Editing Goldberg Variations (section)

== Form ==
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]] ({{audio|GoldbergVariationsBassLine.mid|Play}}) and [[chord progression]]. The bass line is notated by harpsichordist and musicologist [[Ralph Kirkpatrick]] in his performing edition<ref name="Kirkpatrick 1938">{{harvnb|Kirkpatrick|1938}}</ref> as follows.
<score>
\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,
  }
}
</score>

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 (music)|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 [[interval (music)|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,<ref>{{harvnb|Kirkpatrick|1938|p=viii}}</ref> 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 dance]]s (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 signature|3|4}} [[Time signature|time]], and features a heavily [[Ornament (music)|ornamented]] melody:
<score>
\new PianoStaff <<
 \new Staff \relative c''' {
  \key g \major \time 3/4
  g4 g( a8.)\mordent b16 |
  a8 \appoggiatura g16 fis8 \appoggiatura e16 d2 |
  g,4\mordent g4.\downprall fis16 g |
  a32( g fis16) g32( fis e16) \appoggiatura fis8 d2 |
  d'4 d( e8.)\mordent f16 |
  e8 \appoggiatura d16 c8 \appoggiatura b16 a4. fis'!8\turn |
  g32( fis16.) a32( g16.) fis32( e16.) d32( c16.) \appoggiatura c a'8. c,16 |
  b32( g16.) fis8 \appoggiatura fis g2\mordent |
 }
 \new Staff <<
  \new Voice \relative c' {
   \voiceOne \clef bass \key g \major
   s4 f\rest d |
   s4 e\rest d |
   s4 d\rest cis |
   s4 d\rest a |
   s4 d\rest g, |
   s4 d'\rest a |
   r8 c~ c b16 a g fis e fis |
   g8 a b2 |
  }
  \new Voice \relative c' {
   \voiceThree
   r4 b2 |
   r4 a2 |
   r4 g2 |
   r4 fis2 |
   r4 d2 |
   r4 e4. s8 |
  }
  \new Voice \relative c' {
   \voiceTwo
   g2. |
   fis2. |
   e2. |
   d2~ d8 c |
   b2. |
   c2~ c8 d |
   e8 c d2 |
   g,4. d'8[ e8.^\mordent fis16] |
  }
 >>
>>
</score>
{{listen|type=music|help=no|filename=Goldberg Variations 01 Aria.ogg|title=Aria|description=Performed by [[Kimiko Douglass-Ishizaka]] on piano}}
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.

[[Peter Williams (musicologist)|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. ===
{{listen|type=music|help=no|filename=Goldberg Variations 02 Variatio 1 a 1 Clav.ogg|title=Variatio 1. a 1 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
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 (dance)|polonaise]]. The characteristic rhythm in the left hand is also found in Bach's [[Partita for Violin No. 3 (Bach)|Partita No. 3 for solo violin]], in the A{{music|flat}} 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. ===
{{listen|type=music|help=no|filename=Goldberg Variations 03 Variatio 2 a 1 Clav.ogg|title=Variatio 2. a 1 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is a simple three-part contrapuntal piece in {{time signature|2|4}} 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. ===
{{listen|type=music|help=no|filename=Goldberg Variations 04 Variatio 3 a 1 Clav. Canone all'Unisuono.ogg|title=Variatio 3. a 1 Clav. Canone all'Unisuono|description=Performed by Kimiko Douglass-Ishizaka on piano}}
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 {{time signature|12|8}} and the many sets of [[Tuplet|triplets]] suggest a kind of a simple dance.

=== Variatio 4. a 1 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 05 Variatio 4 a 1 Clav.ogg|title=Variatio 4. a 1 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
Like the [[passepied]], a Baroque dance movement, this variation is in {{time signature|3|8}} time with a preponderance of quaver rhythms. Bach uses close but not exact [[Imitation (music)|imitation]]: the musical pattern in one part reappears a bar later in another (sometimes [[Inverted chord|inverted]]).
<score>
\new PianoStaff <<
 \new Staff <<
  \new Voice \relative c'' {
   \key g \major \time 3/8
   r8 b g |
   \voiceOne d'8 a d |
   g4.~ |
   g8 fis r |
   \oneVoice R1*3/8 |
   \voiceOne R1*3/8 |
   r8 a, c~ |
   c16 a b8 r |
  }
  \new Voice \relative c' {
   \voiceTwo
   s4. |
   r8 d fis |
   b,8 g' c |
   b16 g a8 r |
   s4. |
   r8 c, e |
   a,8 d4~ |
   d8 g r |
  }
 >>
 \new Staff <<
  \new Voice \relative c' {
   \clef bass \key g \major \voiceOne
   s4. |
   s4. |
   r8 b g |
   d'4 r8 |
   r8 g, b |
   e,8 a g~ |
   g8 fis16 e fis8 |
   g8 d r |
  }
  \new Voice \relative c' {
   \voiceTwo
   g4. |
   fis4. |
   e4. |
   r8 d fis |
   b,4. |
   c4. |
   d4. |
   r8 b d |
  }
 >>
>>
</score>
Each repeated section has alternate endings for the first or second time.

=== Variatio 5. a 1 ô vero 2 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 06 Variatio 5 a 1 ovvero 2 Clav.ogg|title=Variatio 5. a 1 ô vero 2 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is the first of the hand-crossing, two-part variations; the title means "for one or two manuals".<ref>The Italian usage is somewhat archaic; for details see Wiktionary entry: [https://en.wiktionary.org/wiki/ovvero]</ref> The movement is written in {{time signature|3|4}} time. A rapid melodic line predominantly in sixteenth notes is accompanied by another melody with longer note values, which features very wide leaps:
{{Clear}}
<score>
\new PianoStaff <<
 \new Staff \relative c' {
  \key g \major \time 3/4
  r16 d e fis g fis g a b a g b |
  a16 g fis e d e fis g a fis e d |
  g16 fis e d cis d e fis g b a g |
  fis16 e d cis d a d e fis d fis a |
 }
 \new Staff \relative c' {
  \key g \major \clef bass
  g8 r \clef treble b' r \clef bass g,4 |
  fis8 r \clef treble a' r \clef bass fis,4 |
  e8 r \clef treble g' r \clef bass e,4 |
  d8 r \clef treble fis' r \clef bass d, c! |
 }
>>
</score>
The Italian type of hand-crossing such as is frequently found in the sonatas of [[Domenico Scarlatti|Scarlatti]] is employed here, with one hand constantly moving back and forth between high and low [[Register (music)|registers]] while the other hand stays in the middle of the keyboard, playing the fast passages.

=== Variatio 6. Canone alla Seconda. a 1 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 07 Variatio 6 a 1 Clav. Canone alla Seconda.ogg|title=Variatio 6. a 1 Clav. Canone alla Seconda|description=Performed by Kimiko Douglass-Ishizaka on piano}}
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 signature|3|8}} 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 ===
{{listen|type=music|help=no|filename=Goldberg Variations 08 Variatio 7 a 1 ovvero 2 Clav.ogg|title=Variatio 7. a 1 ô vero 2 Clav. al tempo di Giga|description=Performed by Kimiko Douglass-Ishizaka on piano}}
The variation is in {{time signature|6|8}} 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 [[gigue|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''{{sfn|Schulenberg|2006|page=[https://archive.org/details/keyboardmusicjsb00schu/page/n388 380]}} 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 Suites|French suite]] and the gigue of the ''[[Overture in the French style, BWV 831|French Overture]]''. This kind of gigue is known as a "Canary", based on the rhythm of a dance which originated from the Canary islands.
<score>
\new PianoStaff <<
 \new Staff \relative c'' {
  \key g \major \time 6/8
  b8. a16 b8 d,8. g16 b8 |
  a8.\prall g16 a8 d4. |
  g8.\mordent fis16 g8 a,8. e'16 g8 |
  fis8.\prall e16 fis8 d4. |
 }
 \new Staff \relative c' {
  \key g \major \clef bass
  g4\mordent g,8 g'4.~\mordent |
  g4. fis8.\prall e16 d8 |
  e4 d'8 cis4 a8 |
  d4.~ d8. e16 c8 |
 }
>>
</score>
He concludes, "It need not go quickly." Moreover, Schulenberg adds that the "numerous short [[trill (music)|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 [[siciliana|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. ===
{{listen|type=music|help=no|filename=Goldberg Variations 09 Variatio 8 a 2 Clav.ogg|title=Variatio 8. a 2 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is another two-part hand-crossing variation, in {{time signature|3|4}} 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 note]]s 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 note]]s.

=== Variatio 9. Canone alla Terza. a 1 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 10 Variatio 9 a 1 Clav. Canone alla Terza.ogg|title=Variatio 9. Canone alla Terza. a 1 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is a canon at the third, in {{time signature|4|4}} 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 [[ornament (music)|ornaments]] and somewhat reminiscent of the opening aria's melody.
<score>
\new PianoStaff <<
 \new Staff <<
  \new Voice \relative c''' {
   \key g \major \time 2/2 \voiceOne
   R1*8 |
   g2\mordent g4.\prallprall fis16 g |
   a4 fis d fis |
   b,4 e e, d' |
   cis4\prall b8 c a b c a |
   d4 d, d'2~ |
   d4 d, d'2~ |
   d2 cis |
   d1 | \bar ":|."
  }
  \new Voice \relative c'' {
   \voiceTwo
   R1*10 |
   \once \override MultiMeasureRest.staff-position = -8 R1 |
   R1 |
   a2\mordent a4.\prallprall g16 a |
   b4 g e g |
   e4 a a, g' |
   fis4\prall e8 fis d2 |
  }
 >>
 \new Staff <<
  \new Voice \relative c' {
   \key g \major \clef bass \voiceOne
   \override MultiMeasureRest.staff-position = 4 R1*2 |
   \override MultiMeasureRest.staff-position = 6 R1 |
   \override MultiMeasureRest.staff-position = 4 R1 |
   d2\mordent d4.\prallprall c16 d |
   e4 c a c |
   a4 d d, c' |
   b4\prall a8 b g b a c |
   b8 a b4 e2~ |
   e4 a, d2~ |
   d4 b e2~ |
   e4 d cis e |
   a,8 b a g fis2 |
   g2 r |
   r4 e a2~ |
   a8 a g a fis |
  }
  \new Voice \relative c' {
   \voiceTwo
   g2\mordent g4.\prallprall fis16 g |
   a4 fis d fis |
   e4 a a, g' |
   fis4\prall e8 fis d e c d |
   b8 d e fis g4 b, |
   c2 r4 a |
   fis2 r4 d |
   g4 d' b d |
   g2 r4 e |
   fis2 r4 d |
   g2 r4 e |
   a2 r4 g |
   fis2 r4 d |
   g,4 b g e |
   a2 r4 a |
   d1 |
  }
 >>
>>
</score>
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.

{{listen|type=music|help=no|filename=Goldberg Variations 11 Variatio 10 a 1 Clav. Fughetta.ogg|title=Variatio 10 a 1 Clav. Fughetta|description=Performed by Kimiko Douglass-Ishizaka on piano}}
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. ===
{{listen|type=music|help=no|filename=Goldberg Variations 12 Variatio 11 a 2 Clav.ogg|title=Variatio 11 a 2 Clava|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is a virtuosic two-part [[toccata]] in {{time signature|12|16}} time. Specified for two manuals, it is largely made up of various [[Scale (music)|scale]] passages, [[arpeggio]]s and trills, and features much hand-crossing of different kinds.

=== Variatio 12. a 1 Clav. Canone alla Quarta in moto contrario ===
{{listen|type=music|help=no|filename=Goldberg Variations 13 Variatio 12 Canone alla Quarta.ogg|title=Variatio 12. Canone alla Quarta|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is a canon at the fourth in {{time signature|3|4}} 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 [[appoggiatura]]s (bars 19 and 20) and trills (bars 29–30).

=== Variatio 13. a 2 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 14 Variatio 13 a 2 Clav.ogg|title=Variatio 13 a 2 Clav|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This variation is a slow, gentle and richly decorated sarabande in {{time signature|3|4}} 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 [[mordent]]s. 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):
<score>
\new PianoStaff <<
 \new Staff \relative c'' {
  \key g \major \time 3/4
  cis32 g fis g a g fis g e' cis b cis d cis b cis g' e d e a g fis e |
  << { fis16 cis cis d d g, g fis fis4 } \\ { s4 r8 cis d4 } >> | \bar ":|."
 }
 \new Staff <<
  \new Voice \relative c' {
   \key g \major \clef bass \voiceOne
   a8[ cis] g' e cis4 |
   d8[ e,] f bes a4 |
  }
  \new Voice \relative c {
   \voiceTwo
   a8 a'16. g32 a4. a8 |
   d,2. |
  }
 >>
>>
</score>

=== Variatio 14. a 2 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 15 Variatio 14 a 2 Clav.ogg|title=Variatio 14. a 2 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is a rapid two-part hand-crossing toccata in {{time signature|3|4}} 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."<ref name="Gould Page">{{harvnb|Gould|Page|2002}}</ref>

=== Variatio 15. Canone alla Quinta. a 1 Clav.: Andante ===
{{listen|type=music|help=no|filename=Goldberg Variations 16 Variatio 15 a 1 Clav. Canone alla Quinta.ogg|title=Variatio 15 a 1 Clav. Canone alla Quinta|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is a canon at the fifth in {{time signature|2|4}} 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."<ref name="Gould Page" />

=== Variatio 16. Ouverture. a 1 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 17 Variatio 16 a 1 Clav. Ouverture.ogg|title=Variatio 16 a 1 Clav. Ouverture|description=Performed by Kimiko Douglass-Ishizaka on piano}}
The entire set of variations can be seen as being divided into two halves, clearly marked by this grand French overture, commencing with particularly emphatic opening and closing [[chord (music)|chords]]. It consists of a slow prelude with dotted [[rhythm]]s with a following fugue-like [[counterpoint|contrapuntal]] section. Here Bach follows his custom of beginning the second half of a major collection with a movement in French style, as with the earlier ''[[Clavier-Übung (Bach)|Clavier-Übung]]'' volumes, in both parts of the ''Well-Tempered Clavier'', in the ''[[Musical Offering]]'' (#4 of the numbered canons) and in the early version of the ''[[Art of Fugue]]'' (#7 of P 200).

=== Variatio 17. a 2 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 18 Variatio 17 a 2 Clav.ogg|title=Variatio 17 a 2 Clav|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This variation is another two-part virtuosic toccata. [[Peter Williams (musicologist)|Peter Williams]] sees echoes of [[Antonio Vivaldi]] and [[Domenico Scarlatti]] here. Specified for two manuals, the piece features hand-crossing. It is in {{time signature|3|4}} time and usually played at a moderately fast tempo. [[Rosalyn Tureck]] is one of the very few performers who recorded slow interpretations of the piece. In making his 1981 re-recording of the ''Goldberg Variations'', Glenn Gould considered playing this variation at a slower tempo, in keeping with the tempo of the preceding variation (Variation 16), but ultimately decided not to because "Variation 17 is one of those rather skittish, slightly empty-headed collections of scales and arpeggios which Bach indulged when he wasn't writing sober and proper things like fugues and canons, and it just seemed to me that there wasn't enough substance to it to warrant such a methodical, deliberate, Germanic tempo."<ref name="Gould Page" />

=== Variatio 18. Canone alla Sesta. a 1 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 19 Variatio 18 a 1 Clav. Canone alla Sexta.ogg|title=Variatio 18 a 1 Clav. Canone alla Sexta|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is a canon at the sixth in {{time signature|2|2}} time. The canonic interplay in the upper voices features many [[Suspension (music)|suspensions]]. Commenting on the structure of the canons of the ''Goldberg Variations'', Glenn Gould cited this variation as the extreme example of "deliberate duality of motivic emphasis ... the canonic voices are called upon to sustain the [[Passacaglia|passacaille]] role which is capriciously abandoned by the bass." [[Nicholas Kenyon]] calls Variation 18 "an imperious, totally confident movement which must be among the most supremely logical pieces of music ever written, with the strict imitation to the half-bar providing ideal impetus and a sense of climax."<ref>[[Nicholas Kenyon|Kenyon, Nicholas]]. ''[https://books.google.com/books?id=x1fm8XWwvJkC&pg=PA421 The Faber Pocket Guide to Bach]'', p. 421 (Faber & Faber, 2011).</ref>

=== Variatio 19. a 1 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 20 Variatio 19 a 1 Clav.ogg|title=Variatio 19. a 1 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This is a dance-like three-part variation in {{time signature|3|8}} 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).<ref>Melamed, Daniel. ''[https://books.google.com/books?id=ixadkfy40bwC&pg=PA67 Bach Studies 2]'', p. 67 (Cambridge University Press 2006).</ref>

=== Variatio 20. a 2 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 21 Variatio 20 a 2 Clav.ogg|title=Variatio 20 a 2 Clav|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This variation is a virtuosic two-part toccata in {{time signature|3|4}} 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:
<score>
\new PianoStaff <<
 \new Staff \relative c'' {
  \key g \major \time 3/4
  r16 b r g r d r b r \clef bass g fis e |
  fis8 a \clef treble d fis a d |
 }
 \new Staff \relative c' {
  \key g \major
  g8 b d g b cis |
  r16 d r a r fis r d r \clef bass a g fis |
 }
>>
</score>

=== Variatio 21. Canone alla Settima ===
{{listen|type=music|help=no|filename=Goldberg Variations 22 Variatio 21 Canone alla Settima.ogg|title=Variatio 21 Canone alla Settima|description=Performed by Kimiko Douglass-Ishizaka on piano}}
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.<ref name=Lederer>Lederer, Victor. ''[https://books.google.com/books?id=cWZGBqb5iMMC&pg=PA121 Bach's Keyboard Music]'', p. 121 (Hal Leonard Corporation, 2010).</ref> The bass line here is one of the most eloquent found in the variations, to which Bach adds [[chromatic interval]]s that provide tonal shadings.<ref name=Lederer /> This variation is a canon at the seventh in {{time signature|4|4}} time; [[Kenneth Gilbert]] sees it as an [[allemande]] despite the lack of [[anacrusis]].<ref name=gilbert>Notes to Kenneth Gilbert's recording of the variations.</ref> 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:
<score>
\new PianoStaff <<
 \new Staff \relative c'' {
  \key g \minor
  r2 r16 a bes c d c bes a |
  g8 d' g, c~ c16 fis, g a bes a g fis |
  g8 r r g as g as a |
 }
 \new Staff <<
  \new Voice \relative c' {
   \key g \minor \clef bass \voiceOne
   r16 bes c d es d c bes a8 es' a, d~ |
   d16 g, a bes c bes a g a8 r r a |
   bes8 a bes b c16 d es d c bes a g |
  }
  \new Voice \relative c {
   \voiceTwo
   g4 g' fis f |
   e4 es d16 a bes c d8 d, |
   g16 d' e fis g f e d c8 b c cis |
  }
 >>
>>
</score>
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 ===
{{listen|type=music|help=no|filename=Goldberg Variations 23 Variatio 22 a 1 Clav.ogg|title=Variatio 22 a 1 Clav|description=Performed by Kimiko Douglass-Ishizaka on piano}}
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. ===
{{listen|type=music|help=no|filename=Goldberg Variations 24 Variatio 23 a 2 Clav.ogg|title=Variatio 23 a 2 Clav|description=Performed by Kimiko Douglass-Ishizaka on piano}}
Another lively two-part virtuosic variation for two manuals, in {{time signature|3|4}} 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:
<score>
\new PianoStaff <<
 \new Staff \relative c'' {
  \key g \major \time 3/4
  r8 g b'16 a g fis e d cis b |
  a16 g fis8 a'16 g fis e d cis b a |
  g16 fis e8 g'16 fis e d cis b a g |
  fis16 e d8 r r16 e32 fis g a b cis d8 |
 }
 \new Staff \relative c'' {
  \key g \major
  g8 b'16 a g fis e d cis b a g |
  fis8 a'16 g fis e d cis b a g fis |
  e8 g'16 fis e d cis b a g fis e |
  d8 \clef bass r16 c!32 b a g fis e d8 r r16 c! |
 }
>>
</score>
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. [[Peter Williams (musicologist)|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?"{{cite quote|date=March 2021}}

=== Variatio 24. Canone all'Ottava. a 1 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 25 Variatio 24 a 1 Clav. Canone all Ottava.ogg|title=Variatio 24 a 1 Clav. Canone all Ottava|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This variation is a canon at the octave, in {{time signature|9|8}} 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. {{citation needed|date=April 2015}}

=== Variatio 25. a 2 Clav.: Adagio ===
{{listen|type=music|help=no|filename=Goldberg Variations 26 Variatio 25 a 2 Clav.ogg|title=Variatio 25. a 2 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
Variation 25 is the third and last variation in G minor; it is marked [[Andantino (music)|adagio]] in Bach's own copy<ref>{{cite web|last=Tomita |first=Yo |url=http://www.qub.ac.uk/~tomita/essay/cu4.html#PC |title=The "Goldberg" Variations, Essay by Yo Tomita (1997) |publisher=Qub.ac.uk |access-date=2012-08-11}}</ref> and is in {{time signature|3|4}} time. The melody is written out predominantly in sixteenth and thirty-second notes, with many [[chromaticism]]s. 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''.<ref>{{cite book |last1=Kanwischer |first1=Alfred |title=From Bach's Goldberg to Beethoven's Diabelli: Influence and Independence |date=15 May 2014 |publisher=Rowman & Littlefield |isbn=978-1-4422-3064-4 |page=41 |url=https://books.google.com/books?id=aWqYAwAAQBAJ&pg=PA41}}</ref> Williams writes that "the beauty and dark passion of this variation make it unquestionably the emotional high point of the work",{{sfn|Williams|2001|p=[https://books.google.com/books?id=MKguGysZmA8C&pg=PA82 82]}} and Glenn Gould said that "the appearance of this wistful, weary [[Glossary of music terminology#C|cantilena]] is a master-stroke of psychology."<ref>{{Cite AV media notes |title=Bach: The Goldberg Variations |title-link=Bach: The Goldberg Variations (Glenn Gould album) |first=Glenn |last=Gould |author-link=Glenn Gould |date=1956 |type=liner notes |publisher=[[Columbia Records]]}}</ref> In an interview with Gould, [[Tim Page (music critic)|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 [[Carlo Gesualdo|Gesualdo]] and [[Richard Wagner|Wagner]]."<ref name="Gould Page" />

=== Variatio 26. a 2 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 27 Variatio 26 a 2 Clav.ogg|title=Variatio 26 a 2 Clav|description=Performed by Kimiko Douglass-Ishizaka on piano}}
In sharp contrast with the introspective and passionate nature of the previous variation, this piece is another virtuosic two-part toccata, joyous and fast-paced. Underneath the rapid arabesques, this variation is basically a sarabande.<ref name=gilbert /> Two time signatures are used, {{time signature|18|16}} for the incessant melody written in sixteenth notes and {{time signature|3|4}} for the accompaniment in quarter and eighth notes; during the last five bars, both hands play in {{time signature|18|16}}.

=== Variatio 27. Canone alla Nona. a 2 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 28 Variatio 27 a 2 Clav. Canone alla Nona.ogg|title=Variatio 27 a 2 Clav|description=Performed by Kimiko Douglass-Ishizaka on piano}}
Variation 27 is the last canon of the piece, at the ninth and in {{time signature|6|8}} time. This is the only canon where two manuals are specified not due to hand-crossing difficulties, and the only pure canon of the work, because it does not have a bass line.

=== Variatio 28. a 2 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 29 Variatio 28 a 2 Clav.ogg|title=Variatio 28 a 2 Clav|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This variation is a two-part toccata in {{time signature|3|4}} time that employs a great deal of hand crossing. Trills are written out using thirty-second notes and are present in most of the bars. The piece begins with a pattern in which each hand successively picks out a melodic line while also playing trills. Following this is a section with both hands playing in contrary motion in a melodic contour marked by sixteenth notes (bars 9–12). The end of the first section features trills again, in both hands now and mirroring one another:
<score>
\new PianoStaff <<
 \new Staff <<
  \new Voice \relative c' {
   \key g \major \time 3/4 \voiceOne
   \set Score.currentBarNumber = 13
   fis16 r r8 g16 r r8 a16 r r8 |
   b16 r r8 a16 r r8 g16 r r8 |
   a16 r r8 b16 r r8 a16 r r8 |
   \oneVoice fis16 d cis d \clef bass a fis e fis d4 | \bar ":|."
  }
  \new Voice \relative c' {
   \voiceTwo
   \repeat unfold 8 { r32 d e d e d e d } r cis d cis d cis d cis |
  }
 >>
 \new Staff <<
  \new Voice \relative c {
   \key g \major \clef bass \voiceOne
   \repeat unfold 8 { r32 fis g fis g fis g fis } r e fis e fis e fis e |
  }
  \new Voice \relative c {
   \voiceTwo
   d16 r r8 b16 r r8 a16 r r8 |
   g16 r r8 a16 r r8 b16 r r8 |
   a16 r r8 g16 r r8 a16 r r8 |
   \oneVoice d,16 fis e fis a d cis d fis4 |
  }
 >>
>>
</score>
The second section starts and closes with the contrary motion idea seen in bars 9–12. Most of the closing bars feature trills in one or both hands.

=== Variatio 29. a 1 ô vero 2 Clav. ===
{{listen|type=music|help=no|filename=Goldberg Variations 30 Variatio 29 a 1 ovvero 2 Clav.ogg|title=Variatio 29 a 1 ovvero 2 Clav|description=Performed by Kimiko Douglass-Ishizaka on piano}}
This variation consists mostly of heavy chords alternating with sections of brilliant arpeggios shared between the hands. It is in {{time signature|3|4}} time. A rather grand variation, it adds an air of resolution after the lofty brilliance of the previous variation. Glenn Gould states that variations 28 and 29 present the only case of "motivic collaboration or extension between successive variations."

=== Variatio 30. a 1 Clav. Quodlibet ===
{{listen|type=music|help=no|filename=Goldberg Variations 31 Variatio 30 a 1 Clav. Quodlibet.ogg|title=Variatio 30. Quodlibet. a 1 Clav.|description=Performed by Kimiko Douglass-Ishizaka on piano}}
[[File:Quodlibet.jpg|right|thumb|235px|The [[Quodlibet]] as it appears in the first edition]]
The final variation is titled after the ''[[quodlibet]]'' tradition, in which multiple popular songs are played at once or in succession. According to Forkel, the many musicians of the Bach family practiced this tradition at gatherings:

<blockquote>As soon as they were assembled a [[chorale]] was first struck up. From this devout beginning they proceeded to jokes which were frequently in strong contrast. That is, they then sang popular songs partly of comic and also partly of indecent content, all mixed together on the spur of the moment. ... This kind of improvised harmonizing they called a Quodlibet, and not only could laugh over it quite whole-heartedly themselves, but also aroused just as hearty and irresistible laughter in all who heard them.</blockquote>

Though Bach never noted the sources of Variation 30,<ref name="Alpha">{{Cite AV media notes |title=Variations Goldberg |first=Jean-Paul |last=Combet |others=[[Céline Frisch]] |date=2001 |type=booklet |publisher=Alpha Productions |id=Alpha 014 |location=Paris}}</ref> Forkel's anecdote led to the belief that it is composed from German [[Volkslied]] melodies, as if to evoke the Bach gatherings.<ref>{{harvnb|Kirkpatrick|1938|p=viii}}</ref>

Since folk tunes commonly shared melodies, music alone does not identify the songs intended.{{sfn|Williams|2001|p=90}} For example, part of Variation 30 traces back to the melody of the Italian [[Bergamask]] dance,<ref name="Alpha" /> which not only gave rise to compositions by many musicians (such as [[Dieterich Buxtehude]], under the title of ''La Capricciosa'', for his thirty-two partite in G major, BuxWV 250{{sfn|Schulenberg|2006|page=[https://archive.org/details/keyboardmusicjsb00schu/page/n395 387]}}), but is even sung to various words in regions such as Iceland today.<ref>{{cite news|last=Allen|first=David|url=https://www.nytimes.com/2023/10/20/arts/music/vikingur-olafsson-goldberg-variations.html|title=The Pianist Vikingur Olafsson on 'History's Greatest Keyboard Work'|work=[[The New York Times]]|date=October 20, 2023|access-date=2024-04-23}}</ref>

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.<ref name="CrossAccent">{{cite magazine |last=Marissen |first=Michael |date=Fall–Winter 2021 |title=The Serious Nature of the Quodlibet in Bach's 'Goldberg Variations' |url=https://www.bach-cantatas.com/Articles/Marissen-Quodlibet-Goldberg.pdf |magazine=CrossAccent |location=Valparaiso, Indiana |publisher=Association of Lutheran Church Musicians |access-date=April 23, 2024}}</ref>

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.<ref name="Alpha" /> In contrast, the "Ich bin solang..." text is much more obscure,<ref name="Vikingur">{{Cite AV media notes |title=Goldberg Variations |first=Víkingur |last=Ólafsson |others=[[Víkingur Ólafsson]] |date=2023 |type=booklet |publisher=[[Deutsche Grammophon]] |id=486 4553 |location=Berlin}}</ref> and these words have not been found in any Volkslied archives.<ref name="Alpha" />

Other bars of Variation 30 can be heard as incipits of yet more songs, though none have been identified.{{sfn|Williams|2001|p=89}}

=== Aria da Capo ===
{{stack|{{listen|type=music|help=no|filename=Goldberg Variations 32 Aria da Capo è Fine.ogg|title=Aria da Capo|description=Performed by Kimiko Douglass-Ishizaka on piano}}}}
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."{{sfn|Williams|2001|p=92}}