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Bach - The Art of Fugue, performed on the organ by Anne Page.

The Art of Fugue (Die Kunst der Fuge BWV 1080) comprises14 fugues (each called 'Contrapunctus') and four canons. Bach shows his consummate mastery of the contrapuntal art handed down from preceding generations and his knowledge of the different European traditions which enriched that art. It is a work of the composer's maturity and was in the process of being engraved when Bach died in 1750. The final fugue remained incomplete and performers choose either to end where the autograph score runs out, or to provide a completion. In this performance both options have been included, the final fugue (Contrapunctus 14) having been completed by Paul Binski. The organ arrangement is by Anne Page, performed on the organ of the Dutch Church in London. Copyright (arrangement and performance) Anne Page 2021 Copyright (completion of final fugue) Paul Binski 2021 On the completion of Contrapunctus 14 Paul Binski writes: 'Contrary to some recent arguments (Butler, Wilson etc.) this completion accepts that the ‘fuga a 3 soggetti’ was intended by Bach not only to complete the Art of Fugue but also to introduce the motto theme as a fourth subject, used as a cantus firmus. The objections raised against this are not convincing. My completion is more concerned with appropriate length, musical ‘plot’ and tension-building than with contrapuntal ingenuity or originality, given the difficulty of finding keyboard combinations that have not been published. I have studied and adapted passages in completions by Donald Tovey, Davitt Moroney and Yngve Jan Trede --- which I readily acknowledge. With the exception of Moroney’s 40-bar completion, mine is shorter than many proposed, adding 58 bars to make a total of 291. Few published completions justify their often considerable length, but the scale and internal proportions of any art work are fundamental to its dispositio or ordering (to cite Mattheson’s Der vollkommene Capellmeister). In completing the fugue I draw attention to Gregory Butler and Indra Hughes’s observation that the four sections needed to get smaller by a fixed proportion (30% Butler, 1:1441 Hugues). I suggest that this was the plan, but that the ratio of the four sections was more probably based on the √2 (1.414), recognized as one of the basic ratios in mathematics and proportional theory in the arts since Pythagoras. A4 paper is based on √2 . Expressed decimally or as a fraction this resembles the ‘Bach’ number 14 – a fact that has not to my knowledge been sufficiently stressed in the literature on Bach and numerology. This ratio has a universal validity in the arts that 1:1441 did not: Bach’s name was not only ‘musical’ but embodied a profound numerical harmony. The ratio of the first to second sections including subject overlaps is 114:80 bars, close to 1.4:1; if continued, the BACH section would have continued to 57 bars and the final quadripartite section to 40 bars = 291 bars, indicating a 58-bar completion. That would allow a final section starting with the motto subject as a cantus firmus at bar 251 and about five further combinations – a limitation which would have forced JSB to choose the most elegant solutions while keeping up the tension unleashed in the music dissipated by excessive length. The fugue is thus a ‘14’ fugue which explores that number gematrically and dispositively as a ratio. This suggests that it was indeed intended to be the ‘14th fugue’ in the sequence (pace Butler) and may have been written for inclusion in the corresponding package of the Mizler Society, which was interested in Pythagoreanism, and as a ‘trailer’ for the Art of Fugue itself. My schema is : 239-50 second triple combination 251 motto theme in triple counterpoint 258 motto theme in quadruple counterpoint at the twelfth 269 inversus quadruple combination 277 triple stretto on BACH 282 quadruple combination rectus to 291 coda over motto cantus firmus’