Bach's schematic, as it appears on the page, © Bradley Lehman, 2005-22, all rights reserved.
All musical/historical analysis here on the web site is the personal opinion of the author,
as a researcher of historical temperaments and a performer of Bach's music.

Video Demonstrations

Bach's Well-Tempered Clavier (+ a Sinfonia)

Video demonstration of C major, B-flat minor, and E major music by Bach on YouTube, November 2007 (recorded 2005)

Harpsichord performances of several short compositions by Johann Sebastian Bach: Fugue in C major, Prelude and Fugue in B-flat minor, and Sinfonia in E major. (The C major Prelude is available as a separate video....)

The captions give a brief analysis of the compositions and the books they are in: Bach's "Well-Tempered Clavier" (book 1) and his set of 15 inventions and 15 sinfonias.

The performances are by Bradley Lehman, 2005, demonstrating the musical characters inherent in this tuning method derived from the title page of Bach's "Well-Tempered Clavier".


Harpsichord tuning: Well-Tempered Clavier

Video demonstration of the basic principles on YouTube, August 2007: explaining the Bach drawing and the tuning sequence for "Bach/Lehman 1722"

Keyboard temperament from the title page of Bach's "Das wohltemperirte Clavier" (1722).

The step-by-step explanation here shows how it is derived. Two full-length performances on harpsichord are included: Bach's C major and B major preludes from this book. [CD available for purchase]

Research by Bradley Lehman, 2004, continuing a doctoral project from 1993-4 in "modified meantone" tuning as applied to Bach's music. The interpretation is based on analysis of Bach's extant keyboard music, plus a historical study of tuning methods, plus (in 2004) the suspiciously irregular drawing on Bach's title page.

This research was first published in an Early Music (Oxford University Press journal) article, February-May 2005. Two printed portions and five web files comprise that article.


Tuning a harpsichord in Bach's temperament

Video demonstration on YouTube, August 2007: setting this Bach temperament

Tuning a harpsichord (cembalo, clavecin) in just a few minutes, by ear, using the tuning sequence I believe is illustrated on the title page of Bach's Well-Tempered Clavier (1722).

Research by Bradley Lehman, 2004, continuing a doctoral project from 1993-4 in "modified meantone" tuning as applied to Bach's music. The interpretation is based on analysis of Bach's extant keyboard music, plus a historical study of tuning methods, plus (in 2004) the suspiciously irregular drawing on Bach's title page.

This research was first published in an Early Music (Oxford University Press journal) article, February-May 2005. Two printed portions and five web files comprise that article.

This hands-on demonstration: 2007, Bradley Lehman at home. Flemish-style harpsichord built by Anne Acker.

F-C-G-D-A-E 5ths (or 4ths) double-tempered; E-B-F#-C# pure 5ths/4ths; C#-G#-D#-A# single-tempered (very slight).

Time to set up the temperament by ear, from a single tuning fork: about 5 minutes. Time to do the entire instrument: about 8 to 20 minutes. As reported by Bach's son Carl Philipp Emanuel, it never cost JSB more than a quarter hour for the whole thing. (Get the tuning done quickly so there's more time left for playing or improvising! And it's going to be stable for only a day or two anyway, with normal weather fluctuations, so it's good to develop an efficiency of setting and maintaining this quickly.)


Harpsichord tuning: 17th-Century regular...morphed to Bach's

Video demonstration on YouTube, August 2007: 1/6 comma meantone morphed into Bach

A normal 17th-Century harpsichord temperament is heard first: regular "1/6 comma meantone".

A folk tune (Twinkle, twinkle, little star / A-B-C-D-E-F-G / Ah, vous dirais-je, Maman / Morgen kommt der Weihnachtsmann...) is played in the four keys of D, B, A-flat, and F major. Two of these scales are excellent, and two of them are terrible.

The sarabande from Bach's B minor French Suite illustrates the behavior of this minor key: problems with the too-sharp D#, A#, and E# as they occur in the music. Those notes are too sharp because they were tuned for their more common use as Eb, Bb, and F...and in this style of tuning, the correct spelling of the note names matters that much.

Then, the harpsichord is retuned by moving six of the 12 notes in each octave. The adjustments are based on a drawing that Bach put on his title page of the "Well-Tempered Clavier"...which I take as his method of adjusting that normal tuning into something more flexible and beautiful.

The notes C, D, E, F, G, and A of the C major scale are retained as they were, and the other six notes F#, G#, A#, B, C#, D# (from the B major or F# major scales) are retuned.

The same compositions are then played again, to compare the change in harmonic and melodic quality.

The regular "1/6 comma meantone" system used here is also known as the 55-tet, or simply the "common" tuning described by 18th century writers: Tosi, Sauveur, Telemann, et al. Enharmonic notes such as D# and Eb are one comma apart. Within a whole tone, such as D-E, the D# is at 4/9ths of the distance, and the Eb is at 5/9ths. Only one of the two notes can be on the keyboard...or a compromise can be reached, picking some intermediate pitch that can serve (roughly) as either the D# or the Eb.

This is what the Bach (as interpreted by Lehman) modification then does: it keeps the notes F, C, G, D, A, and E at their usual positions for that system, but it alters B and the five accidentals to carefully controlled intermediate positions where they can serve more smoothly with additional note-names. The F#, C#, and G# are each raised part of the way toward Gb, Db, and Ab. The Bb and Eb are lowered part of the way toward A# and D#.

This hands-on demonstration: 2007, Bradley Lehman at home. Flemish-style harpsichord built by Anne Acker. Folk song arrangement: Bradley Lehman, 2007.


Bach vs Equal Temperament, part 1

Video demonstration on YouTube, November 2007: Bach vs Equal Temperament, part 1. B major, C major, and E major.

As a direct A:B comparison with equal temperament, I have a set of video recordings of five Bach compositions.

I tuned my Flemish single-manual harpsichord in equal temperament and played the WTC 1 preludes in C major (BWV 846), f minor (857), E major (854), e-flat minor (853), and B major (868). These were all on a single 8-foot stop. Then, keeping the same note C I retuned the instrument to the Bach temperament, and played all these preludes again with the same camera placement. The Sony DCR-TRV18 videocamera with built-in microphone was on a stand 2.5 meters from the instrument.

Same performer, same registration, same recording device, less than an hour later for each piece, with the only difference being the temperament. With the current equipment there is no possibility of editing within any of the takes; these are straightforward performances with an attempt to play moderately and simply in each piece. There is some very minor background noise occasionally from traffic and a purring cat. It was a casual and informal living-room session....

My own reaction to hearing this listening exercise is as I expressed in the second half of the Early Music article. They sound almost the same, except that the Bach layout has more intensity and contrast: more expressive range between its calm and its tension. It has a subtle dimensionality that is difficult to describe in words. To 18th century listeners, all of this would have seemed like equal temperament. "All music works so equally well that the lack of problem is unremarkable. In its brilliant highlighting of the music, the temperament does not call attention to itself (nothing ever sticks out to sound 'wrong'), and that is probably why Bach and his contemporaries had so little to say in extant sources. It comes across as 'equal' temperament in which everything is fine all the time, and that is what the 18th-century witnesses described: as a contrast against the bumpiness and modulatory restrictions of regular (mean-tone) temperaments." (Early Music May 2005, p225)

Especially so, as they grew up hearing regular meantone regularly in churches. Sorge in 1747-8 lamented this, in published polemics: that the conservative organ builders were still setting up regular 1/6 comma and its more extreme variants, as normal procedure. Sorge remarked that if they weren't going to go to more equalized systems, to get rid of the barbarity of the four diminished fourths in these regular temperaments, they should at least get with the halfway decent ideas that Werckmeister had laid out 57 years earlier. Or, better, they should go ask Bach in Leipzig what he does and what he thinks of those barbaric diminished fourths (being more than a comma sharp). [For details about this Sorge material, see the Bach-Dokumente and Mark Lindley's article Stimmung und temperatur.]

Likewise, CPE Bach's remarks in his Versuch set up a primary comparison against the conservative holdover of regular temperaments. All of this equality and pseudo-equality sounds both "equal" and "pure" against that conservative background of regular 1/6 comma and its predecessors, with the harsh wolf diminished sixth (typically G#-Eb) and the four wolf diminished fourths (typically B-Eb, F#-Bb, C#-F, and G#-C).


Bach vs Equal Temperament, part 2

Video demonstration on YouTube, November 2007: Bach vs Equal Temperament, part 2. F minor and E-flat minor.

PART 2 OF 2. Preludes from book 1 of Bach's "Well-Tempered Clavier" are performed on harpsichord, twice each.

The first performance of each pair is in equal temperament, and the second is in the "Bach/Lehman 1722" which I believe to have been Bach's own practice for this book of music.

The performances are by Bradley Lehman, May 31 2005. Same instrument, same camera, same day, trying to play as similarly as possible. All of the equal-temperament "takes" were recorded first, then the instrument retuned, and then all of the Bach-temperament takes.

My own impression, hearing these 2 1/2 years later and editing them together into this presentation: the Bach temperament sounds enough like equal to fool just about anybody, and brings both more intensity and more relaxation to the music. In any event, it encourages me as a player to bend the music more freely and naturally, investing it with more nuances, in reaction to the sound. It makes me listen more closely to melody and counterpoint, the way the musical lines interact with one another. Tonality "locks in" with a subtly different character and mood for every key (scale).

Equal temperament, by contrast, goes on and on with a relatively bland inoffensiveness...being less than inspiring, and encouraging "run-on" uninflected performances. The performer has to work harder to make something special of the music. Why not tune instead with a subtle inequality, and let the intonation itself do part of the interpretive work?

Better-miked versions of most of these pieces are on my CD "Playing from Bach's fancy", recorded a few weeks before these videos.

There are also (as of autumn 2007) two complete recordings of the Well-Tempered Clavier book 1 by other harpsichordists using this same Bach tuning: Peter Watchorn and Richard Egarr.


Harpsichord tuning: late 17th century "Ordinaire" style

Video demonstration on YouTube, September 2007: setting late 17th century temperament ordinaire, and playing several short pieces by Henry Purcell

Harpsichord tuning demonstration: in late 17th century style, useful into the early 18th century as well.

A regular system ("meantone") is set up first, with approximately 1/5th to 1/6th comma tempering...i.e. with all the major 3rds slightly wider than pure, and all the 5ths slightly narrow. The whole line of notes is: Eb-Bb-F-C-G-D-A-E-B-F#-C#-G#.

Then, to make the instrument more playable in keys of two or more sharps/flats, a simple modification is made to the several notes at each end of the sequence. The sharps are each raised in pitch, and the flats are each lowered, until they roughly meet one another (and can therefore be respelled as one another in music).

Two short pieces by Henry Purcell demonstrate the flexibility and color of this tuning: a Saraband in G minor, and a Hornpipe in D major.


Harpsichord tuning: building a scale by ear

Video demonstration on YouTube, August 2007: setting meantone accurately (a more advanced video demonstration for harpsichord tuners!) [Transcript of the captions]

Tuning a harpsichord from the reference of a single starting note.

In this demonstration we start from an A, and then we derive all the notes of a pentatonic scale from it: F, G, A, C, and D.

The title of this demonstration could also be: "Starting any meantone temperament accurately, by ear." The notes and intervals are adjusted carefully until they are deliberately impure by the right amounts relative to one another.

Despite some perhaps arcane terminology, this is merely a simple listening skill of controlling the relative pitches carefully. With practice, and knowing what to listen for, this skill can be developed by any reasonably musical teenager working hands-on at a harpsichord.

The basic technique here is to set up four consecutive 5ths (such as F-C-G-D-A) with exactly the same amount of tempering (impurity) in each interval, deliberately. The 5ths all have to be made slightly narrow, or else we would end up with a major 3rd that is unpleasantly wide and ugly. Tempering is always a series of trade-offs.

In this demonstration a size of major 3rd is chosen first, as boundary, and then the intervening 5ths/4ths are fit equally into that confined space. Here we have chosen to start with a pure major 3rd, for simplicity, but the technique works similarly with any other reasonable size. We could have used a slightly wider major 3rd tastefully, according to the milieu and the keys of the music we plan to play.

The resulting layout is called "meantone" because the whole step (the tone) makes an equal and average size within a given size of major 3rd. That is, for example, F to G being the same size step as G to A, within the major third F-A as illustrated here. The G's frequency is at the geometric mean between the other two frequencies.

This hands-on tuning method at the harpsichord is entirely geometric/analog, not involving any calculations or any technology invented later than 1600. (Well, OK, the tuning fork was 1711, but it's not necessary even to have a tuning fork; just some suitable way to assign a resonable pitch to the first note.)

This is the basis for most of the historical keyboard temperaments used on harpsichords, clavichords, organs, and pianos: at least among the natural notes (white keys on a piano), having all or most of them equally spaced in a "meantone" relationship.

After watching the video several times, taking notes if necessary, it might be useful to go through it again only listening closely to the sound (i.e. not looking at the picture or the captions). It might be easier to comprehend in that way, since the technique being taught is a listening skill...not a reading skill.

Of course, nothing substitutes for trying it out oneself at a harpsichord, to get a feel for the types of adjustments necessary.

With enough practice, and using temperaments that are built like this, the whole harpsichord can be tuned accurately by ear in about 7 to 20 minutes.

This same (More...)

JS Bach's six-voiced Ricercar from the Musical Offering

Informal video (on YouTube) of Bach's Ricercar a6 from the Musical Offering

This is the piece that Mark Lindley's 1985 article asserted had a necessity of equal temperament. Subsequently that same assertion has been repeated in later articles, including a New Grove entry ("Temperaments"), where Lindley wrote: "One could readily believe that Bach sometimes exploited the qualities of a particular key as inflected in a typical irregular temperament, sometimes merely accommodated what he knew was likely to be the kind of tuning his published music would be played on, and sometimes -- for instance, in the concluding ricercar of the Musical Offering -- ignored completely the possibility of intonational shadings."

No; the composition's intonational shadings simply sound unpleasant when played in the irregular temperament shapes that Lindley investigated, but they sound ravishingly beautiful here in this one!

JKF Fischer: Ariadne musica preludes/fugues

Video presentation on YouTube, November 2007: six of the preludes and fugues from Fischer's Ariadne musica, with facsimile score to follow along with the music

Preludes and fugues from Ariadne musica (1702/15) by JKF Fischer. The book has 20 of these preludes and fugues in 19 different keys, plus five ricercars based on chorales.

The compositions played here are in E major, F minor, F major, F# minor, G minor, and Bb major...all in 10 minutes. These are very short!

The examples here are from the complete recording by Bradley Lehman, 2005, on the new Taylor & Boody organ at Goshen College (Goshen IN). This is available for purchase as the 3-CD set "A Joy Forever", including music by other composers.

Ariadne musica was an inspiration for Bach to write his own books, going further to use all 24 keys. Bach also borrowed Fischer's F major fugue subject for his own similar F major subject in book 1, and Fischer's E major fugue subject for his own in book 2's E major.

What might this book have sounded like as Bach played through it for his own enjoyment and edification?

The pages of score shown here are from the 1715 edition, written in soprano clef and bass clef.

As a whole, Ariadne musica calls for 19 different notes...and obviously the instrument is not to be retuned between these one-minute pieces! The 19 notes are Cb; Db-Ab-Eb-Bb; F-C-G-D-A-E-B; F#-C#-G#-D#-A#-E#-B#. There is no Gb or Fb, but otherwise we have everything short of double-flats or double-sharps. The occurrence of Cb is prominent in the soprano voice in the A-flat major prelude, in the last phrase of the piece.

A complete roster of the sharp and flat usage, piece by piece:

  • C major: F#
  • c# minor: F#, C#, G#, D#, A#, E#, B#
  • d minor: Bb, F#, C#, G#
  • D major: F#, C#, G#, D#
  • Eb major: Bb, Eb, Ab, F#
  • e Phrygian: F#, G#
  • e minor: F#, C#, G#, D#, A#
  • E major: F#, C#, G#, D#, A#, E#
  • f minor: Bb, Eb, Ab, Db
  • F major: Bb, Eb
  • f# minor: F#, C#, G#, D#, A#, E#, B#
  • g minor: Bb, Eb, Ab, F#
  • G major: F#, C#
  • Ab major: Bb, Eb, Ab, Db, Cb
  • a minor: F#, C#, G#, D#
  • A major: F#, C#, G#, D#, A#, E#
  • Bb major: Bb, Eb, Ab, Db
  • b minor: F#, C#, G#, D#, A#, E#
  • B major: F#, C#, G#, D#, A#, E#
  • c minor: Bb, Eb, Ab, F#

Also interestingly, the five ricercars appear to have been written so they work fine on meantone organs. They use only F#, C#, G#, and Bb; no Eb or D# anywhere, and nothing farther out on either side. But...among the 20 preludes and fugues, only five of them work unproblematically in meantone: C major, d minor, e Phrygian, F major, and G major.


Bach: Bb fugue, & Ach Gott und Herr (BWV 714)

Video presentation on YouTube, November 2007: Bach's fugue in B-flat major (BWV 890) from the "Well-Tempered Clavier" book 2, and chorale prelude "Ach Gott und Herr" (BWV 714) as found in the Neumeister Collection.

Bradley Lehman, organ. From a concert 23 September 2007 at Goshen College, Goshen Indiana. Taylor & Boody Opus 41.

Joseph Kerman wrote of this B-flat major fugue: "This work is one of Bach's more subtle inventions--a light-hearted fugue for connoisseurs, we should probably acknowledge, one that also labors under a further handicap, that of sharing space with one of the composer's most radiant (and longest) preludes." (The Art of Fugue, 2005, p125)

As Mark Lindley pointed out in a 1994-97 article, the chorale prelude "Ach Gott und Herr" BWV 714 has "the most straightforward uses of C#-major (or Db-major) triads that I have found in Bach's organ music." (Michaelstein Conference report, 1997, p50) It therefore makes an excellent tuning test for setting up an organ appropriately....

I like to listen to these two short pieces together because they provide such a beautiful simplicity, and a strong contrast of character. They are both slow and quiet, but so very different from one another.

There are two or three very minor finger and toe slips in this performance, sorry! Audience coughs and rustling at a few places, too.


Kirnberger's keyboard temperament, 1771, playing Bach

Video presentation on YouTube, December 2007: Johann Philipp Kirnberger's keyboard temperament, published 1771 in Die Kunst des reinen Satzes.

Pure: Db-Ab-Eb-Bb-F-C-G-D 5ths.
Pure: C-E major 3rd.
Pure: E-B-F# 5ths.
Heavily tempered: D-A-E 5ths.
Schisma: F#-Db slightly narrow.

Musical illustrations: Bach's prelude and fugue in C major, from the Well-Tempered Clavier (book 1), 1722.


Bach: Adagio Bb, Allemande A, Sarabande Em

Video presentation on YouTube, December 2007: Concert excerpts from March 13, 2007 - Chico (California) Bach Festival

Bradley Lehman, pedal harpsichord

Music by Johann Sebastian Bach: Adagio (from Capriccio in B-flat major), Allemande (from English Suite in A major), Sarabande (from Partita in E minor).

Harpsichord and pedal harpsichord by Keith Hill, courtesy of David Rothe

Program notes from the concert...


Bach: Chromatic Fantasy and Contrapunctus 3

Video presentation on YouTube, February 2008: Two compositions in D minor by Johann Sebastian Bach: the Chromatic Fantasy (BWV 903a) and Contrapunctus III from "Die Kunst der Fuge" (BWV 1080).

Bradley Lehman, organ (live concert Sept 2007) and harpsichord (CD recorded March 2005).

Enjoy! I especially like the contrasts of character whenever the music modulates far away from D minor, into keys of many flats or many sharps.


Couperin: Goat's feet and old gentlemen

Video presentation on YouTube, April 2008: Pieces from Francois Couperin's 4th book of harpsichord music, published 1730: "Chevre-pieds" from Ordre 23 and "Les vieux seigneurs" from Ordre 24.

Bradley Lehman, harpsichord. From a concert March 10 2008, James Madison University, Harrisonburg VA USA. Single-manual harpsichord in Flemish style, tuned with the Bach/Lehman 1722 temperament.

The recording is audio only, with a slide show of selected paintings (c1710-1720) by Watteau.


Bach: Fantasia in A minor, BWV 922

Video presentation on YouTube, April 2008: Organ performance of Bach's Fantasia BWV 922. Bradley Lehman, recorded 2005 at Goshen College, Goshen Indiana USA. The organ is the Taylor & Boody Opus 41.

The recording was part of the sessions for the 3-CD set "A Joy Forever", but eventually we decided the set was already full enough without it. It is published here as an informal video, with a scrolling score.

Bach wrote this music in his late 20s.


Temperament: Werckmeister 3 vs Bach/Lehman

Video presentation on YouTube, May 2008: A comparison of two possible temperaments for Bach's organ accompaniments in Leipzig. One is Andreas Werckmeister's most famous layout from a 1691 publication, and the other is a temperament I believe was Bach's own.

The organ was tuned a whole step higher than the rest of Bach's ensemble, and therefore the organist for cantatas and passions always had to read from a part transposed a step lower. This put him into keys with two more flats, or two fewer sharps, than the other players. (For example, in the F-sharp minor "Buss und Reu" heard here, the organist played in E minor.) What character comes into the music from the keyboard temperament?


Part 2 continues with examples from Cantata #51 and the St John Passion.

Bach: Sinfonias in D minor and E minor

Video presentation on YouTube, June 2008: Two of Bach's three-part inventions, analyzed and performed by Bradley Lehman (harpsichord).

The analyses focus especially on the way Bach modulated: by swapping one note out of a scale and replacing it with the sharp (or flat) version of the same note name.

For example, within an F major scale (F-G-A-Bb-C-D-E), when a C# appears and replaces the C, the listener's ear reorganizes the notes to find another scale that happens to contain them all...and we move to D minor. Similarly, when a G# intrudes into D minor music and a B natural replaces a Bb, these swaps move us from D minor to A minor.

Incidentally, the D minor sinfonia played here makes a great case against meantone tuning. D minor is traditionally the "home" key (along with C major) for regular meantone. However, this composition uses both D# and Eb within the same bar, only half a beat apart! Furthermore, the D# is sounded with a G# only a few seconds before that, and the Eb is sounded with a Bb a few seconds later. The D#/Eb key can't be tuned so it makes a "wolf" 5th/4th with either one of those, yet it has to serve as both functions: and therefore it has to be at some interim position, having both 5ths Eb-Bb and G#-D# be good.



Bach's schematic, rotated for use