Answers to above examples
example 1:
B to G is four semitones. The new vibrating length must
be the old length divided by (1.0595)4 : L = 65.0/1.260=51.6cm
distance from neck = 65.0-51.6 = 13.4cm
example 2
freq ratio is reciprocal of length ratio: 50/30 = 5/3
5/3 interval is a just sixth (such as C-A see table of just ratios)
Thus tone is just sixth above D4 = B4.
For 15 cm string, ratio is 50/15 = 10/3. This ratio is an octave
above 5/3 (since 2x5/3 = 10/3) B5
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