I am committed to teaching my students something about the history of tuning in Western European music. I don’t expect them to retain any details or do any math, I just want them to know that the history exists. In preparation, I continue to refine my explanation of this history to myself.
Before the year 1400 or so, Western Europeans mainly tuned their instruments in three-limit just intonation, which they called Pythagorean tuning. (Don’t be fooled by the name; this system was in use in Mesopotamia centuries before the Greeks described it.) Three-limit just intonation is based on the first three harmonics of a vibrating string. Western Europeans really like the pitch ratios produced by these harmonics, as do people from many other cultures (though not all of them). In this post, I will explain why Europeans liked three-limit just intonation, why they nevertheless eventually abandoned it, and what came after.