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Problem Solving

Assuming the original string is the first note (C), two-thirds of the string will achieve the fifth note of the scale (G).
The ratio of the new length to the original length is
(2 / 3) to 1 or 2 to 3
The ratio of the frequencies is the reciprocal, 3 to 2. i.e. the original has frequency 300 Hz and the new frequency is 450 Hz.
450 Hz to 300 Hz = 3 to 2
For the fourth note (F), you should shorten the length to 3/4 of its original length.
String ratio: (3/4) to 1 or 3 to 4
Frequency ratio: 4 to 3 (a reciprocal)
The new tone will have a frequency 400 Hz or
400 Hz to 300 Hz = 4 to 3