The “squiggle” above the words “Das Wohltemperierte Clavier” in Bach’s handwriting

The following tuning method produces a keyboard temperament based upon Bach’s “squiggle” on the autograph title page of the Well-Tempered Clavier, Book I.

The derivation of this tuning method from the “squiggle” is explained fully in the essay “Decoding Bach’s Temperament” by David Louie. View the essay at the bottom of this page, or download in high resolution at davidlouiepiano.com/Shop.

The “slightly-tempered” and “normally-tempered” intervals, represented by corresponding loops in Bach’s squiggle, are always tempered as wide fourths and correspondingly narrow fifths. It is helpful to perform checks of the major thirds along the way, as described below.

The Method

  • start from F (set pitch as necessary using a tuning fork or an electronic device)…
  • tune B-flat as a pure interval (no beats) from F…
  • tune E-flat/D-sharp as a pure interval (no beats) from B-flat…
  • tune A-flat/G-sharp as a pure interval (no beats) from E-flat/D-sharp…
  • tune C-sharp as a “slightly-tempered” interval, approximately one-eighteenth Pythagorean comma, from A-flat/G-sharp. Check the C-sharp to E-sharp (ie. F) third, which beats quickly, but tolerably…
  • tune F-sharp as a “slightly-tempered” interval from C-sharp. Check the F-sharp to A-sharp (ie. B-flat) third, which beats quickly…
  • tune B as a “slightly-tempered” interval from F-sharp. Check the B to D-sharp third, which beats fairly quickly…
  • tune E as a “normally-tempered” interval, approximately one-sixth Pythagorean comma, from B. Check the E to G-sharp third, which beats moderately quickly…
  • tune A as a “normally-tempered” interval from E. Compare the F to A third, the A to C-sharp third, and the C-sharp to E-sharp (ie. F) third. The F to A third beats moderately, the A to C-sharp third beats moderately quickly, and the C-sharp to E-sharp third beats quickly…
  • tune D as a “normally-tempered” interval from A. Compare the D to F-sharp third, the B-flat to D third, and the F-sharp to A-sharp (ie. B-flat) third. The D to F-sharp third beats moderately, the B-flat to D third beats moderately quickly, and the F-sharp to A-sharp third beats quickly…
  • tune G as a “normally-tempered” interval from D. Compare the G to B third, the E-flat to G third, and the B to D-sharp third. The G to B third beats moderately, the E-flat to G third and the B to D-sharp third both beat fairly quickly…
  • tune C as a “normally-tempered” interval from G. Compare the C to E third, the E to G-sharp third, and the A-flat to C third. The C to E third beats moderately, the E to G-sharp beats moderately quickly, and the A-flat to C beats quickly, but tolerably…
  • to finish, check the interval from C to F. If everything has been tempered well, this residual interval should end up either pure, or tempered marginally.

The setting of the temperament is now complete. The architecture of this tuning method allows the immutable pure fourths/fifths to be tuned first, followed by those that are “slightly-tempered” and ending with those that are “normally-tempered.” Control is maintained over the final result by checking and comparing the qualities of the major thirds while tempering the fourths and fifths.

Decoding Bach’s Temperament
by David Louie

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For useful information on various keyboard temperaments, and comparisons between Bach-Louie and other interpretations of Bach’s “squiggle,” see Carey Beebe’s website.