Johann Sebastian Bach, The Musical Offering, and the Anatomy of a Fugue

On October 18, 2015, NOVA presented a selection of works by Johann Sebastian Bach (1685-1750) dating from his years in Cöthen, where he worked at the court of Prince Leopold from 1717 to 1723. In 1723, Bach moved to Leipzig to serve as Kantor (the music director and instructor) of the Thomasschule, a school connected to the Church of St. Thomas; he would spend the rest of his life in Leipzig. Bach’s output during the Leipzig years was staggering, including his largest religious works (the B Minor Mass, the St. Matthew Passion, and the St. John Passion), the Goldberg Variations, and over three hundred sacred and secular cantatas; but it is the monumentality of these works, the desire to milk every ounce of compositional potential from the smallest musical motif, that marks Bach’s late style.

In 1747 Bach was invited to Potsdam, near Berlin, to perform at the court of Frederick the Great, where Bach’s son Carl Philip Emanuel was employed as a harpsichordist. Frederick was a great lover of music; on May 7, Bach performed in the court’s nightly chamber music concert. Bach’s ability to improvise complex contrapuntal works was legendary, and the king presented him with a thornily chromatic theme upon which to improvise. Bach relished the challenge, and his improvisation was met with great applause. Had the story ended there, the incident would be merely another anecdote in the annals of the Bach biography. Upon his return to Leipzig, however, Bach began a collection of compositions based on Frederick’s theme. In addition to several fugues, he wrote a trio sonata (for flute, violin, and continuo), and a series of diabolically complex canons for a variety of instrumental combinations. This collection, the so-called “Musical Offering” (Musikalisches Opfer), was presented to Frederick in a letter dated July 7 of that year, and will now enjoy pride of place on NOVA’s February 28 concert.

When approaching this work, it is worth developing an understanding of fugues and canons, the compositional principles that structure each piece in the Musical Offering. Both genres are defined by a set of rules establishing how a single tune must be manipulated to form the entire piece. How the composer conforms to these rules––the originality and ingenuity with which s/he does so––is the point of this compositional game.

The rules of the fugue are beautifully illustrated in the following video, in which colors correspond to the different musical motifs in the Ricercare for six voices (one of the most famous pieces of the Musical Offering set). The six lines on the grid below the musical staff correspond to the six individual “voices” of counterpoint. As the work unfurls, each melody is indicated by a different color. Initially, only a single voice is heard: this is the “subject” of the fugue, a melody that will appear at least once in all six voices. This subject (in blue) is played in its entirety, then another voice begins playing the subject while the first voice introduces new material. And so it goes, until the subject has appeared in all six voices. For those who like to get fancy with their fugue terminology, the yellow bars indicate a “counter subject,” a melody that is paired at least twice with the fugue subject. When multiple blue bars overlap, this is a practice known as “stretto” (from the Italian stretto, meaning narrow or dense, since the subject of the fugue is presented “densely”); stretto was (and is) considered the mark of a superbly crafted fugue.

The image at the beginning of the video is the palace of Sanssouci in Potsdam, a few kilometers outside of Berlin. It was here that Bach met Frederick the Great.

I also recommend this 1963 television broadcast, in which the renowned pianist Glenn Gould discusses the principles, both practical and aesthetic, of the fugue: 

Gould composed several examples to musically illustrate his lecture, including a delightfully clever fugue for four voices and string quartet entitled “So you want to write a fugue.” The song is present in the broadcast linked above, but the video below clearly illustrates how the voices interact (each voice is a different color). The piece also includes examples of “inversion” (playing the subject upside down), and “augmentation” and “diminution” (playing the subject more slowly or more quickly, respectively). 

The King’s theme, in Bach’s hand, became some of the most glorious fugues ever written. Yet Bach was not done: he would also use the theme in an array of “canons,” pieces which follow some fore-determined “rule” (the name comes from the Latin canon, “rule”). The simplest form of canon is the round, where multiple singers sing the same melody but begin at different times: think “Row, Row, Row Your Boat.” But composers were infinitely creative in thinking up “rules” for their music to follow. Sometimes one voice sang a melody, while the other sang the melody “upside down.” Sometimes the second voice sang the melody backwards… and so-called “cancrizance” or “crab” canons feature the second voice singing the melody upside-down and backwards! One voice could sing the melody at a slower or faster rate than the other (again, referred to as “augmentation” and “diminution,” respectively).

When compositions are constructed out of such finely fitting parts, puzzle-compositions cannot be far behind. For so-called “puzzle canons,” the rule must be discovered before the work can be performed. Many of the works in Bach’s Musical Offering are of this latter type, offering fiendishly difficult musical riddles that often allude to Frederick in their solutions: one canon in augmentation is inscribed "Notulis crescentibus crescat Fortuna Regis" (“may the fortunes of the King increase with the length of the notes”), while a modulating canon that ends a tone above where it began is inscribed "Ascendenteque Modulatione ascendat Gloria Regis" (“as the modulation rises, so may the King’s glory). The following image is one small work from the set, in Bach’s own hand: observe the upside-down treble clef in the red circle. The solution to the canon is suggested by this clef, and by the title, “Canon of augmentation and contrary motion”: one instrument plays the lower line with the rhythms and notes (according to tenor clef) as written; another instrument plays this line upside down, with the notes according to the treble clef (ergo, the first three notes are G-F-Eb), at precisely half the speed at which they are written (so the first two notes are played as sixteenth notes, rather than as thirty-second notes).

Although separated from Bach by some 300 years, contrapuntal mastery informs the work of the young German composer Matthias Pintscher as well. Pintscher, one of the most sought-after composers working today, has written of his interest in using music to “build a communicative bridge” between the past, the present, and the future. The three works by Pintscher that NOVA will present on February 28 fully embody this principle of looking-forward-by-looking-back: Janusgesicht (“Face of Janus”), for instance, is named for the Roman god of beginnings, transitions, and doorways, who is often depicted facing in two directions at once. In nomine (1999) brings Pintscher’s richly modern musical language to a centuries-old compositional tradition. “The matter of new beginnings and of the imaginary journey from the familiar to the unknown concerns me fundamentally,” Pintscher has written of his work. On February 28, NOVA will embody this approach, offering a journey through old voices and new, antiquated compositional styles and modern musical languages, the familiar, the unfamiliar, and the new beginnings that every musical performance inevitably offers.

-Kamala Schelling, 2.15.16

Nova Chamber Music Series
Nova Chamber Music Series


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