The Saddest Thing I Know about the Integers

It takes a total of 12 steps, and so if we keep all our fifths perfect, the frequency of the C we get at the end is 312/212, or 531441/4096, times the frequency of the C we had at the beginning. Currently, most instruments use equal temperament, which makes all the fifths slightly narrower than perfect so the octaves will be in tune. One solution is to tune an instrument so that the octaves, fifths, and/or thirds are perfect or very close for the important chords from some keys (generally “easy” keys like C, G, and D) but terrible for some other keys.

Source: blogs.scientificamerican.com