The Fifth Desk · Evaluation
Act I · The Map
Johann Sebastian Bach · Das Wohltemperirte Clavier, the first part, BWV 846 to 869 · twenty-four preludes and fugues, one pair in each major and minor key, scored as one book · for keyboard: harpsichord, clavichord, organ and, most widely since the nineteenth century, the piano · about 100 to 130 minutes complete, by instrument and performer
Mode
Keyboard preludes and fugues in pairs; arpeggio, invention, toccata, aria and dance beside fugue in two to five voices
Mythos
An ordered ascent through every region of a world; the circle of keys heard as a figure of order, evoked rather than built
Phase
Twenty-four pairs in chromatic order from C major to B minor, each major followed by its parallel minor; each tonic once, no return
Presentation
Concert music; forty-eight pieces for keyboard, the 1722 text played complete on harpsichord, clavichord, organ or piano
Register
From the wit of the C sharp major pair and the grace of the G major to the lament of the E flat minor prelude and the gravity of the great minor fugues; no word set
Scale
Every key under one tuning, and a teaching book for hands and minds; about 100 to 130 minutes complete
Governing Proposition
Forty-eight pieces climb the chromatic scale from C to B, a prelude and a fugue in every major key and then in its minor, the remote keys written as fully as the near. The wager of the book is that under one tuning every key is habitable and each has its own character, and it makes the claim by walking into all twenty-four; what it builds is a plan, not a story, and it ends in B minor because B minor is last.
Act II · The Essay
Movement I
The title is Das Wohltemperirte Clavier, and the autograph fair copy carries the date 1722 on its title page. Bach was then Kapellmeister at Köthen. The title page offers the book, in substance, for the use of young musicians eager to learn and for the pastime of those already skilled in the art. It is a teaching book, and it says so. What it teaches is laid out in its plan: a prelude and a fugue in every one of the twelve major and twelve minor keys, forty-eight pieces in all.
“Clavier” means keyboard in general, and the book names no single instrument. It has been played on harpsichord, clavichord and organ and, most widely since the nineteenth century, on the piano. The change of instrument is neither credited nor charged. What “well-tempered” meant is disputed: whether equal temperament, or one of the unequal circulating temperaments of the day, in which every key is usable and each keeps a colour of its own. Nothing here rests on the answer. What is certain is that the book requires a tuning in which all twenty-four keys can be played.
Several of the preludes stand in earlier and shorter versions in the Clavier-Büchlein begun in 1720 for Wilhelm Friedemann Bach, the composer’s eldest son. In the book they were enlarged to fill their places in the plan. The earlier versions are evidence of the making, and they show something the finished book conceals: that the plan came to be filled, slot by slot, and that a piece could be grown to fit. A second book of twenty-four preludes and fugues, completed about 1742, now carries the same name. It is a separate work and is not part of this one.
Movement II
The book opens with a single figure. The C major prelude is one arpeggiated pattern carried through a progression of harmonies, bar after bar, with no melody above it: harmony alone, the law of the book shown bare before anything is built on it. In the 1850s Charles Gounod set a melody over it and called the result Ave Maria. Gounod heard the absence of a tune as a space to fill. In the book it is not a space but a statement, and the fugue that follows supplies the line.
The C major fugue is in four voices, and its economy is strict: it lives on its subject and keeps close to it. Then the plan begins to climb. Every major key is followed by its parallel minor, C major by C minor, C sharp major by C sharp minor, and so up the chromatic scale to B major and B minor. Each tonic is used once, each of the twenty-four keys once. Nothing in the order is chosen for effect. The plan is the most impersonal thing in the book, and it is the argument.
Counted by script, the plan reaches far from home. Six of the twenty-four keys carry five or more sharps or flats, and C sharp major needs seven. Of the fugues, one is in two voices, eleven are in three, ten are in four and two are in five. The minor keys carry the heavier writing: eight of the twelve minor-key fugues are in four or more voices against four of the twelve major, a mean of 3.75 voices against 3.33. No prelude is in a form fixed in advance. Each pair is a unit, and the units are all different.
Movement III
The third pair is in C sharp major, a key of seven sharps that keyboard players of the time did not use, and it is played as lightly as C major. The pair is all grace and wit. Nothing in either suggests difficulty or strangeness: the remote key is made habitable by being treated as ordinary. That is the book’s first and plainest disclosure, and it is made by demonstration, not by statement. Under one tuning the same laws of voice and harmony hold everywhere, and the music that was impossible becomes merely music.
The fourth fugue, in C sharp minor, is the first great one in the book. It is in five voices, on a subject of four notes, laid down from the bass and taken up voice by voice. Its grandeur is reached by accumulation: the voices gather, the texture thickens, and the piece grows to a weight that nothing before it in the book has prepared. It is written in the old church style of the ricercar, and the gathering of the voices is the growth of the piece. Change the form and the piece no longer knows what it knows.
The eighth pair is printed as a prelude in E flat minor and a fugue in D sharp minor, the same key spelled two ways. The prelude is a lament of rare stillness. The fugue that answers it is learned, an exercise of the old devices of counterpoint, and it rises by learning into something like awe. Freedom and law are halves of one act: the prelude grieves without rule, the fugue takes the grief and orders it. The book says this again and again, in every pair, and here it says it most plainly.
Movement IV
The tenth fugue, in E minor, is in two voices only, the smallest in the book. It is a bare piece, and it is slighter than its neighbours. A teaching book has many such pieces, whose virtue is grace, wit or clarity: the C sharp major pair, the F major fugue, the G major pair. They are beautiful, and they are not elevated. They are also the pieces most easily exchanged: another E minor prelude, another F major fugue, would serve the plan as well, and the plan would not notice.
That is the book’s first limit. The slots are required; their contents are not. Change one piece and the book knows the same, because what it knows is the equality of keys and the union of free and strict, and those are said by the cycle and the pair, not by the relation of one pair to the next. Within each piece the necessity is high. Across the pieces the order is the key ladder, and nothing more binds them. The book is a plan and a collection at once, and the collection is where it gives.
The twenty-second fugue, in B flat minor, is the second in five voices. It is grave, and it closes in stretto, the entries of the subject crowding on one another, with a weight that has been called choral. Between it and the C sharp minor fugue the book has moved through dance, invention, aria and toccata, from wit to lament, two voices to five. Perhaps nine or ten of the forty-eight rise to the summit, at both ends of the book and through its middle. The rest are its daily work.
Movement V
The book ends with the B minor prelude and fugue. The fugue is in four voices on a chromatic subject that touches all twelve pitches of the scale, and still the subject has a tonic. It is the law of the book pressed to its edge: every pitch present and none secure, and the harmony holding. It is dark, and it resolves only at its close. Set beside the C major prelude, the law shown bare, it is the same law at its farthest reach. But it is not an answer to the beginning. The book ends in B minor because B minor is last.
Most of Bach’s music fell from use after 1750. This book did not. It was copied, taught and played without a break, by Bach’s pupils and through Kirnberger and Forkel; it reached Mozart, who studied it after 1782, and Beethoven, who learned on it; Chopin, by report, played Bach before his concerts. It was first printed in 1801, more than a quarter of a century before the St Matthew Passion was revived. Its plan became a genre: Chopin’s Preludes Op. 28, Hindemith’s Ludus Tonalis of 1942, Shostakovich’s Twenty-Four Preludes and Fugues Op. 87 of 1950 to 1951, and many others.
Landowska, Tureck, Gould, Richter, Gulda, Leonhardt, Schiff and Hewitt are among those who have recorded it, on harpsichord and on piano, and the questions they answer differently stay open: which instrument, which temperament, what tempo for the C sharp minor fugue, how much ornament in the preludes. On this desk the book stands a tenth below the Goldberg Variations, the same maker’s single architecture on one bass, and level with Kind of Blue and the Quartet for the End of Time. It is the greater fact of history and the lesser single form: a plan of every key, which every keyboard student meets and every serious keyboard player returns to.
Act III · The Twelve
The subtractive test cuts two ways. At the level of the plan nothing can go: the book’s claim is every key, so the loss of any pair breaks it, and the order, each tonic once, major before minor, rising by semitone, admits no substitute. At the level of the pieces much could be exchanged without loss to the whole. A different E minor prelude or F major fugue would serve the plan as well, and several preludes began as shorter teaching pieces for Wilhelm Friedemann Bach and were enlarged to fill their places. Within the pieces necessity is high, and the economy of the C major fugue is strict. But the plan requires a piece in each slot, not this piece.
Score: 8.4 / 10
The disclosure can be stated, and it is the work’s: under one tuning every key is habitable, and each has its own character. Before 1722 keys such as C sharp major and D sharp minor were places a keyboard player did not go; the book walks into all twenty-four and shows that the same laws of voice and harmony hold there. That is a truth about the tonal system, made by demonstration, and it held: the next two centuries of music lived in the territory it opened. A second truth runs through the pairs: freedom and law are halves of one act. Beyond these the book discloses states of mind, lament, gravity, near-despair, but as moods. Its plainest truth is about music itself.
Score: 8.4 / 10
Height reaches near the ceiling several times. The C sharp minor fugue, five voices on a subject of four notes laid down from the bass, rises to grandeur by accumulation. The E flat minor prelude is a lament of rare stillness. The B flat minor fugue, again in five voices, closes in stretto with a weight that has been called choral. The B minor fugue ends the book on a dark chromatic plain that resolves only at its close. Frequency is lower by design. A teaching book has many pieces whose virtue is grace, wit or clarity, the C sharp major and G major pairs, the two-voice E minor fugue, the F major fugue: beautiful, and not elevated. Perhaps nine or ten of the forty-eight rise to the summit.
Score: 8.9 / 10
The rubric does not adjust an axis for a form’s limits. What can be called archetypal here is the cosmos: an ordered ascent through every region of a world, the circle of keys as a figure of created order, and the sacred style of the old ricercar in the great minor fugues. Bach signed his church works to the glory of God, and the book has been heard since as music of order itself. But that myth is the listener’s. Nothing in the book builds a figure that carries archetypal weight: no journey with a stake, no figure that returns transformed, no end that answers the beginning. The particular is vivid and stays particular. Myth evoked by scope and learning, not built.
Score: 7.6 / 10
The inheritance is the keyboard collection of preludes and fugues, and the key-set had been approached: J. C. F. Fischer’s Ariadne musica had already gone through many keys. The departures are four: every key, the remote written as fully as the near; the pairing made strict, one prelude to one fugue, each pair a unit; the prelude raised from a warm-up to the fugue’s equal, in forms from figured arpeggio to invention, toccata and aria; and the fugue stretched from two voices to five in one book. The stake was real for a working musician, since the remote keys were unplayable in common tunings. But the book stayed in manuscript among pupils, on a road Fischer had marked: a swerve of completion.
Score: 8.6 / 10
Change the form and the work loses much of what it knows. What it knows is the equality of keys, and that is said only by the cycle: a set of twelve or twenty would claim nothing, and the full twenty-four, in order, is the argument. The pair says the second thing, that free invention and strict imitation belong together. Inside the fugues the form is the instrument: in the C sharp minor fugue the gathering of five voices is the growth of the piece, and in the B minor fugue a chromatic subject makes fugue the form of something like doubt, every pitch present and none secure. Held below the top because within the cycle the form is a collection: substitute one piece and the book knows the same.
Score: 8.9 / 10
Evidence of three centuries. Mozart studied the book after 1782; Beethoven learned on it; Chopin, by report, played Bach before his concerts. Analysis from Riemann and Tovey to the present has not exhausted it, and performance is more open now than in 1900: harpsichord, clavichord or piano, which temperament, Gould’s detachment against Richter’s gravity against Schiff’s voicing, the tempo of the C sharp minor fugue, the ornament of the preludes. The question of temperament has reopened in this century. Every keyboard student meets the book, and every serious keyboard player returns to it. Held below the ceiling because much of the yield is shared with Book II and with Bach’s keyboard work as a whole.
Score: 9.5 / 10
Printed only in 1801, the book was in wide circulation in manuscript long before, and both components are weighed together. Its force is its own: it made the twenty-four keys the territory of keyboard music, fixed the pair of prelude and fugue as a form, and set the standard of fugal writing that later composers measured themselves against. Keyboard music in every key might have come without it; the book showed what such music was for. Achieved reach is scored with intrinsic force: through Kirnberger, Forkel and Bach’s pupils it reached Mozart and Beethoven, trained the nineteenth century’s pianists, fathered the key-cycle as a genre, Chopin, Hindemith and Shostakovich among many, and has been the basic text of keyboard teaching for two centuries. Discounted where Book II shares the reach.
Score: 9.3 / 10
Survival is weighed in form, presence and fabric, and all three are strong. The form survives entire, in Bach’s autograph fair copy, with the earlier versions of the preludes as evidence of its making. Presence is continuous, and unusually so for a work of 1722: while most of Bach’s music fell from use after 1750, this book was copied, taught and played without a break, by his pupils, in the circles of Mozart and Beethoven, and in print from 1801, before the revival of the St Matthew Passion in 1829. It has outlived its instrument without retouching. The surface fixed to its moment is small: a tuning question and some dance types. Charged lightly because the text comes down in more than one state.
Score: 9.6 / 10
Command of the medium at the summit, and load-bearing. The counterpoint is the standard against which fugal writing is still taught: invertible counterpoint, stretto and the learned devices of the old style; five voices kept distinct in C sharp minor and B flat minor; a chromatic subject made to work in tonal harmony in B minor; the strict economy of the C major fugue. The keyboard writing is idiomatic in every key, the remote keys as natural under the fingers as the near. The preludes command a dozen textures. The costs are small and real: a few preludes are figuration studies on one pattern, the C major, the C minor and the D major, though each is shaped, and the two-voice E minor fugue is slighter than its neighbours.
Score: 9.6 / 10
Take the two most distant elements: the C major prelude, an arpeggio through a progression, and the B minor fugue, four voices on a chromatic subject. One law governs both: tonal harmony under one tuning, in which any pitch can be a tonic and every voice is a line. The C major prelude is that law shown bare, harmony without melody; the B minor fugue presses it to its edge, all twelve pitches in a subject that still has a tonic. Every piece obeys it, across the widest range of any work of its kind: two voices to five, dance to lament, every key. The tension is that the law is the system’s: the pieces are bound to one another by the key plan and the pairing, not by shared material.
Score: 9.2 / 10
A book of keyboard pieces holds few orders, and the figure says so. Consciousness, in a range of states from wit to lament. The sacred, in the old church style of the great minor fugues and the chorale-like gravity of several preludes. The social, in dance types, the gigue, the courante, the siciliano rhythm, and in the voices of fugue as equal speakers. Learning and labour, in a book made to teach hands and minds. The natural order, in the claim that one tuning makes a world of twenty-four regions, which the book makes structural rather than illustrates. They are held together by the plan, not listed. What holds the axis here is absence: the family, the state, history and mortality as a built theme do not appear.
Score: 7.4 / 10
Act IV · The Reckoning
8.8 / 10 · Final Average
Placement: Tier IV · Canonical
Strongest Dimensions
The Imperishable and The Made at 9.6 each, then The Bottomless Well at 9.5 and Pressure on Tradition at 9.3. A book copied, taught and played without a break since 1722, in its autograph whole; counterpoint that is still the standard by which fugal writing is taught, idiomatic in every key; a well of performance and analysis still open; and a plan that made the twenty-four keys the territory of keyboard music and the key-cycle a genre.
Limiting Dimension
The Encompassed at 7.4: consciousness, the sacred, the social in dance, learning and the natural order are held by the plan, but the family, the state, history and mortality as a built theme are absent. Next above it, The Archetypal Deep at 7.6: the order of the book is real and structural, but as myth it is evoked by scope and learning, not built, and the book ends where its plan runs out. Then The Inevitable and The Unconcealment at 8.4 each: the slots are required and their contents are not, and the book’s plainest truth is about music itself.
The Necessity Cap clears at 8.4 against a threshold of 7.5. The Coherence Floor clears with room: The Made at 9.6, The Inner Law at 9.2, The Living Form at 8.9, each against 7.0. The Epochal Gate is unmet: The Imperishable at 9.6 and Pressure on Tradition at 9.3 clear the bar of 8.5 with room, and The Swerve clears it by a tenth at 8.6, but The Unconcealment at 8.4 falls a tenth short and The Archetypal Deep at 7.6 falls nine tenths short. The Universal Minimum is met: of the eleven axes it covers, the lowest is The Archetypal Deep at 7.6, a tenth above 7.5. The Encompassed, which it exempts, clears its own floor of 6.0 at 7.4. Four of the five summit conditions are met, and with the Epochal Gate unmet and an aggregate of 8.8 the work stands in Tier IV.
Basis · the score of Das Wohltemperirte Clavier, the first part, BWV 846 to 869, as written in Bach’s autograph fair copy dated 1722, and its performance tradition, read from knowledge under the desk’s convention for concert music; no score, edition or recording was in hand, and no text of the work is in the desk’s files. The unit is the set of twenty-four preludes and fugues in the order of the autograph, scored as one work; no single prelude or fugue is scored. The second book, completed about 1742, is a separate work and stands outside the unit; where the two share credit, under Pressure on Tradition and The Bottomless Well, the share is charged. The earlier versions of several preludes in the Clavier-Büchlein of 1720 are evidence of the making, not part of the unit. The standard performing version is the 1722 text played complete on any keyboard; the change of instrument is neither credited nor charged, and the meaning of “well-tempered” is stated as disputed. The work sets no words; German is quoted only in its title, and the title page is given in substance, not quoted. The key plan and the voice counts of the fugues were counted by script. Details that could not be verified are not given, among them the number of preludes in the Clavier-Büchlein, the publishers of 1801, the spelling of the keys in the autograph and Bach’s older key signatures, the further subjects of the C sharp minor fugue, the particular devices of the D sharp minor fugue, the tempo markings of the last pair, the date and key range of Fischer’s Ariadne musica, Bach’s later revisions, early reports of Beethoven’s playing, a remark attributed to Bülow, and which recording was first; the running time is a range across the recorded tradition, not a measurement. The sound of the work as heard is beyond this reading and is neither credited nor charged.