Goldberg Variations

The aria is a sarabande in ³
₄ time, and features a heavily ornamented melody:

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).

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.

This is a simple three-part contrapuntal piece in 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.

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 ¹²
₈ and the many sets of triplets suggest a kind of a simple dance.

Like the passepied, a Baroque dance movement, this variation is in ³
₈ 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).

First 8 bars of the fourth variation.

Each repeated section has alternate endings for the first or second time.

This is the first of the hand-crossing, two-part variations. It is in ³
₄ time. A rapid melodic line written predominantly in sixteenth notes is accompanied by another melody with longer note values, which features very wide leaps:

First four bars of Variation 5.

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.

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 ³
₈ time. The harpsichordist Ralph 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.

The variation is in 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 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[5] 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.

First 4 bars of the seventh variation.

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.

This is another two-part hand-crossing variation, in 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 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.

This is a canon at the third, in ⁴
₄ time. The supporting bass line is slightly more active than in the previous canons.

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.

The first section of Variation 10.

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.

This is a virtuosic two-part toccata in ¹²
₁₆ 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.

This is a canon at the fourth in 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 appoggiaturas (bars 19 and 20) and trills (bars 29–30).

This variation is a slow, gentle and richly decorated sarabande in 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 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):

The final two bars of the first section of Variation 13.

This is a rapid two-part hand-crossing toccata in 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."[6]

This is a canon at the fifth in 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."[6]

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 chords. It consists of a slow prelude with dotted rhythms with a following fugue-like 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 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).

This variation is another two-part virtuosic toccata. Peter Williams sees echoes of Antonio Vivaldi and Domenico Scarlatti here. Specified for two manuals, the piece features hand-crossing. It is in 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."[6]

This is a canon at the sixth in ²
₂ time. The canonic interplay in the upper voices features many 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 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."[7]

This is a dance-like three-part variation in 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).[8]

This variation is a virtuosic two-part toccata in 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:

First 2 bars of variation 20.

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.[9] The bass line here is one of the most eloquent found in the variations, to which Bach adds chromatic intervals that provide tonal shadings.[9] This variation is a canon at the seventh in ⁴
₄ time; Kenneth Gilbert sees it as an allemande despite the lack of anacrusis.[10] 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:

The first three bars of Variation 21

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.

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.

Another lively two-part virtuosic variation for two manuals, in 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:

The first four bars of Variation 23

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?"

This variation is a canon at the octave, in 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.

Variation 25 is the third and last variation in G minor; it is marked adagio in Bach's own copy[11] and is in ³
₄ 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.[12] Williams writes that "the beauty and dark passion of this variation make it unquestionably the emotional high point of the work",[13] and Glenn Gould said that "the appearance of this wistful, weary cantilena is a master-stroke of psychology."[14] 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."[6]

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.[10] Two time signatures are used, ¹⁸
₁₆ for the incessant melody written in sixteenth notes and ³
₄ for the accompaniment in quarter and eighth notes; during the last five bars, both hands play in ¹⁸
₁₆.

Variation 27 is the last canon of the piece, at the ninth and in 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.

This variation is a two-part toccata in 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:

The last four bars of the first section of Variation 28

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.

This variation consists mostly of heavy chords alternating with sections of brilliant arpeggios shared between the hands. It is in 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."

The Quodlibet as it appears in the first edition

This quodlibet is based on multiple German folk songs,[15] two of which are 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"). The others remain unknown.[16] The Kraut und Rüben theme, under the title of La Capricciosa, had previously been used by Dieterich Buxtehude for his thirty-two partite in G major, BuxWV 250.[17]

Bach's biographer Forkel explains the Quodlibet by invoking a custom observed at Bach family reunions (Bach's relatives were almost all musicians):

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.

Forkel's anecdote (which is likely to be true, given that he was able to interview Bach's sons), suggests fairly clearly that Bach meant the Quodlibet to be a joke.

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."[18]

• Goldberg Variations: Scores at the International Music Score Library Project
• Goldberg Variations on Mutopia
• Animated graphical scores of the Goldberg Variations, with harpsichord performances by Colin Booth

• "Goldberg Variations – The Best Recordings" – theclassicreview.com
• The Goldberg Variations made new – Review of Glenn Gould's and Simone Dinnerstein's renditions
• An essay on the Goldberg Variations by Yo Tomita
• Canons of the Goldberg Variations – graphical analysis enables you to see the leader and follower in the canons
• J.S. Bach, the architect and servant of the spiritual – a closer look at the Goldberg Variations

• Public-domain piano recording by Kimiko Ishizaka (Open Goldberg Variations project), with linked newly edited score.
• Bach-cantatas.com: The Goldberg Variations – Comprehensive discography
• jsbach.org: BWV 988 – Reviews of many recordings