Just intonation tunes intervals as whole-number ratios — 3:2, 5:4 — so their harmonics coincide and nothing beats. The catch is geometry: stack pure intervals and they never quite close. The tiny leftovers have names — commas — and the entire history of temperament is the history of deciding where to hide them. Click around the 5-limit lattice (fifths run left–right, thirds up–down; every node plays against the 1/1), then meet the commas themselves.
← fourths · fifths → | top row: up a pure third (·5/4) · bottom row: down a pure third (·4/5). click = hear it against 1/1