On this amazing page I have learnt that you can calculate the cents between two notes with the following formula: c = 1200 × log2(f1/f0)

I simply wonder if there is an accessible proof of this, I can't seem to find any.

Thanks for helping


It's not as much a statement in want of proof rather than a definition. Interval widths correspond to frequency ratios so when viewed additively, they correspond to a logarithm of a frequency ratio. A cent is defined as a 100th of a semitone of which 12 are defined to be in an octave (which is defined as a frequency ratio of 2), so we have 1200 cent per factor of 2.

Basically, this is the straightforward formulaic rendition of the definition of cent, so there is not a lot to prove.

  • Yep. Another way of putting it: this is a convention, not a fact of nature. – Scott Wallace Dec 9 '17 at 20:27

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