Just Intonation (Part 5)

In Part 3 we saw that in just intonation there are four candidates for the tritone. They are simple fractions close to the square root of 2. We saw that they lie at the corners of a parallelogram in a diagram called the tone network, or Tonnetz:

To get a 12-tone scale from this parallelogram, we need to think about the tiny differences between these 4 numbers. More precisely, since our ear hears frequency ratios, we need to think about the ratios of these 4 numbers, which are close to 1. Be...