The Fifth Desk · Evaluation
Act I · The Map
Johann Sebastian Bach · an Aria with thirty variations, BWV 988, the fourth part of the Clavier-Übung · thirty-two pieces on one bass, the Aria first and last · for harpsichord with two manuals, and now as often on the piano · from under forty minutes to over eighty in performance, as the repeats are taken or left
Mode
Keyboard variations on a ground; canon, dance, fughetta, overture, lament and quodlibet on one bass
Mythos
The journey out and the homecoming; a ladder of canons climbing one interval at a time to the ninth
Phase
An Aria, thirty variations and the Aria again; two halves of sixteen, the second opened by an overture; G major, three variations in G minor
Presentation
Concert music; thirty-two pieces for harpsichord with two manuals, with the print’s repeat signs, issued as the fourth part of the Clavier-Übung
Register
From a slow lament in G minor to street songs and hand-crossing bravura; no word sung or printed in the music
Scale
One bass and the characters of an age: court, church, dance floor, kitchen; under forty minutes to over eighty
Governing Proposition
An Aria of thirty-two bars is laid down and its tune set aside: thirty variations keep only its bass and its harmony, and on them build canons at every interval from the unison to the ninth, dances, a fughetta, an overture, a lament and a pair of street songs, before the Aria returns note for note. The wager of the work is that one law can hold every character of an age, and that the same notes, heard again after the journey, are not the same music.
Act II · The Essay
Movement I
The work begins with a sarabande in G major, in 3/4, thirty-two bars long, in two halves of sixteen, each half repeated. The melody is heavily ornamented, so decorated that the ornament is much of what is heard. Beneath it the bass moves plainly. Its first eight notes are G, F sharp, E, D, B, C, D, G: a falling tetrachord and a cadence. The harmony keeps a fixed plan, from G major at the first bar to a half close on D at the eighth, a cadence in D major at the sixteenth, and home to G at the thirty-second.
The Aria is copied into the second notebook of Anna Magdalena Bach, the book begun in 1725. When it was entered there, and whether Bach himself composed it, have both been questioned, and the question is open. Nothing in the cycle depends on the answer. What the cycle takes from the Aria is not its tune but its bass and the harmony the bass carries, and on those the thirty variations are built.
That is the decision on which everything rests. The tune of the Aria, the thing a listener would carry away from it, is not heard again until the end. For thirty pieces the melody is withheld while its ground goes on under every surface: under canons, dances, a fugue, an overture, a lament and a joke. The listener hears the law by hearing it survive. And because the tune is gone, its return is required. The first piece of the work compels the last.
Movement II
The work was published at Nuremberg by Balthasar Schmid, by the accepted date in 1741; the print itself is undated. It was issued as the fourth and last part of Bach’s Clavier-Übung, after the six Partitas, collected in 1731, the Italian Concerto and French Overture of 1735, and the organ volume of 1739. Its title page names the instrument: “vors Clavicimbal mit 2 Manualen”
“for the harpsichord with two manuals.” And it names the purpose: “Denen Liebhabern zur Gemüths-Ergetzung verfertiget”
“prepared for music lovers, for the refreshment of their spirits.” The most learned keyboard work of its age was offered to amateurs, and few amateurs could play it.
The two manuals are part of the design. On one keyboard two hands crossing would collide; on two they pass through each other, each line keeping its own place. Most of the virtuoso variations are written for the crossing, and several are made of little else. On the modern piano, where the larger part of the work’s modern life has been spent, the crossings are redistributed on one keyboard. That is a change of instrument, not of the work.
The variations fall into ten groups of three. On the usual reading each group holds a character or genre piece, a virtuoso piece and a canon, in that order, and the pattern bends in places. The canons climb. Var. 3 is a canon at the unison, two voices on the same note; Var. 6 is at the second, Var. 9 at the third, and so on, one interval wider at every third variation, each over a free bass that obeys the Aria’s harmony. Between them Var. 10 is a Fughetta, the old learned style on a dance’s bass, and Var. 13 draws a long ornamented line that rises by beauty alone.
Movement III
Var. 15 closes the first half. It is the first variation in G minor, and its canon is at the fifth in contrary motion, the second voice answering the first upside down. It is slow, and it is a lament. The law has not changed: the bass and its cadences are the Aria’s, turned to the minor. A canon at a fixed interval, inverted, over a free bass bound to a given harmony, is among the hardest tasks in counterpoint, and here it sounds only like grief.
Var. 16 opens the second half as a French overture: a dotted, grand opening in the manner of a court, then a fugal second part in 3/8. The cycle has thirty-two pieces, the Aria, thirty variations and the Aria again, and they fall into two halves of sixteen, as the Aria’s thirty-two bars fall into two halves of sixteen. The Ouverture stands where the Aria’s own second half begins. The proportion of the theme is the proportion of the whole.
Var. 21 is the second canon in the minor, at the seventh, over a chromatic descending bass. Var. 22 is marked Alla breve and written in the old motet style, the church’s counterpoint set on a sarabande’s harmony. The court, the church and the dance floor have now all been heard on one bass. Some of the pieces between are lighter, and a few could stand in another group without the plan noticing: the law holds them all, but the order does not need every one.
Movement IV
Var. 25 is the third and last in G minor. It is slow, its line moves chromatically over the bass, and its harmony is as advanced as anything Bach wrote. It is the deepest grief in the cycle, and it comes late. Then the music turns outward. Var. 27, the canon at the ninth, is for two voices only, with no free bass beneath them: the last rung of the ladder is stripped bare. Var. 28 and 29 are brilliance at the keyboard’s limit, trills and hand-crossing, the two manuals played as one instrument.
Var. 30 stands where a canon at the tenth would stand, and it is not a canon. It is a Quodlibet: two popular songs combined in counterpoint over the Aria’s bass. One is the song that begins “Kraut und Rüben”
“cabbage and turnips”, whose singer has been driven away by them. The other, in sense, is a song of having been too long away. Forkel connects the piece with the quodlibets the Bach family sang at their gatherings. The learned ladder, unison to ninth, ends in a kitchen and a street.
The joke is placed. It comes immediately before the return, and both its songs are about home: being driven from it by poor food, and being away from it too long. Instrumental music keeps the particular thinly, and this is the one particular the cycle admits, and it is deliberately small. It names no person and no place. It says only that the traveller has been gone a long time, and in the next piece the Aria comes back.
Movement V
The Aria returns note for note as it began. Nothing in the score is changed, and it cannot be heard as the same. Thirty variations have carried its bass through every character the age knew, and the tune that was set aside comes back carrying all of them. It is the cycle’s last elevation and its largest, and it is quiet. Without it the work has no ending; with it the law is proved at the end, by stripping the surface back to where it began. The same notes are not the same music.
The name comes from J. N. Forkel’s biography of Bach, published in 1802. Forkel tells that Count Hermann Carl von Keyserlingk, Russian envoy at the Dresden court, could not sleep, and asked for keyboard pieces his young harpsichordist, Johann Gottlieb Goldberg, could play to him at night, and that he rewarded Bach with a golden goblet holding a hundred louis d’or. The story is reported, not documented. The print carries no dedication, and Goldberg, born in 1727, was about fourteen in 1741. After Bach’s death the work was known to players and was printed in the collected edition by the 1850s, but it was rarely played in public before the twentieth century.
Wanda Landowska’s harpsichord recording was among the first complete recordings. Glenn Gould recorded the work in New York in June 1955, and Columbia issued it in 1956; it became the central keyboard record of its age. He recorded it again in 1981, and the second recording, released in 1982 shortly before his death that October, reconsiders the first. In 1974 Bach’s own copy of the print was found in Strasbourg, with his corrections and added markings, and with fourteen canons in his hand on the first eight notes of the Aria’s bass. Thomas Bernhard made the work the subject of Der Untergeher (1983), and Richard Powers the frame of The Gold Bug Variations (1991). It has been arranged for string trio, for orchestra and in jazz, and it remains what it was in 1741: thirty readings of one bass, and a return.
Act III · The Twelve
The large plan resists the subtractive test. The canons climb one interval at every third variation, unison to ninth, so no canon can go without breaking the ladder. Ten groups of three, two halves turning on the Ouverture, and thirty-two pieces answer the Aria’s thirty-two bars. The return is compelled by the first piece, whose tune the variations leave unheard until the end. The give is in the free variations: within a group the character piece and the virtuoso piece could change places, and to lose Var. 17 or Var. 20 would cost brilliance, not a step in the argument. Performances without most of the repeats lose less than their length.
Score: 8.8 / 10
The disclosure can be stated, and it holds: the strictest law and the freest play are one activity. Nine canons, each bound to an interval and to the bass, are as unlike as the lament of Var. 15 and the light two voices of Var. 27. A second truth is shown, not asserted: return after a journey is not repetition. The Aria da capo is note for note what began the work, and it cannot be heard as the same. Held down by what it discloses of a human condition: Var. 25 opens grief and the Quodlibet homesickness, but the cycle is a gallery of characters in a frame, not a consciousness passing through them.
Score: 8.4 / 10
Height is reached, and it returns: Var. 25, slow and chromatic in G minor, the deepest grief in the cycle; Var. 15, the inverted canon that closes the first half; Var. 21, a canon over a chromatic descending bass; the Ouverture’s dotted grandeur; and the Aria’s return after the Quodlibet, the last and largest elevation, and quiet. The Aria and Var. 13 rise by beauty; Var. 28 and 29 are the sublime of energy, brilliance at the keyboard’s limit. Held below the top because the register is mostly delight: Var. 4, Var. 19 and the virtuoso pieces are wit, dance and display, elevated in craft more than in transport.
Score: 8.9 / 10
One archetype is built, not evoked: the journey out and the homecoming. The Aria departs, its harmony carries the cycle through thirty worlds, and the last variation before the return is a pair of songs about being driven off by poor food and being too long away. Then the Aria comes home; without it the work has no ending. The ladder of canons is a second figure, an ascent, and it bears weight too. Held down by the particular, which instrumental music keeps thinly: no person, place or act is named. The numbers are allusion the work allows, not construction it needs, and the Quodlibet’s songs, the one particular, are deliberately small.
Score: 8.4 / 10
The inheritance is the keyboard variation set and the ground: Sweelinck and Byrd, Frescobaldi, Bach’s own Passacaglia and Chaconne. The departures are several: a set built as an architecture of halves and threes; a canon at every interval in order, which no keyboard set had attempted; the genres of the age, overture, fughetta, gigue, the old motet style and bravura, on one bass; and a learned ladder that ends in two street songs. The stake was real but bounded: a wager on counterpoint against the galant, in a print for amateurs that few amateurs could play, risking no post and no commission. The ground was a proven path; the swerve is the synthesis.
Score: 8.7 / 10
Change the form and the work stops knowing what it knows: that one harmonic law can hold unlimited character, and that return transforms. The variation on a ground is the instrument of the first: the bass and its cadences stay, the surface becomes canon, dance, lament and joke, and the law is heard by surviving. The da capo is the instrument of the second. As a suite the work would lose the law; as variations on the tune, the hidden return. The two manuals are form too, letting two lines cross without collision. The joint is in the free variations, where the group of three is a container the pieces fill, not a form that thinks.
Score: 9.4 / 10
Evidence, not promise, and mostly of the last century. The work has been answered on harpsichord and piano, with and without repeats, slow and fast, each answer contested; one pianist recorded it in 1955 and again in 1981, the second a documented reconsideration of the first. The questions stay open: whether the Aria is Bach’s, how far the plan of threes governs, what the fourteen canons in Bach’s own copy show of the bass, whether the numbers mean anything. The arrangements and the novels of Bernhard and Powers are a record of yield. Held below the top because the evidence is concentrated after 1900; before then the work was rarely heard in public.
Score: 9.4 / 10
The work reorganised what a variation set could be: from a sequence of ornamentations to a cyclic architecture with a law, a ladder and a return. Delayed influence is credited and discounted: the work was little played in public for a century and a half, and its reach is more of performance than of composition. Achieved reach is scored with intrinsic force: the great variation cycles stand in its line, Beethoven’s Diabelli Variations of 1823 first among them, then Brahms, the line credited, not each link; Glenn Gould’s recording of 1955 made it the central keyboard record of its age and redirected how Bach is played on the piano. The field is Western keyboard music.
Score: 8.9 / 10
Survival is weighed in form, presence and fabric. The form survives whole: the print survives, Bach’s corrected copy was recovered in 1974, and nothing is lost or in doubt beyond the Aria’s authorship. The cost is in presence. Known to players and to Forkel after 1750, and in the collected edition by the 1850s, the work was rarely performed in public before the twentieth century: a gap of hearing, not of loss. Since the 1930s it has been among the most performed and recorded keyboard works. The surface fixed to its moment is small, the dances and the overture now heard as characters, not fashion, and it has outlived its instrument.
Score: 9.2 / 10
The making bears weight throughout. Nine canons at nine intervals each sound like a character piece, not an exercise, and eight carry a free bass that obeys the Aria’s harmony; the canon at the fifth in contrary motion is also a lament. The Ouverture sets a French overture on a sarabande’s bass. The Quodlibet fits two popular tunes into counterpoint over that bass without strain. The chromatic harmony of Var. 25 is as advanced as anything Bach wrote, and the hand-crossing variations use two manuals as a medium, not a convenience. No passage falls short of its intention. A tenth or two below the ceiling, because some free variations are, by Bach’s standard, routine figuration.
Score: 9.7 / 10
Take the two most distant elements: the Aria’s ornamented sarabande and the Quodlibet’s street songs, or the lament of Var. 25 and the bravura of Var. 29. One law governs them all: the same bass, with the same cadences at the same places, under every surface, and the G minor variations keep the plan with the harmony turned to the minor. The range is the widest a keyboard work of its century holds: dance and church style, court overture and folk song, grief and joke, strict canon and free display. The canon ladder is a second law, the halves a third. The axis stops short of the top only where a free variation could change groups unnoticed.
Score: 9.6 / 10
A wordless keyboard cycle holds more orders than its medium suggests, through its genres: the court in the French overture; the church and the learned tradition in the canons and the alla breve; the dance floor in the gigue and the sarabande; the street and the household in the Quodlibet, which Forkel connects with the Bach family’s sung quodlibets; private grief in the minor variations; time and memory in the return. They are held on one bass, not listed. What holds the axis here is absence: the state, labour, history, the natural order and the sacred named as such do not appear, and the family enters only through a joke.
Score: 7.4 / 10
Act IV · The Reckoning
8.9 / 10 · Final Average
Placement: Tier IV · Canonical
Strongest Dimensions
The Made at 9.7, then The Inner Law at 9.6, with The Living Form and The Bottomless Well at 9.4. Nine canons at nine intervals, each a character piece, over a bass whose harmony never fails; one law, the bass and its cadences, governing the sarabande and the street songs, the lament and the bravura; a form whose ground and return are what the work knows; and a well of performance and analysis still open.
Limiting Dimension
The Encompassed at 7.4: court, church, dance floor, street, private grief and memory are held on one bass, but the state, labour, history, the natural order and the sacred named as such are absent. Next above it, The Unconcealment and The Archetypal Deep at 8.4 each, which share a cause: the cycle discloses law, play and time more than a human condition, and the homecoming it builds keeps the particular thin.
The Necessity Cap clears at 8.8 against a threshold of 7.5. The Coherence Floor clears with room: The Made at 9.7, The Inner Law at 9.6, The Living Form at 9.4, each against 7.0. The Epochal Gate is unmet: The Imperishable at 9.2, Pressure on Tradition at 8.9 and The Swerve at 8.7 clear the bar of 8.5, but The Unconcealment at 8.4 and The Archetypal Deep at 8.4 fall a tenth short. The Universal Minimum is met: no axis but The Encompassed falls below 8.4, against 7.5, and The Encompassed, which is exempted, 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 8.9 the work stands in Tier IV.
Basis · the score of the Aria with thirty variations, BWV 988, as published at Nuremberg by Balthasar Schmid, by the accepted date in 1741 (the print is undated), and its performance tradition, read from knowledge under the desk’s convention for concert music; no score, edition or recording was in hand. The unit is the print, thirty-two pieces with its repeat signs, together with Bach’s own corrections and added markings in his copy of it, found in Strasbourg in 1974, which are part of the one work. The fourteen canons on the bass in that copy, catalogued as BWV 1087, are not in the print and stand outside the unit; they are evidence only. Performances, recordings and arrangements are evidence, and no single one is the object. The move from two manuals to the piano is a change of instrument and is neither credited nor charged. The name is the one in use, and nothing here rests on the story behind it. The only words in the work belong to the two songs of the Quodlibet, which are neither sung nor printed with text. German is quoted only where the desk is certain of it: two phrases of the title page and the opening words of one song; every English gloss is the desk’s own. The plan of the cycle was counted by script. Details that could not be verified, among them the station of the Aria’s harmony in its last quarter, the inversion of a second canon, the date of the Aria’s entry in the notebook, the editions after the first collected one and the dates of several recordings, arrangements and studies, are not given; 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.