About the 'Art of Fugue' you may also read:
• An enigma resolved: the Bach's Art of the Fugue by David Peat (on Hans-Eberhard Dentler)
• On Bach's Art of the Fugue by John Stone
• Glenn Gould Discourses on Fugue: Watch and Learn by John Stone
Search for sheet music on the Art of Fugue.
The Bach's Art of Fugue in MIDI files.
The musical examples on this page are designed to be played from the
Musica Antiqua Koln (Archiv 431 704-2) recording of the Art of Fugue BWV 1080.
This method for obtaining sound was intended for my students who have access to this particular disk, but you may listen in if you wish. If
you have obtained the FREE helper application from
Voyager (and configured your computer
to receive these files), you should be able to insert the Archiv disc in the CD drive of your computer and hear the examples.
The Art of Fugue is the last of Bach's great monothematic cycles. Often characterized as the greatest, such a designation demeans aspects
of monothematicism unique to the other three: the Musical Offering, Goldberg Variations, and canonic variations on Vom himmel hoch. Whereas
the Art of Fugue manifests its greatness in thematic transformation and fugue, the Musical Offering and Vom himmel hoch demonstrate the rigors
of canon, while the Goldberg develops a variety of keyboard styles unified by two-part form and bass line.
The Art of Fugue stands as counterpart to Bach's earlier Well Tempered Clavier whose double cycle of preludes and fugues in each of twelve
Major, and minor, keys represents tonal miniatures wherein the primary relationships are procedural, not thematic. By contrast, each fugue
of Die Kunst shares not only the same key, but also subject. The cleverness with which this subject is varied, then fugally revealed, represents
a crowning achievement of western art.
Recent handwriting analysis, and study of watermarks in the autograph, suggest that the Art of Fugue was composed in the early 1740's.
This puts to rest the popular assumption that Bach was composing the Art of Fugue at the time of his death, ten years later. The incompleteness
of Contrapunctus 14 is attributable not to Bach's death, but to carelessness on the part of the executors. At the time of his death Bach was
supervising the publication of the Art of Fugue. Publication had proceeded to the point where engraver's plates had been produced but in no
The lack of a composer specified order has led to considerable speculation with respect, in particular, to the proper insertion point of the
four canons. Upon his father's death, Carl Philipp Emanual ordered the engraver's copies into what is now known as the 1751 printed score.
This score placed the canons toward the end of the cycle and in the following order: augmentation canon, canon at the octave, canon at the
tenth, canon at the twelfth. Carl Philipp Emanuel's order does not agree with surviving fragments of his father's own working copy in which
the octave and augmentation canons appear to demarcate sections of the cycle (the canons at the tenth and twelfth having been lost in the
Large Scale Form of the Cycle
The order of the canons in this study follows Reinhard Goebel's recording to which its musical examples have been calibrated. This decision
was made partly for convenience and partly because of evidence that Johann Sebastian intended the order to be thus: four sections, each section
with four fugues and each section terminated by a canon (i.e. four canons), with the completed cycle rounded off by a quadruple fugue. The
four sections were to have been organized from the simple to the more complex. Out of this grand conception the following works survive:
- Four simple fugues followed by a canon at the octave
- Three stretto fugues followed by a canon at the tenth
- Four double/triple fugues followed by a canon at the twelfth
- Four mirror fugues followed by a canon in augmentation and contrary motion (The 1751 printed score also contained versions of
the mirror fugues arranged for harpsichord duo.)
- Fuga a 3 Soggetti (Contrapunctus 14).
The Subject and its Transformations
Because each movement employs the same d-minor subject, it was essential that Bach avoid monotony by transforming his subject many times
through the cycle. The subject is varied by slight rhythmic or melodic alterations which increase and decrease in complexity so that the final
subject is not immediately heard as related to the first. Some two dozen of these gradients link the new subject to its ancestor.