Bach, retuned
Bach wrote his chorales for voices that could bend a note to whatever sounded right. We play them on instruments that cannot. Every piano in the world is slightly out of tune with itself — a compromise that makes all twelve keys usable by making none of them pure.
This project undoes that compromise. Each chord in a chorale is retuned to whole-number frequency ratios drawn from a tonality diamond, the structure Harry Partch built his instruments around. A simulated annealing search finds good tunings for each chord on its own; a Viterbi pass then chooses the path through those candidates that keeps shared notes from lurching between chords. The result locks in — chords sit still and ring in a way equal temperament never quite manages.
Start here
Hear the difference
The same twelve chorales, BWV 253 through 264, have been rendered in equal temperament, in Werckmeister III (the well temperament of Bach's own era), and in just intonation at the 17-, 19-, and 23-limit. Play the same chorale from each and the argument makes itself — there are 120 recordings across 10 albums.
Watch an orchestra play it
The animation is driven by the same data that produced the tuning, so the instruments on screen play exactly the notes you hear.
How it works
The full explanation — simulated annealing, Viterbi optimisation, and why simplifying the ratios paradoxically makes the music sound more complex — is written up in the notes.