Bach's Goldberg Variations demystified.

If pianists were to play a word association game in which a psychologist said, "Bach's Goldberg Variations," they would almost without fail respond with the name "Glenn Gould." Gould's landmark recording from 1955 has had both positive and negative impacts on modern performers. It has been positive because it introduces pianists to one of Bach's best works, which up to the time had been largely ignored. Thanks to the pioneering vision of Gould, and Wanda Landowska for harpsichordists, one now can choose from literally dozens of recordings by major artists on piano, harpsichord, organ, orchestral transcriptions and even synthesizers. (1) The negative impact of Gould's recording is his tempo extremes--both slows and fasts--and his electric virtuosity that have scared away countless pianists from even touching Bach's masterpiece. After all, who could ever compete with Gould? "Wow, those tempos! How could I ever achieve that?!" These exclamations probably have been uttered, or at least considered subconsciously, by most pianists at one time or another. The restrictive nature of this belief has made the Goldbergs "off limits" to all but the most accomplished virtuosos, which really should not be.

Bach did not live in the time of Lisztian pyrotechnics and did not write his variations for only elite virtuosos, but rather intended his variations to be played and practiced by all--even by less advanced amateurs who might not be able to play all thirty variations. We now live in an "equal opportunity" society and it would be "politically incorrect" to reserve Bach's masterpiece for only the most accomplished virtuosos. This article intends to put to rest the "all or nothing" mentality and make the Goldberg Variations accessible to all, as well as to uncover Bach's overall temporal plan in one of his greatest masterpieces.

In 1741, Bach composed the fourth installment of his Clavierubung (Keyboard Practice) series, which he titled Aria rail verschiedenen Veranderungen (Aria with Diverse Variations) and since has acquired the more common title, the "Goldberg Variations." The Clavierubung series was an ongoing project of which the Goldberg Variations was preceded by three parts: Clavierubung I, the six Partitas (1731); Clavierubung II, Overture in the French Manner and Italian Concerto (1735); and Clavierubung III, a collection of twenty-seven movements for organ (1738). The title "Keyboard Practice" says a lot. All four Clavierubungen were intended as collections that do not necessarily need to be practiced or performed in their entirety, which discredits the "all or nothing" concept. For example, one need not play all six partitas in one concert; usually, one is enough. Likewise, the Overture in the French Manner and Italian Concerto need not be performed together, but can be, and almost always are, performed separately.

Due to the relatively short length of about forty minutes without repeats, the Goldberg Variations certainly can be performed in its entirety more easily than any of the other three Clavierubungen. However, one need not necessarily perform all the variations in one sitting to reap the pedagogical benefits and musical enlightenment Bach intended. Musical amateurs, junior high and high school students, children with exceptional talent and college students of all levels, could benefit from working on several of the less difficult variations and even attempting some of the more difficult variations at a slow tempo. The pedagogical and musical value of the Goldberg Variations is so immense that I recommend it for intermediate-level piano students even more than many of the inventions and sinfonias and preludes and fugues. Let us now traverse through the variations and learn a little more about them.

The chart accompanying this article lists the variations in approximate order of difficulty with brief comments and suggestions for each as well as the suggested tempo. The level of difficulty has been determined by considering such aspects as the number of voices, complexity of polyphony, hand crossings, expression and tempo. I will not discuss each variation here, but rather will emphasize some of the more important points. The reader may consult the chart for details on all the variations.

The least difficult of the variations, technically, is Variation 27. It poses fewer difficulties than many two-part Inventions, is an excellent study in control and balance between the hands and also serves as a superb introduction to turns and trills. Students also could learn sonic advanced theory with Variation 27, since it is a strict canon at the ninth, where the hands play "follow the leader" like in a round.

The next difficult variation is Variation 7, which is even less difficult than the rhythmically similar Gigue from French Suite No. 2. This is an ideal variation for students to learn dotted rhythms, finger precision, mordents and slurring, since the third eighth note in each beat sounds best if it is not connected to the next beat.

The next difficult variation is Variation 19, a delightful piece whose musical charm is sure to please anyone. It would be an ideal variation for students learning to play three voices, since it is less difficult than almost all the three-part Sinfonias. Its tempo is a little faster than a minuet, which Bach indicated by 3/8 instead of the standard minuet meter of 3/4. Less advanced students, however, may play it more slowly.

One of the biggest challenges facing piano students is learning to play polyphonic music with three or more voices. Although teachers have traditionally turned to fugues from the Well-Tempered Clavier or the Sinfonias to meet this demand, the three alla breve variations are probably better. Variations 10, 18 and 22 feature three or four voices and are comparable in difficulty. Variation 22, the least difficult of the three, is an ideal piece for students to learn four-voice polyphony and some finger substitutions. In only one minute, one can gain skills comparable to a three- or four-minute fugue from the WTC. Variation 18, the next most difficult of the three alla breve variations, features a strict canon at the sixth in the right hand, accompanied by an ingenious bass line. The rhythmic patterns in the bass are identical to the rhythmic patterns found in bourrees, like that in French Suite No. 5, suggesting not a leisurely tempo, as often heard on recordings, but a fast tempo, non-legato quarter notes and few or no finger substitutions. Variation 10 ranks as probably the most challenging of the three alla breve variations, due to some particularly knotty and awkward four-voice polyphony in the last four measures of each half. The other twenty-four measures, however, consist of only three voices and only are moderately difficult. This fughetta-style variation would serve as an excellent transition into longer fugues from the WTC. Due to the prominence of eighth notes, its tempo is the slowest of the three alla breve variations.

Let us now turn our attention toward some more difficult or advanced variations. Variation 26 is perhaps the one variation that has scared countless pianists away from even attempting the Goldberg Variations. Many pianists, at least at some point, have thought to themselves, "After all, if I can't play Variation 26 as fast as Gould, then I may as well not play any of the variations!" Unfortunately, this attitude is self-deprecating because it presumes Gould knew more than we do about historical eighteenth-century performance and pianists are riot capable of finding a voice of their own. In reality, Variation 26 is nothing more than a sarabande with ornamental triplet 16ths, which implies not an extremely fast tempo and loud volume, but rather a slow to moderate tempo and a more delicate and expressive performance. Because its tempo is that of a sarabande, it actually is much less difficult than most performers think. I find the difficulty of this variation lies more in expression and voicing than in sheer speed and virtuosity, since it sounds best on the piano if the long, slow notes (the sarabande melody) are voiced a little louder than the light and airy triplet 16ths (the accompaniment).

Pianists looking for speed and virtuosity have plenty of variations from which to choose. The fastest of all variations, at least in terms of quarter-note speed, is Variation 1. This variation is identical in style to the Courante (Corrente) from French Suite No. 5, which implies the same tempo. My research shows this type of corrente (in 3/4 with 16th note motion) to be the fastest of all simple-meter dances, whose usual tempo was a presto of about [crotchet] = 108. (2) I find many performers now play Variation 1 too slowly, which may be a reaction against the much too fast tempo of Gould. It also may be played more slowly, since some writers have described it incorrectly as being in the style of a polonaise. (3) (Variation 12 is the true polonaise-style variation.) Because of its fast tempo and wide arpeggios, Variation 1 ranks as one of the most difficult of all variations.

My research shows the normal or "default" allegro in Bach's music was metronome 84. (4) The eminent Bach scholar Robert L. Marshall agrees with this figure and sets Bach's "tempo ordinario" at about metronome 80. (5) By modern standards this tempo seems too slow, since we have been conditioned to accept nineteenth-century allegros of metronome 120 or faster. This applies mainly to pieces with 16ths as the fastest moving notes. For example, Variations 5, 8 and 17 routinely are played as fast as possible--as if they were Chopin or Liszt etudes. In reality, these three variations cannot be faster than Variation 1, since the corrente at a presto of metronome 108 is the absolute fastest of all Bach's simple-meter styles. The true "fast" variations are 14, 20, 23, 28 and 29, whose fast tempos result more from the presence of triplet 16th or 32nd notes rather than the actual quarter-note speed. But even triplets and 32nds do not give one license to play as last as possible. Bach definitely did not intend any of his music to be played as fast as possible in the vein of Schumann or Liszt.

Let us now turn our attention toward the larger picture--that is, how Bach organized the variations and the tempo relationships he intended for a complete performance. Careful study of Bach's autograph manuscript, the first edition from 1741, shows he did not terminate every variation with a fermata, but that his fermata placements contribute to a virtually symmetrical arrangement of "single" variations (those with a fermata both before and after) and "paired" or "grouped" variations (two or more variations with no fermata between). This shows a highly logical, rational and well thought out symmetrical plan that could not possibly have been coincidental. Alter all, symmetry like this simply does not happen by itself. More specifically, Variations 16 and 17, which have no fermata between them, function as the midpoint, and to either side lie three singles, four groups (either as pairs or groups of three), two singles and Aria. (See Figure 1.) (6)

[FIGURE 1 OMITTED]

Bach's fermatas and the symmetrical variation groupings they produce, have profound implications with respect to tempo relationships, as well as the amount of pause and ritardandos taken between each variation. Upon considering the styles and natural tempos of the thirty variations, those variations grouped together with no fermatas between them have related tempos and should be performed with hardly any pauses, which usually implies very little ritardando and sometimes no ritardando at all. Conversely, those variations separated by fermatas do not necessarily have related tempos, implying there should be a larger pause before going on to the next variation.

Many of the extremely slow and lightening fast "Gouldian" tempos we have become so accustomed to are automatically invalidated simply by honoring Bach's fermatas and implied tempo relationships. For example, Variations 25 and 26 have no fermata between in which a direct tempo relationship of [quaver] = [crochet] makes it impossible to play Variation 25 too slow and Variation 26 too fast (as Gould and countless others do). More specifically, the subdivided Adagio tempo of Variation 25 of about [quaver] = 63 becomes the quarter-note speed of the sarabande-style Variation 26, [crochet] = 63. (7) This relationship works best if one takes little, or no, ritardando at the end of Variation 25 (it is slow enough already) and transforms the eighth-note pulse into the new quarter-note pulse for Variation 26. Since Variation 25 ends softly, the absence of a fermata also implies a similar dynamic level for the beginning of sarabande-style Variation 26. Performers who take a huge ritardando and pause at the end of Variation 25, then attack Variation 26 like the first movement of Schumann's Kreisleriana, are not honoring Bach's notation.

The next pair, Variations 27 and 28, displays the most effective of all tempo relationships, which modern theorists refer to as "metric modulation." The time signatures of these two variations are 6/8 and 3/4, whose eighth notes are merely regrouped from 3 + 3 to 2 + 2 + 2. The best way to highlight this in performance is not to slow down and pause at the end of Variation 27--which most performers do--but rather "barrel in" to Variation 28 with the same eighth-note speed. This creates a highly effective metric modulation that makes Variation 28 seem twice as fast as Variation 27, simply by the addition of 32nd notes as written-out trills. The tempo relationship of [quaver] = [quaver] also makes it impossible to choose a tempo for Variation 27 that is too fast, since this would make Variation 28 unplayable. That is, one should play the eighth note of Variation 27 only as fast as one can play the eighth note of Variation 28, since the tempo of one limits the tempo of the other. In this pair, though, as opposed to Variations 25 and 26, the sudden energy of Variation 28 becomes most effective with a sudden volume increase. I suggest mezzo piano for most of Variation 27 followed by a subito forte right at the beginning of Variation 28. For more details on the tempo relationships, the reader may consult Figure 1.

With the exception of an important but obscure 1992 Festschrift article, I am not aware of anyone addressing the issue of Bach's fermatas in the Goldberg Variations. (8) I also am not aware of any performer, other than myself, who has acknowledged Bach's groupings in commercial recordings or live performances. Most performers use a separate track for each variation separated by a pause and often unrelated tempos, which obliterates the coherence and unity Bach intended. Although some well-meaning artists have at least attempted to make performance groups, their arbitrary groupings have nevertheless been incorrect. For example, Andras Schiff divides them into groups of five. The only true way to honor Bach's intentions is to use just one track for each performance group, such as Variations 3-5, 6-8, 9-10 and 11-12. (9) The main reason virtually all performers--even historically informed scholar-performers--have not realized Bach's groupings seems to be editorial. Unfortunately, most editors have tried to "correct" Bach's "inconsistencies" by adding fermatas where Bach did not indicate them. Even the supposedly most up-to-date and authoritative scholarly edition, the Neue Bach Ausgabe, edited by Christoph Wolff, includes a fermata after every variation (for which Wolff gives no explanation in the critical notes). This clearly is irresponsible editing. If a musicologist of the stature of Wolff has failed to recognize the importance of Bach's fermatas, then it comes as no surprise that artists of the stature of Gould and Schiff have failed to recognize them either. Most performers simply have been working from faulty editions."

The shroud of mystery hopefully has been unveiled from one of Bach's greatest masterpieces. No longer should the Goldberg Variations be only for elite virtuosos; students of several levels and abilities could benefit from practicing them. Any pianist who has the Inventions and Sinfonias in his or her library also should have the Goldberg Variations. And no longer should Gould's recordings intimidate pianists, because many of his tempos are historically incorrect, and he did not group the variations and choose his tempos according to Bach's fermata plan. And, alas, we now know how Bach intended the variations to be grouped in a complete performance and what kind of tempos and tempo relationships he desired. Now, keyboardists, go out and buy an edition if you don't already have one, blot out any extraneous fermatas if the editor added them, and get to work! The musical rewards are too great to be ignored.

Table 1. The Goldberg Variations on approximate order of
difficulty. The tempos have been derived from the tempo
relationships implied by Bach's fermata placements and
are consistent shown in Figure 1.

Variation  Description and comments                Suggested tempo

27         Canon at the 9th,                       [crotchet]. = 48
           two-part invention style                ([quaver] = 144)

7          French gigue in 6/8, dotted             [crotchet]. = 64
           rhythms, finger precision, ornaments    ([quaver] = 192)

19         Three voices, short, a little           [crotchet]. = 48
           faster than a minuet in                 ([quaver] = 144)
           3/8 corrente style

22         Short fughetta with four                [micron] = 84
           voices, mostly legato

18         Canon at the 6th with three voices      [micron] = 96
           texture, fast bourree style,
           non-legato quarter notes

10         Short fughetta with three and           [micron] = 72
           sometimes four voices, mostly legato

11         Two-part invention, 12/16 gigue style   [crotchet]. = 96
           but more introverted than
           extroverted, some octave
           transpositions recommended on piano

9          Canon at the 3rd with three             [crotchet] = 72
           voices, mostly legato

2          Trio style with duet in right hand      [crotchet] = 72
           and continuo-style
           accompaniment in left hand

Aria       Expressive sarabande style,             [crotchet] = 54
           ornaments, some pedal recommended

6          Canon at the 2nd in a moderate          [crotchet]. = 48
           3/8 gigue style, awkward right hand     ([quaver] = 144)

4          Imitative four-voice texture in         [crotchet]. = 56
           3/8 passepied style, very short,        ([quaver] = 168)
           staccato or non-legato eighth notes

5          Two voices, excellent                   [crotchet] = 84
           introduction to hand crossings

30         Four-voice hymn-style texture,          [crotchet] = 72
           mostly legato, some pedal recommended

8          Two voices, energetic and               [crotchet] = 96
           extroverted, some challenging
           hand crossings

1          Two voices in fast corrente style,      [crotchet] = 108
           fastest quarter-note speed of
           all the 3/4 variations

17         Two voices with constant 16th           [crotchet] = 84
           note motion, some octave
           transpositions recommended
           on piano

16         French overture style in two            [crotchet] = 63;
           sections, three-voice fughetta          [crotchet]. = 56
           in 3/8 section

21         Highly expressive canon at the          [crotchet] = 42
           7th with three voices,
           adagio style, some pedal
           recommended

23         Two voices, exciting and                [crotchet] = 72
           energetic display between
           the hands, staccato 16ths

13         Highly expressive sarabande             [crotchet] = 42
           style, some pedal recommended

25         Slowest and most mystical of            [quaver] = 63
           all variations, the only
           variation whose quarter note
           is truly subdivided,
           some pedal recommended

3          Canon at the unison,                    [crotchet]. = 56
           three voices, non-legato eighths        ([quaver] = 168)

14         Two voices, virtuosic                   [crotchet] = 84
           display between the hands

12         Canon at the fourth with                [crotchet] = 72
           three voices in polonaise style,
           the most awkward to play and
           un-pianistic of all the variations

24         Canon at the octave with                [crotchet]. = 72
           three voices, 9/8 pastoral
           gigue style, more extroverted
           than introverted with a robust
           and full tone, legato eighths

26         Moderately paced sarabande              [crotchet] = 63
           with hand crossings, prominent
           melody with light
           and airy accompaniment

29         Brilliant and energetic                 [crotchet] = 84
           featuring triplet 16ths, climax
           and dynamic highpoint
           of the Goldbergs

15         Highly expressive canon                 [crotchet] = 36
           at the 5th with three voices,           ([quaver]) = 72)
           two-note slurs, some pedal
           recommended, andante but not
           adagio (Bach's own indication)

20         Brilliant and energetic                 [crotchet] = 84
           featuring triplet 16ths,
           hand crossings

28         Probably the most difficult             [crotchet] = 72
           of all variations, trill etude

NOTES

(1.) Although the Goldberg Variations had been played by famous pianists before Gould (for example, Tureck, Arrau, Serkin), it was Gould who brought the work to the mainstream.

(2.) "Of Bach and Courante Tempos," Clavier (July/August 2002): 23-25.

(3.) For example, see Peter Williams, Bach: The Goldberg Variations. (Cambridge: Cambridge University Press, 2001): 56.

(4.) This will appear in my upcoming article in Clavier titled "Of Bach and Gigue Tempos."

(5.) Marshall, Robert L., "Bach's tempo ordinario: A Plaine and Easie Introduction to the System," Critica Musica: Essays in Honor of Paul Brainard, ed. J. Knowles. (New York, 1996): 249--78. Marshall sets m.m. 80 as Bach's standard allegro and calls it the tempo ordinario. My research, however, suggests Bach used two standard allegros, m.m. 84 and 96.

(6.) In order for Bach's plan to be precisely symmetrical as opposed to "virtually" symmetrical, I have assumed a fermata after Variation 2. The otherwise perfect symmetry suggests that Bach probably forgot a fermata here. Moreover, I believe Variations 2 and 3 do not have related tempos, which also suggests a fermata.

(7.) This tempo for sarabandes remains consistent with the range given by most dance historians. For example, see Wendy Hilton and Donald Waxman, A Dance Pageant: Renaissance and Baroque Keyboard Dances. (Boston: Galaxy Music Corporation, 1992): 44--49. My research suggests a few different tempos for Bach's sarabandes, of which m.m. 63 is the fastest.

(8.) Franklin, Don O., "The Fermata as Notational Convention in the Music of J. S. Bach," Convention in Eighteenth- and Nineteenth-Century Music: Essays in Honor of Leonard G. Rather. (Stuvesant, NY: Pendragon Press, 1992): 345-381. Franklin also believes the absence of a fermata between variations implies a direct tempo relationship, but does not mention the symmetrical arrangement of the variation groups. I already had studied Bach's manuscript and formulated my theory before the publication of Franklin's article, and thus, my decisions have not been influenced by Franklin's article. Some of Franklin's proposed tempo relationships are different than mine.

(9.) Even though the Aria and Variations 1 and 2 are single variations separated by fermatas (with an editorial fermata added after Variation 2; see endnote 6), I advise grouping them together in performance due to the short length of the variations. The same can be done with Variations 18--20. I also group Variations 29 and 30 Aria together in performance in order not to obstruct the climax as well as to consummate precise symmetry.

(10.) To my knowledge, one of the only editions that reproduces Bach's fermatas correctly is Peters, edited by Kurt Soldan. This is the edition I happened to have used from my first encounter with the work. Popular editions such as Henle and NBA both incorrectly reproduce Bach's fermatas. Gould used the Kirkpatrick edition, which also is incorrect.

Cory Hall teaches music and humanities at St. Petersburg College (Florida). He earned a B.M. degree in piano from California State University-Sacramento, M.M. in piano from the Eastman School of Music and D.M.A. in piano and M.M. in musicology degrees from the University of Kansas. He currently is writing a book titled Breaking the Bach Tempo Code: Tempo and Duration in the Music of J.S. Bach.