Artist Blog

Every week an artist whose single image was published by Der Greif is given a platform in which to blog about contemporary photography.

An Endlessly Rising Canon

Mar 31, 2021 - Michael Swann

“There is one canon in the Musical Offering which is particularly unusual. Labeled simply “Canon per Tonos”, it has three voices. The uppermost voice sings a variant of the Royal Theme, while underneath it, two voices provide a canonic harmonization based on a second theme. The lower of this pair sings its theme in C minor (which is the key of the canon as a whole), and the upper of the pair sings the same theme displaced upwards in pitch by an interval of a fifth. What makes this canon different from any other, however, is that when it concludes-or, rather, seems to conclude-it is no longer in the key of C minor, but now is in D minor. Somehow Bach has contrived to modulate (change keys) right under the listener’s nose. And it is so constructed that this “ending” ties smoothly onto the beginning again; thus one can repeat the process and return in the key of E, only to join again to the beginning. These successive modulations lead the ear to increasingly remote provinces of tonality, so that after several of them, one would expect to be hopelessly far away from the starting key. And yet magically, after exactly six such modulations, the original key of C minor has been restored! All the voices are exactly one octave higher than they were at the beginning, and here the piece may be broken off in a musically agreeable way. Such, one imagines, was Bach’s intention; but Bach indubitably also relished the implication that this process could go on ad infinitum, which is perhaps why he wrote in the margin “As the modulation rises, so may the King’s Glory.” To emphasize its potentially infinite aspect, I like to call this the ‘Endlessly Rising Canon’.”


Douglas R. Hofstadter – ‘Gödel, Escher, Bach: An Eternal Golden Braid’