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Few composers have ended their careers with a work that serves to epitomize their skills.
His Majesty immediately ordered his admission and, upon his entry, went to the so-called ‘Forte and Piano’ and without any preparation personally condescended to play Capellmeister Bach a theme that the latter should improvise into a fugue. This was accomplished by the aforesaid Capellmeister Bach so successfully that not only was His Majesty inclined to indicate his pleasure, but all other persons present were given to great astonishment.[Bach's first biographer, Johann Nikolaus Forkel,reported that the King was so enamored of the new-fangled pianoforte, a forerunner of the modern piano, that he collected 15 of them.] Other accounts add that Bach extemporized not only a fugue in three voices but another in six parts, which Spitta claims was based on his own theme, rather than the King's - an extraordinarily difficult undertaking, as the parts had to be distinct, yet so closely interwoven as to fall within the compass of two hands; indeed, Spitta believes the feat to have been previously unheard of on a clavier without pedals (on which the lowest voice could be played). According to the newspaper, "Mr. Bach found the [King's] theme so exceedingly lovely that he wanted to write it down on paper as a proper fugue and have it engraved in copper." Indeed, upon returning home, Bach composed a three-voice fugue (for which he used the old term of "ricercar," which initially meant a prologue to establish tonality but had evolved into signifying an elaborate composition displaying all the techniques of the fugal style) and sent it to the King along with six canons and another fugue, all based on the royal theme. In the typical toadying fashion of the day, Bach's accompanying dedication, dated July 7, 1747, asserted that: lacking an opportunity for the necessary preparation [for the improvisation], I was unable to give a performance worthy of so excellent a theme. I then determined to develop this right royal theme in a more perfect manner, and immediately applied myself to the task, so that it should become known to all the world.He soon followed with a second beautifully-bound dispatch that added three more canons, a six-part ricarcar, and a four-movement sonata for flute, the King's own favorite instrument. Nikolaus Harnoncourt asserts that, notwithstanding Bach's praise, the royal theme was entirely unsuited for use as a fugue subject (indeed, it's overly long, chromatic and fitful),
The canons enabled Bach to display his astounding technical skill. A canon requires strict imitation by sequential overlapping voices. Its simplest form is a round, in which each voice plays the same melody without any change (such as "Three Blind Mice" or "Row, Row, Row Your Boat"), but Bach takes a vastly more sophisticated approach with brilliant results. Thus, the second canon (and one of the simplest) consists of a single line that generates its two parts by being played simultaneously forward and backward. The fourth (in contrary motion) features the second part as an inversion of the first heard a half-measure later. The subject of the sixth canon is repeated through successively higher keys until finally returning back to home base. The Musical Offering is full not only of invention but considerable wit and a touch of mystery. One canon (teasingly inscribed "he who seeks shall find") is a puzzle, printing only the first part and requiring would-be performers to determine where, of all the possible permutations of transposition, inversion, retrograde, rhythm and note-value, to insert the same theme as the second part to make the most musical sense.
One puzzle that eludes consensus, though, is how to organize the work. Should the pieces be played in the order in which Bach engraved them, or should they lead to a climax with the six-voice ricercar (the most complex invention) or culminate with the flute sonata (which the King would have considered the pinnacle)? Performance, too, poses questions - except for the flute sonata and a canon for two violins (which also requires a cello for a bass accompaniment), Bach did not specify instrumentation - nor, for that matter, any tempos. Due to their origins at the royal concert, the ricercars are generally presumed to be for a single keyboard player, although, perhaps to focus attention upon the complex interplay of its individual lines, Bach wrote the second one in open score on a system of six staves, with one staff per part. The canons, though, can be played on strings (and Bach so specified for one of them), keyboards, winds, or any combination or other variety of ensemble to differentiate the intertwining lines. Indeed, various recordings take each of these approaches. The king apparently never sent Bach any gift, nor even an acknowledgement, in exchange for this marvelous tribute. Yet it served a higher purpose. The meeting with the king enhanced Bach's reputation and Bach was so proud of his six-voice ricercar that he had 100 copies printed. But beyond that, the concept of a relatively abstract, intellectual display of compositional prowess presenting a vast realm of invention on a single theme flowered into a final and even more astounding summation of his art.
Although ignored at the time, and for a century to come, the Art of the Fugue is now universally hailed as not only a supreme treatise on counterpoint and thus the foremost embodiment of Bach's esthetic ideals, but one of the supreme monuments of art, in which a wealth of invention is crafted from a single idea (and in that sense serves to exemplify Bach's core belief in the perfect and inviolate God-given order of the universe). John Stone calls it "tantamount to a sacred text, an artwork so quintessentially perfect in form, so unutterably beautiful from the dual perspectives of the mind and heart, intellect and emotions." While many of us enjoy it on a superficial level, perhaps the most meaningful tribute is from those having a lifetime of expertise and the deepest familiarity, who consistently declare their studies and analyses to be incomplete and its depths to be limitless, not only as an encylopedic complilation of past technique but as a visionary guide to inspire the creativity of future generations.
Bach was able to supervise at least some of the engraving, and provided a correction sheet for five of its 18 pieces, thus suggesting to Geiringer that he was unable to oversee the rest. The remainder has generated considerable controversy over perceived errors. Thus, Malcolm Boyd states that the editors (two of Bach's sons and Marpurg) were "ignorant of Bach's intentions, or perhaps misunderstanding them." Spitta was less charitable, asserting that the editors "put everything on the plates as it came - sketches beside completed movements, original settings beside arrangements, parts that had a connection beside those which had none, in dreadful disorder." Although their work was hardly that haphazard, it is true that they included an earlier, shorter variant of Fugue X as a separate piece and illogically scrambled the order of the canons to lead with the most complex. Entire treatises have dissected the Art of the Fugue in minute detail (far beyond my understanding), so it seems more suitable here to address the first movement and then consider the overall structure. Theme - The choice of a theme to serve as the foundation for such a massive work is crucial, and Bach's creation was masterful.
The First Fugue - Even the first (and the simplest) fugue takes substantial liberties with the established conventions of the genre and asserts its own personality. It begins with the expected regular sequential introduction of the theme in each voice, alternating tonic and dominant, with no overlaps or gaps, each entry beginning at four-measure intervals just as the prior one ends. But immediately Bach eschews strict form. Although the answers (extending the end of the theme) all project an entirely different character, they introduce a persistent eighth-note rhythm that will permeate the movement - indeed, from bar 10 through 70 a new note falls on every single half-beat. Yet, Bach avoids any threat of monotony by distributing the phrases and even single notes among the four voices, so that the overall steady, rapid figures flit in a constant panoply of diverse phrases and textures, even as each individual line retains its own integrity. Indeed, this immediately announces the very essence of Bach's inspired counterpoint - as distinguished from later music in which the inner voices are often of marginal interest by themselves and mostly serve to complete the harmony, here each line is fascinating and lucid on its own, yet they compel full attention in combination. Moreover, typical of the dual nature of this work as performable music and as pedagogy - and Bach's supreme artistry - the interplay is as fascinating to see in score as to hear. Even so, just before the persistent rhythm might become tiring, it serves to set us up for a dramatic close - the only one in the entire work - in which the motion suddenly - and quite unexpectedly - halts for three beats of silence, followed by a single stark d-minor chord, another three-beat rest, a tentative resumption of the prior motion over a deep pedal D, and in a final surprise resolves with an unaccustomed smile into a concluding D-major cadence. Structure - In its published, albeit incomplete, form, the work can be split into five major sections. The first comprises four "simple" fugues (that is, with the theme as the only subject). Fugue I is based on a persistent lively half-note rhythm. Fugue II dots the rhythm of the concluding eighth-note figure to inject a lilting motion that pervades the entire piece. Fugue III inverts the theme altogether, imbuing it, and the entire movement it heads, with a wholly new, yet clearly related, character. It also adds a true countersubject, notable for its chromaticism, that accompanies each appearance of the subject.
The second portion consists of three stretto fugues, in which the traditional techniques are explored. Tovey considers these to be "the fugues for which the theme was designed." Fugue V is a stretto fugue in contrary motion, featuring overlapping statements of a rhythmically-modified version of the theme and its own inversion, increasing the intensity by shortening the intervals between statements of the subject from three measures to a single beat. Fugue VI - "a solid mass of stretto" in Tovey's words - not only overlaps the subject in its direct and inverted forms but thickens the texture by using both versions in diminution (halving the theme's note-values) to yield a total of four variants heard together. Bach also designates the sixth fugue "in the French style," not only heavily dotting the rhythm (possibly to be construed as double-dotting, consistent with the "French" custom of the time) but adding ornamentation of trills and shakes, which Rosen, for one, takes as an invitation to the performer to add his own tasteful elaborations. Fugue VII reaches an apex of density, adding augmentation to diminution, intensifying the appearances of the theme by separating them with only a single brief episode, and building to a weighty conclusion by adding an additional voice to the standard four. C. Herbert Parry describes Fugue VII as "so crowded with allusions to the subject in every conceivable way" that Bach "had to take leave of it for a while" - and so he does. The third major division - "the central business" of the work, to Tovey - introduces new subjects to which variants of the theme become a second or third subject. Samuel Baron notes that all the themes are related to the original, and likens them, as offspring, to the proliferation of a family tree. Fugue VIII lightens the texture to only three voices, but is a triple fugue with three subjects, the first two chromatic and the third a close relative of the main theme, each developed sequentially, and then combined; as Jeffrey Hall notes, at that point "the music simply explodes with energy." Tovey nails the challenge here for a fugues with multiple subjects: the themes must be strongly contrasted and distinctive, yet so disposed that any can be a bass or treble to the others to yield a satisfying harmony - far easier said than done. Next come two double fugues (with two subjects) of contrasting moods, but displaying similar contrapuntal feats - invertible subjects that can be placed above or below each other at intervals of the 12th (Fugue IX) or 10th (Fugue X) - i.e.: an octave plus a fifth or third. As Tovey notes, the object here is to obtain two different harmonic schemes from a single pair of themes. Following this slight respite, the section closes with a staggering feat - a highly chromatic triple fugue based on inversions of all three subjects of Fugue VIII (which eventually are re-inverted to their original form), resulting in "a tremendous conflict and clashing of themes, ideas and feelings … extending from the most inner and secret utterances to the most outspoken defiance" yet all sublimated in the form of "pure music of the most profound order" (Baron) and culminating in "amazing resource and ingenuity." (Boyd)
The fourth section comprises two ingenious mirror fugues, which can be played either as written or with the score inverted - literally turned upside down - and make complete musical sense either way. Fugue XIII is a four-voice fugue, so that the inversion places the soprano in the bass, the tenor in the alto, the alto in tenor and the bass in soprano. The process can be seen in a brief passage showing two systems from Bach's autograph. Fugue XII is for three primary voices, with the inversion rotating them so that the bass becomes the middle part, the middle the treble and the treble the bass. In this fugue alone, Bach steps aside from formal strictures to add a fourth, free voice and specifies "a 2. Clav." - his only suggestion of instrumentation (necessitated by the spread of the voices beyond the realm of two hands). The final section contains four canons. Rather than presented as a puzzle, as in the Musical Offering, Bach's autograph provided the first canon in a single voice, followed by his own "resolutio" on two staves. Bach's realization of the remaining canons is far from simple. Thus, the last one presents its theme along with its inverted augmentation, and then swaps the positions with the lower voice on top. Yet, despite their technical facility, Tovey, for one, considers them a letdown in difficulty or spontaneity and questions their inclusion, commenting that it is no more difficult to extend a two-part canon for 100 bars than to confine it to the length of the subject and suggesting that technique here degenerates into idle mechanism. Indeed, Robert Simpson considers them anomalies and better suited to a separate, unrealized "Art of the Canon." Yet, there is one more piece that has proven the most intriguing of all - a massive, yet fragmentary quadruple fugue of which Bach wrote 239 measures. Bach's son, Carl Phillip Emmanuel, perpetuated the melodramatic view that Bach died in the throes of composing it, and even inscribed on the last page of the autograph: "While working on this fugue, in which the Name BACH appears in the countersubject, the author died"), but Wolff, for one, discounts that assertion by considering it an afterthought while the posthumous engraving was in process. The portion Bach completed drops off after the introduction and working out of three subjects, none of which is directly related to any others in the work. Early scholars questioned its inclusion in the Art of the Fugue. They noted that its title in the first edition was "Fuga a 3 soggetti" ("Fugue on 3 subjects"). Spitta stated that it "has nothing whatever to do with this work" and that it "crept into the original editions" by misunderstanding. That changed in 1881 when Gustav Nettebaum discovered that all three themes fit well with none other than the original theme of the Art of the Fugue and contended that Bach's unrealized intent all along had been to bring his work full cycle to a brilliant conclusion by culminating with the very theme with which it had begun. The significance of the final incomplete fugue is magnified by the third subject which begins with B-flat-A-C-B-natural, or B-A-C-H in German notation, thus serving an autobiographical function and a signature stamp to conclude his life's work - and the first and only time that such a figure appeared in the composer's entire oeuvre. Rosen notes that the portion of the final fugue using the B-A-C-H theme is "tersely chromatic" and "leads to far-reaching modulations, as if Bach were drawing the most significant effects of his art from his own name." (A further intriguing possibility: in an obituary, CPE Bach and Johann Friedrich Agricola stated that Bach's last fugue not only was to contain four themes but in a final bravura demonstration of staggering complexity was to have been inverted note for note with all four voices.) Indeed, Leonhardt reasons that had Bach lived he not only would have finished the fugue but might have substantially revised it. David Johnson goes further to speculate that Bach may have been planning a yet more grandiose finale.
The issue of realizing the Art of the Fugue has challenged performers from the start. Questions have also been posed as to whether the work is best heard as a whole or in excerpts. Lang declares: "An integral performance is the worst that can be done to it and affords perhaps the best proof that we still have to blaze a trail to this summa of the Baroque, for the work is a philosophical breviary, every measure of which invites reflection and thought. It is only through long and intimate acquaintance with the individual fugues that we can arrive at a true understanding of their message." Tovey takes a middle ground, asserting that the first eleven fugues are effective in their given order (although he feels that the stretto fugues tend to sag), but proposing that for maximum impact the others be paired with preludes and movements from Bach's other works. Yet, most fans tend to side with Spitta who considered the entire work to comprise a single gigantic fugue, in which an understanding of the ingenious intricacy of the latter portions requires the preparation provided by knowledge of the rest. Turning from abstract philosophy to the practicality of performance, an immediate issue challenges performers with the order of presentation. Bach's manuscript followed the first fugue with the one having an inverted subject, and then the one with dotted rhythm, whereas the engraving, the first portion of which he supervised, presented the one with dotted rhythm before the two inverted ones. Either order seems logical. The matter becomes more complicated - and controversial - with the canons. Should they interrupt the progress of the fugues, or, as Simpson asserts, be relegated to some sort of appendix? Various editors, arrangers and performers freely assemble the second half of the work to group fugues with similar structures or to vary the organization for a more dramatic progression. A further question looms as to the appropriate instrumentation. As Johann Philipp Kirnberger stated, “if one finds the right style of performance for them, even the most learned fugues sound beautiful.” But how? Bach was silent on the matter, and a wide variety of musicians have supported their choices with exemplary recordings. None is exclusive; reflecting the outlook of those who regard the work in abstract spendor, Stone says, “The amazing thing is, the musical ideas themselves, the pure relation of note to note and voice to voice, are so consummately worked out that the music ‘works’ on virtually any instrumental combination. Timbre really does seem beside the point with such a composition.” Bach himself had fostered the realm of performance possibilities by having written the work in open score, with each line on a separate staff. To some this underlines a didactic purpose to facilitate understanding the interplay of the voices, which admittedly are easier to follow and compare on individual staves. But it also is consistent with the way Bach wrote his scores for ensembles, and thus invites adaptations for multiple players.
Perhaps the best way to explore the huge variety of approaches and performing forces the Art of the Fugue has attracted - surely the most diverse of any musical work - is to consider each in turn, with particular attention to the pioneers and their rationales. Remarkably, the first recording arose only in 1934, although within two years three more appeared before interest waned (and then returned with full force - currently, dozens are available). Harpsichord - It seems curious, to say the least, that the first recording on one of Bach's own two favored instruments arose only after two decades of adaptations. A young Gustav Leonhardt,
Bach left no direct clues as to his own style of playing, but an important guide is found in the obituary notice penned by his son, which asserted that “he generally took very lively” and “was uncommonly sure,” thus suggesting fleet, steady tempos. This is echoed in the biography by Johann Forkel that, although published in 1802, was based upon information gleaned from Bach's sons and contemporaries: according to Forkel, Bach "took the time very brisk but contrived to introduce so much variety in his performances that every piece was like a discourse," thus suggesting personalized touches and creative ornamentation which few modern players dare to interpose, perhaps for fear of seeming arrogant and disrespecting the purity and perfection of the scores. Forkel further credits Bach with developing a technique in which all fingers, including the thumb, were equal so as to enable all voices, including the inner ones, to be of similar import. He also reportedly had huge hands that could span a twelfth, and wrote the Art of the Fugue for that range, requiring artists with smaller reach to resort to occasional arpeggios or pedals. Leonhardt's reading exemplifies both period practice generally and the composer's own interpretive inclinations (except for the faster tempos Bach prescribed). Even so, the harpsichord's sharp percussive sonority creates an illusion of speed that belies the actual moderate pacing. Piano - The mere title to his fine 1968 album of Bach's "Last Keyboard Works" announces Charles Rosen's conviction as to the composer's intended instrumentation. The very first Art of the Fugue keyboard recording presented the entire work in an arrangement for two pianos by the American (but European-trained) Richard Buhlig, a modest intellectual who doted on early and modern music but made no commercial discs. His Art of the Fugue recording with his pupil Wesley Kuhnle was made in Los Angeles around 1935 and was circulated only privately until its release on a Pearl CD in 2002 (80'). Respectful of the esthetic of Bach's time, there is no attempt to exploit the power of the modern concert grand, whose resources are used discretely for subtle gradations of balance and dynamics to afford a limited degree of highlighting of structure and voicing. Although several endings are romanticized through lengthy deceleration, tempos are generally steady. In theory, assigning only a single voice to each hand should enhance the linearity of each musical line, but the benefit is barely audible, and there is a certain amount of blurring resulting from imprecision in striking vertically-aligned notes slightly out of synch, suggestive of a rolled chord. Yet the sheer courage of this pioneering venture merits an honored place in the history of restoring Bach’s luster in modern times. Organ - Bach's greatest lifetime fame involved his other primary instrument - the organ. According to his son C.P.E., he had thorough knowledge of their mechanics and construction, often was called upon to apply his critical facility to severely test and approve new instruments, insisted upon tuning them to his own precise specifications, and was deeply sensitive to the design and acoustic qualities of the halls in which organs were to be installed.
The first organ recording of the Art of the Fugue appeared in 1936 by Fritz Heitmann on Telefunken. Although currently unavailable, its quality may be inferred from two other Heitmann recordings - a 1938 set of other Bach selections (chorale preludes and a fugue) and a 1950 remake of Art of the Fugue excerpts (both currently available as downloads from the International Historical Organ Recording Collection). The early set, on an organ Bach himself had played, was hailed by a May 1939 Gramophone review as "a really outstanding series of records [that] has recaptured to a wonderful degree the splendid voicing of this ancient organ," while the latter, on a modern instrument, seems to better exemplify Bach's own approach to the organ with imaginative registration and lively, precise playing. Although Heitmann's pioneering album was followed in 1940 by another now-obscure RCA set from E. Power Biggs, the most famed organ recording arose in a 1956 Archiv rendition by Helmut Walcha (86'). Among the many other organ recordings of the Art of the Fugue, Glenn Gould's 1962 Columbia LP, although only of the first nine fugues, warrants special mention. Although he claimed that the organ was a great influence on his distinctive (and often bizarre) manner of playing the piano, this was Gould's only organ recording. Quickly paced (31 minutes v. 39 for Walcha in the same portion), and piquantly voiced (abetted by placing the microphones against the pipes to capture their air supply), it stands in marked contrast to the isolated Art of the Fugue movements Gould played as part of recital programs, in which he applied extreme pacing (both fast and slow). Gould's iconoclastic approach to Bach culminated in his final year, when he recorded the final, incomplete fugue in a mesmerizing video. Thoroughly absorbed in a private world of sound, his extreme swaying and grand gestures conjure an extraordinary degree of spirituality right up to a deliberately abrupt broken end that accentuates the magnitude of our loss. Quartets - The notion of expanding the Art of the Fugue
A fascinating variant of the string quartet is a consort of viols, a family of stringed instruments prevalent in Bach's time that developed in tandem with modern violins, violas and cellos but with elements of lutes and guitars, including fretting along the neck, six stings tuned in fourths, and being held vertically with an underhanded bow grip. As played by Fretwork on a 2002 Harmonia Mundi CD (76'), their thinner design, lower-tensioned strings and nasal tone impart a reedy sonority that helps to distinguish the voices within an intriguingly novel blend. At the same time the lighter texture and precision delude the ear into hearing an faster apparent tempo than actually occurs. Other variants of the quartet approach include several for saxophones - not the rude raucous honkers of early rock but tamed to lugubrious melancholy - that seem more oriented to novelty than musical insight. One even includes a segment of "free spatial improvisation" [translation: random noise], a modern conceit that seems vastly more out of place than Bach's final chorale. Yet one extreme arrangement stands out (to me, at least) as altogether extraordinary - a 1988 CBS CD by the Canadian Brass, a quintet playing trumpets, piccolo trumpet, flugelhorn, French horn, euphonium and tuba. Encouraged by Glenn Gould, and arranged by Arthur Frackenpohl, their swift rendition (52½ minutes, omitting the canons) is sharp, bright and consistently intriguing - one of the few small ensemble renditions that manage to hold my attention throughout. Ensembles - For added power and timbral variety, many arrangers have assigned multiple instruments to Bach's individual voices. Indeed, it was a full orchestral performance by Wolfgang Graeser in 1926 that was largely responsible for stimulating modern interest in the Art of the Fugue and thus paved the way to recordings. Similar considerations shape the full orchestral versions. In notes to a fine 1966 album by Karl Ristenpart and the Chamber Orchestra of the Saar of an orchestral realization by Marcel Bitsch and Claude Pascal (Nonesuch, 85'), Jason Farrow presents an unabashed defense of this approach. The first orchestral version to appear was by the Radio Beromunter Orchestra conducted by Hermann Scherchen in 1949 (Decca LPs; Archipel CD) in an arrangement by Roger Vuataz, which Scherchen later rejected as too rich (an impression amplified by his extremely relaxed tempo of 99 minutes). In 1965 he recorded his own adaptation with 40 players from the Vienna Symphony and Vienna Radio Orchestras - 26 strings, 10 winds, two trumpets, two trombones - and a harpsichord to which all four canons are assigned (Westminster LPs). While the Ristenpart recording is consistently light and airy, Scherchen's is far more bulky and serious, due in equal part to its more extended timing (109', including the appended chorale prelude) and its more formal organization - the simple fugues alternate winds and strings, the counterfugues combine both, the triple and mirror fugues are introduced by a solo harpsichord canon, and the full orchestra weighs in for the triple fugues that close each major section (the unfinished one, like Gould's, running over 13 minutes). Yet it's constantly alive with intriguing sonorities, from gentle pastorales to the lushly romanticized, vibrato-laden abundance of the late 19th Century, producing an ample variety of mood and characterization, with the double fugues in turn mischievous (VI), zesty (VII) and playful (VIII), and the triple fugues patiently and inexorably building to massive dramatic climaxes. Perhaps more than any other rendition, Scherchen's illuminate the sheer humanity of the work and thus leave no doubt that in the sonic garb of any era the Art of the Fugue transcends a mere academic exercise to radiate an irrepressible pulse of creativity and life in their infinite variety.
Copyright 2012 by Peter Gutmann | |||||||||||||
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copyright © 1998–2012 Peter Gutmann. All rights reserved. |
Many succumbed long before they could anticipate their demise, while others lingered on as their inspiration and energy dissipated. As his blindness advanced and his health declined, Johann Sebastian Bach poured his final strength into "one of the truly great creations of the human mind" (Karl Geiringer), a "philosophical breviary, every measure of which invites reflection and thought" (Paul Henry Lang) that "even Bach himself never produced before in his life" (Philipp Spitta). Even today Bach's final work, Die Kunst der Fuge (The Art of the Fugue), stands as not only the ultimate monument to his own wide-ranging genius but an enduring shrine to the art of an entire epoch. Yet it is no dry memorial. Rather, although incomplete, quixotic and partly abstract, it has intrigued, challenged and thrilled musicians and listeners of every era. 
The fugue arose long before Bach. The basic components and techniques were in place a century earlier. The subject or principal theme is given alone at the outset and seasons the entire piece. It immediately reappears, perhaps modified, in a second voice as the answer, while the first voice continues with an accompaniment, known as the countersubject. The piece comprises expositions, in which the subject is heard (once in every voice for the first exposition), separated by episodes, which may comprise fragments or variants of the subject such as augmentation (half-speed), diminution (double-speed), inversion (in which all intervals are the opposite of the originals, i.e.: a rising fifth would become a falling fifth), retrograde (backward) or stretto (overlapping by launching a new statement before the prior one ends), as well as rhythmic and harmonic transformations. Yet commentators constantly remind us that despite these basic rules and devices fugue is not a rigid form but a springboard for creativity – Donald Francis Tovey calls it a texture rather than a design, and Glenn Gould considers it "an invitation to invent a form relevant to the idiosyncratic demands of the composition." Indeed, Bach's glory is that he transcended conventions even while exemplifying them, crafting masterworks that combine the seemingly irreconcilable poles of dazzling traditional technique and vast far-reaching imagination to satisfy both intellect and emotion. Although often studied in microscopic detail by the most sophisticated musicians, a Bach fugue rewards even purely intuitive listeners with a sense of structure unifies formality with flights of fantasy, at once soothing and provocative. 
The primary model for the Art of the Fugue often is traced to Bach's prior work, the Musical Offering.
Just as Bach found religious symbolism in the unity of the fugue, so here - he prefaced the sixth canon with an inscription (in Latin): "Like the ascending modulation, may the King's glory also rise" and before a canon of augmented notes: "Like the note values, so may the King's happiness increase." The two ricarcars also display the range of Bach's style - Charles Rosen characterizes the first as light, playful, fanciful, informal and almost improvisatory, perhaps reflecting Bach's extemporaneous playing before the king, whereas the second (which Rosen considers the greatest fugue ever written) is massive, grave, deeply expressive and formally structured. Christoph Wolff further credits the slow middle movement of the flute sonata, "with its melodically twisted, rhythmically differentiated, harmonically surprising and dynamically shaded gestures," as the "Old Bach's" (as he was increasingly called) embrace of the emerging musical fashion of sensitivity, and thus (rare for Bach) a glimpse into the future. 
Why did Bach create the Art of the Fugue? Wolff posits a practical concern. In 1737, a former pupil, Johann Scheibe, possibly in retaliation for Bach having passed him over for a coveted appointment, published an attack in which he savaged Bach's style as "turgid and confused," decrying its "beauty darkened by an excess of art" that buried the melody, detracted from the beauty of the harmony, had excessive ornamentation, and was extremely difficult to play.
At first, it logically was assumed that Bach had written this unfinished work in his final year until, as Spitta put it, “death overtook him.” Scholars now attribute much of the autograph to 1742, although Bach proceeded to supervise its engraving only in 1749. As characterized by Wolff, the autograph, which comprised twelve fugues and two canons, was organized so as to present a rational order and well-rounded structure based on two principles: increasing difficulty and complexity, and increasing animation of the subject. Wolff notes that between the autograph and engraving, “clearly fascinated by the work's perplexing challenges and unique opportunities,” Bach continued to develop it, adding a new fugue and two new canons to broaden the conceptual dimensions of the work. Wolff cites in particular a highly innovative new fugue that altered the intervals of the subject to open up an unprecedented expansion of the harmonic spectrum. Bach also enlarged and rewrote several movements; thus, the autograph version of the first fugue ends with a full cadence right after a dramatic pause, whereas the revised version resumes the former bustle (with some sputtering) before finally coming to a well-deserved rest. Bach also added an entire page to Fugue VIII to introduce and explore its theme, a passage which Tovey considers “one of the most beautiful and profound that Bach ever wrote.”
Performers face a difficult decision of how to treat the final fragment. It has been suggested that Bach stopped on purpose, so as to invite his successors to grasp the initiative to complete it.
For more than a century there was no problem, simply because there were no performances. Indeed, the most fundamental question is whether to perform it at all. Early musicians viewed the work as purely abstract and didactic, fostered from the outset by efforts by C.P.E. to sell copies for that purpose. (As a sad afternote, in September 1756, he offered the copper plates, weighing about 100 pounds, for sale as scrap metal, pledging to accept the first reasonable offer, as only 30 copies had been sold, even at a reduced price.) While hailing its educational purpose, Spitta pronounced portions to be "very difficult, nay impossible, to play." Others consider the work wholly abstract and thus diminished through attempts at performance; thus Lang decries the distortion of "soulful" rendering by instrumentalists and praises its "superhuman aloofness" to "preserve the purest dematerialized spirit of the highest form of Baroque art." Noting that it contains no indications of tempo, dynamics or even instrumentation, Johnson opines that "the human and the emotional are not its real concerns. Like the figures on Keats's urn, it has passed out of time and accident, and wears the changeless beauty of pure thought." Schweitzer contends that it inhabits a "still and serious world … deserted and rigid, without color, without light, without motion; it does not gladden, does not distract; yet we cannot break away from it." Yet, as Geiringer contended: "Even if he had wanted to do so, Bach would have been unable to write only dry instructive precepts. Under his hands, the textbook changed into a poem imbued with the mystery of pure beauty." Leonhardt emphatically calls it "Art of Fugue" rather then "Art of the Fugue," so as to stress that it is a work of art in fugue form rather than a set of craft lessons. 
Imogene Horsley agrees that the ordered presentation produces a broad sense of total form that can only be felt when the work is heard as a unit. Johnson urges: "Put the score away and the infinitude of detail will be subsumed by the massive unity of the thing and the microscopic will give way to the cosmic." 
Any rendition of the Art of the Fugue necessarily must strive for clear articulation (essential for grasping the rhythmic interplay of the lines) and equality of the voices (although Bach's approach to counterpoint flies in the face of the laws of physics, in which the ear naturally gives priority to higher voices}. Yet for those of us who do not approach it as theoretical study, there are two equally important touchstones - the ability to sustain interest throughout its entire length and, above all else, an intangible quality of communicating a sheer sense of awe and enjoyment through commitment and enthusiasm. Scholars have the scores, from which they will wrest their own realizations (or revel in its abstraction), but the rest of us need to savor and relish this work as a living, engaging organism.
who would emerge as a leader of the movement to uncover and revive authentic performance practices of the Baroque epoch, produced the first harpsichord version in 1953 (Vanguard LPs, 97 minutes). In a monograph published the prior year, Leonhardt had asserted multiple justifications, based on his research, for assuming that Bach intended the Art of the Fugue for the harpsichord: 17th and 18th century composers routinely published keyboard works with complex polyphony in open score (and a glance at the clutter of a portion of Bach's autograph of the Musical Offering ricercar on two staves strongly suggests why); the entire work lies easily within the reach of a keyboard player's two hands; Bach revised the score to improve its ability to be played on a keyboard; although Bach was a master orchestrator, none of its individual voices corresponds with the range of the ensemble instruments of Bach's time; the characteristic melodic "shapes" of Bach's orchestral writing are absent; the fugue "types" and "hidden homophony" resemble those Bach wrote for keyboards; and the bass voice occasionally rising above the tenor precludes doubling or continuo, as would characterize Bach's orchestral style. Yet all of these rationales could apply to any keyboard instrument, including the equally prevalent clavichord, which Leonhardt tersely dismisses as "limited." Yet, more than with any other medium, it's the very limits of the harpsichord, lacking any variation in its soft volume or percussive timbre, with no opportunity to adjust the actual sound of the instrument, that invest its performances, and Leonhardt's recording, with an extraordinary purity, such that any drama must emerge from the interplay of the notes themselves. The hushed result is also deeply intimate, creating a close personal connection between performer and product. Leonhardt's performance is further informed by his central tenet that while the 19th century used music as a means of expression, the 18th century used expression as a means of making music, such that primary emphasis must be placed upon refinement of taste.
In accompanying notes he bolsters Leonhardt's view ("an entire work of such contrapuntal complexity does not lie within the compass of two hands by accident") but then departs by considering the problem of which keyboard instrument to use to be a false one. He reasons that since there was no possible opportunity in Bach's time to play the work in a public concert (much less to record it), it must have been intended for whatever instrument was available in a private home setting. He further notes that the work makes no demands of the special characteristics of any particular instrument of the time (such as the contrasting tone quality of a double-manual harpsichord, the vibrato of a clavichord, or the sustained breath of an organ), but rather has an innate purity that accommodates all keyboards with ease. He concludes that modern performance demands a piano, simply so that our familiarity will avoid calling attention to the medium and thus distracting from the music. Yet there is a problem with that approach - Bach labeled one of the mirror fugues (and its inverse version) "a 2. Clav" - for two keyboards - and indeed its density and range require a second player. Some solo artists simply omit that fugue. Others, including Rosen, extend their penchant for modern instrumentation by using tape technology to synchronize their playing of both parts. 
In his accompanying notes, Walcha promotes the use of the "king of instruments" for its "incomparably richer variety of tone-colours [that is] more suitable for interpreting the large number of similar fugal compositions in plastic relief" and because it "can hardly be surpassed in the realization of the work when notes have to be sustained with consistent intensity." He concludes that the organ "certainly meets the demands of the contents of this music to an extraordinary degree." Playing of necessity from memory due to his complete blindness (and having to assemble each piece from hearing the separate parts - an astounding mental feat), Walcha fulfills his claims with a greater variety of timbres than Heitmann, abetted by improved sonic fidelity that brings out the subtly shifting quality of the voices, creating a complex sense of diversity within an integral conception that eludes less versatile keyboard instruments. Indeed, the organ redresses other keyboards' unavoidable rapid decay of held notes that Bach writes as pedal points or final chords with fermatas, thus reinforcing the harmonic underpinning and a sense of completion. Walcha’s tempos tend to be measured and endings weighty, adding to an overall aura of dignity that reinforces Bach's pedagogical purpose. 
beyond the range and a timbre of a single instrument has led many performers to adaptations for various instrumental groupings. The most elementary use ensembles of similar instruments while sacrificing an explosion of color that some consider to be an inherent invitation of the abstract score. Taking a cue from the open score's four separate staves, the most patent approach is for a string quartet, whose members neatly coincide with the range of each part. Indeed, the very first Art of the Fugue recording was cut in late 1934 by the American-based Roth Quartet (Feri Roth, Jeno Antal, Ferenc Molnar, Janos Scholz) in an arrangement by Roy Harris (the composer) and Mary Norton (Columbia ROX 8001-10, Divine Art CD, 75'). (The arrangement was necessitated, in part, because some notes extend below the range of conventionally-tuned string instruments.) A June 1936 Gramophone review championed the approach: "The long sequence of fugues in the same key stand in no need of the extraneous attraction of orchestral colouring to relieve what one might imagine to be an inevitable monotony." Yet IT hailed the arrangement "for its greater clarity being given to the parts than is possible at the keyboard; and also, it must be added, in a greater dynamic expressiveness." While the reviewer's urge to proselytize "the many lovers of Bach who have not yet made acquaintance with this great work" is evident, when heard today, this first exposure is quite modest and unassuming, with deliberate tempos, mild dynamic swelling and a feeling of persistent gentleness and calm that risks lapsing into mournfulness. One feature, though, serves to distinguish it from the keyboard renditions - prominent vibrato, especially in the first violin, which endows it with a somewhat more personal communication than the steady notes of keyboards can impart. The canons are all omitted, but, as a bonus of considerable historical importance, the twentieth side presented Sir Donald Tovey playing his own conjectural completion of the unfinished final fugue on a piano.
Whether Fretwork's sharp inflection reflects authentic period practice, it contributes to an absorbing, lucid and altogether fresh approach, and their sheer sound evokes a by-gone era that joins those of the harpsichord and Baroque organ to transport us back to share the experience of listeners in Bach's own time. 
The third Art of the Fugue recording, by the Collegium Musicum Instrumentale of Berlin (presumably named after the Leipzig coffeehouse-based student band to which Bach had devoted himself in the 1730s) directed by Hermann Diener (Electrola, 1935, 70'), sounds like a mere string quartet despite the title of the ensemble. Its light feel, allied with a scrappy, spirited vigor, give it a propulsive quality. A transitional approach was issued in 1962 by the Fine Arts String Quartet and the New York Woodwind Ensemble (flute, oboe, clarinet, French horn and bassoon) on Concert-Disc. The arrangement by Samuel Baron (the Ensemble's flutist) strives for tonal variety by astute combinations of the instruments - thus, Fugue I is for quartet alone, II is for two strings and two winds, III is for winds alone, and IV is for all nine. Within each movement, each phrase is played by a different solo or combination, which adds a constant shifting of color but at the expense of any sense of continuity, integration or overall architecture. 
He dismisses the significance of Bach's open score manuscript, noting that the mid-eighteenth century was the mid-point between earlier use of that format for keyboards and its later use for ensembles. Rather, he aligns himself with two adaptors - Graeser, who held that this "most powerful work in occidental music" could only be fully realized through orchestration, and David, who conceded that "Bach probably did not think of orchestral performance," yet rationalized that "the work was conceived and almost completed according to so monumental a plan of symmetrical unity that it seems to cry out for complete performance [in which] an orchestra can provide a sense of variety and increasing contrapuntal density that is hard, if not impossible, to obtain with a string quartet or a keyboard instrument." Pascal likens his choice of instruments to render the internal structure through shifting timbres to an artist's use of colored pencils to tastefully enhance a bare outline. Yet, while the playing is delightful and the entire recording is thoroughly enjoyable, a fundamental problem remains - the consistent density of the augmented resources provides a greater realm of sonic options and appeals to us with the comfort and familiarity of modern garb, but at the cost of detracting focus from the all-important evolution of abstract musical thought.
What would Bach have thought of all this? I suspect he might have been deeply pleased, and perhaps even thrilled. 
After all, he constantly adapted his own works to suit available forces and occasions. More important, he had to have died saddened that his art was being supplanted by the next generation of composers (led by his own children) and wrote the Art of the Fugue as a sort of time-capsule to preserve the style he had perfected and to which he had devoted so much of his life - not as a vain attempt to impede the inevitability of esthetic evolution but as a signpost along the way, not as a grasping for personal immortality but as a humble memorial to a moment in time that eventually might take its rightful place in history. Yet here we are a dozen generations later when his art not only is acknowledged by historians, analyzed by theoreticians and studied by scholars but is being outright enjoyed by modern performers and listeners alike, and without compromising the integrity of his vision. That, it seems to me, is the ultimate tribute to any artist. 
I am indebted to the following scholarly sources for the facts, critical perspectives and quotations in this article:
