On Teaching: The Art of the Fugue, part 2

The Art of the Fugue, part 7

I begin this column with an account of something that happened in a recent lesson, something surprisingly germane, by complete coincidence, to what I had already been planning to write about this month. I notice recently that between when I finish one column and when I am due to start writing the next, something often crosses my path, completely by chance, that is relevant to what is coming next in the column. Sometimes it provides an example, other times an interesting sidelight. Often it essentially ratifies and strengthens what I had been planning to write; yet sometimes it suggests a bit of a change.

Before I get to my story, it occurs to me that the fact that I encounter these coincidences as often as I do is itself a commentary on the philosophy and purpose of the column. My hypothesis is that everything is relevant to performing music and to teaching others about music and performance. I believe everything we encounter in life might be potentially fruitful for our music and our teaching.

This series of columns on The Art of the Fugue is meant to be an account of my working process. Part of that working process is to be aware of anything that might lead to an interesting thought about the piece or the performance. If we notice things and assume that they will be interesting and relevant, we cannot lose. If they are relevant, the gain from having noticed them is clear and describable; if they are not, the thought process sparked by noticing them is still rewarding.

The teacher-student experience

A week or so ago a harpsichord student of mine brought up The Goldberg Variations, partly as a step in thinking about whether to work on the piece, partly to ask a few questions. What is the overall structure of the piece? Did the composer write the movements in the order in which we see them? Does the order matter in performance? If so, why? Is it about individual transitions or something else? We talked about all of this a bit, mentioning “official” sources of structure and continuity. These start with the basic fact that each variation shares some version of the same underlying harmonic pattern and includes the phenomenon of every third variation’s being a canon. We talked about the formal layout of the canons, in which each one is a canon at a one-greater interval—Variation 3 a canon at the unison, Variation 6 at the second, Variation 9 at the third, and so on, up to Variation 27, which is a canon at the interval of a ninth. We discussed, but did not resolve the question of whether this formal layout is palpably meaningful to a listener, or is just meaningful as a formality.

Then we tried a live-action version of something similar to an experiment I described in a recent column, about electronic listening. I played a movement, or the last few lines of one, and my student turned some pages at random. I then started the movement on the new page, randomly chosen, after the one that I had just completed. We did not go through the whole piece in this fashion—not enough time, and other things to do. But we got a good sample of what it felt like to move from one variation to another when that transition is neither what the composer had in mind nor what we are used to.

The result was that each transition sounded fine (“worked”, nothing jarring) but also sounded odd. The oddness came from the confounding of fixed expectations, fixed by years (or for me, decades) of listening. It is hard or impossible to sort out what each of those transitions would have sounded like to someone who had never heard the piece before. I strongly suspect that they would each have been just fine, but I cannot be sure of that. This was a reminder that structure comes in part from expectation. The kind of expectation that comes simply from having heard the work before can be very powerful. But I assume (or perhaps I hope) that expectations created intrinsically by the music are even more powerful.

Sources of overall structure in The Art of the Fugue

It is my working hypothesis that in The Art of the Fugue there are two main sources of overall structure. The first is the nature of the theme itself and the way that it sets up other themes and musical gestures to be meaningful. The second is the recurrence of specific themes. I mentioned both of these in my 1985 program notes that were reprinted here in two recent columns. But I want to delve into both of them in more detail in this column and in next month’s. Of these two ideas, the recurrence of specific themes is, perhaps, the more clear-cut. It is not remotely unusual to include as a source of continuity and of structure. This includes all of the uses of the main theme and its variants: the top level of what we get by contrapuntal analysis. But there is also more below the surface.

My thoughts about the nature of The Art of the Fugue theme are perhaps more speculative. That theme starts on a note, goes up a perfect fifth, goes down a major third, then down a minor third, then down a semitone. After that it goes up by that same semitone, and up and down by step until it ends. Every musical theme, of course, has some pattern of intervals that I or anyone could describe in words. What is striking to me about this theme is how comprehensively, systematically, almost encyclopedically, it lays out all of the intervals that define tonal music. They occur in what could plausibly be considered their order of importance, there is essentially no redundancy: almost no interval is repeated until each interval has been heard (the exception is the semitone), and the inversions of intervals are assumed rather than stated.

My own experience as a listener has been that throughout the piece I hear any interval as a reference to this theme. This starts right away, as soon as there is anything to hear other then the theme itself. The scale notes that make up the counterpoint to the second entry of the theme at measure 5 fill in the opening interval of the theme itself (Example 1).

Does a listener hear it this way? Does a listener spontaneously think, “that is that same theme” or “that is a reference to that same theme?” I believe I do, and that I began to do so after repeated listening years ago, before I thought that I might have any idea why.

The chromatic countersubject in Contrapunctus III seems to arise out of that original semitone that is the interval from the fourth note to the fifth note of the opening theme. The leaping thirds that are one of the characteristic gestures of Contrapunctus IV seem to answer the thirds that make up measure 2 of the theme. Contrapunctus V plays around further with the idea of the third. First of all, when the theme comes in the second time, it is a third away from the note that accompanies it. (In Contrapuncti I–IV, this has always been the interval of a fifth.) Second, this movement contains a pervasive gesture that is the interval of a third filled in by step, and there are also a lot of parallel thirds!

The thirty-second-note flourish that pervades Contrapunctus VI, and that is a principal justification of the heading of this movement as being “in French Style,” sounds like a reference to the last four notes of the opening theme. The mordent-like figure that enters Contrapunctus VII in measure 3 is related to the semitone-based gesture in the opening theme going (in Contrapunctus I) from the end of measure 2 into measure 3. For me, the nature of the opening theme itself turns the whole piece into a tapestry of familiar, known, referential themes and gestures.

A complement to this is the gradual introduction of the octave into the picture. The opening subject, while displaying all of the discrete intervals of its tonal language, almost pointedly fails to encompass an octave. However, the first thing that happens after the filled-in reference to the opening interval that I pointed out in Example 1 is a drop of an octave: the first octave in the piece. When the second voice to enter (the soprano voice) finishes its statement of the fugue subject, it immediately makes an octave leap: one not in any way required by the counterpoint or harmony (Example 2).

Then, later on, whereas each of the first seven contrapuncti begins with the interval of either a fifth or a fourth, Contrapunctus VIII beings with a step, a very striking change. While the compass of the theme of each of the first seven movements has been never more than a sixth, the compass of the opening subject of Contrapunctus VII is a tenth, but one that could also be seen as outlining an octave. (The first and last notes of the subject are an octave apart, and the note that creates the tenth is off the beat and somewhat ornamental.) Then Contrapunctus IX begins with the brand-new gesture of a leap of an octave. The compass of this subject is a ninth, and that of the next movement a tenth, so that we are in a region of expanded compass of themes.

All of this is enough to make me feel that it makes sense to say that the subject or fundamental building block of The Art of the Fugue is not “the AOTF fugue subject” but the very concept of the melodic interval. This in itself does not create structure in the sense of linear shape. But it establishes the conditions for the creation of that structure.

The repetition, recurrence, and referencing of identifiable individual themes is the foundation of counterpoint, and probably the major defined source of contrapuntal structure. At the level of “this theme is the inversion of that theme” or “this theme is the same as that theme, but with altered rhythm,” this is fundamental and definitional. And there is an abundance of that sort of correspondence in The Art of the Fugue. What interests me beyond that is the more fleeting or hidden thematic connections. There are quite a few of these in the piece. The phenomenon that I have tried to describe above (the tendency of this piece to permit any interval, even in an isolated occurrence, to seem meaningfully thematic) is a background against which it becomes clear, I think, that small, individual thematic connections are meaningful to a listener and almost certainly intentional on the part of the composer. Some of the ones that stand out to me are as follows:

This seems to be an isolated event in the bass line in measure 35 of Contrapunctus IV. The notes seem like a filler in a kind of quasi-cadence (Example 3).

All of the eighth-note motion in the movement prior to this has been by step, as is almost all of it after. This is then picked up in Contrapunctus X (Example 4). The figure that enters in the tenor voice at the beginning of this example is passed back and forth among all of the voices and then culminates in an exact statement (at a different pitch level) of the theme from Contrapunctus IV cited above.

The beginning of the main theme of Contrapunctus X (Example 5) is referenced in passing in the bass voice near the end of Contrapunctus XI (Example 6) and again in the middle of the final movement (Example 7).

That latter one is an “answer” rather than a literal quoting of the motif. Are these parallels valid? It could certainly be argued that the fragments of themes that I am pointing to here are just routine cadential figures or other tropes that are too non-specific to be meaningful. I do not hear them that way. Again, I think that the structure of The Art of the Fugue subject itself predisposes any motivic entity to be significant, and the ways in which some of these fleeting motifs are deployed seems too systematic to be non-intentional.

As I said above, I think that there is more to be gained by assuming that correspondences are real than by resisting hearing them that way. Next month I will bring forward several more examples—perhaps even more important to the actual overall structure of the work as a whole—and talk more expressly about that structure.

To be continued.

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.

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.

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.

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 8

In the last few columns, I have started writing and thought of a suitable and effective name for each column somewhere along the way, even at the end of the process. However, today I was able to start with the title, because it is time to get back to writing about Johann Sebastian Bach’s The Art of the Fugue!

This is still an uncertain time, no less so than a month ago. And it is still true that there are things that are unknown as I write this that will be known when you read it: will there be a Major League Baseball season? Who will be the Democratic nominee for vice president? Will there be a post-Memorial Day spike in COVID-19 cases? Will Broadway theaters really reopen on September 6? And there are things that are unknown now that will probably remain unknown, at least with any certainty by then: will there be a second wave of the virus? What will Advent and Christmas be like—for church musicians, for retailers, for families? Will the practice of going to the movies survive?

When I wrote my first Art of the Fugue column a year ago, I could not have imagined that over the succeeding year I would be unable to practice or perform the work, so this column really was my only study of the piece. I also could not have predicted what the content of the columns would actually be. I thought that I could, but it turned out to be very different from what I initially planned. But that is all eerily appropriate. When Bach first set out to compose the work he certainly did not know that he would be forced to leave it incomplete or that he would not see it published. Uncertainty has to be an underlying theme of The Art of the Fugue.

I strive to organize some of my thoughts about how the uncertainties surrounding the order of the movements interact with my thinking about the work in general. In my column from May 2020 I wrote of “the basic definition of counterpoint, namely two or more things that are different from one another happening at the same time.” The second consistent characteristic of counterpoint as we usually know it—for me, just below the level of “definition”—is that things that are the same happen at different times. Paradoxically this is perhaps even more important in shaping our range of reactions to counterpoint: esthetic, emotional, intellectual, etc. It is the source of our need, when we analyze pieces of this sort, to know about and recognize themes, subjects, countersubjects, motifs: anything that happens more than once. And this phenomenon is entirely dependent on memory. We know that a theme has recurred because we remember it from before. This is true immediately when a fugue subject appears for the second time. That part is relatively easy. (And it is assisted by expectation, if we have been told that what we are hearing is a “fugue” and we have just heard a theme in one voice unaccompanied.)

When a theme comes from elsewhere, as in a chorale prelude, for example, the process of recognizing that theme takes on another layer or two. I find it interesting that chorale-based pieces have a kind of double life. They come across differently to listeners who already know the tune and those who do not. Presumably most chorale-based pieces have been written in the first instance for listeners who knew the tunes extremely well—almost instinctively. In a multi-movement chorale-based work like Bach’s Canonic Variations on Vom Himmel hoch da komm’ ich her the recognizability of the chorale creates unity that perhaps makes the exact order of the movements function differently than it might in another situation. That is not to say that it is not important: it is manifestly a somewhat different piece with the movements in one order from another. It is interesting that Bach did indeed present the work in two different orders: first, in a published version, with the most complex and imposing of the five variations as the closing movement; later, in an autograph manuscript, with that variation in the exact middle. (This could be a rationale for considering it possible that the triple/quadruple fugue from The Art of the Fugue could function not as a culmination but as an interior building block, way station, or destination.)

When a theme has been altered, perhaps through augmentation, diminution, inversion, or something else well defined, perhaps by just a small change or two, recognizing it becomes more abstract and mediated by the subconscious. For many contrapuntal works this creates a kind of layered structure in which as elements recur in different ways, they evoke different kinds of memory. The development of the sense of “this is answering that” or “this edifice has that kind of shape or structure” is a multi-faceted, interlocking, overlapping experience.

In my December 2019 column, I wrote that “the subject or fundamental building block of The Art of the Fugue is not ‘the AOTF fugue subject’ but is ‘the very concept of the melodic interval.’” That column develops some of the reasons I believe that this is so, which I will not repeat here. If this is true, it sets up a condition in which the layers and facets of what we recognize as we listen, what we rely on to create structure in our minds, is infinitely complex and varied. The more the status of recognized themes or ideas is different (some more obvious, some more subliminal), the more complex that structure will be. 

I believe this relates to the question of the order of the movements. Since these connections are so numerous—effectively infinitely numerous, since there is very nearly nothing within the universe of the piece that does not connect to other things—and since the nature of those connections is so varied and fluid, convincing, engaging patterns will form themselves in the listener’s mind regardless of the order in which the components are encountered. The structure is then not “x follows y, which follows z” but “a, b, and c are all connected.”

So the nature of the opening theme and the ways in which it is developed in the first contrapunctus set up this focus on any and all melodic intervals, which in turn creates an infinitely fluid set of ways of hearing connections and perceiving or synthesizing shape. This explains why the piece can be effective almost regardless of the order in which the movements are heard. And it is not just that it is effective: it takes on a convincing overall shape, a strong sense of arc, direction, and structure. This does not mean that Bach did not have an order in mind. It just explains perhaps why the piece works so well even though we do not and very likely cannot know what that intended order was.

I say “almost” regardless. I believe, based on this analysis and intuition, that it is important for Contrapunctus I to be first, since it sets the stage for all that follows. I also think that not placing the triple/quadruple fugue at the end makes the biggest difference among all possible ordering choices. I am reluctant to say that it is “wrong” or would not work, but I know that it would be a big statement to place it elsewhere.

Conventional ordering of musical content

With certain sorts of pieces convention gives us an expectation as to how the ordering of types of musical content will create shape. This is true of suites, sonatas, symphonies, and other similar types of works. These conventions are not ever absolutely fixed, and they vary with time and place. But there is no convention as to the ordering of twenty or so contrapuncti. The content must create the possibility of shape and arc if there is going to be such a possibility.

This thought leads to an idea that I have held for a long time, have never been able to implement, and will likely never be able to implement. It would be a logistic tour de force and extraordinarily expensive as well. The analysis above helps to explain why I think that it could in theory work. Consider a performance of The Art of the Fugue by twenty different performers or performing ensembles, each playing one contrapunctus in a different room. Each movement in its room would be played over and over, and the listeners would be free to wander from one room to another. Each audience member would create their own path and could come and go from rooms at any time. Timing considerations would make it close to impossible to hear all of the movements in any order without also hearing fragments, since each movement in each room would be a different length from the others. The experience for any listener would not be that of “hearing the piece” exactly, but of getting absorbed in it. This is not a type of deconstruction that I would suggest for, for example, the Goldberg Variations or most other multi-movement works. But I think that it would work beautifully here.

Some of the observations that I have been trying to pull together in the last several months’ columns have led this thought to occur to me. The Art of the Fugue is a fully, rigorously contrapuntal work, and that is a large part of the lens through which we think about it. There is a body of music out there that is clearly imbued with counterpoint, but that is not fully contrapuntal. For me one quintessence of this sort of music is the keyboard music of William Byrd. There are passages that are fugal, there are passages that are chordal, and there are fugal bits in which the number of voices seems to fluctuate, or in which it is not always clear which notes belong to which voice. There is music by Mozart, Beethoven, and many subsequent composers that fits this profile. I have always had a nagging tendency to be uncomfortable with this: is it counterpoint or not? Fundamentally there is no reason to consider this anomalous or problematic, though some of us do. Looking at counterpoint as an analogy to the structure of the world or of the universe in the manner that I described in my previous column, and noticing that under some circumstances entities other than complete, defined subjects can be fodder for contrapuntal development, both tend to mediate between and reconcile contrapuntal and non-contrapuntal textures and make sense of the sorts of pieces that flow from one to the other.

Another less esoteric part of my recent Art of the Fugue experience has been that circumstances have led me to practice quite a bit on the piano. Using the piano in our home as a practice machine has been interesting. Vestigial memories of studying piano in my youth have come to the fore and have caused me to drift into doing things with volume that I am not very good at and that are not really relevant to this music.

But that raises a good question: does the “volume temptation” reveal things to me about the piece that are valid and that I can make use of, or is it just a distraction? Or is it actually misleading? These are not questions that I have never heard people ask. But they feel more vivid to me now as I have sat at the piano more in the last couple of months than I had in the previous many years. Many students do a fair amount of practicing on instruments other than the one on which a lesson or performance will take place: piano for harpsichord, piano for organ, electronic keyboard for either, or of course harpsichords and organs that are just very different from others. I have had too much tendency to see this as a necessary evil, to believe that ideally practicing on the exact right instrument is always better. I still believe that practicing on the performance instrument is better, more efficient, and that it should make up as significant a portion of practicing as possible. But since I am finding sitting at the piano to be enriching and interesting, I find myself rethinking all of this a bit. 

This is my twelfth consecutive column that is either about The Art of the Fugue or framed by my inability to write about The Art of the Fugue. It is my plan to put writing about the piece on the back burner, while getting back to actually working on the piece.

Just as I used the titling of this column as a boost of morale, I will reuse my mini-bio from 2019 below to express a bit of optimism about getting back to performance. It turned out not to be true then. Perhaps it will be now.

The Art of the Fugue, part 6

I recently had a concert performance anxiety dream. This one was specifically about The Art of the Fugue, and it followed a common pattern: I was aware I was to perform the piece, and I sat down at the organ, but when I looked at the score, I realized that I had never seen the music before. I started to panic, but also to try to scheme: could I get away with sight-reading this? How slow could I play it without giving away what was going on? Could I leave out the hardest bits? I remember looking around hoping to see something happening that would force the concert to be abruptly canceled. The music on the page was not actually The Art of the Fugue. It was dense, chordal, and chromatic. The typeface looked like something French from the late nineteenth century. But within the dream I accepted that this was indeed the work that I was supposed to be playing. I had just somehow neglected to learn it.

I have this kind of dream once or twice a year, but I am pretty sure that these dreams usually involve playing at someone else’s behest, in chamber music or in a church service, not solo performance. My Art of the Fugue project is something that is being carried out only at my own behest. My decision to do it is a choice to focus on something that is specifically important to me and that I am utterly convinced I can only do well if I am very committed to doing it the way I want it to be done.

So why the dream? My only thought so far is that I am trying to remind myself that I should really learn the thing! There are always traps in any project, and maybe the trap with this one is that my sense of “ownership” over this work, my awareness that I have been studying it and interacting with it for nearly fifty years, my experience of being comfortable with it at a conceptual level will disguise how hard it is to play and lead me into complacency about the business of learning the notes. Maybe that is what the dream was about, or maybe not. Yet, any interpretation of a dream that reminds me to work as hard as I can to become as certain of the notes as possible is worth paying attention to!

Connections

The connection between the sense of understanding, inner commitment, ownership, and the nitty-gritty practical learning of a piece is a complicated one. At one level, there is the fact that, for almost everyone, focus and concentration are easier and more successful working on something we love than on something that we do not care about, or at least not very much. This is why I want students who endeavor to become more accomplished players to work on music they care about. The translation of time and effort into growth as a player is most efficient this way. Students do not know what music is out there as well as I do or another teacher does. The process of helping them to explore things that they do not know interacts in complicated ways with the goal of working on music they love.

Yet, I am wondering about something deeper. If one feels a deep bond with the music one is working on, what dangers does that invite? I believe there is a risk of assuming that the bond with a piece or a composer or a repertoire is in itself enough to make something come across to listeners. If I feel something while I am playing and listening, am I interpreting the music a certain way because of my love of the music? Is this hiding the necessity of doing something interpretively from me?

Overall structure of The Art of the Fugue

I now turn to some thoughts about the overall structure of The Art of the Fugue. There are two salient facts I would like to discuss. The first is that one of the movements is incomplete—the one that most of us take to be the final movement. Second, that there is some uncertainty as to the order in which Bach intended the movements to be played. There has been a lot of serious, thorough, and fascinating scholarship about both of these matters, each of which has a different set of interactions with performance. Regarding the final movement, there is the question of whether to play it as it has come down to us, breaking off abruptly, or to alter it in some way, either by completing it or by ending it at an earlier point than the break-off. As a set of choices this is probably more about philosophy than about scholarship or research. Scholarship, research, and analysis can, for those who wish to perform a completed version of the piece, elucidate different possibilities for that completion. There is also, however, the question of whether to play it at all. This is a matter that has to be addressed by a combination of scholarship and philosophy. It used to be fairly common for performers or scholars to entertain the possibility that this movement was actually never meant to be part of this work. I believe this is a rarely held view nowadays, and indeed the musical connections between this movement and the rest of the work are convincingly strong. To be fair, though, there are one or two quite recent recordings of the work that omit the long, unfinished fugue.

Anyone who sets out to perform The Art of the Fugue has perforce to end up making a decision about an order in which to play the pieces. And, speaking of recording, I have just completed a quick and random survey of a dozen or so CDs of the work, and no two recordings present the movements in the same order! This includes performances on organ, harpsichord, piano, and by chamber ensembles, such as saxophone ensembles, consorts of viols, and so on. These are mostly recent recordings, subsequent to the burgeoning of Art of the Fugue scholarship that we have seen over the last few decades.

(Further regarding recording: nowadays it is easy to set up a recording of the piece with each movement in a separate file, and with playing order to be determined by the listener. This could be as a set order or as a random “shuffle.” So I should say that any performance of The Art of the Fugue presupposes a choice by the performer about movement order. Only a live performance does so of necessity.)

There are two underlying causes of uncertainty about movement order. The first is there are two primary sources for the piece: a manuscript of most of the movements in Bach’s own hand from the mid-1740s, and the edition published in 1751 by Bach’s heirs. These sources have different numbers of movements and are presented in different order. The second source of uncertainty is we do not know how much input J. S. Bach himself had in the preparation of the printed edition. Therefore we do not know that he had signed off on the order represented there.

For example, it is possible for a performer to assume that, since the people who finished the preparation of the 1751 edition were close to J. S. Bach and worked with him directly on at least much of the project, the order that they created is probably the correct order. But this would be at best just an assumption, and there is a significant amount of scholarship to call it into question. A further complication is that the published edition contains elements that almost everyone agrees are not really part of The Art of the Fugue at all, at least not part of the integral structure of the work as a whole. For instance, there are alternate versions of two of the movements and a chorale prelude, the latter manifestly added to the end of the publication as a kind of compensation for its incompleteness and a memorial to the composer. I have never encountered or even heard rumored any performance of literally every note in that original edition in the order in which those notes are found there. So what were these early editors up to, and what did or didn’t they understand about the composer’s intentions?

You will probably not be surprised to read that we cannot answer that question. As I said, there is a lot of good scholarship on the matter, but that scholarship is often in disagreement. Every argument rests on assumptions, and while many of those assumptions seem sound, none of them seem rock-solid certain.

As a performer I must come up with an order. I notice, reading my 1985 program notes, that I then completely accepted the order that I had grown up with. This is the order that Helmut Walcha used in his recording, and I used the same order. This is almost the same as the order used by the early twentieth-century scholar Wolfgang Graeser, who is credited with rediscovering The Art of the Fugue, and whose edition was used as the basis for the first known public performance of the work, which took place in 1927. As best I remember, I did not particularly know at the time there were issues about movement order, since much of the scholarship on the matter has been carried out since then.

I found considerable structural logic in the shape of the piece with this order of movements. For example, I considered the placement of the group of four canons, with their two-voice and therefore relatively light texture right after the dense and complex Contrapunctus XI, to be aesthetically and structurally significant. However, the canons as a group are not placed after Contrapunctus XI in either original source, and they are differently placed in the two sources. Other performers find logic in spreading them out around the other mostly four-voice fugal contrapuncti. This uses the lighter texture to define groupings in the successive fugal pieces. Some performers place them after the long unfinished fugue, displacing it as the ending, and instead ending the work using the lighter textures to create a relaxed sort of coda.

I also found logic in the gradual introduction of the B-A-C-H motif, successively more open and clear in Contrapuncti IV, VIII, XI, and XVIII. Likewise, I find logic in the immediacy of the motion from the flourish ending Contrapunctus XVI—the four-voice mirror fugue—to the opening subject of Contrapunctus XVIII of which it is a very close pre-echo. This happens only if the appropriate section of Contrapunctus XVI is the last item before Contrapunctus XVIII. I also found the juxtaposition of Contrapunctus VIII—the first one whose subject opens with an interval smaller than a fourth—and Contrapunctus IX—the first one whose subject opens with an interval greater than a fifth—to be meaningful. This is only a juxtaposition if those two movements are indeed next to each other.

There are a number of questions that arise out of this complicated picture. If I see a convincing overall structure in this piece with a particular movement order, does that mean that this is likely to be the “correct” order, the order that the composer had in mind? (I will answer this one: no.) Or am I simply imposing that sense of structure because I am accustomed to that order and fondly want to believe the piece has a meaningful overarching shape? (Maybe.) Is it possible that if we really knew for sure what order Bach had in mind we would see that order gave to the work an even more compelling overall shape than we experience now?

Musical entities that are not just clearly one unit have a variety of shapes. To stick with Bach for the moment, The Well-Tempered Clavier is one thing (a collection of completely separate pieces, but ones constructed along similar lines to one another); a suite or partita is something else (a piece clearly intended to have an overall shape, but made up of movements that are in different forms from one another, each of which could stand as a piece in itself); The Goldberg Variations is something completely different yet a piece made up of clearly separate movements, but also with a clear unifying principal among the movements. Das Orgelbüchlein falls into the same category as the WTC. How about Clavierübung III? Unlike all of the above, it gets part of its unified or structured feeling externally, through the associations that we have with the hymns on which the pieces are based. It is also given a circular structure by the prelude at the beginning and the fugue at the end.

Which of all of these would seem very different if the order of the component parts were changed? It would probably depend on the specifics of the changes. For example, if in The Goldberg Variations, the return to the opening “Aria” were taken away from the end and placed somewhere in the middle, that would feel like a drastic change, probably a change for the worse. If the imposing “Variation 16” were moved away from the position that it occupies in the middle of the work that would probably seem odd and weaken the overall shape of the piece. Moving other movements around might make considerably less difference. In Clavierübung III, if the closing fugue were moved into second position right after the prelude, leaving the work to end with the four duets, the structure of the whole would seem radically different. If the four duets were distributed throughout the piece rather than placed in a group at the end that would seem like a real change as well.

In all of these cases we have reason to believe that we know what order Bach intended. With The Art of the Fugue we approach the same sorts of issues from a less anchored place.

I will continue this discussion next month, attempting to tie it in as closely as possible to some of the specific compositional details of The Art of the Fugue and, in turn, to performance as such.

To be continued.