The Well-Tempered Clavier …what does it actually imply?

In this episode I seek (in 18 minutes) to demonstrate mathematically pure intervals, alongside ‘tempered’ intervals. The circle of fifths is in fact a spiral of fifths— it is infinite. We seek to make it a circle for convenience, but this means that the distance between what would be mathematically pure intervals must be altered (!) in order to force the spiral into a circle.

The question remains: how do we do that? Music today is heard in equal temperament, where all keys, all tonalities sound the same. Pure intervals have been forced into identical ‘impure’ ones— convenient, but this deprives us not only of a beautiful natural simplicity, but also the individual character of each key found in unequal temperaments. From the earliest European music, numerous solutions to this immortal problem have been offered. By the time Bach arrives, his solution, laid out for us in The Well-Tempered Clavier, is certainly an elegant one…but we don’t quite know exactly what it is.

The remainder of the episode analyzes the prelude and fugue, no. 13, in F-sharp major, BWV 858. A look at the opening of the prelude in earliest version offers lovely insights into Bach’s working mind:

In revision Bach changes the repeated note — a recognizable motif of the early version— into a trill, now acting as its own motif:

Particularly fascinating is the way Bach changes the harmonic rhythm from the early version here, bar 17:

Now again from measure 17 in the revision. Bach inserts two full bars, extending the harmonic length of g# minor and C# Major:

“Thank Bach for God.”

A huge thanks to Bradly Lehman for helping preparing this episode. I haven’t even scratched the surface of what his work covers, but hopefully you’ve got some idea how deep the topic of tuning can go. Lehman has some great online resources illuminating the fascinating world of temperament. For starters, try:

www.larips.com (Spiral spelled backward)

Dig deeper with this essay here, published by the Reimenschneider Bach Institute:

And finally, more Articles and Essays by Bradley Lehman

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Concepts Covered:

Pure vs tempered intervals, ‘spiral of fifths,’ vs. the circle of fifths, equal temperament, loss of key character, Bradly Lehman temperament, historical tuning systems, Bach’s Well-Tempered Clavier, temperament and tuning, F-sharp major Prelude and Fugue No. 13, Bach’s compositional revisions, and BWV 858

A double canon from Bach’s Orgelbüchlein! A bit late, but Bach’s take on this Christmas tune is really wonderful. See how both melodies combine to make a double canon:

German mystic, Heinrcih Seuse, author of ‘In Dulci Jubilo’

English composer R. J. Pearsell’s setting of the melody.

Spread the Love, Doubly Canonic:

N.B. I’ve been wanting to make this rebrand for a while: The title of this podcast is no longer “The WTF Bach Podcast” but simply, “WTF Bach” — I hope this doesn’t cause any problems, if you run in to any issues as all, please alert us! Thanks!

Want to help this resource? Here’s how:

We encourage our listeners to become a paid subscriber atwtfbach.substack.comFree subscriptions are also beneficial for our stats. You can make a one-time donation:

https://www.paypal.me/wtfbachhttps://venmo.com/wtfbach

Supporting this show ensures its longevity. Thank you for your support!

I had the great pleasure of speaking with Mr. Paul Jacobs. On the 250th anniversary of Bach’s death, July 28th, 2000, Jacobs played Bach’s complete organ works in one giant 18 hour concert— he was 23.

Our conversation spans how to memorize, scholars vs. performers, pianists playing the organ, pop music, music for consumption, ‘social media musicians,’ music as a substitute for God, The Art of Fugue (harpsichord or organ?) and more…

Become Your Best Buxtehude:

Some links mentioned in the chat:

Organmaster Shoes

The Robertsbridge Codex

Schumann’s advice for young musicians

and of course, Paul’s website.

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We encourage our listeners to become a paid subscriber atwtfbach.substack.comFree subscriptions are also beneficial for our numbers.

You can make a one-time donation:

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Supporting this show ensures its longevity. Thank you for your support!