J.S. Bach's The Art of Fugue: An Enigma Resolved
I am very happy to use this Web site 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 seventh, which would be Earth, is 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. 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. The
next performance will be on 28 May, 2001 in the beautiful church of
Santa Maria presso San Satiro in Milan. Maestro Dentler also hopes to
perform the work in Bach's church in Leipzig and is looking into the
release of a CD. He will also be recording, on three Cds, a number of
Bach's pieces over the next three years including the Brandenburg
concertos.
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.)
Those wishing to learn more could write (English, German or Italian) to info@fdavidpeat.com and I will pass on messages to Maestro Dentler.
Contact F. David Peat
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