For as much as I love, have written about, and continue to listen and perform the music of John Cage, I'm equally drawn to the music of Johann Sebastian Bach, in many ways Cage's polar opposite. Cage composed with chance operations, and some of my favorite Cage works (like the number pieces) produce sound events differently at every performance, epitomizing what has come to be called "open form." Bach's music presents an inexorable logic, to the point with his fugues where the harmonic and contrapuntal possibilities are contained within the first few measures, which might be considered the ultimate closed form.
Yet Cage selected Bach's The Art of Fugue as an early example of indeterminate music in his lecture "Composition as Process" because it was originally published as an open score, each voice on its own stave and with the instrumentation unspecified. "Timbre and amplitude characteristics of the material, by not being given, are indeterminate," he wrote. "This indeterminacy brings about the possibility of a unique overtone structure and decibel range for each performance of The Art of Fugue." And indeed, contemporary recordings of the work exist for orchestra, keyboard (piano, harpsichord and organ), string quartet, wind quintet, saxophone quartet, and many other combinations. Despite a now prevailing scholarly opinion that The Art of Fugue was written for keyboard, its open score has seemingly licensed a timbral imagination that exceeds the normal orchestral transcriptions that one finds for Bach's organ works. (The orchestral versions of The Art of Fugue that I've heard are in fact relatively colorless compared to, say, Schoenberg's transcription of the St. Anne Prelude and Fugue or Webern's magnificent transcription of the ricercar from A Musical Offering.) And I confess, I have embarked on my own set of realizations on the computer, having completed four of the set to date, half simulating acoustic instruments and half for overtly synthetized sources.
One of the most commonly known trivia about The Art of Fugue is that the last fugue in the set, a quadruple fugue erroneously entitled "fuga a tre soggetti" (fugue on three subjects) in the first edition, was unfinished at Bach's death in 1750. The first edition, published by Bach's sons a few years later, closes with the music trailing off into nowhere and a note in the handwriting of C. P. E. Bach, "N.B. While working on this fugue, in which the name BACH appears in the countersubject, the author died." The vast majority of The Art of Fugue recordings perpetuate this message, breaking off in mid-phrase. The first editors stuck in a chorale that Bach dictated from his deathbed to terminate The Art of Fugue, but it's clearly unrelated to the rest of the work and therefore seldom recorded.
In a gesture that might be seen as hubris, some musicians and scholars have attempted to complete this fugue. My love of Bach was instilled by the English composer, musicologist and critic Donald Francis Tovey, whose 1924 edition of Bach's Well-Tempered Clavier includes detailed and entertaining commentaries for each piece. This edition, still in print from the Royal Schools of Music in London, was the first Bach music I studied, and his commentary was as much a part of the education as learning the music. I knew Tovey had published a completion in 1931, but it's fairly difficult to locate even though his monograph Companion to The Art of Fugue is available at many used book shops (generally for an exorbitant price). After several unsuccessful attempts at obtaining Tovey's completion through inter-library loan, I finally located one fairly cheap from a used bookseller in England, and it's now part of my library. Tovey wasn't the only one to attempt a completion of Bach's final fugue. Probably the most well-known version is by the composer and virtuoso pianist Ferruccio Busoni. Busoni actually incorporated the whole fugue into his Fantasia Contrappuntistica, a massive twelve-part piano piece published in 1910. I've got a recording of the piece, and it sounds a lot more like Busoni than Bach, and I'm a bit repelled by the piece's virtuosic nature.
The most recent scholarly research puts forward that Bach was considerably more open about The Art of Fugue than even Cage had thought, specifically that Bach deliberately left the final fugue unfinished as a puzzle for performers to complete. Bach left us other puzzles, including but not limited to the "quaerendo invenietis" canons from The Musical Offering. Printed on a single stave but with two clefs, a tenor clef right side up and a bass clef upside down, Bach's directive to "seek and ye shall find" incites two performers facing each other across the score to devise a solution. An organist from New Zealand, Indra Hughes, uses numerology, handwriting analysis, and solid detective evidence to support his thesis that Bach had a solution to the final fugue, which I find fairly compelling. Bach wrote many of his works for didactic purposes, and Hughes suggests that The Art of Fugue belongs in large measure in this category, a compendium of fugal technique, so that the completion of the final fugue was left as an exercise for the students.
Tovey and Busoni may be the most celebrated final fugue finishers, but recent years have seen other performers release their own completions. The Henle edition of The Art of Fugue was edited by harpsichordist Davitt Moroney, who includes his version. Organist Michael Ferguson from St. Paul, Minnesota, published one and has included it in an organ recording of the entire The Art of Fugue. The Hungarian composer and organist Zoltàn Göncz also used higher mathematics to demonstrate its permutational matrix. His version of the score comes with an endorsement from Györgi Ligeti, who taught counterpoint and fugal technique. Hughes' thesis doesn't include a completion, but he extends the numerological analysis to show how long he thinks the completion should be, along with where the four themes should show up, both normal and inverted.
So, as I hinted three years ago, my summer project is an orchestration of this final fugue. It's one of Bach's longest fugues, so I still have plenty of time to decide whose completion I'll use — I've always been curious to hear Tovey's. But who knows, maybe I'll compose my own….