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Bach and Die Kunst der Fuge

June 9, 2003
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Jan Overduin is Professor of Music at Wilfrid Laurier University in Waterloo, Ontario, where he teaches organ and church music. He began studies in The Netherlands, where he was born, and continued in Canada at the University of Western Ontario, where he received the Masters degree in performance. The list of his teachers includes Marie-Claire Alain, Peter Hurford, and Jean Langlais. He has directed many choirs including the Wilfrid Laurier University Choir and Chapel Choir, the Niagara Chamber Choir (which he founded), the Menno Singers, the Mennonite Mass Choir. He has been actively involved in church music for over 40 years, most recently as director of music at St. Matthew's Lutheran Church in Kitchener, Ontario from 1985 to 1997. As organ soloist, he has recorded numerous broadcasts for radio and has played concerts in Europe, North America, and the Far East. His discography includes nine CDs with trumpeter Eric Schultz (on the German labels 'ebs' and 'Arte Nova Classics'), a solo album recorded at Ottobeuren, Germany (on 'ebs'), and a recent CD with recorder virtuoso Matthew Jones. Forthcoming is a book on improvisation for organists, published by Oxford University Press, and a new organ edition of the Art of Fugue. Jan Overduin may be contacted at [email protected] and welcomes visitors at his website http://info.wlu.ca/ ~wwwmusic/overduin/index.htm

The Kunst der Fuge, BWV 1080, a work consisting of 14 fugues and 4 canons all on one theme, is Bach's farewell, his testament. It is a very solemn and personal work, and ends with Bach's only fugue on his name, the notes B-flat, A, C, and B-natural (B, A, C, and H in German). Never before did he use this chromatic theme on such a grand scale or with such clarity as here at the end of Contrapunctus XIV. It is as if he puts his signature not only to the KdF, but also to his life's work. In fact it is uncanny, this very clear reference to his own name. The aural effect is almost dizzying, as is the visual appearance of the last page, with C.P.E. Bach's handwritten note about his father's death: "In this fugue, where the name BACH appears as a countersubject, the composer died." Like Shakespeare in the character of Prospero in The Tempest, Bach himself appears on stage, but it is to say "good-bye."

It is fitting that Bach reserved the 14th fugue for the use of the plain theme in clearest form, because of the relationship between the number 14 and his name. By allowing each letter of the alphabet a number (a=1, b=2, c=3, d=4 and so on), Bach's name adds up to 14 (2 + 1 + 3 + 8). Moreover, the name J.S. Bach adds up to its retrograde 41 (9 + 18 + 14). Though Bach's familiarity with numbers is not documented, the cabalistic numerical ideas were common knowledge.1 The work may have been intended as his third and final offering to the Mizler Society, which he had joined in June 1747, waiting until he was the 14th member to join. He also had his portrait painted for this society with 14 buttons on his jacket. Perhaps his aim was to finish the KdF by June 1749, as his third and final offering, since a condition of membership obliged him to submit a published "scientific" work every year until the age of 65.2

The more I play this work, the more aware I become of how saturated it is with personal references or "signatures." The B-A-C-H theme in the obvious four-note form or more subtly through the use of themes that contain 14 or 41 notes permeates the entire KdF. A casual listener or player is not likely to be conscious of some of these allusions, but the fact that they are there in such abundance imbues the work with a personal intensity and warmth that can easily be felt. While some or even many of the "B-A-C-H's" may occur spontaneously as a result of Bach's use of chromatic language, there are reasons to suspect that their incorporation is part of the overall design of the work and intention of the composer. Bach is not merely scribbling his name all over the score or playing numerological games. The chromatic language itself, the use of the key of D minor, the shape of theme and its inversion with its hymn-tunes analogies, the dramatic use of silence, various other motifs--it is all these and more, together with the "signatures," that give the work its deeply personal flavor.

The following examples include only appearances of the B-A-C-H theme that use the four actual notes B-flat, A, C, and B-natural. Excluded are all transpositions of the motif, e.g. E-flat, D, F, E etc., of which there are numerous examples. All examples have the four notes in the same octave.  Again, by relaxing this restriction, the list could be greatly expanded. Included however are those statements of the motif that are decorated with unessential notes, especially between the second and third notes; the unessential notes may serve to hide the visual but usually do not obscure the aural impact of the motif. These observations do not pretend to be profound, but are merely the result of a growing familiarity with and fondness for this stupendous work. If they have any validity, it is in underlining the deeply personal nature of the KdF.

Immediately in Contrapunctus I, in the most obvious voice, i.e. the soprano, in measures 10-12 Bach features the four-note name theme. Bach "hides" the eighth-note E by having it dip below the alto note G, so that even though the soprano part by itself really spells B-E-A-C-H (not a word in German), the ear perceives it as B-A-C-H. (Example 1)

The B-A-C-H motif is more hidden in Contrapunctus II, though increasing chromaticism causes it to occur more frequently. It appears twice in measures 35 to 37, both times in the dotted note motif that dominates this fugue. Though the first two notes are separated from the third and fourth by a complete measure, they occur in adjacent statements of the dotted note motif, and therefore appear related and connected. (Example 2)

Measures 22-23 of Contrapunctus III contain a very clear statement of B-A-C-H, shared between the upper two voices (B-A in the soprano, C-H in the alto).  While this sharing serves on the one hand to hide the motif, it also underlines it, since the effect is that of an ornamented version: the B-A-C-H motif beautified in a flowery way. (Example 3)

One of the most poignant of all references to the name of Bach occurs in Contrapunctus IV. The shape of the regular inverted theme is such that there is a noticeable high point on the notes B-flat and its "resolution" to the semitone below. There is also a marked similarity to the hymn-tune "Aus tiefer Noth schrei ich zu dir," a hymn paraphrase of Psalm 130 (De profundis). The resemblance in fact is too obvious to ignore.3 In Contrapunctus IV, and only here, Bach transposes the second half of the theme up a whole tone, so that the high point of the theme now is C-H (C and B-natural) instead of B-A (B-flat and A). This causes a sudden modulation to another key, the dominant of the dominant, a rather wrenching and quite dramatic shift of key. It happens first in bar 61, and thereafter four more times (in other words, not every time the theme is heard). The change from the expected high point B-A to C-H may not be exactly an obvious reference to Bach's name, but certainly for the player, the alteration of the climax of the theme is all the more dramatic and personal, especially when the personal nature of the hymn "Aus tiefer Noth schrei ich zu dir" is taken into consideration as well. Not only the personal pronoun is emphasized by this veiled reference to B-A-C-H, but also the idea of "calling" (schreien).   (Examples 4a and 4b) 

"Calling" is also happening constantly throughout this fugue through the use of the pervading "call-motif" of the descending minor third. Towards the end of Contrapunctus IV occurs another and much more traditional example of the use of the B-A-C-H motif: in bars 135-136 it is slipped in once into the tenor voice, like a hardly noticeable signature. (Example 4c)

In Contrapunctus V, the KdF theme appears consistently in 14-note form, as it will continue to do in much of the rest of the KdF, with the two descending thirds smoothed out with passing notes. Thus the theme itself is being identified with the name of Bach. Moreover, it is especially interesting that the B-A-C-H motif is heard quite plainly and in the most obvious voice (soprano) exactly in bar 41. (Examples 5a and 5b)

Contrapunctus VI states the B-A-C-H motif near the beginning, in measures 4 and 5 in the soprano. Again the first two notes are separated by a measure from the third and fourth, but they are perceived to be related to each other through their rhythmic emphasis. (Example 6)

Contrapunctus VII features the B-A-C-H motif in much the same way, for example in the tenor part of measures 17-19. Within the context of a statement of the KdF theme in 14-note form (and in diminution), the notes B-A are again separated from C-H by a measure, but each pair of notes comes at a similar point, i.e. the end of two parallel phrases. (Example 7)

With the introduction of a new theme that is rather chromatic, numerous instances of B-A-C-H occur in Contrapunctus VIII. In measure 11 a very clear statement of B-A-C-H is shared between the two lower voices (Example 8a). In measures 85-86, the motif is featured in the soprano and in measure 112 in the bass (Examples 8b and 8c). The main KdF theme (inverted), which occurs as theme III in this fugue (beginning in measure 95, in the alto), consists always of exactly 14 notes. More noticeably, each measure begins with a quarter rest (Example 8d). The use of silence on the downbeat is a technique often used by Bach to symbolize eternity and/or death.4 Thus the form of the theme in this fugue forms associations not only with the name "Bach" (14 notes), but also with "death" (silence on the downbeats). A convincing example of this technique to express longing for death is often encountered in Bach's chorales, such as at the end of Cantata #56 (Ich will den Kreuzstab gerne tragen). (Example 8e)

In Contrapunctus IX, in bars 84-85, the B-A-C-H motif is shared between the soprano (B-flat, A) and alto (C, B-natural), but because the voices cross, the motif appears to remain in the same voice, the alto. (Example 9)

In Contrapunctus X, again exactly in bar 40-41, the B-A-C-H motif makes an appearance in the two upper voices. (Example 10)

The 14-note version of the main KdF theme, with rests on every downbeat, now  "rectus," boldly opens Contrapunctus XI (Example 11a). The inversion of the second theme of Contrapunctus VIII, which in this fugue appears as theme III, very clearly spells B-A-C-H. Donald Tovey rejects this allusion to the name of Bach, since strictly speaking the theme misspells his name as B-A-C-C-C-H, yet to a listener (as opposed to a mere score-reader) this is almost as obvious an allusion to the name of Bach as in the final fugue.  (Example 11b) The B-A-C-H motif occurs frequently, not only in connection with the third theme, but elsewhere as well. An example is found in measure 144, with the motif shared between the alto (B-flat, A) and the soprano (C, B-natural).  (Example 11c)     

Contrapunctus XII and XIII, the two completely invertible "mirror" fugues, leave the composer with very little room to maneuver.  The listener has no idea of the strict rules behind these wonderful pieces, especially the playful Contrapunctus XIII. Even here the B-A-C-H motif pervades everything, though not as overtly as elsewhere in the KdF. The descending semitones B-A and C-H permeate the texture, but the four notes never occur together, and seldom within the same octave. One reason that Bach chose D minor as the key for this work may well have been that it allowed him to "season" fugues like Contrapunctus XII and XIII with these notes.  For example, C-H (the more unusual of the two pairs of notes) is used six times in measures 25-26 of Contrapunctus XIIb, just after several highly exposed B-A's. Appearances of the motif within one voice and within the compass of a minor third also occur (though somewhat more separated than usual) in measures 14-16 of Contrapunctus XIIa (bass) and measures 46-47 of Contrapunctus XIIb (bass). Similar concentrations of B-A and C-H occur in Contrapunctus XIII, imbuing the whole with the flavor of the BACH motif (e.g. in Contrapunctus XIIIa: eight times B-A in measures 32-35, followed by eight times C-H in measures 37-41).

Theme II of Contrapunctus XIV consists of exactly 41 notes, as if in direct preparation for the next theme, that of B-A-C-H itself (Example 12). There are also numerous examples of the B-A-C-H motif in the earlier part(s) of this fugue, again as if to prepare us for the plain statement of Theme III in measure 183. To list just three examples: measures 16-17 (tenor), 59-60 (alto/soprano), and 133-134 (alto).  (Examples 13, 14, and 15)

The evolution of the B-A-C-H motif is but one of many marvels of the KdF.  A constant companion in the background, like a quietly-flowing underground stream,5 in Contrapunctus XIV it finally appears quite alone and "naked," like a new-born babe. It is a paradoxical moment of loneliness and pity, sadness and comfort, weakness and strength. Almost immediately it is used in stretto and inversion, and "with the boldest and most mysterious harmonies"6 that are wrenching in their effect on us. It is at this point that this great composer, for whom nothing seemed impossible, especially in this work, leaves us forever. But the unfinished ending in which the composer is "called by name" also contains the promise of what "eye has not seen, nor ear heard." (I Cor. 2:9)

Notes

                        1.                  William Wright, The Organ--The Instrument and Its Literature (University of Toronto: private publ., 1994) 96.

                        2.                  J.S. Bach, Die Kunst der Fuge, ed. Davitt Moroney (Muenchen: G. Henle, 1989) vii.

                        3.                  The main theme in "rectus" form vaguely hints at "Vater unser" (Lord's Prayer). The descending thirds in Contrapunctus IV are also striking characteristics in some chorales, e.g., "Wie schön leuchtet der Morgenstern" (How lovely shines the morning star) and "Wer weiss, wie nahe mir mein Ende" (Who knows how near is my life's end). The most ornamented of all versions of the theme, as found in the Canon per Augmentationem in contrario Motu shows a striking resemblance to the "Agnus Dei" from the Mass in B minor.

                        4.                  Many of the more ornate chorale settings such as those in Schemelli's Gesangbuch illustrate this, e.g., "Lasset uns mit Jesu ziehen," "Es ist vollbracht," and "Liebster Gott, wann werd ich sterben?"  Examples in Das Orgelbüchlein include "Alle Menschen müssen sterben," and "Wir danken dir, Herr Jesu Christ, dass du für uns gestorben bist" (BWV 623 and 643).

                        5.                  In other words, like a Bach (German: brook).

                        6.                  Donald Francis Tovey, Essays in Musical Analysis: Chamber Music (first published in 1944; London: O.U.P., 1972) 88.

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