Well Temperaments (Part 5)

Okay, let’s study Kirnberger’s three well-tempered tuning systems! I introduced them last time, but now I’ve developed a new method for drawing tuning systems, which should help us understand them better.

As we’ve seen, tuning theory involves two numbers close to 1, called the Pythagorean comma (≈ 1.0136) and the syntonic comma (= 1.0125). While they’re not equal, they’re so close that practical musicians often don’t bother to distinguish them! They call both a comma.

So, my new drawing sty...