[chrisshroba]

A little more intuitively, 1 semitone is one "note", aka the interval between two successive notes on a piano (including white and black keys) such as C to C#, and to talk about intervals less than that, we use cents as 1/100 of a semitone.

Musically, two notes an octave apart vary by a factor of 2 (e.g. Middle A (A4) is 440Hz and the next A (A5) is 880Hz), and our ears hear frequencies logarithmically rather than linearly, so each of the 12 semitones in an octave is a factor of 2^(1/12) higher than the previous one (so that 12 of them in a row result in doubling the frequency), and therefore the 100 cents between each semitone are each (2^(1/12))^100 = 2^(1/1200) greater than the previous one.