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Kunst der Fuge (Art of Fugue)
 Composed by Bach, Johann Sebastian
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J.S. Bach (1685-1750)

Art of Fugue (Kunst der Fuge BWV1080))

Although it was once thought that Johann Sebastian Bach’s Art of Fugue was his last composition, one that remained unfinished at his death in 1750, we now know that it actually occupied him throughout the entire decade of the 1740s, a fact that makes its incomplete status all the more tantalising. It is a work that must be placed alongside the other speculative works of Bach’s last decade also devoted to the exploration of a single theme - the Goldberg Variations, the Canonic Variations on ‘Vom Himmel Hoch’ and the Musical Offering. In the Art of Fugue, an encyclopaedic work devoted to the fading world of learned counterpoint, Bach took a modest theme, and in a progressive series of distinctive fugues and canons, explored how the old devices could be exploited to display every conceivable contrapuntal machination. The title of the work can in fact be understood as a kind of provocation, since, for many of Bach’s contemporaries, the learned devices of fugue were no longer considered ‘art’ so much as intellectual vanity far removed from the requirements of a ‘natural’ music. ‘Mind games’ (Sinnenspiel) writes Johann Mattheson, ‘cannot appeal to affects’, and he knows of no one who can assert that strict counterpoint ‘has moved his heart, stirred this or that affect, or has been in one way or the other to his liking. As long as this has not happened, one has accomplished nothing in music.’ The title of Bach’s collection suggests that his goal was very much to assert the status of fugue as musical ‘art’ (Kunst ) rather than merely artifice (Künstlichkeit) and that the deeply moving result was to appeal not only to the mind and to the eye but most particularly to the ear.

Although Bach wrote the Art of Fugue so that most of it was playable by one person seated at a keyboard, it is not, strictly speaking, a keyboard work. Its aim is rather to explore the various forms of fugue rather than to provide mere examples of playable keyboard music. This is why Bach called each movement a ‘Contrapunctus’ and in some sources appended the arcane academic names denoting the specific technique that underlay a particular fugue. This speculative feature of the work is also underscored by Carl Philipp Emanuel Bach, who in 1751 advertised a published version of his father’s Art of Fugue. In this newspaper advertisement, discovered not so long ago, the younger Bach speaks first of the singability of each individual voice which could be observed in the open score format and only thereafter mentions, as kind of bonus, that the work was at the same time ‘expressly arranged for the use of harpsichord or organ.’ Since the key to appreciating the Art of Fugue is to hear the profound message it imparts about Fugue, it is particularly advantageous to hear the piece performed by a quartet of viols, that is, by an ensemble very much at home with projecting the lines of strictly imitative music. The idea here is not to claim this version as an ‘authentic’ realisation of the Art of Fugue but rather to approach the underlying ideas of expression underlying the counterpoint. At the same time, we take pains to characterise throughout the Contrapuncti the references to a wide variety of instrumental styles and genres - both historical and contemporary - upon which the Art of Fugue weaves a fascinating commentary.

The Art of Fugue embraces three kinds of fugues: from the simple fugues of Contrapunctus 1 through 4, the counter- or augmentation fugues found in Contrapunctus 5 through 7, and the invertible or double fugues on multiple themes found in Contrapunctus 8 through 11. The set concludes with the unfinished double fugue based on four themes which embraced not only the audacious inclusion of Bach’s monogram (B-A-C-H understood ‘in German’ as Bf-A-C-Bn) but also elements of melodic inversion (or counterfugue) and stretto (or canon). Despite its status as incomplete, the quadruple fugue amounts to a kind of extended fugal peroration which sums up the entire collection, even though the work remains, alas, incomplete.

It enhances the experience of listening to the Art of Fugue if one is aware of the characteristic traits of the kinds of fugues heard . A simple fugue, first, is closest to composition not based on imitation and gives free reign to the composer’s imagination and inventive powers. It is not at all uncomplicated in a technical sense but is called ‘simple’ because it traffics in Contrapunctus simplex, which avoids double or invertible counterpoint. This means that when the composer writes other parts to accompany the melodic subject of the fugue, he is free to compose voices that need not either be turned on their head when they exchange places or else need to be devised so that they can simultaneously be layered atop each other at different rates of speed.

Bach’s conceit in the opening four fugues can be understood as a principle of non-repeatability, in which the free counterpoint that accompanies each statement of the subject furnishes a fresh harmonic environment for the theme. In the first two fugues, the theme is heard in its so-called proper form and in the second two fugues is heard upside down in its melodic inversion. The theme itself appears embedded in the free counterpoint rather than having been ‘harmonised’ by seeking out mere embellishments of triadic chords that make up the subject. Not only does Bach make use of the proper and inverted versions of the Kunst der Fuge subject; he also crafts a host of varied forms of the subject once he has established the basic forms.

One of the properties of the Art of Fugue theme is that its invention ensured that both the ‘right’ form and the inverted form are usable fugue subjects, even if they are also intentionally somewhat plain. Contrapunctus 2 and Contrapunctus 3 alter the rhythms of the fugal subject but it isn’t until Contrapunctus 4 that Bach begins to stretch the theme itself, a liberty that compromises the triadic identity of the Art of Fugue subject. As one experiences this piece, it becomes apparent how Bach is far from demonstrating the limits placed on him by strict composition but, quite the contrary, asserts how a composer is thus free to think through ever more inventive combinations.

The next set of fugues, called counterfugues, start combining simultaneously both versions of the subject heard both in their normal length as well at successively slower and faster rates of speed, called augmentation and diminution. The experience of a counter-fugue is quite different from a simple fugue in that one can perceive overlapping musical objects of widely contrasting magnitudes. This is why one hears musical time proceeding according to several different simultaneous clock speeds. There are three counterfugues in the second group, of which Contrapunctus 6 is a particularly brilliant piece which Bach labels ‘in French style’. Here the composer alludes to the pompously dotted rhythms that characterised the French entrée or overture associated with Jean-Baptiste Lully and the Sun-King, Louis XIV. By combining this idea of diminution with the traditional learned use of diminution - playing the fugue theme against itself at differing rates of speed - Bach ends up composing a utterly mad evocation of French overture which literally decomposes into sets of majestic gestures posturing at incompatible velocities. (For this reason, we don’t assimilate the rhythms of the augmentations to the faster moving themes -turning quavers into semi-quavers - but rather reinforce what seems to be Bach’s intentionally wild metric conflict.) The kind of majesty Bach is representing here is therefore far more speculative than the kind concerned merely with vain monuments to worldly glory. Note, however, that the same temporal separation of musical strands can result in the most astounding kind of contemplative art, as in Contrapunctus 7, which recalls so movingly the magisterial cantus firmus organ works at which Bach especially excelled.

To understand the idea of double fugues one has to grasp the idea that the Art of Fugue theme (or subject) will be heard simultaneously in each piece with at least one or two other subjects which will all then be rotated topsy-turvy in a series of permutations. Without delving into the mathematics of invertible counterpoint at the octave, tenth or twelve, suffice it to say that the musical message of the double fugues is disclosed not by listening just for the Art of Fugue subject alone, but rather its awesome combination with other repeated themes. For example, in Contrapunctus 9, perhaps the most accessible double fugue, Bach displays two versions in what is called invertible counterpoint at the 12th when the bustling opening subject combines with the Art of Fugue theme. And because inversion in this kind of counterpoint displaces the intervallic relations so palpably, each version possesses a distinctly individual harmonic flavour.

The listener’s task in the three types of fugues therefore differs in some interesting ways. In the simple fugues, Contrapunctus 1 through 4, one takes pleasure in the contrasting harmonic abodes for the subject and in the various forms of alteration undergone by the subject itself. In the augmentation or counter-fugues, Contrapunctus 5 though 7, one concentrates on hearing forms of the subject played against themselves at contrasting rates of speed. And in the double fugues, Contrapunctus 8 through 11 and in the final incomplete piece, one rejoices in the intimate cohabitation of the subject with as many as three new themes, all of which exchange places in a dazzling choreography.

Much has been written about Bach’s cryptic unfinished double fugue on four themes, which breaks off in the 238th bar shortly after the striking exposition of Bach’s personal signature melody has been finally combined with the two other new themes developed earlier in the movement. This fugue was to conclude the Kunst der Fuge not so much because of its extreme difficulty, perhaps, but because it would sum up Bach’s personal vision of fugue by the composer making a cameo appearance in it as one of the countersubjects to the Art of Fugue theme. It was a work that was in any case to be heard as mysterious because the Art of Fugue subject was not to make an appearance until quite near the end of the piece. There it was to be shown to combine seamlessly with the other three themes which had already been extensively developed. This glove-like fit was really only discovered in the nineteenth century when it was observed that Bach had surely intended to combine the three themes in the Contrapunctus with the Art of Fugue subject itself in a final contrapuntal tour de force. You can imagine what this fugal complex would have sounded like if you listen carefully to the very last combination of the three themes just before the fragmented torso ends and substitute the Art of Fugue subject for the free counterpoint in the first treble viol part. Indeed, this fugal complex in four parts must have been Bach’s basis for the invention of the movement.

Many scholars are now of the opinion that Bach had in fact completed the final fugue, but that, due to the confusion of manuscript sources after his death, incompetent editors failed to put the pieces of the puzzle together correctly. But given the most reliable dating for the manuscript of the final fugue torso, it becomes difficult to understand why Bach never supplied a conclusion to the engraver. On the basis of a careful study of Bach’s gradually deteriorating handwriting and the watermarks found in the relevant paper, the most recent scholarship has dated this manuscript to the period between August 1748 and October 1749, perhaps as much as two years before his death. Bach’s first eye operation took place much later, during the last days of March, 1750, and thereafter, according to the Obituary, ‘he no longer had use of his eyes.’ Bach died on the 28th July, 1750. There were therefore at least five months before his first operation and possibly far more than that during which Bach apparently did not work on this fugue. It seems difficult to claim, therefore, that pressures of time prevented him from bringing the work to completion.

One is left wondering why it was, then, that Bach delayed completing the Art of Fugue, even if it were more or less obvious to him how he would want to proceed. Although there is no further evidence that would help answer this question, it is certainly worth considering whether the composer had second thoughts about issuing a work in which his boldly embroidered family emblem was proclaimed, no matter how appropriate and well-deserved this proclamation. So even if he could easily have finished filling in the details of the final fugue, of which no one can have the slightest doubt, it is worth considering whether Bach did not through his inaction choose to leave it unfinished at his death. Certainly this was Emanuel Bach’s view when he supplied the last page of the unfinished fugue manuscript with the following inscription: ‘NB. At this point in the fugue where the name B A C H was introduced in a countersubject, the author died.’ Though in a literal sense Emanuel was surely engaged in myth-making, his inscription also surely contains within it a kernel of truth: namely, that as a composer of fugues, Bach had in fact died at that very moment when he decided not to complete the final fugue breaks. As the fortunate inheritors of this work, we are nonetheless compelled to wonder at the conclusion of a stirring musical fragment at the same that we reflect on the loss of someone so passionately dedicated to its cultivation.

Laurence Dreyfus©

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