As a follow-up to my previous post on Thomas Daniel and his completion of Bach's last fugue, I would like to offer some thoughts on a doctoral dissertation by Indra Hughes (2006). Hughes, an early-music specialist living in New Zealand, completed his dissertation four years before the publication of Daniel's book, but is not mentioned by Daniel. Both authors share an interest in Bach's use of numbers and gematria. However, the conclusions reached by Hughes differ radically from those of Daniel.
The dissertation seeks to explore the idea that the unfinished state of Contrapunctus 14 is not to be explained as a result of Bach's sudden death. Rather, Bach's intention in the first place was to leave the final fugue of The Art of Fugue unfinished, and to provide a number of hidden hints as to how the performer might complete the fugue. In other words, according to this hypothesis, Contrapunctus 14 should be viewed as a type of exercise in composition! The basis for the hypothesis is the observation that Bach's fragment breaks off after 239 bars. The sum of the digits of this number is 14, a number of great significance to Bach. (If the value of each letter equals its position in the alphabet, the letters BACH can be combined by summation to yield the number 14.) Taking Gregory Butler's 1983 article as a starting point, Hughes argues that the number of missing bars is exactly 47. Markings at the end of the score are used as corroborative evidence for this inference. However, these considerations do not lead up to a full completion of the fugue. Instead, the reader is introduced to a schematic solution that involves a number of "building blocks."
The background material on gematria is well worth reading. However, a general impression is that Hughes's interpretations of the evidence are too speculative to warrant serious consideration. The idea that Bach intentionally refrained from completing the fugue is in fact a recycled version of the notion that, with this fragment, Bach wished to create a deliberate torso. As pointed out by Daniel, such a notion is anachronistic (see Daniel, 2010, p. 9, n. 4). A further weakness is that it is not clear from the dissertation why Bach would wait until the final forty-three bars of this long fugue to introduce the main theme of the cycle. Finally, it is understandable, yet disappointing, that Hughes declines to compose a completion of the fugue, declaring the task to be "outside the scope" of the dissertation.
Hughes's dissertation is available for free public access via the following page:
- Butler, Gregory (1983). "Ordering Problems in J S Bach's 'Art of Fugue' Resolved," in: The Musical Quarterly, 69, pp. 44-61.
- Daniel, Thomas (2010). Bachs unvollendete Quadrupelfuge aus "Die Kunst der Fuge." Studie und Vervollständigung. Cologne: Verlag Dohr.
- Hughes, Indra (2006). "Accident or Design? New Theories on the Unfinished Contrapunctus 14 in J. S. Bach's The Art of Fugue BWV 1080." Doct. diss., University of Auckland.