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.

Variant of the temperament for vocal ensemble accompaniment

The main layout, for the chamber and solo music (including the organ repertoire and service-playing), is: F-C-G-D-A-E 1/6 comma each; E-B-F#-C# pure; C#-G#-D#-A# 1/12 comma each; very slightly wide (but nearly pure) A#-F resulting.

But, to play keyboards in the Bach passions, masses, oratorios, and most of the cantatas there is a different version to use!

Tuning a harpsichord or continuo organ at Cammerton to that main Chorton organ in the church (for example, preparing a second organ for the St Matthew Passion's second orchestra), the temperament gets transposed as follows:

G-D-A-E-B-F# 1/6 comma each; F#-C#-G#-D# pure; Eb-Bb-F-C 1/12 comma each; very slightly wide (but nearly pure) C-G resulting.

That is: to play Bach's continuo parts to vocal works today, using modern scores that have been transposed so the keyboard continuo is playing at the same pitch as the orchestra, it is best to use this latter version. It simulates the resulting sound as if the organist were reading his/her part a whole tone lower. (The temperament is transposed to offset the transposition of the part, in print.)

That's the version for the harpsichord, organ, or rehearsal piano when rehearsing or performing most of Bach's vocal music.

Why does it matter to use this transposed version?

The attempt here is to find the sounds that may have influenced Bach's compositional process. The tuning helps to indicate how strong or gentle the various musical elements might be, in accent or articulation or dramatic progression. The assumption is that Bach did some of the compositional work either at or checking with the organ, for the sound created by the basso-continuo chording: providing a harmonic backdrop of tensions and resolutions for each composition as a whole. This has the organ continuo part in its originally-notated key, i.e. for the first performances: what harmonic layout did that organ create, with the assumption that it had the normal "C" version of the temperament? And then, to the rest of the orchestra and the singers, that sounds like a "D" temperament (from the perspective of the page they are looking at) because the organ is producing a sound a step higher than the rest of the ensemble.

Within that scenario, with the composer working or checking at the keyboard while composing (or at least with knowledge how it would sound in the first performance), how might those sounds influence the direction or balances in the composition? (This is rather like the question: what can we deduce from Stravinsky's or Schoenberg's orchestral music by looking at the piano sketches and playing them in their standard, equal temperament? Did those sets of pitches influence the composing imagination, for orchestra and singers?)

To whet the appetite, here are several observations from the way the tuning sets up on the organ, through its interaction with the orchestra and singers. Everything comes around to the sound created in practice by this tuning, and the way it provides contrast and dramatic motion. In the cantatas and passions a whole world opens up, simply by setting up the organ/harpsichord in the tuning for which he wrote this music, and then listening to the way it interacts with the texts being sung. Bach was a brilliant composer, and his strongest medium of expression was the sounds he deployed to create approprate effects.

A few short illustrations from the St John Passion:

  • Early in part 1 there is a spot where Malchus's ear is stricken off, in recitative, by the angry character of Peter. There are two diminished-7th chords in succession in the continuo, but they have different effect from one another because they have objectively different sound, in the placement of their intervals. The one on the word "Ohr" downbeat sounds especially startling and violent, appropriately making a strong effect within its the thrust of a knife.
  • In Jesus's trial scene in part 2, "Und gaben ihm Backenstreiche" is followed by the strongest tonic/dominant minor cadence available: G minor 6-4, D major, G minor (the darkest minor key, in this tuning, while D major is the most resonant major). Then Jesus puts on the purple cloak, and Pilate addresses the crowd: "Und er sprach zu ihnen: Sehet, welch ein Mensch!" The harmony in "zu ihnen" is cadencing into F major, which happens to be of medium/average tension...and then the harmonies on "Sehet" and "Mensch" are startlingly strong. And then the crowd yells for Jesus to be crucified, doing it in the strongest and most evil-sounding G minor.
  • Part 2 has an Adagio aria for bass, with chorus, "Mein theurer Heiland". It starts off in the calmest D major with some excursions to G...a very still mood. Then at the choir's "In der letzten Todesnoth" it has tensed up to B minor/major and an F# major half cadence: with a brighter sound and considerably more intensity. The bass soloist's "Ist aller Welt" brings us back around through E minor and A major, to G and D again...and the piece calms toward the end.
  • Suddenly after this, the recitative "Und siehe da" starts off with the bright and unprepared B major (inverted). The bass whooshes down, and the "Und die Erde erbebete" is wholly startling with the Neapolitan-harmony sound of B-flat major! We cadence into the medium-bright E minor.
  • And then through the next recitative and on into the F minor "Zerfliesse mein Herze" the mood changes to very intense sorrow.
  • The temperament magically imparts this shifting series of characters to the whole thing, always appropriately to the spot in the drama...because Bach knew exactly what he was doing before he composed the piece.

And the St Matthew Passion? Set up a piano or harpsichord, and get a piano/vocal score. Then, to hear the contrasts of Affekt, play through at least the following sequences:

  • The B minor aria "Ach, nun ist mein Jesus hin" at the beginning of part 2 (with the bright tension/despair in its sound!), through the B-flat chorale "Mir hat die Welt".
  • The A-flat recitative "Ach Golgatha" all the way through the crucifixion scene, burial sequence ("Am Abend" with such a dark sound!), and to the end of the passion. Notice how the sequence of flat-keys walks the line between profound grief at the loss of life, and personal comfort.

The organ, with its layout of harmonic contrasts objectively available as the expression-keeper, is the primary reference point for the ensemble. The compositions stem from the way the (transposing) basso-continuo part will sound, as to its dramatic tensions and resolutions in forward motion. The basic Affekt is laid down by the organ's temperament. Bach took that into account before writing the music, and he used those effects objectively to create music appropriate to the motion/meaning of the words.

That is: all the musicians in the ensemble do not have to work as hard to create the appropriate musical effects, artificially. It suffices to listen closely to the way the music is already revealing itself (in overall shifts of Affekt and in specific strokes), and then react appropriately as sensitive musicians, going with the flow of the emotions. The music has already been composed, brilliantly.

That's evidenced both in the resulting sound in these Leipzig compositions (playing through them in the temperament that Bach wrote down for use on the Leipzig organs, allowing for the transposition!), and in Bach's well-known pedagogical remark that thorough-bass is the soul of music and composition.

"The thorough-bass is the most perfect foundation of music, being played with both hands in such manner that the left hand plays the notes written down while the right adds consonances and dissonances, in order to make a well-sounding harmony to the Glory of God and the permissible delectation of the spirit; and the aim and final reason, as of all music, so of the thorough-bass should be none else but the Glory of God and the recreation of the mind. Where this is not observed, there will be no real music but only a devilish hubbub." (New Bach Reader, pp 16-17: Bach dictating his basic principles to his students of thorough-bass; Wolff, Johann Sebastian Bach: The Learned Musician, p 309.)
To experience this directly: Set it up on a harpsichord, organ, or rehearsal piano according to the instructions here, and then spend several hours playing through each piece with a piano/vocal score, or from full score, to hear and see what's going on in the drama. All these tonal colors emerge on their own, and show the player how to weight them according to the meaning of the words.

Another exercise: play through the Bach four-part chorales in an edition that respects their original keys. (Thank you to Margaret Greentree for her cross-referenced catalog of chorales, in open-score PDF format!) Listen carefully to the characteristic sounds of the scale and the harmonies, with the meaning of the text that is being sung or the overall spiritual themes of the cantata.

[Note: If the chorale came directly from a cantata written in a transposing-organ situation, either play the chorale by reading everything down a whole step, or transpose the entire temperament to the "D" version as described in the article or here.]

Details about this are in the "Ensemble music" section of part 1 of the article. See also the math page, where this secondary transposed version is presented next to comparative charts of the main one.

Thanks are due also to Jos van Veldhoven, Siebe Henstra, and the Netherlands Bach Society: using this temperament for twelve performances of the St Matthew Passion in the Easter 2006 season. One of these performances has been recorded for radio broadcast: 13 April 2006, Netherlands Radio, channel 4, 1:00-4:00 pm (GMT +1).

Similarly, the St John Passion has been performed using this temperament: by Jeannette Sorrell and Apollo's Fire.

B Minor Mass

van Veldhoven - B minor Mass Channel Classics 25007: - Netherlands Bach Society, Jos van Veldhoven. Bach's B Minor Mass. This was recorded in December 2006. It was released in the Netherlands February 2007, with the rest of Europe and North America soon to follow. The performance uses this recommended tuning (transposed version) in the organ continuo.

The following observations about the Mass in B Minor are based on the original organ keys from the cantata movements that were rewritten as Mass movements. And unfortunately, the transposition situations are especially problematic. Of the completed Mass, performing parts survive only for sections 1 (Kyrie/Gloria) and 3 (Sanctus), and that organ part is written out in Chorton...apparently for performance at a venue away from Leipzig. On the other hand, Bach composed these in Leipzig; and if he ever had occasion to try them out in performance -- such as the three Gloria movements of BWV 191, from 1743 or 1746 -- their (lost) organ continuo part would have been transposed to Chorton, i.e. C and F major, instead of D and G. (These movements in the completed Mass were the "Gloria in Excelsis", "Domine Deus", and "Cum Sancto Spiritu".)

  • From the perspective of the organ and its intonation, if a Leipzig tryout or performance ever happened, all the B minor movements are in the simple key of A minor; and all the D major movements are in C major. This makes them especially open and resonant, the way the organ was tuned, and especially normal-sounding (by 18th century standards!) to play and sing with. C major is also the trumpet-and-timpani perspective, for those loudest and most festive movements.
  • "Deprecationem nostram" at the end of the "Qui sedes" movement (B minor; Chorton organ presumably A minor) cadences into the most spicy and urgently tense major chord available anywhere...and it has to resolve into the opening of the next movement. "Who takes away the sins of the world, hear our prayer..." resolving into "...who sits at the right hand of God the Father, have mercy on us." The tension in the tuning keeps the action moving along as the text does.
  • The "Et in unum Dominum" movement, in G major, is from the organ's perspective in F major. This, even more than C major, is the calmest (and one might say "most comforting") key available; see also the first movement of the organ Pastorale in F, BWV 590. And then, in the last line where the text is either "and was made man" or "came down from heaven" (depending which of the two alternate versions is performed), the music turns to F minor (from the organ's perspective) coming down from the perfect spiritual realms to a decidedly troubled and troublesome earth. The key here gives some of the darkest and murkiest mood available, for that contrast, due to the ways those harmonies are tuned.
  • If the Crucifixus is played in its final key of E minor, and if a putative Leipzig organ part therefore would have been in D minor: the "Et sepultus est" lays him in the grave to the calm and restful F major. The drama's apparently over, he's dead and buried, all is at rest...and then C major blazes out, startling everybody with the resurrection. But, on the other hand: this movement is borrowed from "Weinen Klagen" in BWV 12, from 1714, where the original continuo part was in Chorton F minor; and when Bach reused the piece in 1724 in Leipzig, he kept the continuo in F minor (while everybody else is in G minor). So, arguably, the "real" character of this movement's conception was F minor, not D minor. In "Weinen Klagen", which is a da capo chorus instead of having a passage analogous to "Et sepultus est", the big cadence before the repeat is into A-flat major. That is at least an observation that the Weimar organ, back in April 1714, could handle that notoriously problematic key!
  • In the "Et exspecto resurrectionem mortuorum" passage of the "Confiteor", the juxtapositioning of various keys is simply magical, the way the transformations happen through the suspensions and surprises. That's presuming, of course, that the singers and players are listening to the organ and matching the way its harmonies move!
  • The "Agnus Dei" is notated in Cammerton G minor (in the score; we don't know about any original parts). But, it stems from a lost wedding cantata(!) of November 1725...and so does another copy, "Ach, bleibe doch" in the Ascension Oratorio, BWV 11...where it is in A minor. Does this indicate that the original organ continuo part was therefore notated in Chorton G minor? Or, if Bach ever tried out the final "Agnus Dei" with the violin and singer in G minor, would there have been an F minor part for the organist? It is not clear; and Bach had used both G minor and F minor (from organ perspective) in other penitential pieces, elsewhere.... If we can hypothetically assume an F minor copy, it recalls such other F minor organ pieces as Bach's "Ich ruf zu dir" (BWV 639) in Orgelbüchlein and "Jesus Christus, unser Heiland" (BWV 689) in Clavierübung III. Or if

Electronic device instructions

This is the transposed version for Bach's vocal music. (The main version for solo or instrumental music is elsewhere.)
  • Establish the tempered D, E, F#, G, A, B: copy them exactly from the "Young's #2" setting on an electronic device.
  • Turn off the device.
  • Tune C# pure to F#.
  • Tune G# pure to C#.
  • Tune D# pure to G#.
  • Tune C pure to G (this is temporary).
  • Tune F pure to C.
  • Set Bb very slightly impure from both Eb and F. This is a midpoint between the places where it would be pure to either one of them, and getting only a vaguely slow wobble from each.
  • Go back to C and give it this same vaguely impure quality against F, by lowering it slightly from pure.
  • Check everything by ear: F#-C#-G#-D# pure 5ths, Eb-Bb-F-C 5ths with only the slightest wobble, and G-D-A-E-B-F# 5ths with a bit more wobble.
If your electronic device doesn't have a "Young's #2" setting, but only an equal-temperament meter:
  • Tune A exactly to its equal-temperament position.
  • Tune C, F, Bb, and Eb exactly to their equal-temperament positions.
  • Tune D 2 cents higher than its equal-temperament position.
  • Tune G 4 cents higher than its equal-temperament position.
  • Tune E and G# each 2 cents lower than their equal-temperament positions.
  • Tune B and C# each 4 cents lower than their equal-temperament positions.
  • Tune F# 6 cents lower than its equal-temperament position, i.e. a pure 5th from C#.
  • Check everything by ear: F#-C#-G#-D# pure 5ths, Eb-Bb-F-C 5ths with only the slightest wobble, and G-D-A-E-B-F# 5ths with a bit more wobble.

Sorge 1758, transposed for this same purpose

The following temperament published by Bach's colleague and admirer, Georg Andreas Sorge, is also explicitly for Chorton organs. And it too reveals the vocal-music effects I have described above, when set up in its simulated-Chorton transposed version. It has the same set of colors, only slightly paler and less intense (i.e. moderated toward equal temperament) and may be a good all-around compromise for modern ensembles:
  • 1. G-D-A-E-B-F# in regular 1/6 Pyth.
  • 2. F#-C#-G#-D# pure.
  • 3. G-C-F pure.
  • 4. Put Bb equally tempered between Eb and F.
  • 5. Nick F# upward so it's equally tempered between B and C#.
  • 6. Retune C# pure to this new F#.
  • 7. Retune G down so it's now pure from D.
  • 8. Nick C downward so it's equally tempered between G and F.
  • 9. Nick Eb downward so it's now pure from Bb.
The result of this layout:
F -1/12 C -1/12 G 0 D -1/6 A -1/6 E -1/6 B -1/12 F# 0 C# -1/12 G# -1/12 D# 0 A# -1/12 F.


Bach's schematic, rotated for use