When my father listened to a rich and many-voiced fugue, he could soon say, after the first entries of the subject, what contrapuntal devices it would be possible to apply, and which of them the composer by rights ought to apply, and on such occasions, when I was standing next to him, and he had voiced his surmises to me, he would joyfully nudge me when his expectations were fulfilled.

So reported Carl Philipp Emanuel Bach to Johann Nikolaus Forkel in December 1774, as Forkel was beginning to gather material for the groundbreaking biography of Johann Sebastian Bach he would eventually publish in 1802. We see in this anecdote not only J. S. Bach’s perhaps unsurpassed knowledge of fugal writing, but also his evident delight in matching wits with lesser contrapuntists. In the late 1730s, Bach’s music had been attacked by Johann Adolf Scheibe: “This great man would be the wonder of entire nations . . . if he did not deprive his pieces of all naturalness through excessive and confusing ornamentation and obscure their beauty with a surfeit of artistic effects. Because he judges according to his own fingers, his pieces are most difficult to play, for he demands that the singers and instrumentalists execute with their voices and instruments what he can play on the clavier. But such a thing is impossible.”

Defending Bach, Johann Abraham Birnbaum explained his very concept of music: “The true amenity of music consists in the connection of an alternation of consonances and dissonances without hurt to the harmony.” And in Bach’s view, the succession and alternation of consonances and dissonances was governed, above all, by counterpoint. Birnbaum elucidates: “Indeed, the well-founded opinion of a musical ear that does not follow the vulgar taste [exemplified by Scheibe’s desire for greater simplicity] values such alternation, and rejects the insipid little ditties that consist of nothing but consonances as something of which one very soon becomes tired.”

Bach was perfectly capable of writing in the simpler galant style of which Scheibe approved when it suited him to do so, as he demonstrated in many pieces, among them the third movement of the Musical Offering trio sonata, written after a 1747 visit to the court of the flute-playing Prussian king Frederick the Great. But the Musical Offering as a whole takes its place among a series of monumental composition projects Bach undertook during the last decade or so of his life. Setting aside the B Minor Mass, a work of kaleidoscopic variety and complexity in which Bach embodied the summa summarum of his artistry as a church musician—as Kapellmeister and Cantor—these last works include several which are severely monothematic, including not only the Musikalisches Opfer, but also the Goldberg Variations, the Canonic Variations on “Von Himmel Hoch,” and the focus of our attention this evening.

With The Art of Fugue (Die Kunst der Fuge—or its earlier bi-lingual title Die Kunst der Fuga, entered on Bach’s autograph manuscript by his son-in-law J.C. Altnikol), Bach systematically laid out all of the possibilities inherent in a simple four-bar theme that he had specifically designed for such manipulation, both exhibiting his contrapuntal mastery, and demonstrating his vision of a comprehensive and well-regulated structure reflecting divine order. Because of the way that it has been transmitted to us, The Art of Fugue was long held to be the last of Bach’s works, but it now appears clear that a great deal of it was completed by about 1742, the date of an autograph manuscript containing most of the fugues, or, as Bach called them, contrapuncti. On Bach’s death, the project, which was being prepared for publication, was not yet complete, and his executors, in recognition of this fact, chose to conclude their edition (published in 1751, and reissued the following year with an expanded explanatory preface) with a setting of the chorale Vor deinen Thron tret’ ich hiermit (“I come before Thy throne”) purportedly dictated by the blind composer in extremis, but actually a variant of an earlier chorale setting. The posthumous versions of some of the contrapuncti and the canons that accompany them are rather different than their earlier forms as transmitted in the autograph, and there are several more pieces in the published edition of the work. As is clear, however, from the fragmentary state of the last fugue, the conceptually perfect unity Bach had envisioned for the work remains elusive in the published version.

Nonetheless, the overall outline of Bach’s design can be established. The first four contrapuncti, which can be classified as simple fugues in which only one subject is manipulated, present the theme either in its original form or inverted (that is, with the intervals turned upside down). The next several contrapuncti are counterfugues, in which the subject and its inversion appear together. The designation “in Stylo Francese” of the sixth contrapunctus refers to the dotted rhythms of the French overture that pervade the piece as the theme is presented at two different rates of speed. Bach’s subtitle of the seventh contrapunctus, “per Augment et Diminut,” refers explicitly to such rhythmic augmentation and diminution, now expanded to three levels. The ninth and tenth fugues are double fugues, each opening with a new subject that is later combined with the original theme. The counterpoint is invertible (either the subject or countersubject can appear in the bass without producing errors of musical grammar) at the intervals of the 12th and 10th, respectively. The eighth and eleventh contrapuncti are triple fugues, combining the main subject with two countersubjects derived from it. The collection next presents two mirror fugues, in which the entire three- or four-voice structure of the complete piece is inverted, note for note, as if one were to hold a mirror along the bottom of each staff system and read the resulting image. Four two-part canons follow in the print, an expansion from the two canons contained in the autograph. Our performance tonight omits these pieces, as their extended ranges far exceed those of the other contrapuncti, and seem better suited to execution on a keyboard than on viol-family instruments. (Several writers, prominently among them the harpsichordist Gustav Leonhardt, have made strong, if not water-tight, cases for The Art of Fugue having been designed originally as a keyboard work. Indeed, numerous fine recordings present it on harpsichord or organ. But there are also convincing traversals by viol consorts, string quartets, or—in a tradition going back at least to Wolfgang Graeser’s 1926 edition—mixed ensembles, all of which, it might be argued, allow the ear to track more easily the individual voices.) In any case, attending a performance of any sizable portion of The Art of Fugue is a rather Zen-like experience, as attempting to follow the contrapuntal niceties can rather easily provoke a kind of out-of-body trance state, lending some credence to the thought that, for the advanced musician, one perfectly legitimate way to appreciate The Art of Fugue might be simply to realize it in one’s head, rather than perform it at all.

Despite its designation a 3 Soggetti (“on three subjects”), the final, incomplete fugue was in fact designed as a quadruple fugue, with the fourth subject to have been the original theme. It must have been worked out, at least mentally, by Bach to its very end, since he would have had to ensure that all four themes could actually be melded together before embarking on writing the piece. The third subject, B-flat–A–C–B-natural, is the musical rendering of the name BACH using the German musical alphabet. (Although neither the canons nor the Fuga a 3 Soggetti are numbered in the 1751 print, the fugue would logically be the 14th contrapunctus. According to one simple numerological system, “Bach” = 14 [2 + 1 + 3 + 8], and “J. S. Bach” = 41. Thus, that the 14th contrapunctus would contain Bach’s “musical signature” seems almost predestined.) Where it breaks off, the autograph manuscript contains C.P.E. Bach’s inscription: “NB: At this point in the fugue where the name BACH was introduced as a countersubject [to the main theme], the author died.” Though various writers have attempted, with varying degrees of success, to complete the fugue, our performance ends here, suggestively incomplete, as well.

—Kenneth Slowik