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.

LaripS 1003 - Playing From Bach's Fancy

This is a single CD, released January 4th 2006. It is a companion to LaripS 1002. The pre-release selection of the C major prelude has been heard on BBC Radio 3, Sunday 8/28/05.

LaripS 1003: Playing from Bach's fancy
Cover art for LaripS 1003
Graphic design: Gwen Stamm
Photo: Gloria Rhodes

Order this recording through the Goshen College Music Center
(phone: (574)535-7361)
or through Bradley Lehman,

Single CD with 29 tracks, 77 minutes of music, and a deluxe booklet.
$15.00 plus postage.

Audio Samples

Some streamed programs are available here.


1     Bach    Sinfonia in D, BWV 789
2     Bach    Sinfonia in g minor, BWV 797
3     Bach    Modulation canon, BWV 1079	[c, d, e, f#, g#, bb]
4-5   Bach    WTC 1 Prelude/Fugue in C, BWV 846
6-7   Bach    WTC 1 Prelude/Fugue in f minor, BWV 857
8     WF Bach Polonaise in eb minor
9-10  Bach    WTC 1 Prelude/Fugue in f# minor, BWV 859
11    Bach    Sinfonia in E, BWV 792
12    Bach    Wer nur den lieben Gott, BWV 690	[a]
13    Bach    Contrapunctus 3 of Die Kunst der Fuge, BWV 1080	[d]
14    Bach    Suite BWV 832 in A, Sarabande
15    Bach    Sinfonia in d minor, BWV 790
16    Bach    Sinfonia in f minor, BWV 795
17    Bach    Suite BWV 819a, Menuets in Eb & eb minor
18-19 Bach    WTC 1 Prelude/Fugue in bb minor, BWV 867
20    WF Bach Polonaise in e minor
21-22 Bach    WTC 1 Prelude/Fugue in B, BWV 868
23    Bach    Sinfonia in e minor, BWV 793

BONUS TRACKS played on organ:
24    Bach    Modulation canon, BWV 1079
25    Bach    O Mensch, bewein dein Sünde groß, BWV 622 [Eb]
26-29 Bach    Four Duetti, BWV 802-805 [e, F, G, a]

"Playing from Bach's Fancy"


In J. S. Bach's obituary it was reported: "In the tuning of harpsichords, he achieved so correct and pure a temperament that all the tonalities sounded pure and agreeable. He knew of no tonalities that, because of impure intonation, one must avoid."

The present album and its companion set for organ (LaripS 1002, "A Joy Forever") explore the specific temperament I have proposed as reconstruction of his practice, the discovery of his documented expectations. This tuning method is deduced from historical context and Bach's written evidence: his drawing at the top of the Well-Tempered Clavier's title page (1722) plus an analysis of his music--in that book and elsewhere. The article about this discovery is published in the February and May 2005 issues of Early Music (Oxford University Press), and further details are at <>. For the reasons I have stated there, I believe that Bach probably preferred this specific system for much or all of his career, instead of equal temperament or the various unequal methods around him. This also solves classic problems in the music of his sons, as to harmonic flexibility and surprises within their styles.

The layout is:

F-C-G-D-A-E 1/6 comma narrow 5ths;
E-B-F#-C# pure 5ths;
C#-G#-D#-A# 1/12 comma narrow 5ths;
A#-F a residual diminished 6th, 1/12 comma wide.

In this tuning, every major scale and minor scale sounds different from every other, due to the subtle differences of size among the tones and semitones. This allows music to project a different mood or character in each melodic and harmonic context, with a pleasing range of expressive variety as it goes along. It builds drama into musical modulations.

The result sounds almost like equal temperament in its smoothness, and it similarly allows all keys to be used without problem, but it has much more personality and color. In scales and harmony it sounds plain and gentle around C major (most like regular 1/6 comma temperament), mellower and warmer in the flat keys such as A-flat major (most like equal temperament), and especially bright and exciting in the sharp keys around E major (like Pythagorean tuning, with pure 5ths). Everything is smoothly blended from these three competing systems, emerging with an emphasis on melodic suavity.


Bach's first biographer, Forkel, wrote: "Nobody could install the quill-plectrums of his harpsichord to his satisfaction; he always did it himself. He also tuned both his harpsichord and clavichord himself, and was so practiced in the operation that it never cost him above a quarter of an hour. But then, when he played from his fancy, all the 24 keys were in his power; he did with them what he pleased. He connected the most remote as easily and as naturally together as the nearest; the hearer believed he had only modulated within the compass of a single key. He knew nothing of harshness in modulation; even his transitions in the chromatic style were as soft and flowing as if he had wholly confined himself to the diatonic scale. (...)"

"In the modulation of his instrumental works, every advance is a new thought, a constantly progressive life and motion within the circle of the keys chosen and those nearest related to them. Of the harmony which he already has he retains the greatest part; but at every advance he mixes something related to it; and, in this manner, he proceeds to the end of a piece so softly, so gently and gradually, that no leap or harsh transition is to be felt; and yet no bar (I might even say, no part of a bar) is like another. With him, every transition was required to have a connection with the preceding idea and to appear to be a necessary consequence of it. He knew not, or rather he disdained, those sudden sallies by which many composers attempt to surprise their hearers. Even in his chromatics the advances are so soft and tender that we scarcely perceive their distances, though these are often very great: we fancy that he has not deviated a step from his diatonic scale. Thus he knew how to combine everything in the whole extent of the dominion of sound which could by any means be connected together.

"From the manner in which Johann Sebastian Bach treated harmony and modulation, his melody necessarily assumed a peculiar form. In the union of several concurrent melodies which are all to be flowing and expressive, no single one can be so prominent as to attract to itself alone the attention of the hearer. This prominency the melodies must, as it were, divide among them; so that sometimes the one, sometimes the other may shine in particular, though its brilliancy seems to be diminished by the equally singing concomitant parts, because the attention of the hearer is shared by them. I say, seems to be diminished; for, in fact, it is not diminished, but rather increased when the hearer has practice enough to survey and to comprehend the whole at once. (...)"

"When he was asked by someone, as frequently happened, for a very easy clavier piece, he used to say: 'I will see what I can do.' In such cases, he usually chose an easy theme, but, in thoroughly working it out, always found so much of importance to say upon it that the piece could not turn out easy after all. If complaints were made that it was still too difficult, he smiled, and said: 'Only practice it diligently, it will go very well; you have five just as healthy fingers on each hand as I.' Was this caprice? No, it was the real spirit of the art.

"This true spirit is what led him to the great and sublime as the highest object of the art. We owe it to this spirit that Bach's works do not merely please and delight, like what is merely agreeable in art, but irresistibly carry us away with them; that they do not merely surprise us for a moment, but produce effects that become stronger the oftener we hear the works, and the better we become acquainted with them; that the boundless treasure of ideas heaped up in them, even when we have a thousand times considered them, still leaves us something new, which excites our admiration, and often our astonishment; lastly, that even he who is no connoisseur, who knows no more than the musical alphabet, can hardly refrain from admiration when they are well played to him and when he opens his ear and heart to them without prejudice."

About Wilhelm Friedemann Bach, who had been one of his own friends and correspondents, Forkel wrote: "Bach's sons were the most distinguished of his scholars. The eldest, Wilhelm Friedemann, approached the nearest to his father in the originality of all his thoughts. All his melodies have a different turn from those of other composers, and yet they are not only extremely natural, but, at the same time, uncommonly fine and elegant. When performed with delicacy, as he himself performed them, they cannot fail to enchant every connoisseur. It is only to be regretted that he loved more to play from his fancy, and to seek after musical delicacies only in improvisation, than to write; the number of his beautiful compositions is therefore small."

For this album I have chosen a variety of short pieces by Johann Sebastian and Wilhelm Friedemann Bach, attempting to hear what their "playing from their fancy" might have encompassed within their own expected tuning system. The sequence juxtaposes compositions that explore all the keys, either as tonic or through their modulations. I have found that this temperament emphasizes contrapuntal listening to melodies: textural clarity in forward motion, rather than harmonic stasis. The resulting music is progressive, as Forkel appreciated.

These sinfonias, preludes, and fugues demonstrate not only the range of characters among the keys, but also the way the temperament handles enharmonic equivalencies (such as D# and Eb being played by the same lever on the keyboard), sometimes within the same short piece. The D minor sinfonia employs 13 different notes from D# to Eb.  The E minor sinfonia has 14 notes from Eb-Bb up to D#-A#.  The F minor sinfonia has 15, from Bbb-Fb up to A-E-B. Contrapunctus 3 of Die Kunst der Fuge (BWV 1080) plays games of close mutation with Eb/D#, Ab/G#, and Db/C#. And, the modulation canon of Das musikalisches Opfer (readily playable as either a keyboard solo or duet, among other options) has an incalculable number of notes as it continues to rise infinitely through enharmonic swaps. To play it merely six times is to use all twelve minor scales in turn, by a spiral-of-5ths progression...and the pitch level of the piece has gained an octave!

I have included an earlier version of the B major prelude and fugue, as found in the "alpha" reconstruction published in the Neue Bach-Ausgabe. This presents an interesting musical alternative to the more frequently heard readings: several of the octave placements and rhythms are different, giving what I feel is an even richer sound. The two polonaises by Friedemann are from his set of twelve, composed between 1756 and 1764. There is quite a difference of character between E minor (one sharp) and E-flat minor (six flats)! The other short pieces are here simply because I enjoy them, and to provide additional variety of key-characters.

The organ selections are included here both for "bonus" pleasure-listening, and as illustrations for the Early Music article mentioned above. The recording session was a delightful opportunity to play these two instruments in the same fine hall, tuned identically and recorded with the same microphones. The organ's specification is provided in LaripS 1002.


According to a later church official in Leipzig, recounting a local legend, Bach had been both modest and forthright about his own style of organ-playing. "There is nothing remarkable about it. All one has to do is hit the right notes at the right time, and the instrument plays itself." Whether Bach actually played that simply or not, the method is attractive and it works well in practice. Prepare the notes carefully, and then react to them with a free and easy manner of delivery, a natural flow.

I have tried to pattern my harpsichord and organ technique along that line of strategy: merely playing the notes at what seems to be "the right time" in reaction to the tensions and resolutions caused by the music and the temperament, letting my phrasing and articulation be governed by melodic/contrapuntal listening. I cultivate a quiet, unostentatious approach to the instrument and the compositions: seeking to let the music reveal itself in its sound, with very little extra assistance from the performer.

Indeed "the instrument plays itself"...if it has been set up correctly (via tuning and voicing) and approached with an adequate technique. The tuning and the contrapuntal writing already have plenty of interest in the multi-layered sound produced, without too-imaginative intervention from the performer's will. At least for my own work, I do not think a performance should draw undue attention to itself: but it should merely reveal the composition, reacting flexibly to its moods, starting from a basic position of relaxed muscles and alert attention.

I am influenced also by the naturally paced dysfluencies in human speech--letting the different thoughts have various bits of space as they end and begin. Music works the same way as speech, putting forth rhetorical points. Notes as syllables are grouped into meaningful units of words, phrases, and ideas, with a natural hierarchy to them. The especially important points tend to have additional space around them, with a more dramatic and noticeable presentation. Infants know how to use this, to get their needs and wishes met. So do cats. It is basic communication. The goal is direct clarity of intent. Breathless run-ons are unintelligible and unpersuasive! They betray ungrammatical thought: an unwillingness (or inability) to discriminate between the naturally strong and weak elements in a sentence.

Musical time is a liquid. Notes on a page do not have any specific length or accent until they are played within the flow of a piece of music. They describe little semi-determinate particles of sound at some relative positions within a field of possibilities. When a performance converts them to organized groups of sounds, they get stretched or compressed slightly, according to the way the music around them is going. As with the syllables of speech, context determines their precise pronunciation (articulation and accent), and the proper amount of time they deserve within larger thoughts. Phrasing--to hit all the right notes at "the right time"--is therefore to be decided in the moment, at least somewhat, by the composition's tensions, resolutions, surprises, and inevitabilities: as the music speaks.

There is no way to notate these speech-like nuances adequately, but that basic process of reactive flexibility is natural. Natural shapes tend to be irregular. Slight dysfluencies of flow help listeners to "get" the music immediately without having to think about it. Time flows around obstacles. The most important thing to do while playing is to listen to the composition. Then, in response to its well-organized yet free thoughts, one may let the music go where it will in the given occasion, having its own living intention.

Alfred Cortot reported playing Debussy's preludes to the composer's widow and daughter, and then asking: "Is that the way your papa played?" Eight-year-old Chouchou replied: "No, Papa listened more."

- © Bradley Lehman, 2005

The harpsichord is a Franco/Flemish double by Knight Vernon [photo 1, photo 2] modeled on 17th century Ruckers instruments.

Bradley Lehman, harpsichord and organ

Recorded: March 13-14, 2005
Producer: Bradley Lehman
Engineers: Matthias Stegmann, Todd Hershberger
Editing: Matthias Stegmann, Bradley Lehman

Bradley Lehman

Bradley Lehman, born in Indiana and now living in Virginia, is a harpsichordist, organist, composer, researcher, and developer of business software. He has performed solo and ensemble concerts in the US, Canada, Costa Rica, England, and Germany, and as a regular church organist for ten years.

Lehman's publications include a dozen recordings, a hymnal concordance, hymns and arrangements, CD reviews for Christian Century, radio theme music, and a scoring system for the game of bridge. His 2005 article in Early Music (also featured here at describes this keyboard tuning method from JS Bach's evidence: giving the historical context and analyzing its musical and mathematical properties.

Lehman holds a doctorate in harpsichord performance from the University of Michigan. His other degrees, variously from Michigan and Goshen College, are in the fields of musicology, church music, mathematics, and interdisciplinary study of early keyboard instruments.

Order this recording through the Goshen College Music Center
(phone: (574)535-7361)
or through Bradley Lehman,

Single CD with 29 tracks, 77 minutes of music, and a deluxe booklet.
$15.00 plus postage.

Score of the modulation canon:

Performance score for keyboard, arranged by Bradley Lehman for this recording:


Bach's schematic, rotated for use