The Well-Tempered (and not-so-well-tempered) Clavier

Posted byEthan

Bach wrote The Well-Tempered Clavier as a showcase for a new tuning system that could play in all twelve major and all twelve minor keys. Up until that point, the various European tuning systems only worked for some keys, not all of them. If you were in or near the key of C, you were usually okay, but as you moved further out on the circle of fifths, things got ugly fast. So this new tuning system that actually sounded good in all the keys was an exciting development.

However… no one knows what tuning system Bach used. All we know is that it wasn’t twelve-tone equal temperament, the one we all use now. There were many systems in circulation at the time that people called “well temperament.” Was Bach using Werckmeister? Kirnberger? Kellner? Some idiosyncratic system of his own invention? No one knows. This video sums up the situation well:

Until this gets resolved, at least technology makes it easy to hear these different systems for yourself. I used Oddsound MTS-ESP to run some of the Well-Tempered Clavier preludes through various historical tuning systems. Here’s what I got:

Here are the tuning systems I used:

I got these tunings from MTS-ESP’s presets and the Huygens-Fokker Scala archive. I got the MIDI files from the web. The MIDI files follow tempo maps that I made by warping out Glenn Gould recordings in Ableton.

Here are my subjective takes on each tuning system.

  • 12-TET sounds fine throughout. But only fine. It’s never offensive, but it lacks the spiciness and character of the other systems.
  • Five-limit just intonation sounds unsurprisingly great in C because it’s based on the natural harmonics of C. The chromatic pitches in the C major prelude sound a bit odd, but you get used to them. However, five-limit sounds extremely weird in the other keys. I explain why that is here.
  • Three-limit just intonation sounds pretty bad everywhere, even in C. In just intonation, you have to choose whether you want the fifths or the thirds to be in tune. In three-limit, all the fifths are perfect, but the thirds are dreadful. Apparently, medieval Europeans were fine with this, because thirds were considered dissonances anyway. But for Bach (and us), thirds are supposed to sound good, so three-limit is pretty useless.
  • Quarter-comma meantone sounds good in C, but pretty terrible everywhere else. It has good-sounding thirds, but most of the fifths are flat, except for a few which are wildly sharp. So when meantone is in tune, it’s very in tune, but when it’s out, it’s way, way out. The C major prelude mostly sounds nice in meantone, but C-sharp sounds horrendous. Fifth-comma sounds better than quarter, and sixth-comma sounds better than fifth.
  • Werckmeister is also pretty sour outside of C, but it’s not as seasickness-inducing as meantone.
  • Kirnberger sounds better than Werckmeister. In places, its out-of-tuneness even enhances the vibe.
  • Thomas Young sounds smooth and right to me. This is Kyle Gann’s favorite tuning, the one he uses for his home piano. It’s very similar to 12-TET, but without the bland sameness across keys and intervals.
  • Bradley Lehman sounds the best to my ears. Maybe that’s just because it’s the closest of all these tunings to 12-TET, but it has a slight edge to it in the remote keys. I have no idea whether there’s any historical merit to Lehman’s claim that this is the tuning system Bach really used. Mark Lindley and Ibo Ortgiesse argue that Lehman is totally wrong. It’s a good-sounding tuning, anyway.

The harmonies in this music sound radically different in these different tunings, especially outside of C major. It makes me wonder if the same rules could be meaningfully said to apply universally across them. There are plenty of intervals that clash horribly in meantone that are perfectly unobjectionable in 12-TET. Maybe Europeans started embracing chromaticism because post-meantone tuning systems made it sound good. How many rules of Western tonal theory are holdovers from a pre-12-TET world?

Update: some valid criticism of my approach.