What does The Well-Tempered Clavier sound like in actual well 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 (https://oddsound.com/mtsespsuite.php) . 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 (https://en.wikipedia.org/wiki/Quarter...) , Andreas Werckmeister's temperament III from 1681 (https://en.wikipedia.org/wiki/Werckme...) , and Johann Kirnberger's well temperament as described in a letter to Johann Nikolaus Forkel in 1779 (https://en.wikipedia.org/wiki/Kirnber...) .

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:    • G. Sabbatini: Derelinquat impius viam suam  

Daniel Adam Maltz demonstrates Kirnberger:    • Wolfgang Amadé Mozart: Sonata in F Major, ...  )

Carl Radford demonstrates Young’s temperament:    • Classical vs Modern Tunings - C# Major Pre...  

John Moraitis demonstrates quarter-comma meantone, Rameau and Kirnberger:    • Comparison between meantone and Rameau tem...  

Alice M. Chuaqui Baldwin demonstrates quarter-comma meantone and Werckmeister III:    • Meantone Temperament and Other Historical ...  

I decided not to talk about Bradley Lehman’s proposed Bach tuning (https://bpl.rf.gd/larips/?i=1) ; 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 (   • Bach: demonstration of piano in Lehman's '...  ) , and if you have a longer attention span than I do, you can watch Lehman tune a harpsichord (   • Tuning a harpsichord in Bach's temperament...  ) .

Wikipedia has a good summary of the various theories about Bach's tuning: https://en.wikipedia.org/wiki/Bach_Te...

John Carlos Baez explains quarter-comma meantone with math and diagrams: https://johncarlosbaez.wordpress.com/...

Kyle Gann's web site has lots more material on historical tuning with audio examples: https://www.kylegann.com/microtonalit...

For a deeper dive, try the tuning and temperament chapters in The Cambridge History of Western Music Theory: https://www.cambridge.org/core/books/...

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