Deze bezat een exemplaar van de Goldbergvariaties waarin Bach persoonlijk enige fouten had verbeterd. Op de laatste pagina van deze druk echter ontdekte men een handgeschreven vel papier met 14 canons over de eerste 8 basnoten van de Goldbergvariaties. De titel van dit blad luidt: Verschillende canons over de eerste acht fundament-noten van de aria hiervoor van J. Bach Het manuscript werd voor Raadselschrift[ bewerken brontekst bewerken ] Al was de Goldberg cyclus al in in druk verschenen, toch heeft Bach blijkbaar gezien dat er meer compositorische mogelijkheden in het materiaal scholen.
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The bass line is notated by Ralph Kirkpatrick in his performing edition  as follows. The digits above the notes indicate the specified chord in the system of figured bass ; where digits are separated by comma, they indicate different options taken in different variations. Goldberg Variations bass line Problems playing this file?
See media help. 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 Ralph 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, 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. 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.
Performed by Kimiko Douglass-Ishizaka on piano. This file is available in "flac" format here Problems playing this file? 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. 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.
Performed by Kimiko Douglass-Ishizaka on piano Problems playing this file? Williams sees this as a sort of polonaise.
Variatio 2. 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. Variatio 3. 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. Variatio 4. 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. Each repeated section has alternate endings for the first or second time. Variatio 5. 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. Variatio 6. Canone alla Seconda. 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". Variatio 7. The variation is in 6 8 meter, suggesting several possible Baroque dances. 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.
Bach  the scholar and keyboardist David Schulenberg notes that the discovery "surprised twentieth-century commentators who supposed gigues were always fast and fleeting. This kind of gigue is known as a "Canary", based on the rhythm of a dance which originated from the Canary islands.
He concludes, "It need not go quickly. The pianist Angela Hewitt , in the liner notes to her 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. 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 Francois 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. This is a canon at the third, in 4 4 time. The supporting bass line is slightly more active than in the previous canons.
Variatio The first section of Variation 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 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 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.
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. Canone alla Quarta in moto contrario[ edit ] Performed by Kimiko Douglass-Ishizaka on piano Problems playing this file? 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 In the second section, Bach changes the mood slightly by introducing a few appoggiaturas bars 19 and 20 and trills bars 29— 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 : Variatio 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. Canone alla Quinta. 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.
14 Canons, BWV 1087 (Bach, Johann Sebastian)