Exploring the Richness Beyond 12-Tone Equal Temperament

This episode features Glenn Gould's 1963 recording of Johann Sebastien Bach's Prelude No. 1 in C Major from The Well-Tempered Clavier Book I, BWV 846 (1722). I also tempo-mapped Gould's performances of other WTC preludes and used them for the tempos of the MIDI versions of the various movements.

A small correction: I say in the episode that five-limit just intonation is the basis for Western European tuning systems. This is only true from the Renaissance onwards. Medieval Europe used Pythagorean (three-limit) tuning. Also, just intonation was probably more of a theoretical ideal than a practical tuning method.

Also, at one point I refer to Bach’s F-sharp major prelude as the F-sharp minor prelude.

I did the alternative tunings using MTS-ESP. I used the following tuning ratios for the just intonation parts:

* C - 1/1

* C# - 16/15

* D - 9/8

* Eb - 6/5

* E - 5/4

* F - 4/3

* F# - 45/32

* G - 3/2

* Ab - 8/5

* A - 5/3

* Bb - 9/5

* B - 15/8

I also used quarter-comma meantone, Andreas Werckmeister's temperament III from 1681, and Johann Kirnberger's well temperament as described in a letter to Johann Nikolaus Forkel in 1779.

In actual practice, Europeans tended to center their tuning around D rather than C. I stick to C for ease of explanation, not historical accuracy.

Here are some real humans performing music in historical European tuning systems:

* Alice Borciani, Eva Saladin, Brigitte Gasser and Johannes Keller perform a Sabbatini motet in quarter-comma meantone

* Daniel Adam Maltz demonstrates Kirnberger

* Carl Radford demonstrates Young’s temperament

* John Moraitis demonstrates quarter-comma meantone, Rameau and Kirnberger

* Alice M. Chuaqui Baldwin demonstrates quarter-comma meantone and Werckmeister III

I decided not to talk about Bradley Lehman’s proposed Bach tuning; I like how it sounds, but the controversy around it was too complicated for me to get into. You can hear Dr Charles Tebbs demonstrating Lehman’s tuning, and if you have a longer attention span than I do, you can watch Lehman tune a harpsichord.

Wikipedia has a good summary of the various theories about Bach's tuning.

John Carlos Baez explains quarter-comma meantone with math and diagrams.

Kyle Gann's web site has lots more material on historical tuning with audio examples.

For a deeper dive, try the tuning and temperament chapters in The Cambridge History of Western Music Theory.