A Pythagorean Enigma
The theory is advanced by the cellist Hans-Eberhard Dentler (a pupil of Pierre Fournier's, and Fellow of the World Academy of Art and Science) that the Art of the Fugue was written to display Pythagorean philosophical principles. The arguments revolve upon Bach's friendship with Johann Matthias Gesner, whom he had known in Weimar and who in 1730 moved to the Thomasschule at Leipzig (where Bach was Cantor) as rector. There Gesner taught Greek philosophy with an emphasis on Pythagorean thought.
Among Gesner's students was Lorenz Christoph Mizler, who became a pupil and friend of Bach's. Bach was one of four distinguished dedicatees of Mizler's 1734 doctoral dissertation on Music as part of a Philosophical Education. Mizler founded the Korrespondierenden Sozietät der Musikalischen Wissenschaften (Corresponding Society of Musical Sciences) in 1738, which Bach joined in June 1747, and of which Handel and Telemann were also members. The society was concerned with the union of music, philosophy, mathematics and science in Pythagorean theory, and required each member to contribute a practical work in demonstration of this approach, for which Bach produced his Canonic Variations on "Vom Himmel hoch da komm' ich her" for organ, BWV 769, and the Canon triplex a 6 voci. The Society's work commenced with the publication of a Bibliography (in its Musikalische Bibliotek) referencing works of Marcus Meibom, John Wallis, Leibniz, Kepler and Robert Fludd.
The points of this analysis are that the work constitutes an enigma in the classical sense of a puzzle contained within its structure. This subsists in the numerical and philosophical relations of Unity (one key signature throughout and the thematic synthesis); Tetraktys (the relation of 1, 2, 3 and 4 as arranged to form the perfect triangle), the mirror or speculum principle, Contrapunctus as derived from Aristotelian terminology referring to balancing opposites, the Music of the Spheres is possibly reflected in Fugues 1-7, and in the term Fugue, meaning 'flight', which refers to the flight of the musical phrases.
Against the theory is Bach's apparent indifference to the Society in its early years, and his hesitancy in joining it. The Society had in fact attempted to establish principles for the writing of cantatas which were not in line with his own approach. Since any musical structure was susceptible to Mizler's Pythagorean analysis, the case for any specific precedent influence on The Art of Fugue remains conjectural.
It has also been argued that the hidden theme in Edward Elgar's Enigma Variations may derive from The Art of Fugue.
Read more about this topic: The Art Of Fugue
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—Ralph Waldo Emerson (1803–1882)
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