Two compositional projects played a major role in shaping Bach’s work on The Art of Fugue: The Well-Tempered Clavier, whose score accommodated many but not all fugal devices, and the Goldberg Variations, which exhibited the potential of a multimovement monothematic cycle. Thus, in the absence of a datable composing score of The Art of Fugue, we can logically trace its true genesis to the beginning of the 1740s, when the composition of both part II of The Well-Tempered Clavier and part IV of the Clavier-Übung were completed. Indeed, an early version of The Art of Fugue emerged by around 1742, when Bach made a fair copy of the work.31
The governing idea of the work, whose title came later (the title page of the autograph fair copy was originally left blank), was an exploration in depth of the contrapuntal possibilities inherent in a single musical subject. The carefully constructed subject would generate many movements, each demonstrating one or more contrapuntal principles and each, therefore, resulting in a self-contained fugal form. Bach selected the key of D minor (closely related to the traditional first, or Dorian, mode) and crafted an easily identifiable subject with distinct melodic contours and a sharp rhythmic profile, whose regular and inverted versions, if sounding together in a contrapuntal relationship, resulted in flawless and attractive harmony, and whose chordal structure presented a pivotal cadential scheme (Ex. 12.1).
In the course of the work, the main subject (theme) would be joined by various kinds of derived and freely invented counterpoints, would itself be gradually subjected to variation, and would also be combined with contrasting countersubjects (new themes).
The early version of The Art of Fugue (still without title)32 comprised a total of fourteen movements (also lacking headings), which can be regarded as a complete cycle in that the twelve fugues and two canons present a rational order and well-rounded structure (the first column in Table 12.2 indicates the movement sequence in Roman numerals). Its overall organizational design is based on two points.
First, types of counterpoint are introduced according to increasing difficulty and complexity, and sometimes—if particularly significant—are designated in customary Latin or Italian terminology (in the later printed edition): per augmentationem et diminutionem = with the subject in augmented (doubled) and diminished (halved) note values; in contrario motu = with the entire part in contrary motion; contrapunctus inversus = the entire setting inverted, that is, read in mirror image; in contrapunto alla terza, quinta, decima, or duodecima = the distance between the subject and its counterpoint at the interval of the third, fifth, tenth, or twelfth.
Second, Bach gradually increases the animation of the subject, giving us a sense of developing variations, with the rhythmic-metric arrangement adding a new dimension to the compositional makeup of the movements.
The changing rhythmic-melodic textures contribute significantly to the overall stylistic variety of the work, which takes as its point of departure the classic simplicity reminiscent of sixteenth-century counterpoint, then touches on prominent models such as the French style, and proceeds to the most sophisticated contemporary mannerisms, as exposed particularly in the translucent web of the capricious two-part canons:
TABLE 12.2. The Art of Fugue, BWV 1080: Synopsis of Earlier and Later Versions
Earlier Version: Autograph MS (1742)a
Later Version: Original Edition (1751)
Structural Design of Later Version
I
Contrapunctus 1
Simple fugues: main theme introduced in regular or inverted form
III
Contrapunctus 2
II
Contrapunctus 3
—
Contrapunctus 4
IV
Contrapunctus 5
Counterfugues: main theme introduced together with its inversion
VII
Contrapunctus 6 a 4 in Style Francese
VIII
Contrapunctus 7 a 4 per Augment: et Diminut:
X
Contrapunctus 8 a 3
Fugues with multiple themes: main theme combined with countersubjects
V
Contrapunctus 9 a 4 alla Duodecima
VI
Contrapunctus 10 a 4 alla Decimabb
XI
Contrapunctus 11 a 4
XIII
Contrapunctus inversus 12 a 4
Mirror fugues: complete score inverted
XIV
Contrapunctus inversus 13 a 3
IX
Canon alla Ottava
Canons
—
Canon alla Decima in Contrapunto alla Terza
—
Canon alla Duodecima in Contrapunto alla Quinta
XII
Canon per Augmentationem in Contrario Motucc
—
Fuga a 3 Soggetti [Contrapunctus 14]dd
[Fugue with multiple themes]
The autograph fair copy from around 1742 represents The Art of Fugue in this fourteen-movement version. Bach, however, clearly fascinated by the work’s perplexing challenges and unique opportunities, continued to develop it. Between 1742 and 1746, he revised and expanded individual movements—notably the fugues nos. I–III, which received longer concluding sections, and the augmentation canon no. XII, which was completely rewritten. He also added four entirely new movements, two fugues and two canons. The revisions and additions considerably broadened the conceptual and compositional dimensions of the work. For example, the newly composed Contrapunctus 4, added to the group of simple fugues, introduced a highly innovative modification of the inverted theme by breaking traditional rules of interval order (Ex.12.2).
This change allowed the subject to trigger modulations, within the key of D minor, to E major and B major, an unprecedented expansion of the harmonic spectrum. Bach also added a quadruple fugue (mislabeled “Fuga a 3 soggetti” in the original edition) in which he presented, as the fourth theme, a subject constructed on the musical letters of his own name: B-A-C-H (B and H being the German note names for B-flat and B-natural).33 This chromatic motive permitted him to explore chromatic harmony, prevalent in a number of movements, on a plain thematic level as well—apart from the fact that the B-A-C-H theme emphatically personalized the work. But, most important, Bach completely reorganized the work so that the various movements make up a practical textbook on fugue in five chapters: simple fugues, counterfugues, multiple-theme fugues, mirror fugues, and canons—remarkably predating any theoretical textbook on the subject.
It was at this point, in 1747 or later, that Bach formulated the title Die Kunst der Fuga (added in the hand of his son-in-law Altnickol to the autograph fair copy of the earlier version) or, entirely Germanized, Die Kunst der Fuge (the title of the 1751 edition).34 Although the title does not appear in Bach’s own hand, there is no reason to doubt its authenticity. Moreover, the fact that he used the term “contrapunctus” for the individual fugues indicates that he wanted the pieces to be seen not exclusively as fugues but, more generally, as examples of contrapuntal settings.35 Bach intended, probably from the start, to publish the work. However, not before 1748, and definitely after the publication of the Musical Offering, the Canonic Variations on “Vom Himmel hoch,” and the Schübler Chorales, was The Art of Fugue ready to go into production. For the most part, Bach was able to supervise the engraving process, even though he would not see it through to the end. A note written posthumously on the proof sheets by his second-youngest son, Johann Christoph Friedrich, indicates how meticulously Bach went about movement headings:
Canon p[er] Augmentationem contrario motu.
NB: The late Papa had the following heading engraved on the plate: “Canon per Augment: in Contrapuncto all ottave,” but he had crossed it out on the proof plate and put it in the above-noted form.36
Bach apparently composed the quadruple fugue as an afterthought while the engraving of The Art of Fugue was already in progress. The composing manuscript, which dates from 1748–49, belongs among the latest musical manuscripts from Bach
’s hand, and its unfinished state (it breaks off after 239 measures) may tempt us to think that death stayed the composer’s pen. Even Carl Philipp Emanuel was misled, as shown in a note he appended many years later to the last manuscript page: “NB. While working on this fugue, in which the Name BACH appears in the countersubject, the author died.”37 But the incomplete form in which the fugue has been transmitted does not correspond to what actually existed at the time of Bach’s death. Before composing the quadruple fugue, Bach would have had to test the combinatorial possibilities of the four themes. His draft of such contrapuntal combinations has not survived, but a description, at least, of the composer’s intentions is included in the Obituary, which mentions the “draft” for a fugue that “was to contain four themes and to have been afterward inverted note for note in all four voices.”38 From this statement, we can reasonably surmise that The Art of Fugue at the time of Bach’s death was less incomplete than what has come down to us. But whatever the lost draft contained, it must not have been sufficiently worked out to bring the quadruple fugue to an end.
Nevertheless, even in its unfinished state, The Art of Fugue stands before us as the most comprehensive summary of the aged Bach’s instrumental language. At the same time, it is a highly personal statement; the letters BACH woven into the final movement represent much more than a fanciful signature. Theory and practice merge in this work. By letting the substance of the musical subject be logically uncovered and systematically exhausted, by employing traditional and novel techniques of composition as well as old and new elements of style, Bach created an autonomous work of art that embodies the character and universality of his art. The significance of the work at an important historical moment was captured well by Marpurg in dedicating the second volume of his own fugal treatise to the two elder Bach sons:
I take the liberty of laying before Your Honors the principles of an art that owes its improvement particularly to the excellent efforts of your famous Father. One need not look back even half a century to discover the happy moment when a beginning was made of combining imaginative harmonic changes with an agreeable and unified melody [referring to the new Italian style of the Vivaldi generation]. At the very time when the world was beginning to degenerate in another direction, when light melody making was gaining the upper hand and people were becoming tired of difficult harmonies, the late Capellmeister was the one who knew how to keep to the golden mean, and taught us how to combine an agreeable and flowing melody with the richest harmonies.39
The grand-scale project of The Art of Fugue seems to have occupied the composer’s mind throughout the last decade of his life. Seen in this light, however, the work is less the crowning conclusion of a representative series of monothematic compositions (beginning with the Goldberg Variations and including the Musical Offering and the “Vom Himmel hoch” Variations) than the conceptual background and theoretical underpinning for many of Bach’s works written during the 1740s. Yet the language of The Art of Fugue, despite its remarkably broad stylistic palette, is marked by significantly greater systematization, concentration, and abstraction than any of the other monothematic instrumental cycles, let alone the magnificent B-minor Mass. Nevertheless, the Mass similarly reflects a long-term engagement and—within the limitations dictated by vocal composition, a fixed liturgical genre, and a long historical tradition—a comparable systematic musical exploration that Bach defined for himself.
Bach’s grandiose plan to set a solemn Mass can already be discerned in the layout of the Kyrie-Gloria Mass of 1733 (Table 12.3). This aim is apparent in the five-part texture of the vocal writing, the large orchestral contingent, and especially the sophisticated design of its individual movements. The opening three-movement Kyrie group clearly proclaims the composer’s ambition: Kyrie I is an extended fugue with obbligato orchestra, the Christe adopts the style of a contemporary opera duet, and Kyrie II draws on retrospective vocal counterpoint, thereby relegating the orchestra to the role of doubling the choral parts. The entire Kyrie complex shows the great value Bach placed on highly contrasting compositional styles and techniques. Its movements also outline a sequence of keys from B minor to D major to F-sharp minor, forming a B-minor triad, thereby signaling a broadly conceived harmonic scheme for the entire work that centers on D major (the trumpet key).
The Gloria complex of the musically self-contained Kyrie-Gloria Mass of 1733 resolutely builds on the stylistic variety of the Kyrie group by offering four large-scale choruses (“Gloria in excelsis / Et in terra pax,” “Gratias agimus tibi,” “Qui tollis peccata mundi,” “Cum sancto spiritu”) interspersed with four equally large-scale solo movements with obbligato instruments, each with a full polyphonic orchestral accompaniment. Thus, the Gloria section gives a solo aria to each concertist of the five-voiced choir and an obbligato part to each family of instruments in the orchestra (strings, flutes, reeds, and brass): combining solo soprano II with solo violin (“Laudamus”), soprano I and tenor with flute (“Domine Deus”), alto with oboe d’amore (“Qui sedes”), and bass with horn (“Quoniam”).
When did Bach begin to expand his Kyrie-Gloria Mass into a complete setting of the Mass? A possible clue lies in an early version of the Credo intonation,40 but this merely indicates that the Credo added to the Mass during the years 1748–49 had a prehistory. We do know that in the late 1730s and early 1740s, Bach copied, performed, and examined numerous Masses by composers ranging in time from Palestrina to his own contemporaries.41 For example, he performed the six-voice Missa sine nomine by Palestrina, with added cornettos, trombones, and continuo, and the Missa sapientiae by Antonio Lotti. And compositional studies with a direct impact on the B-minor Mass include a “Credo in unum Deum” intonation, BWV 1081, added to a Mass in F major by Giovanni Battista Bassani, and a contrapuntal expansion of the “Suscepit Israel” movement, BWV 1082, in a Magnificat setting by Antonio Caldara. In its first version, the Symbolum Nicenum (Credo section) of the B-minor Mass comprised only eight movements, as the duet setting of “Et in unum Dominum” also incorporated the text portion “et incarnatus est…” After finishing this duet, however, and possibly after finishing the entire score of the Symbolum, Bach decided to reapportion the text underlay of the duet, free up the “et incarnatus est” section, and compose a separate movement for this liturgically pivotal text traditionally treated with special musical emphasis. In its overall design, now comprising nine movements, the Symbolum gained a strengthened symmetrical layout. Bach turned what had been a 2+1+2+1+2 design (eight movements, choruses boldface) into an architecture of 2+1+3+1+2.
TABLE 12.3. Mass in B Minor
The Symbolum opens and closes with a pair of contrasting choruses: “Credo” (motet, on the liturgical chant) together with “Patrem omnipotentem” (concertato fugue) at the start, and “Confiteor” (likewise on the liturgical chant) together with “Et expecto” (again, concertato fugue) at the end. By including two settings in an emphatically retrospective style (“Credo” and “Confiteor”) based on medieval chant, Bach added a theological, historical, and compositional dimension that the Kyrie-Gloria Mass of 1733 lacked. Thus, in setting the chants, Bach uses the (musical) canon technique in order to accent the (liturgical) canonical value of the Mass text in general and the Nicene Creed in particular, while the archaic style of the two cantus firmus settings allows the work to embrace a wide span of the compositional history of the Mass genre. In the theological realm, we find that following the “Confiteor,” which is set in imitative counterpoint, two different settings of the text “Et expecto resurrectionem” (And I await the resurrection) draw a line between “the expecting” and “the expected”: an expressive Adagio, filled with unprecedented chromatic and enharmonic devices that illustrate the suffering in this world, contrasting with an upbeat Vivace that portrays, in anticipation, the life of the world to come. The two framing choral pairs of the Symbolum are each adjoined by two arias that function as connecting links to the central choral complex. This center emphasizes in a musically per
suasive way the Christological core of the Nicene Creed: “And he was made incarnate,” “He was crucified,” “And he was resurrected.”
This central group of three choruses includes both the oldest and the most recent compositions of the entire Mass: “Crucifixus,” a movement based on the chorus “Weinen, Klagen, Sorgen, Zagen” from cantata BWV 12 of 1714, and “Et incarnatus est,” an inserted afterthought and apparently Bach’s last choral setting, dating from 1749. In the scheme of things, the “Crucifixus” coming immediately after “Et incarnatus est” would seem to threaten a stylistic and aesthetic clash of incompatible music.42 Bach, however, avoids such a conflict: he subtly links the two movements by providing both with a similar structural underpinning, and unifies them by using a repeated melodic pattern in each. The six-note violin figure that shapes the “Et incarnatus est” from beginning to end (and, for the concluding measures, even slips into three-part canonic counterpoint) gives way to the seven-note ostinato bass line of the “Crucifixus.”
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