The basic awkwardness of harmonics-based tuning systems has caused musicians a lot of confusion and irritation over the years. Depending on your starting pitch, some intervals can be perfectly in tune, but others can’t be. And the more harmonically complex you want your music to be, the worse the tuning issues are going to get.

The word “hemiola” originates from the Greek words “hemi,” meaning half, and “holos,” meaning whole. In other words, one and a half. And so, a hemiola is a rhythmic pattern that uses a ratio of three to two, and the Greeks, ever concerned with ratios, noticed that three divided by two gives you one and a half, thus their description “hemiola.”

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