After a statement of the aria at the beginning of the piece, there are thirty variations. The variations do not follow the melody of the aria, but rather use its
bass line () and
chord progression. The bass line is notated by harpsichordist and musicologist
Ralph Kirkpatrick in his performing edition as follows. \relative { \key g \major \clef bass \omit Staff.TimeSignature \repeat volta 2 { g1 fis^"6" e^"3,5,6♯" d b^"6" c^"3,5,6" d g, \break g' fis^"6" e a^"♯" fis^"6" g^"6" a^"♯" d, } \break \repeat volta 2 { d' b^"6" c^"6" b^"♯" g^"6" a^"3,5,6" b^"♯" e, \break c^"6" b^"6" a d g, c^"3,5,6" d g, } } The digits above the notes indicate the specified chord in the system of
figured bass; where digits are separated by comma (stacked vertically in a proper figured bass), they indicate seventh chords in first inversion. Every third variation in the series of 30 is a
canon, following an ascending pattern. Thus, variation 3 is a canon at the unison, variation 6 is a canon at the second (the second entry begins the interval of a
second above the first), variation 9 is a canon at the third, and so on until variation 27, which is a canon at the ninth. The final variation, instead of being the expected canon in the tenth, is a
quodlibet, discussed below. As Kirkpatrick has pointed out, the variations that intervene between the canons are also arranged in a pattern. If we leave aside the initial and final material of the work (specifically, the Aria, the first two variations, the Quodlibet, and the aria da capo), the remaining material is arranged as follows. The variations found just
after each canon are genre pieces of various types, among them three
Baroque dances (4, 7, 19); a
fughetta (10); a
French overture (16); two ornate arias for the right hand (13, 25); and others (22, 28). The variations located
two after each canon (5, 8, 11, 14, 17, 20, 23, 26, and 29) are what Kirkpatrick calls "arabesques"; they are variations in lively tempo with a great deal of hand-crossing. This ternary pattern—
canon,
genre piece,
arabesque—is repeated a total of nine times, until the Quodlibet breaks the cycle. All the variations are in G major, apart from variations 15, 21, and 25, which are in G minor. At the end of the thirty variations, Bach writes
Aria da Capo e fine, meaning that the performer is to return to the beginning ("
da capo") and play the aria again before concluding.
Aria The aria is a
sarabande in
time, and features a heavily
ornamented melody: \new PianoStaff > >> The French style of ornamentation suggests that the ornaments are supposed to be parts of the melody; however, some performers (for example
Wilhelm Kempff on piano) omit some or all ornaments and present the aria unadorned.
Williams opines that this is not the theme at all, but actually the first variation (a view emphasising the idea of the work as a
chaconne rather than a piece in true
variation form).
Variatio 1. a 1 Clav. This sprightly variation contrasts markedly with the slow, contemplative mood of the aria. The rhythm in the right hand forces the emphasis on the second beat, giving rise to
syncopation from bars 1 to 7. Hands cross at bar 13 from the upper register to the lower, bringing back this syncopation for another two bars. In the first two bars of the B part, the rhythm mirrors that of the beginning of the A part, but after this a different idea is introduced. Williams sees this as a sort of
polonaise. The characteristic rhythm in the left hand is also found in Bach's
Partita No. 3 for solo violin, in the A major prelude from the first book of
The Well-Tempered Clavier, and in the D minor prelude of the second book. Heinz Niemüller also mentions the polonaise character of this variation.
Variatio 2. a 1 Clav. This is a simple three-part contrapuntal piece in time, two voices engage in constant motivic interplay over an incessant bass line. Each section has an alternate ending to be played on the first and second repeat.
Variatio 3. Canone all'Unisono. a 1 Clav. The first of the regular canons, this is a canon at the unison: the follower begins on the same note as the leader, a bar later. As with all canons of the
Goldberg Variations (except the 27th variation, canon at the ninth), there is a supporting bass line. The time signature of and the many sets of
triplets suggest a kind of a simple dance.
Variatio 4. a 1 Clav. Like the
passepied, a Baroque dance movement, this variation is in time with a preponderance of quaver rhythms. Bach uses close but not exact
imitation: the musical pattern in one part reappears a bar later in another (sometimes
inverted). \new PianoStaff > \new Staff > >> Each repeated section has alternate endings for the first or second time.
Variatio 5. a 1 ô vero 2 Clav. This is the first of the hand-crossing, two-part variations; the title means "for one or two manuals". The movement is written in time. A rapid melodic line predominantly in sixteenth notes is accompanied by another melody with longer note values, which features very wide leaps: \new PianoStaff > The Italian type of hand-crossing such as is frequently found in the sonatas of
Scarlatti is employed here, with one hand constantly moving back and forth between high and low
registers while the other hand stays in the middle of the keyboard, playing the fast passages.
Variatio 6. Canone alla Seconda. a 1 Clav. The sixth variation is a canon at the second: the follower starts a major second higher than the leader. The piece is based on a descending scale and is in time. Kirkpatrick describes this piece as having "an almost nostalgic tenderness". Each section has an alternate ending to be played on the first and second repeat.
Variatio 7. a 1 ô vero 2 Clav. al tempo di Giga The variation is in meter, suggesting several possible Baroque dances. In 1974, when scholars discovered Bach's own copy of the first printing of the
Goldberg Variations, they noted that over this variation Bach had added the heading
al tempo di Giga. But the implications of this discovery for modern performance have turned out to be less clear than was at first assumed. In his book
The Keyboard Music of J. S. Bach the scholar and keyboardist David Schulenberg notes that the discovery "surprised twentieth-century commentators who supposed gigues were always fast and fleeting." However, "despite the Italian terminology [
giga], this is a [less fleet] French gigue." Indeed, he notes, the dotted rhythmic pattern of this variation (pictured) is very similar to that of the gigue from Bach's second
French suite and the gigue of the
French Overture. This kind of gigue is known as a "Canary", based on the rhythm of a dance which originated from the Canary islands. \new PianoStaff > He concludes, "It need not go quickly." Moreover, Schulenberg adds that the "numerous short
trills and
appoggiaturas" preclude too fast a tempo. The pianist
Angela Hewitt, in the liner notes to her 1999 Hyperion recording, argues that by adding the
al tempo di giga notation, Bach was trying to caution against taking too slow a tempo, and thus turning the dance into a
forlane or
siciliano. She does however argue, like Schulenberg, that it is a French
gigue, not an Italian
giga and does play it at an unhurried tempo.
Variatio 8. a 2 Clav. This is another two-part hand-crossing variation, in time. The French style of hand-crossing such as is found in the clavier works of
François Couperin is employed, with both hands playing at the same part of the keyboard, one above the other. This is relatively easy to perform on a two-manual harpsichord, but quite difficult to do on a piano. Most bars feature either a distinctive pattern of eleven
sixteenth notes and a sixteenth rest, or ten sixteenth notes and a single
eighth note. Large leaps in the melody occur. Both sections end with descending passages in
thirty-second notes.
Variatio 9. Canone alla Terza. a 1 Clav. This is a canon at the third, in time. The supporting bass line is slightly more active than in the previous canons.
Variatio 10. Fughetta. a 1 Clav. Variation 10 is a four-voice fughetta, with a four-bar subject heavily decorated with
ornaments and somewhat reminiscent of the opening aria's melody. \new PianoStaff > \new Staff > >> The exposition takes up the whole first section of this variation (pictured). First the subject is stated in the bass, starting on the G below middle C. The answer (in the tenor) enters in bar 5, but it's a tonal answer, so some of the intervals are altered. The soprano voice enters in bar 9, but only keeps the first two bars of the subject intact, changing the rest. The final entry occurs in the alto in bar 13. There is no regular counter-subject in this fugue. The second section develops using the same thematic material with slight changes. It resembles a counter-exposition: the voices enter one by one, all begin by stating the subject (sometimes a bit altered, like in the first section). The section begins with the subject heard once again, in the soprano voice, accompanied by an active bass line, making the bass part the only exception since it doesn't pronounce the subject until bar 25.
Variatio 11. a 2 Clav. This is a virtuosic two-part
toccata in time. Specified for two manuals, it is largely made up of various
scale passages,
arpeggios and trills, and features much hand-crossing of different kinds.
Variatio 12. a 1 Clav. Canone alla Quarta in moto contrario This is a canon at the fourth in time, of the inverted variety: the follower enters in the second bar in
contrary motion to the leader. In the first section, the left hand accompanies with a bass line written out in repeated quarter notes, in bars 1, 2, 3, 5, 6, and 7. This repeated note motif also appears in the first bar of the second section (bar 17, two Ds and a C), and, slightly altered, in bars 22 and 23. In the second section, Bach changes the mood slightly by introducing a few
appoggiaturas (bars 19 and 20) and trills (bars 29–30).
Variatio 13. a 2 Clav. This variation is a slow, gentle and richly decorated sarabande in time. Most of the melody is written out using thirty-second notes, and ornamented with a few appoggiaturas (more frequent in the second section) and a few
mordents. Throughout the piece, the melody is in one voice, and in bars 16 and 24 an interesting effect is produced by the use of an additional voice. Here are bars 15 and 16, the ending of the first section (bar 24 exhibits a similar pattern): \new PianoStaff > | \bar ":|." } \new Staff > >>
Variatio 14. a 2 Clav. This is a rapid two-part hand-crossing toccata in time, with many trills and other ornamentation. It is specified for two manuals and features large jumps between registers. Both features (ornaments and leaps in the melody) are apparent from the first bar: the piece begins with a transition from the G two octaves below middle C, with a lower mordent, to the G two octaves above it with a trill with initial turn. Bach uses a loose inversion motif between the first half and the second half of this variation, "recycling" rhythmic and melodic material, passing material that was in the right hand to the left hand, and loosely (selectively) inverting it. Contrasting it with Variation 15,
Glenn Gould described this variation as "certainly one of the giddiest bits of neo-Scarlatti-ism imaginable."
Variatio 15. Canone alla Quinta. a 1 Clav.: Andante This is a canon at the fifth in time. Like Variation 12, it is in contrary motion with the leader appearing inverted in the second bar. This is the first of the three variations in G minor, and its melancholic mood contrasts sharply with the playfulness of the previous variation. Pianist Angela Hewitt notes that there is "a wonderful effect at the very end [of this variation]: the hands move away from each other, with the right suspended in mid-air on an open fifth. This gradual fade, leaving us in awe but ready for more, is a fitting end to the first half of the piece." Glenn Gould said of this variation, "It's the most severe and rigorous and beautiful canon ... the most severe and beautiful that I know, the canon in inversion at the fifth. It's a piece so moving, so anguished—and so uplifting at the same time—that it would not be in any way out of place in the St. Matthew's Passion; matter of fact, I've always thought of Variation 15 as the perfect Good Friday spell."
Variatio 19. a 1 Clav. This is a dance-like three-part variation in time. The same sixteenth note figuration is continuously employed and variously exchanged between each of the three voices. This variation incorporates the rhythmic model of variation 13 (complementary exchange of quarter and sixteenth notes) with variations 1 and 2 (syncopations).
Variatio 20. a 2 Clav. This variation is a virtuosic two-part toccata in time. Specified for two manuals, it involves rapid hand-crossing. The piece consists mostly of variations on the texture introduced during its first eight bars, where one hand plays a string of eighth notes and the other accompanies by plucking sixteenth notes after each eighth note. To demonstrate this, here are the first two bars of the first section: \new PianoStaff >
Variatio 21. Canone alla Settima The second of the three minor key variations, variation 21 has a tone that is somber or even tragic, which contrasts starkly with variation 20. The bass line here is one of the most eloquent found in the variations, to which Bach adds
chromatic intervals that provide tonal shadings. The bass line begins the piece with a low note, proceeds to a slow
lament bass and only picks up the pace of the canonic voices in bar 3: \new PianoStaff > >> A similar pattern, only a bit more lively, occurs in the bass line in the beginning of the second section, which begins with the opening motif inverted.
Variatio 22. a 1 Clav. alla breve This variation features four-part writing with many imitative passages and its development in all voices but the bass is much like that of a fugue. The only specified ornament is a trill which is performed on a
whole note and which lasts for two bars (11 and 12). The
ground bass on which the entire set of variations is built is heard perhaps most explicitly in this variation (as well as in the Quodlibet) due to the simplicity of the bass voice.
Variatio 23. a 2 Clav. Another lively two-part virtuosic variation for two manuals, in time. It begins with the hands chasing one another, as it were: the melodic line, initiated in the left hand with a sharp striking of the G above middle C, and then sliding down from the B one octave above to the F, is offset by the right hand, imitating the left at the same pitch, but a quaver late, for the first three bars, ending with a small flourish in the fourth: \new PianoStaff > This pattern is repeated during bars 5–8, only with the left hand imitating the right one, and the scales are ascending, not descending. We then alternate between hands in short bursts written out in short note values until the last three bars of the first section. The second section starts with this similar alternation in short bursts again, then leads to a dramatic section of alternating thirds between hands.
Williams, marvelling at the emotional range of the work, asks: "Can this really be a variation of the same theme that lies behind the adagio no 25?"
Variatio 24. Canone all'Ottava. a 1 Clav. This variation is a canon at the octave, in time. The leader is answered both an octave below and an octave above; it is the only canon of the variations in which the leader alternates between voices in the middle of a section.
Variatio 25. a 2 Clav.: Adagio Variation 25 is the third and last variation in G minor; it is marked
adagio in Bach's own copy and is in time. The melody is written out predominantly in sixteenth and thirty-second notes, with many
chromaticisms. This variation generally lasts longer than any other piece of the set.
Wanda Landowska famously described this variation as "the black pearl" of the
Goldberg Variations. Williams writes that "the beauty and dark passion of this variation make it unquestionably the emotional high point of the work", and Glenn Gould said that "the appearance of this wistful, weary
cantilena is a master-stroke of psychology." In an interview with Gould,
Tim Page described this variation as having an "extraordinary chromatic texture"; Gould agreed: "I don't think there's been a richer lode of
enharmonic relationships any place between
Gesualdo and
Wagner." Forkel's anecdote led to the belief that it is composed from German
Volkslied melodies, as if to evoke the Bach gatherings. Since folk tunes commonly shared melodies, music alone does not identify the songs intended. For example, part of Variation 30 traces back to the melody of the Italian
Bergamask dance, A handwritten note found in a collector's copy of the
Clavier Ubung claims that Bach's student,
Johann Christian Kittel, identified two folk tunes making up Variation 30 by their first lines.
Siegfried Dehn of the Prussian royal library later appended purported full texts to this note: • ''Ich bin solang nicht bei dir g'west, ruck her, ruck her'' ("I have so long been away from you, come closer, come closer") and • ''Kraut und Rüben haben mich vertrieben, hätt mein' Mutter Fleisch gekocht, wär ich länger blieben'' ("Cabbage and turnips have driven me away, had my mother cooked meat, I'd have opted to stay"), ascribed to the Bergamask theme. Dehn's texts, though unsourced, stand as the only historical evidence for the provenance of Bach's Quodlibet and are commonly quoted. Today, the identity of "Kraut und Rüben..." is uncontroversial, since multiple versions of the text, including some explicitly set to the Bergamask theme, are preserved. and these words have not been found in any Volkslied archives. Other bars of Variation 30 can be heard as incipits of yet more songs, though none have been identified.
Aria da Capo A note-for-note repeat of the aria at the beginning. Williams writes that the work's "elusive beauty ... is reinforced by this return to the Aria. ... no such return can have a neutral
Affekt. Its melody is made to stand out by what has gone on in the last five variations, and it is likely to appear wistful or nostalgic or subdued or resigned or sad, heard on its repeat as something coming to an end, the same notes but now final." == Canons on the Goldberg ground, BWV 1087 ==