You got it right! Good for you.J

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

Click here to go to Fibonacci.