It keeps the six main notes of the C major scale (C, D, E, F, G, A) in evenly-spaced positions, at their normal spots within the context of late 17th century practice. The tuner is then to install the keyboard's six remaining notes (B and the sharps F#, C#, G#, D#, A#) in tastefully raised positions, with adjustments as indicated by the diagram, so they can also serve well as flats.

This process of minimal but necessary compromises makes the keyboard ready to play music in all 24 major and minor scales. Every scale has a subtly different expressive character, as the steps are not all exactly the same size. The harmonies have various tensions and spice, when the notes of the scales are built together into chords.

Bach demanded and exhibited a system of this enharmonic flexibility not only in the diagram, but also through the music in Das Wohltemperirte Clavier. It presents his tuning challenge (and gives the solution!), where most of the preludes and fugues each require the smooth handling of more than 12 notes. For example, his D major prelude and fugue use all of Bb, F, C, G, D, A, E, B, F#, C#, G#, D#, A#, and E# in the same piece: 14 notes. Some of the other pieces require 13, 15, up to 25! The last piece in the book, the B minor fugue, requires 17 (Eb up to Fx), and presents 13 of them as early as the subject: six naturals C, G, D, A, E, B, and seven sharps F#, C#, G#, D#, A#, E#, and B#.

The resulting temperament has been absent from our history books. It was lost under layers of assumptions and habits that have led away from it.

I believe its particular sound, as an integrated part of musical practice, has profound implications for all of Bach's instrumental and vocal music that uses keyboards: either with written-out parts or in the basso continuo. Since every scale has a different Affekt or mood, from the different musical tension within the intervals, the music sounds colorful and "alive" as it moves.

Bach obviously knew how to set up his keyboards appropriately before writing his music for them. The aim is to restore the specific intonation scheme of his everyday keyboard tuning, the sound relationships he expected to hear in his melodies and harmonies, as they may have influenced his creative imagination. By hearing how these musical elements work through composition and improvisation, we gain new clues into the interpretation of Bach's music: affecting at least the areas of articulation, phrasing, dynamics, timing, intensity, and drama. The tensions and resolutions within the music suggest fresh ideas in performance, both through intuitive reactions and through close analysis.

This "LaripS.com" web site clarifies and explains the material, both through theory and practice. It provides various introductions to this work, for different levels of readers' interest. It serves as an archive of ideas as this temperament is used and discussed among musicians, researchers, and enthusiasts.

The recipe

• We set up the notes of the C major scale first, and then we fit the remaining notes into carefully compromised spots: not like the old style, where you were forced to choose either a sharp or a flat, and have it sound bad as the other one.
• Tune your natural 5ths F-C-G-D-A-E with your everyday process of making all the 5ths (or 4ths) waver with gentle equal quality, and checking that F-A and C-E each end up "a little sharp"; your checkpoint here is that F-A is wide at about 3 per second in the tenor. Here's the little jot on one side, showing the 3 beats.
• You normally would have finished everything else with that same type of 5ths: E-B-F#-C#-G#, and F-Bb-Eb, leaving a gap there between the Eb and G# where it doesn't connect. Instead, we are going to put all those remaining notes into tastefully compromised positions so we can play music that has either sharps or flats, all the way around.
• From E, put the next three notes higher than usual, simply doing pure 5ths E-B-F#-C#. You'll notice that C# gets up fairly high and bright against A, but when you check it as Db-F, the A-C# and Db-F have the same quality as each other. That's how it works well playing all music.
• Continuing on from C#, fit the last three notes G#-D#-A# into place with only half as much tempering as you used on the natural 5ths: only a very slight waver, each. That is, when you do each one, put each one into its pure-5th spot but then take it flat the tiniest bit. Check that you're making your Ab-C a little better than E-G#, the Eb-G better than B-D#, and the Bb-D better than F#-A#.
• As your final checkpoint from A# back to F, that leftover spot is a slightly wide 5th but not troublesome (nobody will hear it, a couple of paces away from the instrument): it wavers the same amount as the C#-G#-D#-A# you just finished, but in the opposite direction. Here's the jot on the other side, showing the quality of the A#-F leftover.
• Finish the instrument by octaves in both directions. This diagram shows you the quality of all the 5ths, if you want to check your octaves with them as you go.
• Now, play and improvise music in all possible scales; it all works! You'll notice that it matches the physical layout of the keyboard: whenever you have to stretch a finger to play a sharp or flat, the music sounds a little more spicy than when you're playing on only the natural notes.

Articles

A supplementary article "The 'Bach temperament' and the clavichord" is available in the November 2005 issue of Clavichord International. It contains further discussion of practical issues: some specifically for clavichord, some more generally in analysis of Bach's keyboard music, scale structure, enharmonic considerations, and by-ear tuning instructions. The compositions presented include BWV 772-801, 802, 808, 849, 887, 988, 1079, and 1080. [Outline] [Full text]

A November 2005 essay "The Tuning" gives a two-page summary of the temperament and its musical character. [Full text] It is printed in the booklets of Peter Watchorn's CDs.

The 2006 article "Bach's Art of Temperament" for BBC Music Magazine further explains this temperament from several additional practical angles, focusing especially on the blend of the C major and B major scales. (C, D, E, F, G, A, B; B, C#, D#, E, F#, G#, A#) [Full text] The BBC's version was shortened and given the title "In Good Temper".

Other articles about this temperament are listed here. There is also a page of my responses to other people's articles and books where they present their agreements or disagreements with this temperament.

My October 2008 lecture notes for James Madison University turn out to be almost a complete article, in themselves.

In Early Music November 2009 I have a letter to the editor, calling for fair argumentation on this topic...especially from Mark Lindley, who has mis-represented and disdained my work three times in that journal.

Quick start!

What might a beginner to this material read first, most productively? Open the streaming audio page and start up some music in the background. Then, start reading either the "Bach's art of temperament" article or the informal lecture. I have prepared a more formal set of notes (slides in a PowerPoint presentation) for a public lecture at James Madison University, 22 October 2008. Also, take a look at the videos showing a harpsichord being tuned and played. Enjoy!

Audio samples and video demonstrations

New! Additional sample recordings are available variously on Last.fm, on iLike, and Facebook as featured excerpts from LaripS 1002 (organ) and LaripS 1003 (harpsichord and organ).

New! More than a dozen recordings by other musicians using this "Bach/Lehman 1722" temperament: on harpsichords, fortepianos, pipe organs, digital organs, synthesizers, and more....

A survey of the temperament's use in public performances and recordings by hundreds of musicians, and built into pipe organs and other instruments....

The LaripS Recordings label....

There is a growing collection of video demonstrations, showing how to tune harpsichords by ear in this and several related temperaments.

Other resources

A temperament diagram with remarks about the scales and intervals.... Dozens of Frequently Asked Questions (FAQ), answered.... The historical and practical assumptions within my research.... Several sets of instructions for tuning instruments by ear, or with electronic devices.... Several additional temperaments to set by ear: see especially my ordinary temperament to play 17th century German music ("Bonus 5" on that page).... New in November 2008! Jean-Philippe Rameau's published preference in 1726 was apparently for a system with regular tempering in Bb-F-C-G-D-A-E-B, and the other four notes tastefully arranged to fill the gap. My presentation of this is in section 6 of the "practical instructions" page.

A historical survey of other "Bach" temperaments as hypothetical reconstructions....

Additional resources for music theory, practice, and history....

Features / Site Map....

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Bradley Lehman, A.Mus.D. (harpsichord), info@larips.com [Biography] [Home page]