sounding the tone C. The other tones of the ascending major scale
require strings of such fractional length as are indicated by the
fractions beneath them. By taking accurate measurements you can
demonstrate these figures upon any small stringed instrument.

Funda- | Major | Major | Perfect | Perfect | Major | Major | Oc- |
mental |Second | Third | Fourth | Fifth | Sixth | Seventh | tave |
| | | | | | | |
C | D | E | F | G | A | B | C |
1 | 8/9 | 4/5 | 3/4 | 2/3 | 3/5 | 8/15 | 1/2 |


To illustrate this principle further and make it very clear, let us
suppose that the entire length of the string sounding the fundamental
C is 360 inches; then the segments of this string necessary to produce
the other tones of the ascending major scale will be, in inches, as
follows:

C | D | E | F | G | A | B | C |
360 | 320 | 288 | 270 | 240 | 216 | 192 | 180 |


Comparing now one with another (by means of the ratios expressed by
their corresponding numbers) the intervals formed by the tones of the
above scale, it will be found that they all preserve their original
purity except the minor third, D-F, and the fifth, D-A. The third,
D-F, presents itself in the ratio of 320 to 270 instead of 324 to 270
(which latter is equivalent to the ratio of 6 to 5, the true ratio of
the minor third). The third, D-F, therefore, is to the true minor
third as 320 to 324 (reduced to their lowest terms by dividing both