Introduction 
7 
preserved form was the form in which it was sung; all that 
can be said is that that is how it was sung at least by some. 
“Scales” were unknown, and “bars” also; and that it is pos¬ 
sible to confine the old wild-song melodies within modern scales 
and bars is proof that the ancient artless music and the modern 
art of music have a common basis. All that is claimed for 
birds is that this common basis is the one on which their song, 
too, is built. 
An objection may here be anticipated. The notes of the scale 
as used in modern music, where keyed instruments play such 
an important part, *are not. in every instance the natural 
notes;—some have been slightly altered in pitch, either raised 
or lowered, in order that all keys might equally be used in the 
production of harmony. The notes thus changed are said to 
be “tempered,” and the modified scale is called the “tempered 
scale,” to distinguish it from the “natural scale.” D. Clarence 
Miller (MM, p. 64) has drawn up a table of the harmonics of 
C, showing the natural notes and the nearest corresponding 
notes of the tempered scale, with their respective number of 
vibrations per second : 
Number of 
harmonic 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
Vibrations per ( 
second 
129 
259 
388 
517 
647 
776 
905 
1035 
1164 
1293 
1423 
1552 
1681 
1811 
1940 
2069 
2199 
LL 
2328 
2457 
2586 
Nearest note of f 
tempered scale < 
C 
C 
G 
C 
E 
G 
eb 
C 
D 
E 
ob 
G 
4 
eb 
B 
C 
4 
D 
4 
E 
Vibrations per [ 
second 
129 
259 
388 
517 
652 
775 
922 
1035 
1161 
1304 
1463 
1550 
1642 
1843 
1953 
2069 
2192 
2323 
2461 
2607 
Difference 
0 
0 
0 
0 
5 
1 
17 
0 
3 
11 
40 
2 
39 
32 
13 
0 
7 
5 
4 
21 
Taking the first eight harmonics, it is seen that the first four 
coincide; the fifth differs by five vibrations, the sixth by one, 
the seventh by seventeen. The eighth notes again coincide. 
