Go up 12 semi-tones from frequency f on a guitar, and the
frequency interval difference in terms of f is f = 2f - f. What
is the formula for the intermediate 11 non-trivial intervals? So
for k=2, that's two semi-tones. If I start at frequency f on
guitar, and go up two frets, what is the frequency interval
length? With g being the new frequency, f being the frequency of
reference, and k being the interval in number of semitones: In
between, you get an exponential curve (power of two). For the
frequency difference between g and f: Note also that k needs not
be positive, and may also have decimals. If the interval you are
looking for is 3 semitones and 14 cents down, take