The oldest tunings are octave divisions. So for example an octave might perhaps be tuned to 400 and 800 hz. The 5th then is the mean average: 600 hz. The major third then is the mean of 400 and 600 = 500 hz. These divisions are ratios of small integers. If you play 400, 500, 600 hz together you'll have the pleasant sound of a major triad. But such simple tunings have problems with dissonance. There is a "wolf fifth" between the 4th and the 7th tone. Also, the circle of 5ths doesn't actually close to a circle since (3/2)^n != 2^m for all integer n and m != 0. In other words repeated movement by a 5th will never be equal to any other number of repeated movements by an octave. This breaks modulation, modes, and borrowed chords. So the modern tuning is simply a 12 tone even division of the octave. We take the octave ratio = 2/1 and say each of 12 halfsteps is the ratio r=2^(1/12), therefore r^12 = 2. So if A is 220 hz then C is 220 * r^3 = 261.62557 since C is 3 halfsteps above A. C# is 220 * r^4 and so on.