 
to a musical composition. The essence of tonality, therefore, is simplicity 
of tonal measurement. 
Let us examine the tonality of the scale-notes on this basis. 
The notes of strongest tonality will certainly be those of the central 
interval (C G, Diagram II), and of these two the keynote (C) is the 
stronger; we therefore mark them 1, 2, as in the centre of Diagram VIII. 
Next will come the fundamentals F and D ; we take F first, as measured 
immediately from the tonic, and D second, as measured from the dominant; 
3, 1, 2, 4, as shown in the middle row. 
Now come the mediants, E and Eb, or 5, 6, first the upward-measured 
third and then its co-functionary. 
Then the leaders Ab and B, or 7, 8. 
There now remain the extremes, and we deal with them in the same 
way, taking first the more upward measurement from the tonic (A), and 
then its co-functionary (Bb), 9, 10 in the diagram. 
And lastly, the chromatic extremes, Db and F$, measuring first from 
tonic and then from dominant, 11, 12 as in the diagram. 
Diagram VIII. 
Tonality of Scale-notes. 
1. Tonic . 
2. Dominant 
3. Subdominant . 
4. Supertonic 
5. Major mediant 
6. Minor mediant 
C 
G 
F 
D 
E 
Eb 
9 
5 
8 
j 12 
3 
1 
2 
4 
11 
7 
6 
10 
7. Minor leader . Ab 
8. Major leader . B 
9. Submediant . A 
10. Minor seventh Bb 
11. Flattest note Db 
12. Sharpest note F$ 
The whole subject of related keys, major and minor, may be studied 
with great advantage along the lines of Diagram VII. 
The fact of supreme significance, which we have tried to expound in 
this short treatise, is the tonal order of the chromatic scale, and its identity, 
on one hand, with the Ptolemaic ratios, and on the other, with the select 
harmonic series. 
We have indicated only a small part of all that this involves, but enough, 
we trust, to invite a wider study of the musical scale, and a closer inspection 
of “ the wonders of its hidden order.” 
(Issued separately January 22 , 1921 .) 
