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Bach’s Art of Fugue: An Enigma Resolved

I am very happy to use this website as a vehicle for announcing the solution by Hans-Eberhard Dentler of the enigma surrounding J.S. Bach’s Art of Fugue.

At his death Bach left an fair copy manuscript of several contrapuntal pieces. The fugal pieces, but not the canons, bore the unusual name of Contrapuntus. The last of these was unfinished and his son Carl Philipp Emanuel wrote “While writing this fugue the composer died where the name B A C H appears in the counterpoint.” Bach gave no title to the piece, the title we know it by today, the Art of Fugue, was added to the fair copy by the hand of Bach’s son-in-law Johann Christoph Altnickol and in the first edition of 1751.

The work has long remained an enigma for there are no indications of tempo markings, instrumentation or suggestions as to how it should be performed. A year after Bach’s death the suggestion was made that it was in fact a keyboard piece, for clavier or organ. Others believed it is a piece for private study and the “inner ear”. Mozart, one of the greatest composers to come after Bach, did not agree and made his own arrangement for strings. Most musicologists clung to the theory that it was either absolute music above all performance or a piece for keyboard. Nevertheless less in our own time a variety of performing versions have been made for everything from small orchestra, keyboard, string quartet, saxophones and even the Canadian Brass.

After considerable research Hans-Eberhard Dentler has resolved this mystery and had allowed us to hear the work, as it was intended, for the very first time. Maestro Dentler was one of Pierre Fournier’s most outstanding cello pupils. After taking a degree in medicine he decided to devote himself to the concert hall. As well as making a special study of Bach, he was also interested in the approaches of the philosophers of science, Karl Popper and Thomas Kuhn, whose methodology he called upon in deciphering the enigma.

An important aspect of the solution comes the fact that Bach was conversant with Pythagorean philosophy. Bach had known Johannas Matthias Gesner in Weimar and in 1730 Gesner moved as Rector to the Thomasschulen, where Bach was Cantor. Gesner taught Greek philosophy with an emphasis on Pythagorean thought. He even changed one of the school statutes to reflect the Pythagorean practice of repeating all one had learned in the day before retiring to sleep.

Gesner was a close friend of Bach and, since the two men’s rooms were close together at the school and music was an important part of Gesner’s life, we can assume they had many discussions on music. Gesner also introduced one of his pupils, Lorenz Christoph Mizler, to Bach. Mizler then became a student of Bach.

Mizner went on to create the Societät der musikalischen Wissenschaften and lists Bach as having joined the society in June of 1747. (Other members included Handel and Telleman. Mozart joined after Bach’s death.) The society devoted itself to the the study of Pythagorean philosophy and the union of music, philosophy, mathematics and science. Each member had their portrait painted in oils and was obliged to contribute a theoretical or practical piece with the aim of developing music along the philosophical lines of Pythagoras.

In the first publication of the society, the Musikalische Bibliotek, Mizler lists Marcus Meibom’s Antiquae Musicase Auctores, Septem, Graece et Latine. This book, published in Amsterdam in 1652, attempted to reconstruct the music of ancient Greece. It must certainly have been known to Bach.

Mizler also refers to the collected works of John Wallis, Opera Mathematica. Wallis was Savilian professor of geometry at the University of Oxford. He made many important contributions to mathematics and Newton admitted that his development of the calculus owed much to Wallis. But in addition to its work on infinitessimals, conic sections and exponents he also makes specific Pythagorean references to music and harmony. References in the Musikalische Bibliotek are also made to Leibniz, Kepler and Robert Fludd’s Monochord of the World. Flood was a doctor and student of occult works and sympathies From his writings it is also clear that Mizler was a close friend of Bach and their shared common interests.

The Art of Fugue was one of three pieces written for the society. Bach probably began the piece in 1738 and began to rework and add to it shortly before his death, or his blindness, prevented him completing the work.

For Maestro Dentler, Bach’s immersion in Pythagorean thought and the Pythagorean elements in the Art of Fugue are clear:

The Basic Enigma: Enigma was of the essence of Greek teaching. Indeed the 2,3,4 pattern of the Riddle of the Sphinx underlies the work.

Contrapuntus: Bach refers to his fugal pieces (not the canons) with this curious term which evokes the notion of opposites as in Aristotle’s “puntus contra puntum”. Note that the term contrapunta was used by Kepler in his chapter on Universal Harmony

Mirror Principle:The speculum is central to Pythagoras – Bach’s mirror counterpoint is strikingly visual in the fair copy

Tetraktys: The perfect triangle created by arranging the numbers 1,2,3,4 is central to Pythagorean thought and is present in the pattern of voices of the Art of Fugue

Four: The number underlies the whole piece as its principle of order

Unity: The work is created out of a single theme and is in a single tonality

Music of the Spheres: This is reflected in the first seven contrapunctus. The Earth itself is represented by a Canon in the Octave.

Fugue: Of course Fugue is central to many of Bach’s works but one should not forget that it also means the flight of the soul towards God

Maestro Dentler’s study of Bach’s fair copy of the work convinced him that it was never intended for keyboard – the physical impossibility of paying certain sections makes that clear. Neither could it be a work for the inner ear alone – such music would have no need to accord to the limits of range of ordinary physical instruments.

For Mastro Dentler the piece is very clearly based on Pythagorean philosophical principles and for that reason, as befitted the Pythagoreans, it is deliberately presented as an enigma. His patient detective work, musicianship and scholarship has finally enabled him to resolve this enigma.

Maestro Dentler’s announcement of the resolution was made at a music conference in Spoleto organized by the composer Luciano Berio The more detailed argument has recently been published in a recent book – L’Arte della fuga di Johann Sebastian Bach: un’opera pitagorica e la sua realizzazione” Skira, Milano, 2000 and presented by the National Academy Santa Cecilia, Rome. The title refers to the music as being based upon Pythagorean principles. A German version of the book has also bee published. Unfortunately an edition is English is not yet available. (The leading musicologists in Italy have given the book golden reviews.)

Maestro Dentler’s version – for four strings and bassoon – was first performed by the group “L’arte della fuga” [(Marco Rogliano (violin), Raffaele Mallozzi (viola), Hans-Eberhard Dentler (cello), Francesco Bossone (bassoon), Franco Petracchi(contrabass and artistic direction)] in the Church of San Francisco at Grosseto, Italy. Other performances followed at Teatro Reggio, Parma; Teatro delle Palme, Naples; Prinzregententheatre, Munich; Schaezlerpalais, Augsburg, Santa Maria presso San Satiro in Milan and and at Massa-Carrara. Maestro Dentler also hopes to perform the work in Bach’s church in Leipzig .

Further information on Maestro Dentler’s discoveries will be posted on this page. I should add say that Maestro Dentler lives not far from the village of Pari where I have settled and it was a great joy for me to have him play Bach’s cello suite, No 3, on the occasion of our Roundtable Conference The Future of the Academy, an occasion on which Maestro Dentler was elected a Fellow of the World Academy of Art and Science. Also on the weekend 27-29 January, 2001 I was happy to attend the Scuola Communale de Musica de Grosseto where Maestro Dentler presented an elaboration of his thesis in six hours of lectures. (I must also apologise if I have made any errors or misinterpretations of Maestro Dentler’s thesis in my notes above.)