Proportional relationships in Bach’s Die Kunst der Fuge and the intended duration of Contrapunctus XIV

Colin MacKnight

Colin MacKnight is a C. V. Starr Doctoral Fellow at The Juilliard School, New York City, where he also received his bachelor’s and master’s degrees. He is in the studio of Paul Jacobs and is working on his dissertation entitled “Ex Uno Plures: A Proposed Completion of Bach’s Art of Fugue.” He currently serves as associate organist and choirmaster at the Cathedral of the Incarnation in Garden City, Long Island.

A frequent competition prizewinner, MacKnight holds the Fellow and Choirmaster certificates from the American Guild of Organists (having won the prize for top score for the latter) and is a member of The Diapason’s “20 Under 30” Class of 2019. Upcoming performance highlights include recitals in Ingelheim, Germany; Kingston, Jamaica; and at Saint Matthew’s Cathedral in Washington, DC. Colin MacKnight is represented in North America by Karen McFarlane Artists, Inc. For more information, media, and a calendar of performances, visit colinmacknight.com.

“Miss no opportunity to practice on the organ; there is no instrument that takes such immediate revenge on the impure and the careless, in composition as well as in the playing, as the organ.”¹ This description from Schumann was likely referring to the organ’s ability to execute—one might even say affinity for—complex counterpoint. It is only fitting then that his only organ work would be a set of six fugues on Johann Sebastian Bach’s surname, a homage to music’s greatest contrapuntist, one of Schumann’s principal influences, and the composer who dominates the organ repertoire to a degree that no other composer dominates any other repertoire. Schumann stated, “What art owes to Bach is to the musical world hardly less than what a religion owes to its founder.”² He also acknowledged the influence that Bach exerted on his own music; Schumann’s compositional style was unusually motivic, and he attributed his disdain for what he called “lyric simplicity” to his study of Bach and Beethoven.³

In German musical parlance, B is B-flat and H is B-natural, allowing one to turn Bach’s surname into the motive B-flat, A, C, B-natural. By composing a set of fugues based on the theme
B-A-C-H, Schumann was participating in a long tradition of composing pieces (particularly for the organ) that include the B-A-C-H motive.

This tradition began with Johann Sebastian Bach himself and continues to the present. Two notable examples of Bach encrypting his own name occur in the Toccata in F Major for organ, BWV 540i (in transposition), and Contrapuncti 8, 11, and 14 of Die Kunst der Fuga, BWV 1080. Felix Mendelssohn was the next composer of a substantial body of organ music to encrypt the B-A-C-H motive into one of his pieces. In measure 56 of the first movement of his Sonata IV in B-flat from the Six Organ Sonatas, op. 65, he prominently includes the B-A-C-H motive in the pedal, transposed down a whole-tone (Example 1).

Schumann was close friends with Mendelssohn and even wrote a glowing review of the organ sonatas in his journal, Neue Zeitschrift für Musik, so Mendelssohn’s encryption may not have been unnoticed by him. Perhaps it is not coincidence that Schumann composed his set in 1845—the year in which Mendelssohn’s organ sonatas were published.⁴ In addition to Mendelssohn’s organ sonatas, Mendelssohn’s Six Preludes and Fugues for Piano, op. 35, and Three Preludes and Fugues for Organ, op. 37, were almost certainly strong influences on Schumann’s B-A-C-H fugues.⁵

Schumann was, however, the first composer to write a large work based on this theme. This proved to be influential; other composers who would later write substantial organ works based on B-A-C-H include Franz Liszt (Prelude and Fugue on the Name B-A-C-H, S. 260, versions of which exist for piano and organ), Sigfrid Karg-Elert (Passacaglia and Fugue on B-A-C-H, op.150), Max Reger (Fantasy and Fugue on the Name B-A-C-H, op. 46), Ernst Pepping (Three Fugues on B-A-C-H), etc. Schumann’s set is the longest of these works.

The year 1845 is often called Schumann’s contrapuntal year because of his and Clara Schumann’s intense study of counterpoint, resulting in such compositions as the Six Studies in Canonic Form, op. 56, and Four Sketches, op. 58, both for pedal-piano; Six Fugues on B-A-C-H for organ, op. 60; and Four Fugues for piano, op. 72.⁶ During this year of “Fugenpassion,”⁷ to use Schumann’s own term, they studied Friedrich Wilhelm Marpurg’s Treatise on the Fugue and Luigi Cherubini’s A Course of Counterpoint and Fugue.⁸ Schumann also studied counterpoint intensely from 1831 to 1832 under Heinrich Dorn and from 1836 to 1838, a period which yielded more contrapuntally complex and rich works such as Kreisleriana.⁹

Schumann finished the first fugue on April 7 and the second on April 18.¹⁰ Soon after the second fugue was completed, a rented pedal-piano arrived at the Schumann house.¹¹ This would have been a useful tool for composing the Sketches, Canonic Studies, and Fugues, but, surprisingly, this is also around the time Schumann began to eschew the use of the piano as a compositional tool.¹² Perhaps, then, the pedal-piano was mainly used to assist in pedal-writing.

After the second fugue, progress on the set slowed for a variety of reasons including illness, work on the latter movements of the Piano Concerto in A Minor, op. 54, and organization of an orchestral concert series in Dresden.¹³ By the end of September, Schumann had drafted the third, fourth, and fifth fugues¹⁴ and in late November, Schumann completed the set.¹⁵ The influence of the B-A-C-H project can also be seen on his next opus, Symphony No. 2 in C Major; the second trio of the scherzo uses a theme beginning with the B-A-C-H motive, and the adagio contains a fugato (Example 2).¹⁶

Schumann’s set of six fugues is in many ways similar to and likely inspired by Bach’s The Art of the Fugue since both are thorough explorations of the contrapuntal potential of one musical idea. Schumann was, however, somewhat disdainful of The Art of the Fugue for being excessively cerebral.¹⁷ Part of this is probably due to what Schumann may have perceived as a lack of variety in The Art of the Fugue. Since The Art of the Fugue is based on a single subject and the Schumann B-A-C-H fugues are only based on a motive, Schumann has considerably more flexibility in his thematic material. (Interestingly, this is not unlike Bach’s use of the B-A-C-H motive in The Art of the Fugue. In Contrapunctus 8, the motive is masked with repeated notes and inversion; in Contrapunctus 11, he un-inverts it but retains the repeated notes. It is not until Contrapunctus 14 that Bach plainly reveals the motive, a technique of which Schumann surely would have been proud.)

Schumann, like Bach, derives several distinct fugue subjects from the B-A-C-H motive. The first, third, and sixth fugues, for example, all plainly feature the motive as the main substance of the subject. The fifth fugue, however, treats it just as the starting point for further elaboration. The fourth fugue also uses the motive overtly but changes its contour by leaping down a sixth from A to C, instead of up a third. By modifying and developing the theme, Schumann reveals and incorporates one of his favorite compositional genres: the character piece. John Daverio describes this important difference between fugues and character pieces by saying, “If the essence of a fugue is a fixed subject, then that of the character piece is the transformation of an eloquent motive.”¹⁸ By combining elements of these two genres, Schumann is not just taking a neo-baroque diversion but is “updating” the fugal form to include the most modern musical trends.

Each of Schumann’s fugues also has specific tempo and dynamic indications to contrast the movements. The work is framed by two large accelerando, crescendo fugues; the second fugue is a virtuosic allegro; the third, serene and lyrical; the fourth, a more austere study; and the fifth, a charming scherzo. In this way, the work is not just a compilation of fugues but also a suite of complementary movements. Schumann also provides tonal variety by including G minor and F major movements into an overarching B-flat major—something The Art of the Fugue does not do despite its much greater length. Additionally, there is greater variety of texture in Schumann’s set than The Art of the Fugue. Schumann is not averse to devolving to homophony as he does in all but the third fugue. He also frequently composed in what looks like a “lazy” five-voice texture by writing five-voice expositions but not maintaining a strict five-voice texture (until the last fugue). This is, however, more likely another attempt at textural variety than contrapuntal ineptitude on Schumann’s part; by moving the bass line between the pedal and left hand, he is varying the sound and texture even while maintaining the same number of voices.

As previously stated, the first fugue is an accelerando, crescendo fugue. The quintessential example of this, and likely inspiration for Schumann, is the first movement of Mendelssohn’s Sonata No. 3 in A Major from his Six Organ Sonatas, op. 65. Schumann’s subject comprises two bars, the first of which is the B-A-C-H motive plainly stated, and the second of which includes the B-A-C-H motive in retrograde in its first, second, fifth, and sixth pitches (Example 3). At the point at which Schumann indicates to begin crescendoing and accelerating, he combines the B-A-C-H motive (or a variant thereof) in the pedal with a two-voice stretto of the diminished form of the subject in the manuals (Example 4).

The piece builds to a very exciting homophonic climax, particularly when the performer has accelerated enough (Simon Preston starts at 92 beats per minute and comes close to doubling the tempo, reaching 168 beats per minute at the fastest), with double-pedal before a five-bar coda that returns to a polyphonic texture, although without the B-A-C-H subject. Because of the lower register and reduction in texture, it is not uncommon to decrescendo through the coda, even though this is not indicated in the score.

The second fugue is the allegro movement and the most unabashedly virtuosic. It is also the only fugue in a triple meter, a trait of which Schumann takes full advantage through the use of hemiola. Its subject begins with a quick dotted B-A-C-H before beginning a sequence that is almost certainly taken from the fugue from Bach’s Toccata and Fugue in D Minor for organ, BWV 565. Schumann would have known this work from Mendelssohn’s famous Bach recital at the Thomaskirche in Leipzig, which he enthusiastically reviewed in his Neue Zeitschrift für Musik (Examples 5 and 6).¹⁹

In measure 48, Schumann combines the subject with its augmentation in the pedal. Then in measure 74, there is a rest for performer and listener alike when Schumann quietly strettos the augmented B-A-C-H motive with occasional interruptions from the BWV 565 motive. (These fragments of the BWV 565 motive make the connection to Bach’s fugue even more obvious.) This motive gradually takes over the texture while crescendoing until the piece devolves into a virtuosic toccata, complete with double-pedal, arpeggios, octave doublings, and no hint of B-A-C-H. He then briefly alludes to the quiet B-A-C-H stretto passage again—this time with neighbor-tones on the B-flat—before a passage of triumphant homophony. There is one more fugal interruption before the chorale-style writing returns and a hemiola passage with sforzando chords every two beats. The movement ends with a coda over a B-flat pedal that continues to use the BWV 565 motive while eschewing the B-A-C-H motive, a final confirmation of this fugue’s inspiration.

The third fugue is the only one that is entirely quiet; there is a piano indication at the beginning with the description “Mit sanften Stimmen”—with gentle stops—and no further performance instructions. This is the only fugue that begins in two voices with the counter-subject present from the beginning. It is also the simplest and technically easiest fugue. The B-A-C-H theme only occurs in one form, and the emphasis is on lyricism rather than intellect or virtuosity. It is also the only fugue in a minor key, G minor, but ending in a tranquil G major.

The fourth fugue is the most austere and perhaps the least accessible of the set. This is clear from the outset when Schumann uses a jagged version of the B-A-C-H motive; instead of an ascending minor third between A and C, he writes a descending major sixth, meaning the subject outlines a pungent diminished octave. This is one of Schumann’s cleverest techniques: to utilize the B-A-C-H motive as a collection of pitch classes with no specific contour rather than a traditional theme with a set shape.   

Schumann further adds to the complexity and austerity of this movement by introducing the retrograde of B-A-C-H for the first time and immediately combining it with the subject’s normal form. The retrograde form of the subject almost always has staccato markings on the first and third notes to draw attention to itself, retrograde being among the more obscure contrapuntal techniques (Example 7).

This movement continues to use retrograde pervasively and eventually transitions into loud chordal writing with flashy pedal scales. Like the second fugue, it alternates between passages of strict counterpoint and homophony. The passagework and homophony bring what was an ascetic contrapuntal exercise—perhaps worthy of Schumann’s own questionable criticism of The Art of the Fugue—to a dramatic and exciting close. The climax in measures 96 to 99 is particularly thrilling and one of the highlights of the whole work, as if to apologize for the trials through which he has just put the listener.

As an additional conciliatory gesture, Schumann placed his charming scherzo-fugue next. The presence of a scherzo—an unusual template for a fugue—in this set is further proof that Schumann conceived this set as a suite of complementary pieces and not just miscellaneous movements based on the same theme. The fifth fugue is the only movement in F major and the shortest of the set. This movement’s subject begins with a fleeting B-A-C-H that sounds almost like a perfunctory after-thought—or pre-thought. It is a refreshing relief after the previous four movements which all employ the B-A-C-H motive so plainly.

Nevertheless, the scherzo is still a contrapuntal tour de force. It includes augmentation, inversion, retrograde, and retrograde augmentation, and combines the augmented form of the subject with the original form and the augmented retrograde form with the plain retrograde, an astonishing amount of artifice for a movement of less than three minutes. The technique, however, never hinders the charm. This fugue demonstrates well Schumann’s outlook on fugal composition: “Anyway, this will always be the best fugue the public for instance regards as a waltz by Strauss—in other words, where the artificial rootage is covered like the roots of a flower so that we can see just the flower.” For Schumann, artifice and contrapuntal ingenuity were always subservient to beauty and emotion.²⁰

The sixth and final fugue, the longest of the set, is another accelerando, crescendo fugue. It is also the only double fugue in the set, giving it more in common with the first movement of Mendelssohn’s Sonata No. 3 in A Major, op. 65, which, as previously mentioned, is also a crescendo, accelerando, double fugue. The three-bar subject begins with the B-A-C-H motive and ends with a short descending scale that is the source of the second subject. The first section also prominently features a five-note motive as a counter-subject, beginning in measure 16. This motive, intentionally or not, sounds like a quotation of the main motive in Bach’s chorale prelude on Valet will ich dir geben, BWV 736. The descending scale that closes the first subject becomes the second subject in measure 58 and begins a new section that is marked Lebhafter and più forte. This section does not use the B-A-C-H motive but instead develops the second subject, including stretto and inversion, and uses the same five-note countersubject.

In measure 95, Schumann finally combines the subjects and countersubject signaling the third and final part of this fugue, the only instance of strict five-part counterpoint in the entire set (Example 8).

The strict counterpoint continues until measure 116 when Schumann switches to grand, fortissimo, chorale writing with a few quasi-contrapuntal interruptions. The homophonic texture allows him to compose abrupt and distant modulations that are unusual in strict fugal textures: most notably, the modulation to G major in measure 139 and back to B-flat in measure 142. As in the second fugue, Schumann eventually eschews the B-A-C-H motive (after measure 144 in the sixth fugue), choosing instead to close the entire work not with either of the subjects but with the counter-subject.

As previously mentioned, Schumann “updates” the fugal form by incorporating elements of the character piece, which he does by developing and transforming the B-A-C-H motive. By examining the different transformations of B-A-C-H, as well as other motives, one can see certain relationships between movements beyond the obvious thematic unity of a monothematic work. Specifically, the movements can be organized into three related pairs: movements one and four, two and three, and five and six.

The first fugue is related to the fourth by merit of the fact that it utilizes a countersubject, itself derived from the B-A-C-H motive, which prominently features leaps of sixths, the same interval that is so characteristic of the fourth fugue’s subject (Example 9). 

While this relationship by itself may seem somewhat tenuous, Schumann retroactively confirms it with what is probably the most shocking harmony of this fugue: the false ending at measure 60, in which an F dominant-seventh chord resolves to a secondary-dominant ninth of the subdominant. What sounds like a dramatic change in register is actually the jagged contour of the fourth fugue’s subject in the soprano! The soprano and tenor lines also continue to prominently feature leaps of sixths through the coda of this movement (Example 10).

The second and third fugues are also connected by an allusion in the second fugue to the third fugue’s subject. In measure 48 of fugue two, the B-A-C-H motive appears in the pedal in augmentation with three extra notes that together with B-A-C-H will form the third fugue’s subject (Examples 11 and 12).

Just like in the first fugue, the relationship between fugues two and three may seem weak, but Schumann once again confirms it by developing the tail of the third fugue subject in the tenor and bass voices later in the second fugue (measure 135) (Example 13).

The connection between the fifth and sixth fugues is perhaps the most obvious. The fugue subject of fugue five has a five-note figure that occurs in the second (C, B-flat, A, B-flat, C) and third (G, F, E, F, G) measures of the subject (Example 14).

Schumann later inverts this theme, so it also occurs in an up-down shape. The inverted form of this motive (the aforementioned quotation of Valet will ich dir geben, BWV 736) then becomes the countersubject to the final fugue and is combined with both of the last fugue’s subjects. It is introduced in the first exposition in measure 16 and is combined with both subjects in measure 95 (see Example 8).

On the surface, nothing could have been more conservative in nineteenth-century music than a set of six fugues for organ. Further examination reveals, however, how progressive Schumann’s B-A-C-H fugues were. They were likely the first set of pieces to be based entirely on Bach’s name, they constitute a complementary “suite” of fugues—not just a collection of movements—and there are connections and developments between the movements that foreshadow Brahms’s developing variation. Schumann himself wrote, “I worked on this set for the whole of last year in order to make it somewhat worthy of the exalted name it bears; [it is] a work that will, I believe, long outlive my other works.”²¹ His prediction that his reputation would be based largely on these fugues did not prove to be accurate, but it was surely right of him to hold them in such high regard.

Notes

1. Helga Scholz-Michelitsch, “Robert Schumann and the Organ,” trans. Susanne Weber, The Franz Schmidt Organ Competition, http://orgelwettbewerb.kitz.net/Franz-Schmidt-OrganCompetition/Robert_Schumann.html. 

2. Eric Frederick Jensen, Schumann (New York: Oxford University Press, 2001), 145.

3. Ibid., 145–146. 

4. Scholz-Michelitsch, “Robert Schumann and the Organ.”

5. John Daverio, Robert Schumann: Herald of a “New Poetic Age” (New York: Oxford University Press, 1997), 308.

6. Daverio, Robert Schumann, 306.

7. Ibid., 307. 

8. Scholz-Michelitsch, “Robert Schumann and the Organ.”

9. Daverio, Robert Schumann, 306.

10. Ibid., 307.

11. Ibid.

12. Jensen, Schumann. 284.

13. Daverio, Robert Schumann, 307.

14. Ibid.

15. Ibid., 308.

16. Jensen, Schumann, 289.

17. Ibid. 144.

18. Daverio, Robert Schumann, 309.

19. Scholz-Michelitsch, “Robert Schumann and the Organ.”

20. Ibid.

21. Daverio, Robert Schumann, 308.

Bibliography

Daverio, John. Robert Schumann: Herald of a “New Poetic Age.” New York: Oxford University Press, 1997.

Jensen, Eric Frederick. Schumann. New York: Oxford University Press, 2001.

Scholz-Michelitsch, Helga. “Robert Schumann and the Organ.” Translated by Susanne Weber. The Franz Schmidt Organ Competition. http://orgelwettbewerb.kitz.net/Franz-Schmidt-OrganCompetition/Robert_Schumann.html.

Gavin Black

Gavin Black, director of the Princeton Early Keyboard Center, Princeton, New Jersey, is preparing performances on Bach’s The Art of the Fugue on both harpsichord and organ for the next two concert seasons.

The Art of the Fugue, part III

This month’s installment picks up exactly where last month’s left off.

Notes on the Individual Movements

Contrapunctus 1 is a four-voice fugue on the original and simplest form of The Art of the Fugue theme (Example 1). There is no regular countersubject. The mood is forthright and powerful, but with underlying calm.

Contrapunctus 2 is a four-voice fugue on the same theme, except that the last notes are changed from eighth notes to dotted eighths and sixteenths (Example 2). This dotted rhythm pervades the piece. The sounds jump rather than flow from one beat to the next. The effect is, at least intermittently, unsettling. The dotted rhythms convey a suggestion of French musical style, though the piece is not fully worked out in that style.

Contrapunctus 3 is a four-voice fugue on the inversion of the original theme (Example 3). The piece moves slowly and gently, and the mood is quiet. The subject is accompanied (after the first entrance) by a chromatic countersubject loosely derived from the subject itself (Example 4). This countersubject also provides a short motive (Example 5) on which two episodes are based. This motive will return later in the work. In measure 23 the subject enters in a new form: with passing tones (Example 6). Although it is abandoned in the next movement this will become the most important form of the theme later on.

Contrapunctus 4 is also a four-voice fugue based on the inversion of the main theme (see Example 3). The theme is accompanied by a short chromatic motive, more explicitly dissonant than that of Contrapunctus 3 (Example 7). The movement is also characterized, however, by long episodes of almost exaggerated consonance. These are based mainly on a simple two-note descending third (which can be heard as a reference to the thirds in the original, non-inverted theme, although that theme is not explicitly present in this movement) and a four-note stepwise fourth, both ascending and descending, which is derived from the last four notes of the main theme, in both its inverted and non-inverted forms. There are several lushly beautiful internal cadences, almost hypnotic in their effect. The last measures conceal a single reference to the B-A-C-H motive.

Contrapunctus 5 opens with a statement of the inverted theme with passing tones, introduced in Contrapunctus 3. Before the end of the theme, this is joined by the non-inverted theme with passing tones in the bass (Example 8). This overlapping of themes, called “stretto” by theorists of fugue writing, is by no means characteristic of the opening of a fugue. Nor is it characteristic for the second subject entry to be an inversion rather than a transposition of the first. This is a gesture of union of the two essential forms of the main theme. They are the opposite of each other, but they can be joined together. In measure 53, an even closer union is suggested with a four-voice stretto at the interval of one quarter note. The inverted and non-inverted themes, however, are treated to this process separately (measured 53–57 and 65–69)! The mood of Contrapunctus 5 is alternately urgent and dreamy, or perhaps both at once. In the last measures of the movement the two versions of the theme are heard simultaneously, somewhat concealed by an unexpected six-voice texture.

Contrapunctus 6 is marked in Stile Francese. Thus it realizes the suggestion made by Contrapunctus 2. It is not easy to define what the “French style” is. For the purposes of this piece, however, it is enough to recognize that it involves the use of dotted rhythms, very fast short runs, and moderately fast longer runs. It also aims to create a feeling of power and grandeur in the context of rather static (non-flowing) rhythm. Native French pieces in this style would never have been fugues, so Bach was doing something new. This piece, like the last, opens with a stretto, at the interval of only one measure. The impatient quality of the second voice, created by its insistence on coming in early, is here intensified by the fact that is comes in “too fast,” that is, in diminution. The very rapid four-note runs, heard from measure 7 on, are a standard characteristic of the French style, but they can also be seen as a double diminution of the last four notes of the main theme.

Contrapunctus 7 is a fugue on the main theme with passing tones, sometimes inverted and sometimes in diminution. To this is added the theme in augmentation (Example 9) that is heard first in the bass and once in each voice. Almost every note in this contrapunctus is derived directly from the theme, by augmentation, diminution, or double diminution. The effect is one of extreme concentration and intensity, but also of rather jovial power and good humor.

Contrapunctus 8 opens with a short fugue exposition on a brand new theme, not derived in any way from what has come before (Example 10, but see under Contrapunctus 18, below). After several short episodes and a cadence in the tonic, a second exposition begins, based on the same theme and another brand new theme (Example 11), simultaneously. These two themes work themselves out with increasing intensity and exuberance, until they are joined in a somewhat hidden manner, that is, in an inner voice, by a new version of the main theme (Example 12). The intensity and exuberance, the latter quality created mainly by the almost exaggerated repetitions of the second theme (Example 11), continue to the end.

Contrapunctus 9 is a fugue on a new subject (Example 13) that is loosely derived from the main theme. Whereas Contrapunctus 8 opened with a descending whole-step (see Example 10), this movement opens with an upward leap of an octave. This is a contrast to Contrapuncti 1–7, all of which opened with the interval D–A or A–D. Contrapunctus 9 is a lively, flowing piece in which exuberance, though present, is restrained. The main theme enters in augmentation in the soprano voice in measure 35 and is heard several times thereafter.

Contrapunctus 10 opens with a fugue exposition on a subject (Example 14) whose rhythmic and melodic peculiarities create more of a sense of expectation than of fulfillment. The expectation is met with the entry of the main theme in the soprano voice in measure 23. What follows is a fugue on this subject, in which Example 14 serves as a countersubject. So many new motives are introduced, developed briefly, and then abandoned, that the movement becomes a celebration of fecundity (or perhaps of profligacy!). The countersubject (Example 15) that appears in measures 22–26, and does not appear again in this movement, will supply the subject of the second section of Contrapunctus 18 (see below).

Contrapunctus 11 is the centerpiece of The Art of the Fugue. It is probably the most complex contrapuntal creation of J. S. Bach, as well as one of the most deeply and powerfully expressive. It is a contrapuntal fantasy making significant use of at least ten different themes and including five fully worked out fugue expositions. It is related to what has come before and what will come after in more ways than it is possible to describe. All of the thematic material is taken from earlier contrapuncti, mostly from Contrapunctus 8, but also at least from 3 and 10. The richness of thematic material is reminiscent of 10, while the compactness with which it is used is reminiscent of 7. The sectional construction is reminiscent of 5 and 8. The compellingly powerful cadences suggest number 4. The most powerful of these cadences is followed by the introduction of the B-A-C-H motive, which looks forward to Contrapunctus 18 and also back to number 8 (see above under B-A-C-H). At measure 158, the main theme and its inversion are again, as in Contrapunctus 5, united in absolute simultaneity, this time without the concealment that marked this event in the earlier movement.

Contrapunctus 11 opens with a fugue exposition on the main theme, with passing tones and altered rhythmically as in Contrapunctus 8. The opening rhythm is the same as that of Contrapunctus 10. Following a cadence in measure 27 there is a loosely constructed fugal exposition on the two new themes: the inversion of the first theme of Contrapunctus 8 and a chromatic theme filling out the interval of a fifth. These themes are joined by a motive taken from Contrapunctus 3. This section ends with a cadence in measures 70–71. The next section is a short fugal exposition on the inversion of the opening theme, in which the motive borrowed from Contrapunctus 3 is also used. In measure 89 there begins a long, rather freely constructed fugue based primarily on the new eighth-note theme that incorporates the B-A-C-H motive. All of the thematic material that has been introduced so far in this movement participates in this section, which lasts until measure 158. At this point The Art of the Fugue theme and its inversion enter simultaneously in the soprano and alto, and then in the tenor and bass. The remaining thirty bars are concerned with a limitlessly joyous uniting of themes in all possible combinations. The main theme appears for the last time (in this movement) in the soprano in measure 180. The last note of this theme is also the last note of Contrapunctus 11 (see Example 16 a–j for all the thematic material of Contrapunctus 11).

At this point, power, grandeur, complexity, repetition, development, and intensity have gone as far as they can. The next four movements are relatively short, quiet, and simple, though not any less expressive. They are strict canons in two voices. Contrapunctus 12 is a canon at the octave based on an ornamented version of the main theme in triplet sixteenth notes (Example 17). It is a good-humored, even humorous, piece. Contrapunctus 13 is somewhat darker in mood. It is a canon at the twelfth, based on a close variant of the main theme (Example 18). Its rhythmic interest comes from an alternation between triplets and duple rhythms. Contrapunctus 14 is a canon at the tenth, based on a completely straightforward version of the inverted main theme. This is accompanied by a quiet, rather wistful triplet figure (Example 19). Contrapunctus 15 is a canon by augmentation in contrary motion. That is, the second voice enters with an inversion of the first voice, at half speed. The second voice falls progressively farther behind, and by the end it has presented less than half the musical material of the first voice. As if to be fair, Bach has arranged the work in two sections, with the upper and lower parts changing roles halfway. This canon is based on a chromatically altered version of the main theme (Example 20, p. 24). The effect is rather weird, both disquieting and humorous.

Contrapunctus 15 reintroduces a principle of inversion that was so important through number 11. Contrapuncti 16 and 17 carry this principle farther than before. Each is in two sections, and, in each case, the second section is a note-by-note inversion of the first. These are contrapuntal tours-de-force of the highest order, all the more so since in both cases the inversions sound just as natural, spontaneous, and free as the original forms. Contrapunctus 16 is in three voices, and based on a triplet version of the main theme, reminiscent in different ways both of Contrapunctus 9 and of Contrapunctus 12 (Example 21, p. 24). The style is that of a moderately lively trio sonata movement. Contrapunctus 17 is a four-voice fugue based on a version of the main theme that is identical to the original version (Example 1), except that it is in triple time (Example 22, p. 24). The texture is very thick. With many voice crossings, the contrapuntal nature of the work is somewhat obscured. The mood is dreamy and brooding. In measure 21 a new version of the subject enters (Example 23, p. 24), which is derived from a short countersubject figure (Example 24, p. 24), which was, in turn, derived from the last four notes of the subject itself. Each half of the work ends with a flourish in sixteenth notes.

Contrapunctus 18, the last movement of The Art of the Fugue, is a monumental work, surpassing even Contrapunctus 11 in scale, and equaling it in expressive power. It was left incomplete. Bach died either before he wrote the ending down or before he was even able to conceive of an appropriate ending to a work of this stature. In its present form, the movement has 239 measures. Any formally adequate continuation and ending would bring the length of the work to over four hundred measures, making it very likely the longest fugue from the Baroque era. This, however, was not to be.

The movement opens with a fugue in four voices on an apparently new theme (Example 25). The first four notes of this theme, however, are identical to the first four notes of the main theme (with passing tones). After the fourth note the theme doubles back on itself, in an allusion to the mirroring process whereby the previous two movements were created. Thus this theme is a version of the first half of The Art of the Fugue theme. This new theme can also be derived directly from the second half of the first subject of Contrapunctus 8 (see Example 10). Furthermore, the very first two notes of Contrapunctus 18 are an exact echo of the last two notes of Contrapunctus 17; and the whole of Example 25 is essentially the same as the flourish that ended the first half of that movement. The fugue built on this subject—one of extraordinary grandeur—lasts 115 measures. It overlaps with a new fugue on a new subject (Example 26). This subject is derived closely from a theme that was introduced briefly in Contrapunctus 10 (see above and Example 15). It also includes, on strong beats, all of the notes of the main theme that are missing from the first theme of Contrapunctus 18: it completes that theme. This fugue is livelier in character than the first fugue. The first theme does enter, however, five times as a kind of cantus firmus. The last two such entries are in stretto with each other. This fugue ends in measure 193. A third fugue now begins, on the B-A-C-H theme in the simplest, most straightforward possible form (Example 27). This section brings a return to the majestic quality of the first section, but it is much shorter. In measure 233 it gives way to a return of the second subject in (partial) stretto with itself. This is joined one measure later by the first theme in the bass, and, one measure later still, by the B-A-C-H theme in the tenor. The three themes are united; the main Art of the Fugue theme is present only by implication or by transfiguration. At this moment the work ends. There is no cadence, no resting place. It ends as abruptly as could be. We are challenged to accept that the meaning, quality, and completeness of a work of art, as of a human life, do not come from the timing or nature of its end, but from what it is and what it does.

The Clavier-Übung Third Part

Michael Radulescu

Michael Radulescu, born in Bucharest, Romania, studied organ and conducting in Vienna at the Academy (now University) of Music and Performing Arts where he taught as professor of organ from 1968 to 2008. His career encompasses work as a composer, organist, and conductor. Since his debut in 1959 he has presented concerts throughout Europe, North America, Australia, South Korea, and Japan. He regularly gives guest lectures and masterclasses in Europe and overseas, focusing mainly on the interpretation and elucidation of Bach’s organ and major choral works.

As a composer, Radulescu has written sacred music, works for organ, voice and organ, choral and chamber music, and orchestral works. He is also in demand as a jury member in international organ and composition competitions and as an editor of early and ancient organ music. Radulescu conducts international vocal and instrumental ensembles in performances of major vocal works. As an organist, he has recorded among other things Bach’s complete works for organ, without any technical manipulation.

For his musical and pedagogical contributions Radulescu was awarded the Goldene Verdienstzeichen des Landes Wien in 2005. In 2007 he received Würdigungspreis für Musik from the Austrian Ministry of Education and Art. In December 2013 Michael Radulescu’s book on J. S. Bach’s spiritual musical language, Bey einer andächtig Musiq . . .,
focusing on the two Passions and the B Minor Mass was published.

When approaching Baroque music in general and spiritual music in particular, it is of greatest importance to take into consideration the fundamental difference between the function and the aims of music in the Roman Catholic rite and the Lutheran conception of music. While Roman Catholic music mainly embellishes and adorns the liturgy, Lutheran music wants to preach, to impress, to move, to convince every single listener. Whereas the mystery of the Canon is at the center of the Roman Catholic Mass, the announcing and the elucidation of the Word of God, spoken by the minister and sung or performed by the church musician, stand at the core of the Lutheran Divine Service.

From this dichotomy results the overwhelming importance of rhetoric, of the musical speech (Klangrede) in Lutheran music. Both the ancient rules of rhetoric and the use of the rhetorical-musical figures determine respectively the overall formal concept of a work as well as the invention of characteristic “speaking motifs.”

In the case of J. S. Bach’s music, however, there also seems to be a more subtle, profound, and hidden means of communicating a message, an interpretation of a text. This happens through the ample use of symbols such as allegories, certain characteristic motifs and specific numerical ratios between different sections of the overall formal concept of a piece, and also, most controversial of all, as numerological entities. The latter aspect has been both heartily emphasized and strongly questioned and even ruled out by scholars and practical performers in recent decades. Nevertheless, a surprising hint at the possibility of Bach’s interest in the use of the “numeric alphabet” seems to be, among others, the theoretical work called Cabbalologia by Johannes Henningius (Johann Henning), published in Leipzig in 1683. This publication is said to have been found also in the famous private library of Bach’s neighbor and colleague Johann Heinrich Ernesti, former rector of Saint Thomas Church in Leipzig.

I

Bach published the Third Part of his Clavier-Übung for the feast of Saint Michael at the end of September 1739 on the occasion of the bicentenary of the Lutheran Reformation in Leipzig. This collection of keyboard compositions is generally known under the titles “The Organ Mass” or “The Dogma Chorales,” neither of which can suggest the complex meaning and the message of the entire opus.

It should be remembered that when Luther introduced his Reformation in Leipzig in 1539 he preached on Pentecost Monday in the Leipzig Pleissenburg Castle on two most crucial themes: the Mystery of the Trinity in the Lutheran Mass and the Lutheran Catechism. Most significantly, Bach takes both these theological categories into consideration and, obviously referring to Luther’s sermon of 1539, treats them consistently in his Third Part of the Clavier-Übung. Of the total of twenty-one chorale settings in the collection, the first nine deal with the Lutheran Missa brevis (which includes only the “Kyrie-Christe-Kyrie” and the “Gloria”), while the remaining twelve chorales follow exactly, chapter by chapter, Luther’s Catechism of 1529.

Seen as a whole, the entire Clavier-Übung III seems to suggest a most striking resemblance to Bach’s own organ improvisations as described by his first biographer, J. N. Forkel, in 1802:

a) a great prelude and fugue in Organo Pleno as an opening;

b) a long series of different kinds of chorale settings with a varying number of parts;

c) a great fugue in Organo Pleno at the end.

In Bach’s Clavier-Übung III, these correspond to the following sections:

a) the E-flat Preludium in Organo Pleno also containing the two fugal sections;

b) the 21 chorale settings in 3, 4, 5, or 6 parts, as well as four duettos;

c) the E-flat Fugue in Organo Pleno.

Two further allusions to the Trinity are most interesting in the overall plan of the entire collection. These are manifest already in the title, “Third Part of the Clavier-Übung,” and also in the use of the majestic key of E-flat major, with its three flats in the signature, for both the opening Prelude and the closing Fugue. Also striking is the fact that both the Prelude and the Fugue appear to be determined by the number 3 (three main musical ideas in the prelude and three themes in the triple fugue).

Another obvious hint at the Trinity is the fact that the first 9 chorales dealing with the Lutheran Mass are organized in 3 groups of 3 each: 3 “great” settings for Kyrie-Christe-Kyrie, 3 “small” alio modo settings for the same cantus firmi Kyrie-Christe-Kyrie, and 3 settings for the German Gloria, “Allein Gott in der Höh’ sei Ehr.”

The remaining 12 chorales, which follow Luther’s Catechism, are arranged by 3 + 3 groups of 2 each, the first group dealing with the 3 main chapters of the Catechism (The Law of the Lord = The Ten Commandments, The Creed, and The Prayer of the Lord = The “Our Father”), and the second with the 3 chapters concerning the Sacraments and the Penitence respectively (Baptism, Penitence as continual renewal of Baptism, and the Communion). Each of these cantus firmi is treated twice, in a “great” version with pedal and in a “small” version without pedal, mostly in another key.

It has often been suggested that these two contrasting versions may allude to Luther’s “Great Catechism” versus its reduced form, the “Small Catechism” for younger and “more modest people.” This double treatment of the “catechism settings,” however, seems also to allude to the double form of liturgy: as the great, official one “in churches,” versus its “small,” intimate, personal form “at home,” within each Christian family. Interestingly enough, this dualism appears also in the original subtitle of the Clavier-Übung III dedicated to both amateurs (Liebhaber) and connoisseurs (Kenner).

II

The opening Praeludium pro Organo pleno, Bach’s largest organ prelude, suggests, in spite of the original slurring of the dotted rhythms of its beginning, the pattern of a French overture:

a) majestic homophonic section with dotted rhythm, measures 1 to 70;

b) Fugato section, measures 71 to 97;

c) majestic homophonic section with dotted rhythm, measures 98 to 129;

d) Fugato section, measures 130 to 173;

e) majestic homophonic section with dotted rhythm, measures 174 to the end.

The three different musical ideas used by Bach seem to illustrate in a marvelous way the three Persons of the Trinity:

1. majestic five-part homophonic section for God the Father (Example 1);

2. transition passage with staccato notes suggesting drops of tears (as in the Passions and in several cantatas) and a plaintive theme in the right hand, full of suspensions and chromaticisms and going to the “extreme” keys B-flat minor and E-flat minor, respectively (musical-rhetorical figure of parrhesia), suggesting the human sufferings, the Passion and Death of God, the Son (Examples 2 and 3);

3. The fugal sections using the most spiritual writing, the fugue, and a theme which by its shape (musical-rhetorical figure of hypotyposis) suggests the movement and the shape of the flames, the fire of God, the Holy Spirit (Example 4).

III

Considering the 9 chorale settings of the Missa brevis, the great “Kyrie-Christe-Kyrie,” the small “Kyrie-Christe-Kyrie,” and the 3 “Allein Gott” settings, one notes the following characteristics:

• The first three settings of the great “Kyrie-Christe-Kyrie” are written in the ancient vocal, a cappella style, the stylus gravis, using the so called white notation (breves, whole notes, half notes, quarter and, more rarely, eighth notes as note values). According to Bach’s cousin
J. G. Walther the stylus gravis is “majestic, serious . . . and best appropriate to elevate the human soul to God.”

• The respective cantus firmus descends within this first triad from the soprano in Kyrie, Gott Vater in Ewigkeit (highest part ~ God Father as the Highest) into the tenor in Christe aller Welt Trost (middle part ~ God the Son as the Mediator) and finally into the pedal-bass in Kyrie, Gott, heiliger Geist (bass part ~ God, the Holy Spirit as the universal Basis). This katabasis, i.e., “descending movement,” suggests the descending of God’s mercy upon us and depicts the “eleison” (“have mercy”).

• The tenor cantus firmus in Christe aller Welt Trost stresses the idea of Christ as the Mediator between God and Man, as strongly emphasized by Luther.

• The bass cantus firmus in Kyrie, Gott, heiliger Geist, on the other hand, represents the fundamental Lutheran idea of Justification through the power of Faith; the text of the chorale also prays for “the reinforcement of our Faith.” The final section of this setting, “eleison,” is excruciatingly dissonant, once again stressing human misery awaiting God’s mercy.

• The total number of measures of all three large chorale-settings is a primary, indivisible number:

Kyrie (42 measures) + Christe (61 measures) + Kyrie (60 measures) = 163 ~ indivisibility of the Holy Trinity!

• The three small settings of “Kyrie-Christe-Kyrie” strongly contrast with the preceding three works. The cantus firmus is only hinted at by quotation of its first phrase. Their writing is manualiter, without pedal, and in a soft “cantabile clavier style.” This might suggest love and the soft breath of the Holy Spirit by its “cantability.”

• All three small settings end modally on an E-major chord.

• The time signatures of all these 3 chorales also allude to the Trinity, being “progressions” of the number 3: 3/4; 6/8; 9/8 (= 1 x 3/4; 2 x 3/8; 3 x 3/8).

• The three Allein Gott in der Höh’ sei Ehr settings fulfill a wonderful anabasis (ascending movement) by the sequence of their keys: following the small “Kyrie-Christe-Kyrie” settings ending all on E major, they rise up to F major, G major, and finally to A major, thus obviously alluding to Gloria in excelsis (Allein Gott in der Höh’/“Glory to the Lord in the Highest”).

• All three settings are trios and written in an “instrumental keyboard style,” the first and the last in a brilliant, light style, the second à 2 Claviers et Pedale imitating violins or flutes accompanied by a basso continuo in the pedal.

• The G-major trio on “Allein Gott” seems to stress Jesus’s role as Lamb of God, alluding to the third stanza of the chorale, “Lamb of God, holy Lord and God, accept the prayer of our misery,” by citing these two verses in canon, a most simple symbol for “one part following another part:” first between the right hand and pedal in measures 78 to 83, and in measures 87 to 92 between the left hand and pedal, and thus alluding to the Gospel of John, 1:29–30: “The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which taketh away the sin of the world. / This is he of whom I said, After me cometh a man which is preferred before me: for he was before me” (Example 5).

IV

The density and complexity of Bach’s dealing with the theological message through music is most impressively revealed in the settings of chorales treating the main chapters of Luther’s Catechism: the Ten Commandments, the Creed, and the Lord’s Prayer.

The large setting of Dies sind die heil’gen zehn Gebot is written in five parts distributed on two manuals and pedal. The cantus firmus is carried out as a canon between the two tenor parts played by the left hand while the right hand plays the two free upper parts. Surprisingly, these free parts never imitate or cite the cantus firmus.

Most interesting is the fact that in Bach’s treatments of this cantus firmus (Orgelbüchlein, the cantata BWV 77 Du sollst Gott, deinen Herrn, lieben, and the two settings in the Clavier-Übung), he uses the same key, Mixolydian on G, the “pure” key without accidentals in its signature. Never does this cantus firmus appear transposed: this obviously suggests the “immutability of the Divine Law.” Most consistently, the treatment of the cantus firmus as a canon also evokes the “severity of God’s Law.”

A further symbolic meaning of the musical texture is the setting of the canonic cantus firmus in the two middle parts, which clearly refers to Luther’s commentary in his Catechism, regarding the way to keep the Divine Law through “Christ’s the Mediator’s Intercession.”

The beginning of the chorale is most serene, diatonic, and calm, and takes place over an organ point in the pedal. After four measures of “complete harmony” the character changes in the fifth measure: the alto plays a “harsh” descending chromatic figure (the figure of parrhaesia) while the soprano plays three times a “sighing figure” consisting of a sixteenth rest followed by three sixteenth notes, and followed by two groups of stepwise descending eighth notes (Example 6).

This seems to be a strong allusion to the Book of Genesis describing the Garden of Eden (= full harmony~4 measures) and Adam’s Fall in the fifth measure (Adam in Hebrew meaning man and being symbolized, according to Andreas Werckmeister, by the number 5 for man’s 5 senses, 5 fingers and toes, and also hinting at Jesus’s 5 wounds on the Cross).

Interestingly enough, this “sighing” figura suspirans is played by the two upper parts during the whole piece exactly 33 times, reminding of the 33 years of Jesus’s earthly life.

From measure 6 on this figure appears also “transformed” into another figure called kyklosis or circulatio and suggesting a “turning around,” an “insecurity” or, as in our case, a great joy.

This “transformation” of suffering (“sighing figure”) into joy (“turning around in joy”) perfectly matches Luther’s commentary about the Commandments, stressing that those who keep the Law apparently suffer in this earthly world, but that through Christ they shall live in joy.

Luther also considers the First Commandment as being the most important of the Decalogue. It is this very commandment that is cited in the second stanza of the cantus firmus, the stanza to which the great chorale setting seems to allude the most: “I alone am your God and Lord. Thou shalt not have other gods; thou shalt love me from the bottom of your heart. Kyrieleis.”

It is when the cantus firmus expounds the phrase “Thou shalt not have other gods” that the pedal plays a “huge” and “exaggerated” interval of two octaves,
C – c′ (the figure of hyperbole = exaggeration) and obviously referring to God’s immensity (Example 7).

Astonishing is the fact that the motif of measures 47 and 48 appears altered in measures 51 and 52, transformed insofar as it is now divided between the two upper parts: one part continuing the other, and thus suggesting the idea of “two parts becoming one” (the figure called heterolepsis = meaning this continuity, the unification of two parts, i.e., love, as described by J. G. Walther). It is striking to note how often Bach makes use of this figure when alluding to love, to unification in and through love. Not surprisingly, this figure appears in our chorale setting only two times, exactly where each of the two canonic cantus firmus parts play the notes for lieben mich (love me); as one can easily see in the “transformed” version, the motive is played by two “unified” parts according to the text line “Thou shall love me” (Example 8).

If we take a look at the pedal part we note that it is divided into several sections either by rests or by the recurring long organ point on A in measure 29. A most intriguing and striking speculation presents itself in this context when considering the number of notes of each of these sections:

a) measure 1 to 10 = 37 notes

b) measure 10 to 20 = 60 notes

c) measure 21 to 28 = 47 notes

d) measure 29 to 55 = 147 notes

e) measure 56 = 5 notes

f) measure 57 = 5 notes

g) measure 58 to 60 = 14 notes

 

a) Could 37 represent the monogram JCHR for Jesus Christ? (the number alphabet with the correspondence between the letters of the alphabet and the natural numerical order: A = 1, B = 2, C = 3, . . ., Z = 24, with I = J and U = V as in old Latin: J (9) + C (3) + H (8) + R (17) = 37);

b) Could 60 allude to the Old Testament, to the 6 Days of God’s Creation, and also to the 10 Commandments = 60?

NB! Bach occasionally uses the number 6 as allegory for the Creation, for the Entire World (also Orgelbüchlein: Christum wir sollen loben schon, measure 6, where the whole range of the organ is encompassed by the lowest C in the pedal and the highest C in the treble part).

NB! Luther always sees and treats the Old Testament considering the New Testament and vice versa.

c) Could 47 recall the 47th Psalm, mentioned by Luther in his Great Catechism: “O, clap your hands, all ye people; shout unto God with the voice of triumph. / For the Lord most high is terrible; He is a great King over all the earth”?

NB! This third section of the pedal starts in measure 21 where the cantus firmus plays the phrase “Thou shalt not have other gods.” Also, it is here where the pedal plays the enormous, exaggerated interval of the double octave, which also perfectly matches the second verse of Psalm 47.

d) Could 147 recall the 11th verse of the 147th Psalm: “The Lord taketh pleasure in them that fear Him, in those that hope in His mercy”?

NB! Luther himself quotes Ps. 147, 11 in his Catechism, in the chapter dedicated to the Ten Commandments. This could make the assumption mentioned above quite plausible!

e) & f) Could the number 5 possibly allude in this context to mankind (five senses; the five wounds on Jesus’s crucified body) as “the Old” vs. “the New Man”?

g) 14 might well suggest Bach’s own name (B [2] + A [1] + C [3] + H [8] = 14) as his personal commitment as a believer, as the pro me (= “for me”), a central point in Luther’s theology.

Another interesting symbolic connotation is suggested by the general form of the chorale setting. The total of 60 measures is clearly divided into two unequal sections considering the sort of “recapitulation” of the beginning, in measure 29:

28 measures (= 7 x 4) + 32 measures (= 8 x 4) = 60 measures, or 28 : 32 = 7 : 8.

Could 7 allude to the seven days of the week, of the 6 + 1 days of the Creation of the earthly world and 8 to the eighth day (the day of Messiah)? Could this overall form and its “articulation” transmit the message of Redemption?

The “small,” manualiter version of Dies sind die heiligen zehn Gebot seems to have a more obvious, more straightforward approach to the text. It is a fughetta using the theme in both normal and inverted position. The gigue-like theme is characterized by the strongly repeated notes at its beginning and by strong leaps followed by stepwise passages. It is most interesting to note some aspects of this piece:

1) the title in the original print from 1739 is Dies sind die heiligen zehen Gebot consisting of exactly 10 syllables (Ten Commandments?)

2) the repeated G in the theme appears 14 times (BACH’s commitment? See above).

3) the theme appears 4 times in normal, 4 times in inverted, and again 2 times in its normal forms, i.e., 4 + 4 + 2 = 10 times (see above).

4) there is quite a long interlude without the theme between measures 18 and 31, lasting 14 measures (see above).

V

The large chorale setting dealing with the Creed, Wir gläuben all’an einen Gott (Schöpfer) is striking because of its dynamism, abundant syncopations, “modern” 2/4 time signature, constant movement in sixteenth notes, and lack of organ points in the pedal, by the six times of the pedal ostinato, and the flamboyant movement of the manual parts. The theme treated in the manual is rooted in the first phrase of the cantus firmus, and it is this very phrase that appears literally quoted in the tenor in the last 12 measures of the piece. The overall flamboyant, dynamic character of this setting might be surprising, but it seems in perfect coherence with Luther’s idea of a willful, powerful, and passionate personal commitment of each believer aiming to attain personal justification.

Some characteristics of this composition might elucidate its possible further message:

a) the total of exactly 100 measures of the piece might suggest the idea of the totality of the Creation (Gott Schöpfer = God, the Creator);

b) the 6-fold appearance of the pedal ostinato might hint at the 6 “working” days of God’s Creation (see above);

c) the quotation of the first cantus firmus phrase in the tenor, starting in measure 89 might allude to Christ as the Mediator;

d) the last pedal entry is longer than its other entries and has exactly 43 notes; this may well mean: (C [3] + R [17] + E [5] + D [4] + O [14] = 43: CREDO) “I believe.”

NB! Interestingly enough, the score of the first Credo chorus in the B Minor Mass shows the word “Credo” written 43 times and heard 41 times, i.e., J-S-B-A-C-H’s creed.

The small version of the same chorale is written as a short manualiter fughetta in the style of a brilliant French overture. This surprising setting can be seen as an introduction to the large version of The Lord’s Prayer, Vater unser im Himmelreich, written in the same key of E Dorian. More likely, however, it also seems to have the function of dividing the whole set of 21 chorales into 12 + 9. One should remember that, on the other hand, the 21 chorales are also divided into 9, dealing with the Lutheran Mass, and 12, treating Luther’s Catechism and the Sacraments. A very beautiful parallel, indeed!

VI

The large version of Vater unser im Himmelreich is possibly Bach’s most difficult and intricate organ work. It is written in 5 parts distributed once again among the two manuals and the pedal, with the cantus firmus in canon. Unlike the Ten Commandments however, each hand here plays a free voice and a canonic cantus firmus part.

Some characteristics may help understand and elucidate the enormous complexity of this composition:

a) the slow, majestic tempo in the 3/4 time signature suggests the austere character of a slow sarabande;

b) the pedal is treated as a basso continuo without quoting the cantus firmus;

c) the cantus firmus is treated in canon suggesting our intimately repeating the prayer spoken by Jesus according to Saint Mark and Saint Matthew;

d) the alternating order of the canonic parts at each new entry seems to suggest a still dialogue between the believer and Jesus;

e) the free manual parts are based on a theme quoting the richly embellished first phrase of the cantus firmus (Example 9);

f) each hand expounds this theme 3 times, alluding probably once more to the Trinity;

g) the two free manual parts display an enormous rhythmical richness with frequent use of the “plaintive” Lombard rhythms and the staccato triplets (Example 10);

h) this “plaintive” Lombardian rhythm and the overall rhythmical complexity seem to depict Luther’s comment on The Lord’s Prayer expressing the “multitude of human miseries;”

i) the staccato triplets obviously describe Saint Matthew 7:7: “Ask and it shall be given to you; seek and ye shall find; knock and it shall be opened unto you.” As a matter of fact, this very verse appears quoted in practically all older Lutheran hymn books on the page where the chorale Vater unser im Himmelreich is printed. The staccato triplets may also allude to drops of tears;

j) there is only one spot where the pedal quotes the “plaintive” Lombardian rhythm and this happens in measure 41 (J [9] + S [18] + B [2] + A [1] + C [3] + H [8] = J. S. BACH), alluding to the composer’s personal commitment.

After this extraordinary piece, the alio modo manualiter version of the same cantus firmus is a simple, quiet meditation on the Prayer, devoid of all further speculative symbols.

VII

Following Luther’s Large Catechism exactly, Bach now treats the Sacraments of Baptism in Christ, unser Herr zum Jordan kam, Penitence in Aus tiefer Not schrei ich zu dir, the latter considered by Luther as the continuation and constant renewal of baptism, and finally the Sacrament of Communion in Jesus Christus, unser Heiland.

The large version of Christ unser Herr zum Jordan kam treats Jesus’s baptism as described in Saint John, Chapter 1. The piece is set for two manuals and pedal with the cantus firmus in the latter, the bass in the left hand and the two upper parts in the right hand. This setting is quite full of important symbolic meanings:

a) the tenor cantus firmus in the pedal suggests, as the middle part of the setting, Christ’s role as Mediator between God Father and mankind;

b) the almost constant movement in sixteenth notes in the left hand bass part seems to allude to the flow of the waters of the Jordan River;

c) the two upper parts of the right hand can be seen as a symbol for the Holy Spirit floating above the scene of Christ’s Baptism by Saint John the Baptist. The beginning four notes in each of the two upper parts seem to depict, as a hypotyposis, a cross motif. Also, the most intricate imitations between the small motives of the two upper parts can be seen as a hint to the Holy Spirit proceeding from the consubstantiality of God Father and God Son, as mentioned in the Nicene Creed (Example 11).

d) NB: the final note of the fifth chorale phrase in the pedal d° seems to generate a “wrong” 6/4-chord d° - g° - b′: This is to be seen as a hint to avoid the wrong harmony by the use of a 4′ reed in the pedal if the left hand were based on 8′, or a 16′ basis for the left hand, should the pedal be played only on an 8′ basis!

e) The total number of measures, 81, equals 3 x 3 x 3 x 3 as a most impressive symbol for the Trinity.

The small manualiter version of the same chorale is quite a short fughetta based on the first phrase of the chorale, combined with an “obbligato” counter-subject, both treated in normal and inverted position. Could the theme itself represent Christ and its inverted form Christ’s descent on Earth? Could the countersubject stand for Saint John the Baptist? Interesting enough is the fact that this fughetta consists of 27 measures (3 x 3 x 3) with exactly 81 quarter notes (see above).

The large version of Aus tiefer Not schrei ich zu dir, the German version of Psalm 130, “De profundis,” is an exceptional work, as it is written in the old, solemn, majestic vocal stylus gravis or motet style, which, according to Johann Gottfried Walther’s Musicalisches Lexicon of 1732, is able to “elevate the soul to God.” This setting marks a pinnacle in Bach’s entire organ music insofar as it is written in six parts, four in the manual and two in the pedal, with the augmented cantus firmus of Luther’s chorale melody in the right foot’s part. This obviously seems to be an allusion to the significance of the upper bass part as the voice of the Old Testament psalmist. Most impressive is also the fact that at the beginning of the last verse of the chorale Wer kann, Herr, vor dir bleiben? (Who can, Lord, stand before Thee?) in the seventh to last measure, the upper bass part playing the cantus firmus is the highest part in the whole texture (Example 12).

• The registration should be the Organo pleno, i.e., an 8′ based Plenum  in the (coupled) manual(s) and 16′ Plenum in the pedal, without mixtures but with reeds 16′, 8′, and 4′.

• This setting is obviously inspired by the great pleno settings in five parts, with double pedal, in Matthias Weckmann’s great chorale settings with the cantus firmus in the upper pedal part.

NB! In one of the Lüneburg tablatures containing Weckmann’s majestic hymn on O lux, beata Trinitas the opening first movement in five parts with double pedal and the cantus firmus in the upper bass bears the indication that the cantus firmus of the upper bass could be played in the pedal by the right foot, or on the manual by the left hand, or also by both the pedal and the left hand together. This comment seems to confirm the registration mentioned above, with the result that the left foot bass is playing in the reeds-pleno, the manual parts in the mixture-pleno and the cantus firmus in both the reeds- and the mixture-pleno, and thus strengthening the cantus firmus.

The following alio modo manualiter version of the same chorale is written in four parts. Learned contrapuntal imitations in the three lower parts—in normal and inverted form—of each phrase of the chorale, anticipate each phrase of the augmented cantus firmus expounded each time by the treble part.

• Each section of the piece begins with five contrapuntal measures in intricate counterpoint between the three lower parts, followed by eight bars expounding the respective phrase of the chorale in the treble and one supplementary bar concluding each section.

• The overall organization of the piece is quite extraordinary:

Sections a), b), c) & d): 5 + 8 + 1 bars; section e): 5 + 8 + 5

• But 5 + 8 + 1 = 14  [= B-A-C-H = 2 + 1 + 3 + 8] and 8 : 5 stands for the golden ratio.

The large version of Jesus Christus, unser Heiland, der von uns den Zorn Gottes wandt is a trio for the two manuals and pedal with the cantus firmus in the latter. It seems quite interesting that the pedal oscillates between playing the tenor and bass parts. Could this hint at Jesus’s double nature, as God and Man?

• The two manual parts seem to actually symbolize the “Wrath of God” by their extremely virtuosic, agitated, and aggressive movements in sixteenth notes and eighth notes.

• The main theme in the manuals starting with big and then diminishing intervals (tenth-octave-sixth) could possibly hint at Man’s approach to God, whereas, on the other hand, these leaps sometimes occur also in the opposite direction, from smaller to larger (sixth-octave-tenth). The message of these patterns seems to be the “struggle” between God and sinful mankind expecting redemption through communion, Luther’s second sacrament.

The following alio modo version of the same chorale is a very complex fugue in F minor, using as a main theme the first phrase of the cantus firmus. The extremely rich counterpoint and the surprisingly daring new motives seem to recall the big, learned fugues of the Well-Tempered Clavier, Book II.

• The augmented entry of the main-theme in the tenor part in measure 57 might be another symbol for the praise of Christ the Lord, as the mediator between God and Man.

• NB! In order to emphasize this augmented theme in the tenor it should be helpful to use a registration of foundations (principals) 8′ and 4′ and a trumpet 8′.

VIII

Most intriguing and surprising part of the work are the following four duettos preceding the final Fugue in E-flat Major. Some speculations might help justify their presence:

a) Luther adds a “Short Admonition of Confession” after the chapter about Communion. In this short appendix he quotes the various ways of confessing: 1. to the priest/pastor; 2. as an open and common confession in front of the congregation; 3. to the neighbor; and 4. to God;

b) in the first part of his Large Catechism Luther quotes the four elements of the world: 1. Fire; 2. Air; 3. Water; 4. Earth;

c) in his Neu vermehrtes Hamburgisches Gesangbuch (New Hymn Book) from 1739, Vopelius inserts after the Catechism Hymns other hymns for: 1. the morning; 2. the evening; 3. before meals; 4. after meals;

d) taking into consideration the Baroque Theory of Affects one can easily imagine a certain parallel with the four temperaments: 1. choleric; 2. sanguine; 3. phlegmatic; and 4. melancholic temperament;

e) the duettos form a tight unity: their tonal progression ascending from E to F, to G, and finally to A corresponds strikingly to the sequence of keys in the “Trinity chorales” 4 to 9, and thus leading to the first note, B-flat, starting the following fugue;

f) two of the duettos are in a major (II and III) and two in a minor key (I and IV);

g) two are in a ternary (I: 3/8 and III: 12/8) and two in a binary (II: 2/4 and IV: 2/2) time signature.

h) two start with the right hand (I and II) and two with the left hand (II and IV).

It also seems quite remarkable how well the duettos match—by their astonishing variety and by their individual character—both the conception of the four elements (mentioned by Luther in his Great Catechism) and that of the four temperaments and even maybe of the four archangels (Michael, Gabriel, Raphael, and Uriel) as well as the four Evangelists (?).

Duetto I: E-minor key; 3/8 time signature; right hand starts, left hand follows; 73 measures; perfectly symmetrical form based upon the golden ratio (28 measures + 17 measures + 28 measures = 73 measures // 28:17 = ~ 1.64; 45 (= 28 + 17) : 28 = ~ 1.7; 73 (= 28 + 17 + 28) : 45 = ~ 1.62); flamboyant themes and countersubjects suggesting flames of fire; Archangel Michael (with attributes: fire, sword, perfect balance); choleric temperament (?); element Fire (?).

Duetto II: F-major key; 2/4 time signature; right hand starts, left hand follows; 149 measures; perfectly symmetrical form of: 37 + 31 + 13 + 31 + 37 measures. NB! 37 could stand for Christ’s monogram in the Greek alphabet [ChRistos]: X ~ CH (= 20) + P ~ R (= 17); 31 may stand for the Latin “In Nomine Jesu” (In Jesus’s Name): [I (= 9) + N (= 13) + I (= 9) = 31]; 13 could allude to Jesus and his Twelve Apostles at the Last Supper. NB! This section of 13 measures from measures 69 to 78 is the center, the middle of the whole piece in which the measures 74 to 78 are the exact “inversion” of measures 69 to 73; could that maybe hint to Jesus’s death?; element Air (?) (Example 13).

The overall form of the piece is quite complex, insofar as the first section and its da capo recapitulation (both 37 measures) are in major and in a serene, joyous mood, whereas the second and penultimate sections (both 31 measures) are in minor and written as canons; might this “discrepancy” remind one of the sanguine temperament (?); Air; could the three references to Jesus Christ (see above) suggest a link to the Archangel Gabriel, Jesus’s messenger (with the attributes: lily and fish); could the perfect formal symmetry represent the symmetrical beauty of a lily?; could the inversion, the crossing of the parts in measures 69–78 hint at a symbol for Christ’s Cross and Death?

Duetto III: G-major key; 12/8 time signature; left hand starts, right hand follows; 39 measures:

15 + 8 + 15 + 1 = 39 measures; 15 (= 3 x 5) + 24 (= 3 x 8) = 39 (= 3 x 13) = golden ratio (cf. Fibonacci); melancholic temperament (?); could the very serene character of the piece remind of the Archangel Raphael (with attribute: fish)? element Water?

Duetto IV: A-minor key; 2/2 (Alla breve) time signature; left hand starts, right hand follows; two themes are used (a and b); 108 measures arranged as 8 (a) + 8 (a) + 16 (b) + 8 (a) + 8 (a) + 8 (b) + 13 (b) + 8 (a) + 8 (b) + 10 (b) + 13(a); NB! The grouping of measures and themes reveals the scheme of: 9 x 8 (= 72 measures) + 2 x 13 (= 26 measures) + 2 x 5 (= 10 measures), an order once more based upon the progression 5, 8, and 13 as quantities of the Fibonacci progression hinting at the “golden ratio;” the quite robust character of the music seems to allude to the strong phlegmatic temperament, while the very intricate formal scheme of the piece might possibly be a hint to the archangel Uriel (with attribute: fire); element Earth?

IX

The concluding Fuga à 5 Pro Organo pleno in E-flat major perfectly continues the ascending keys movement of the duettos (E-F-G-A) by its starting with a B-flat in the tenor.

The main theme suggests by its shape the form of a cross: connecting on paper the first note with the fourth and the second with the third, respectively the second with the fifth and the third with the fourth, respectively the third with the sixth and the fourth with the fifth, respectively the fourth with the seventh and the fifth with the sixth, one obtains three times (Trinity again!) the Greek letter X = Chi used as a symbol of the Cross, for crossing: cf. also Bach’s original title Da Jesus an dem X stund’ and the English No X-ing or Merry X-mas (Example 14).

This majestic theme dominates the whole first section of the fugue written in the ancient stylus gravis (see above, chorales 1 to 3). The second section of the fugue is in 6/4 meter and based on a strongly contrasting theme characterized by its constant movement representing a lengthy kyklosis (“turning around-figure”), with the main notes E-flat—F—G and thus quoting the first phrase of the first large chorale Kyrie, Gott Vater in Ewigkeit (Example 15).

Exactly in the middle of this second section, the majestic first theme reappears, rhythmically strengthened by its syncopations, and dividing the whole fugue into two equal parts of 36 + 22½ : 22½ + 36 (Example 16).

Finally, the third and last section of the fugue written in 12/8 time signature, expounds a third theme that will later be combined with the first and with a varied form of the second theme. This third theme seems to use a bass cadence formula of C–F, and B-flat–E-flat (Example 17).

Most impressive is the perfect formal symmetry of the whole fugue organized in: (20 + 16 =) 36 measures + (22½ + 22½ =) 45 measures + (16 + 20 =) 36 measures.

Considering the fugue as a whole and the most natural tempo relationship of its three time signatures (half note = dotted half note = dotted quarter note), one can conclude the following:

a) the first and the third sections of the fugue are equal in length lasting 36 measures each, divided into 20 + 16, respectively, into 16 + 20;

b) applying the tempo relationship “half note = dotted half note = dotted quarter note” and taking as a common unity of measurement the smaller quantity, i.e., the measure length of the second fugue (which has only two beats per measure vs. the four beats of the first and the third sections respectively), one obtains the following measurements for the three sections:

72 (= 36 x 2) half-measures; 45 measures and again 72 (= 36 x 2) half-measures

c) all these numbers being multiples of 9, these ratios can be reduced to:

72 (= 8 x 9); 45 (= 5 x 9); 72 (= 8 x 9), or just 8 + 5 (= 13) + 8 = 21

d) this series of numbers 8, 5, 13, 21 belongs to the famous “Fibonacci progression” starting by 1:1:2:3:5:8:13:21 and reaching the golden ratio or divine proportion (= “proportio divina”) in the infinite.

e) NB! according to the Italian Renaissance mathematician Luca Pacioli the golden ratio might symbolize the Holy Trinity:

A (the greater quantity/God Father) : B (the smaller quantity/God the consubstantial Son) = (A + B) : A, or, theologically speaking:

A (God Father) engenders B (the consubstantial Son) and, out of these two, proceeds A + B (the Holy Spirit);

f) could this majestic, astonishingly built fugue thus represent once more the ultimate Symbol of the Holy Trinity?

g) its perfectly symmetrical construction is most impressive:

First section (40 half measures—cadence—32 half measures),

Second section (22½—22½ measures)

Third section (32 half measures—cadence—40 half measures), or, more simply:

40 – 32 – 22½ – 22½ – 32 – 40 measure lengths of the second section.

X

Taking a more attentive, new look at the Third Part of Bach’s Clavier-Übung, one discovers some interesting facts concerning the overall compositional plan, a plan corresponding also to Bach’s work, the B Minor Mass:

a) both cycles contain a total of 27 movements each.

b) these 27 movements are divided into two groups of: 6 “free” works without a cantus firmus (prelude in E-flat, the four Duettos, and the final fugue) and the 21 chorales; NB! the “Missa” and the “Symbolum Nicenum” in the
B Minor Mass have together 12 + 9 = 21 movements and the last section of the B Minor Mass (“Sanctus,” “Osanna,” “Benedictus,” “Osanna,” “Agnus Dei,” and “Dona nobis pacem”) also contains 6 movements.

c) the 21 chorales in the Clavier-Übung are divided twice into: 9 for the Lutheran Mass (“Kyrie-Christe-Kyrie – Gloria:” Trinity) and 12 dealing with Luther’s Catechism plus Sacraments.

d) The 21 chorales are also divided (“musically”) into 12 and 9 chorales by the 13th chorale written as a French overture and thus opening the rest of 9 chorales.

[NB! All these numbers are multiples of 3 (Trinity again!).]

e) could the total number of 27 pieces possibly recall in both the Clavier-Übung and the B Minor Mass the 27 books of the New Testament?

f) could the number of 21 pieces allude to the “Teaching Books” of the New Testament, the 21 Epistles, and the 6 “free works” to the four Gospels, the Acts of the Apostles, and the prophetic Apocalypse of John?

g) could one not consider the overall architecture of Bach’s most impressive cycles, Clavier-Übung III and the B Minor Mass, as huge symbols for the New Testament and thereby also for Martin Luther’s Theology?

Michael Gailit

Michael Gailit graduated from the University of Music and Performing Arts in Vienna with both performance and pedagogy diplomas in organ as well as in piano. Teaching piano at this institute since 1980, he has also conducted the organ studio at the Musik und Kunst Universität in Vienna since 1995. As church organist he served at St. Augustine’s Church, 1979–2008; in 2011 he was appointed organist at the Jesuit Church (Old University Church).

Both in his performance and teaching repertoire, Gailit includes all style areas on the base of their individual performance practices. He has toured with solo recitals on both instruments in Europe as well as in North America and appeared with leading orchestras and renowned conductors. Recordings, masterclasses, invitations to juries, musicological publications, editing sheet music, compositions, arrangements, supporting the piano-organ duo repertoire, commissioned works, first performances, and finally occasional trips into the theatre and silent movie repertoire should be noted.

Particular attention was received in 1989 for the first performance of the complete piano and organ works of Julius Reubke (1834–1858), the performance of the complete organ works of Franz Schmidt (1874–1939) the same year, as well as in September 2005 a series of six recitals with the trio sonatas of Johann Sebastian Bach, the organ sonatas of Felix Mendelssohn-Bartholdy, and the organ symphonies of Louis Vierne. Currently Gailit is working on a book The Enigma BWV 565, a study elucidating new answers and new questions.

Editor’s note: Part 1 of this series appeared in the June 2021 issue of The Diapason, pages 18–19; part 2 appeared in the July 2021 issue, pages 12–14.

The first and second articles of this series examined the first thirty measures up to the fugue of Johann Sebastian Bach’s Toccata and Fugue in D Minor, BWV 565. Does it make sense to break down this most famous organ work into its smallest parts? Where is the benefit in lining up countless musical terms to describe one note combination after the other? Due to new evidence, the case of BWV 565 deserves a fresh review. Facts that were considered certain became open questions. This concerns first of all the compositional characteristics, but then also the earliest manuscript and its scribe, the dating, and finally, in the search for the author, the localization of a prime suspect.

In the toccata, hitherto undiscovered thematic processes of surprising density and an abundance of motivic metamorphosis has come to light. We apply now this note-by-note investigation to the fugue, the larger section of BWV 565. Measures 12 and 13 have already prepared the theme, as an adjusted stemming reveals (Example 28). Removing the repeating A from the fugue theme, a line emerges that strings together four tetrachords in the upbeat form of a figura suspirans. In addition, eight notes at the beginning represent the nucleus idea (as we labeled the opening mordent and the following descent). Both toccata and fugue start with the mordent A–G–A.

The general layout for the fugue provides for four voices. Actual four-voice texture, however, is only reached in eight measures:

• in measures 52 and 53 with the first pedal entry,

• fragmentarily in measures 100 and 101,

• in measures 120 and 121, where the first tetrachord of the fugue theme lines up in the pedal four times, accompanied by a homophonic texture on the manual,

• and in measures 126 and 127, supporting the climax character of the closing cadence.

Table 1 shows the structure of the fugue. Counting the measures of relevant sections, the sums happen to be all prime numbers. To assign any symbolic meaning to these numbers would be pure speculation. Their common property of avoiding regularity, however, makes them worthy of mention. There are:

• 13 theme entries,

• 29 full measures of the toccata section, the closing chord not included,

• 17 measures for the recitativ section, the closing chord in measure 30 included (with this closing chord both toccata and recitativ avoid an integer, as do all interludes but the first),

• 23 × 2 measures of toccata and recitativ sections together (23 measures on average for each section, but also here an instance to avoid exact 1:1 proportion),

• 71-measure compass of all interludes in the fugue,

• 97-measure compass of the fugue,

• 127 measures from measure 1 to the end of the fugue, and finally,

• 143-measure compass of the complete piece.

At this point, it can be assumed that the inclined reader has become familiar with the constant use and changes of the central motives of the work. Allow yourself the adventure of going on the motive quest yourself. You are welcome to take the role of a fictitious musical CSI agent and find out what all sorts of things the motives go through. Perhaps you like to report circumstantial evidence. Or read on right away.

Entries and counterpoints

The fugue coordinates thirteen theme entries in three groups. Two of the entries are one voice only, the first one of course, and then the twelfth, the pedal solo. Eleven of them are accompanied by a counterpoint in the sense of the word origin punctum contra punctum, Latin for note against note. Table 2 lists the counterpoints in pitch notation, grouped in context with the theme into four sections of four notes. This results in 44 motives that are all related to the main material, among them 21 tetrachords, all of them ascending (green notes in the table) and 14 cross motives (red notes in the table). On beat 1 we localize 24 mordents (highlighted with a gray box). The two immanent voices of the counterpoint to the eighth entry are notated in the table simultaneously, with the accessory notes grayed out.

The criticism regarding counterpoint in BWV 565 fixates on the lack of contrasting qualities. If these were present, however, any contrasting counterpoint would need to waive relationships to the thematic material. The motivic substance of the counterpoints mirrors clearly the ever-present thematic work in BWV 565, as does the variety to the concept of metamorphosis. The motivation for creating a work like BWV 565 may have been, among other things, to explore new qualities away from contrapuntal skills.

While the toccata opening moves almost exclusively in tonic and dominant harmonies, the fugue strongly inclines toward the subdominant G minor. Its theme allows the answer only in that key. Thus, the entries in the first development (the exposition) follow the unusual key sequence: D minor–G minor–D minor–G minor.

The second development starts in measure 57 with an entry in the parallel key of F major and returns with the next entry to D minor in measure 70. After the longest interlude in the fugue, the second development continues with two entries in C minor, rounded up with a fifth entry in G minor. The choice of C minor for two consecutive theme entries is not as far-fetched as sometimes described. If the answer to the theme has to join on the subdominant, only one step further in the circle of fifths is necessary to arrive at the double subdominant C minor.

The theme entry in measure 105 marks the beginning of the third development. Consolidating the main key, all entries remain in D minor. Observing the number of accidentals that belong to the keys of the entries, together with the indication in which voices they occur, the construction plan becomes apparent. The tenor entries are given in red capitals to underline their structural significance (Example 29).

The eleventh entry in measures 107 through 109, sometimes not counted as such, consists of four consecutive tetrachords and is therefore to be regarded as an entry of its own. This variant completes the entries in the final development in the number of four, and it occupies the allotted space in the soprano voice. On the one hand, the theme of a fugue has to remain true to its melodic shape throughout. On the other hand, small deviations from the original shape are justifiable when the theme appears four times in a row in the main key, especially in a piece so dedicated to thematic development. The four entries differ by the following properties:

• entry in measure 105: no changes;

• entry in measure 107: the first tetrachord replaces the repeated A by steps, the last two tetrachords take other positions (Example 30);

• entry in measure 109: waives all other voices as a pedal solo;

• entry in measure 124: the last two notes take other positions.

It looks like the modification of the last entry was necessary to insert another cadence to reach beat 1 with the closing chord. If the theme remained unchanged, the ending would have arrived half a measure early (Example 31).

The interludes

The figurations of the first interlude, measures 34 through 39, combine two tetrachords with almost only cross motives. For a clear graphic presentation, we combine the notes to chords in pitch notation and then project them colored on an open score. As before, the tetrachords are green, the cross motives red (Example 32).

The next interlude stacks only tetrachords across measures 41 through 45 (Example 33). The passage contains a maximum of motivic density. It is like one of those circulating riddles: how many tetrachords can you spot in these measures? The left hand twice has the Phrygian cadence D–C–B-flat–A an octave apart (red notes), plus G–F–E–D (brown notes), prepared by the upbeats F–E–D–C-sharp (green notes). The right hand has four descending tetrachords (red notes) answered by four ascending retrograde derivatives (cyan notes), the last one incomplete. Counting the colored groups, we add seven tetrachords since the last group lacks the last note; counting the ones with notes at the same positions (marked with gray slurs) we add another seven of them for the same reason of the last missing note. On top sits one more tetrachord with A–G–F–E (green notes). We finally arrive at a grand total of 19 tetrachords in four measures (Example 34).

Measures 45 and 46 serve as a transition and combine three turn motives with another variant of the tetrachord (Example 35). Measures 47 and 48 change to a polyphonic texture in complementary rhythms. The nucleus idea appears twice in D minor and split into its three-note groups, mordent—trichord—mordent (Example 36). Subsequently, the chain of sixteenth-note motives in measures 49 and 50 develops three four-note motives: the first four notes of the theme, the tetrachord, and the cross motive, the latter widely stretched (Example 37). Furthermore, the passage also hides two nucleus derivatives (red notes in the example). The counterpoint parts descend with a new aspect. Two tetrachords are notably extended in length and colored with chromaticism (Example 38).

The theme entries of the exposition each have gradually increased the number of voices. The maximum of four voices is reached with the pedal entry in measure 52. The following interlude in measure 54 goes back to three voices. The section repeats the tetrachord in the form of descending steps (Example 39). Since the pattern ascends four steps in measures 54 through 55, we discover eight more tetrachords and therefore a total of 16 tetrachords (Example 40). The pedal picks up the previously introduced idea and extends a tetrachord in length and with chromatic coloring (Example 41).

Three further half measures prepare the beginning of the second development. Modulating to F major, they are filled in the top voice one by one with two turn motives, two new tetrachord derivatives, and finally two simple tetrachords. The lower voice follows in parallel motion in four cases (Example 42). The theme appears with its counterpoint only, the number of voices shrinks further down to two. The next interlude, spanning measures 59 through 61, reduces further. The descending scales combine a pentachord and a tetrachord and ascend along a pentachord. So, this thin texture creates a mass of nine simultaneously ascending pentachords of the notes at the same position in the scales (Example 43)!

Still two voices, but due to the unison C again a thinner texture, measures 62 through 65 shift the mordent to the weak beats of simple figurations. As a result, the constant presence of the main motive of the piece goes surprisingly unnoticed (Example 44).

In measure 66, the reduction of voices finally reaches the texture minimum of one single voice. Simple broken chords suggest that all developmental procedures have ceased. The source of inspiration could have been the arpeggio in measure 2 as another welcome element to develop.

Each harmony is rolled twice, a performance practice best known from the Prelude in C Major, BWV 846, by Johann Sebastian Bach (1685–1750), which dates back to the collection of piano pieces of 1720 for Wilhelm
Friedemann Bach (1710–1784). Again, we combine the notes into chords in pitch notation and then project them on an open score. This reveals five lines with two tetrachords on top and three derivatives below (Example 45).

At 143 measures in total length, the center of BWV 565 is in the middle of measure 71. That is also the center of the D minor entry that in turn marks the center of the whole piece. In the earliest manuscript, measure 72 comprises only three beats of four sixteenth notes. A fitting filler dating from the beginning of the nineteenth century came into use up to the present. It completes measure 72 smoothly, but it deviates too much to claim authenticity. The author discovered that each theme entry appears unabridged, only in measure 72 it lacks a full beat in the earliest manuscript. Completing the theme and the counterpoint, measure 72 is automatically completed as well. Measure 72 regained in all probability its true original form (Example 46). The Diapason thankfully premiered this correction with the publication of “BWV 565: The Fitting Filler for the Fugue” by the author in January 2021, page 17.

Developing a piece with thematic processes gives numerous possibilities to create a diverse variety of music on the basis of unifying motivic material. Examples show, however, that one’s powder can be shot too quickly, that no further development could be found, and that initial momentum and power did not continue. Part 4 will pursue the question as to how or if the composer mastered this challenge.

To be continued.

Gavin Black

The Art of the Fugue, Part 1

Before delving into the principal topic of this column, I must first briefly revisit the subject of the last two columns, which dealt with aspects of the practice of listening to music. Shortly after I finished the May column, I was in New York City for the day, and I happened to notice, walking along one of the avenues, some bins of used LPs outside an antique store. I had a few minutes to spare, so I started leafing through the boxes. Midway through I saw a record of Brahms’s First Symphony. This is a favorite piece of mine, and part of my program for that day was to hear a concert performance of it at Lincoln Center. I pulled it out to take a look, as I wanted to know who recorded it. But there was nothing: no orchestra name, no conductor, no date, no recording venue, no clues.

I had just written of my experience noticing that students and other listeners have a habit of seeking out recordings online and listening to them without noticing anything about who the performers are. I presented this as being a characteristic of the structure of modern listening technology and a strong and well-accepted modern ethos. But it is interesting to be reminded that it also is not a new concept. This Brahms LP, monaural as far as I could tell, is an artifact reflecting the view that it is perfectly acceptable to listen to a performance not only without noticing who is playing, but also without having any way to find out.

Some of the implications of this would be fascinating to explore at greater length, and I will write more about it at some point. When we listen to a performance, especially when we listen to the same one repeatedly, what do we feel about letting that particular way of performing the piece shape our way of defining it? Do we think about this consciously and give the performance permission consciously and deliberately to affect us in certain ways? The history of this has been more complicated than I was remembering when I touched on it before. That in turn ties in with questions of authenticity, which we tend to think of as being about composers, and authority, which can come from any number of places—writings, performances, teachers—and which can influence us with or without our being aware of it.

Questions concerning Bach’s The Art of the Fugue

For this month’s discussion, I turn to Johann Sebastian Bach’s The Art of the Fugue, BWV 1080. There are a myriad of issues surrounding this monumental opus that open windows into our thinking about authenticity and authority in particular, as well as many different aspects and dimensions of what we do as performers, listeners, students, and teachers. With its length, complexity, and importance in the arc of the work and career of Bach, crucial questions about the work are unanswered and perhaps unanswerable.

So, what is The Art of the Fugue?

It is a work written by Bach over the last decade or so of his life, consisting of many movements—about twenty, but that is one of the areas that can be looked at a number of different ways—each constructed contrapuntally, some as fugues and some as canons. The movements are all based to some extent and in some way on a particular theme. The piece was published shortly after Bach’s death in an engraved edition, and while Bach certainly composed the bulk of the music, the work was completed by others. There are also surviving earlier manuscripts of some but not all of the work.

The theme mentioned above is found in Example 1. The theme in this form opens the first movement, which is a four-voice fugue on this subject. The first movement is the only one to open with a simple statement of the theme in exactly this form and the only one that is based primarily on this form of the theme. The variants of the theme that form the basis of the other movements include inversions, diminutions and augmentations, rhythmic variations, and versions with added passing tones.

One question that intrigues me, and that I will broach here and come back to in the course of these articles about The Art of the Fugue, is, why this theme? One answer could be, why not? After all, Bach wrote fugues on a large number of different subjects and must have improvised fugues on many, many more. However, I think that it is worth interrogating the ways in which this theme in particular might have lent itself to the extended and varied treatment that constitutes this long work. The Art of the Fugue theme was not, as far as we know, or as far as I have ever heard, taken from somewhere else. (As, for example, the theme of A Musical Offering was, or as the themes of all chorale-based pieces are.) Bach wrote a number of other fugues on themes that are largely based on a minor triad, like this one. That is true of the subject of the fugue from the Fantasia and Fugue in G Minor, BWV 542, and, in an even more thoroughgoing way, of the stand-alone Fugue in G Minor, BWV 578. The Canzona in D Minor, BWV 588, is based on a subject that could in fact qualify as a variant of The Art of the Fugue theme (Example 2).

(If that piece were dropped into the middle of The Art of the Fugue it would be quite possible to justify it, at least as far as themes and motifs are concerned, as part of the work. It would seem an interesting variant that the semitone by which the subject departs from the confines of the perfect fifth is the one going up, whereas in the original subject it is the one going down, and that the two of those outline the notes that give the minor mode its harmonic flexibility or instability.)

I have heard or read suggestions that this theme or subject is so simple, basic, plain, that it is astonishing that Bach could construct a massive edifice upon it: that his ability to do so is a particular proof of the power of his genius. I do not disagree with that conclusion, in that it took a genius to create this work. However, I am not inclined to agree with the premise. It seems to me that constructing this theme was indeed part of the genius: that it is specifically and purposely designed to carry the weight of all that was developed out of it, and potentially more. I will come back to this later on.

That brings us to one of the most famous and important things about The Art of the Fugue: that it is incomplete. The movement we regard as the final one, while already the longest in the piece, breaks off in the middle of a measure. It is not a neat ending; it is not the end of a section—just an abrupt crashing from music into silence.

The reason that fugue is incomplete is that Bach died before he could finish it. Perhaps, he had it composed in his head. It seems likely that Bach or any composer would have had to have a fairly strong idea as to where a big contrapuntal structure such as this movement was going before venturing on starting it. It is a complicated fugue with multiple themes. But that does not mean that he had worked out the ending in detail.

In any case, we do not have the last measures of this movement, and therefore we do not have all of The Art of the Fugue. This creates a set of dilemmas for performers. Should one simply break off, playing all and only those notes that we have, allowing the “ending” to be jarring? Or should the performer or performers play one of the many endings that composers, scholars, and performers have composed over the last hundred years or so? Or should one look for a nice closing cadence as close as possible to where the piece currently ends and stop there? The fundamental fact is that none of these portrays Bach’s true intentions.

I have always favored the practice of ending abruptly. This preserves a certain “purity” of playing only Bach. It also forces us to confront in the most direct way the fact that things do not always go the way we want. That breaking off is beyond jarring: it can be deeply distressing and filled with anguish. It is an ending determined, as endings often are, not by any person but by death itself.

There is no way to maintain that this troubling breaking off is what Bach intended. I have had colleagues point out to me that by playing only and all of what we have on the page, we guarantee that we are doing something that Bach could not possibly have wanted. And every completion that has been attempted has been predicated on some analysis of what Bach might have been planning. Therefore any one of them has a chance at least of being similar in concept to what Bach would have envisioned. If nothing else, the length of the piece gets closer with each added measure to wherever it would have ended up if Bach had been able to finish it. And the abrupt breaking off is replaced by a normal ending. In between, the further working-out of the counterpoint might well be something like what Bach would have done. That is presumably the goal for those who have written such continuations, and each person has brought knowledge, care, and analysis to that project. But it is not Bach’s ending, and the piece is no longer just a Bach piece.

The first published edition, supervised by some of Bach’s surviving family and colleagues, chose a version of the third plan. The printed edition ends with the last solid chord, so to speak, before the spot where the manuscript source breaks off. This is an A-major chord in a piece in D-minor and indeed sounds like a dominant. It is a chord, and the rhythmic structure of what has preceded it gives it some solidity. But it does not sound stable, which raises an interesting question about authority. This is the approach apparently sanctioned by those closest to Bach. What authority do we give to that? What do we know or believe about how likely it was that they got that idea from J. S. Bach himself?

We tend to believe that this movement, an ostensible triple fugue that was very likely intended to end up as a quadruple fugue, was clearly meant to be the last section of the overall work. It certainly looks the part. However, we do not know for certain that if he had had several more years, Bach would not have added much more. Perhaps this triple (quadruple?) fugue would have ended up as a centerpiece rather than a culmination. Or perhaps it was really intended to be a centerpiece even without more movements. We do not have absolute certainly about the intended order of the movements, only very well-informed guesses.

Speaking of performance: we also do not know for certain what Bach’s intentions were for the performing forces that are brought to bear on this work. The surviving manuscript sources and the first edition say nothing about what the music is “for.” It is all in open score—four staves for a four-voice piece, three for a three-voice piece, and so on. There are no instrument names or any words on the pages of music talking about instrumentation or performance. There is a significant amount of evidence that this was probably intended to be a work for keyboard instruments, though that is not absolutely certain. And accepting that, it is less clear whether it was for harpsichord or for organ. There is a tantalizingly similar amount of suggestive evidence for each. Another real possibility is that the piece was intended equally for each of those two instruments. There was a long tradition of writing music that fits that profile, mostly from the generations before J. S. Bach. And there is a great deal about this piece that suggests that the composer wanted it to resonate in part as a throwback to those older generations.

The question of what instrument or instruments to use in playing a piece is crucially relevant to performance, to put it mildly. And since this series of columns is really about my own efforts to grapple with The Art of the Fugue as a performer, I will return to this in considerable detail.