Many people, if they wonder how music is made up, suppose that it consists of a tune and an accompaniment. The paradigmatic guitarist in front of a campfire croons the melody, while his hands create the harmonies that give it color. In the bel canto operas of Bellini, the diva astonishes with her delivery of the top line while the orchestra provides dutiful underpinning, moving from tonic to dominant keys with an occasional foray further afield. Frédéric Chopin admired Bellini, and his nocturnes reproduce the same model: the right hand unfurls a line of singing melody on the piano, and the left provides (in his case) exquisite harmonic support.
Much of the music of the Baroque era proceeds on a different model. The early eighteenth century witnessed the zenith of counterpoint, a compositional method in which there is not a dominating tune and a subsidiary accompaniment, but contrariwise a democratic parity between the voices. (They are called voices even when they are instrumental, not sung.) A choral piece by Johann Sebastian Bach or Handel typically shares out the elements equally between soprano, alto, tenor, and bass, so that the distinction between melody and harmony does not apply; every line contributes to both.
By the Classical period and even more in the Romantic era, the age of all-pervading counterpoint was past, though the best composers remained masters of it or, like Schubert at the very end of his life, sought to improve their skills in it. Even before his death in 1750, Bach was seen as persisting in archaic and unfashionable forms; when music lovers at that time spoke admiringly of “the great Bach,” it was one of his sons, composing in a quite different style, that they had in mind. Moving forward to the next century, anyone who has sung the lower parts of Samuel Sebastian Wesley’s hymn “The Church’s One Foundation” can attest to the dreariness of the experience: for most of the time you are confined to one note. This is the antithesis of counterpoint.
Of all the exemplifications of contrapuntal composition, none is more characteristic, more austere, and yet more intriguing than fugue. It should be acknowledged at the outset that the fascination is toward the nerdish end of the spectrum. The word “mathematical” is often used of fugues, and it is true that they contain elements of self-conscious calculation. But if that were all that was involved, any clever student could write a fugue like Bach’s, whereas it is the latter’s ability to combine architecture, emotion, and spirit that the fugue perfectly accommodates. Despite the variety of composers who have written them, and despite too the breadth of his non-fugal output (though the idiom is rarely far distant), Bach is the writer of fugues par excellence, and the fugue is perfectly brought to consummation in his compositions.
All fugues start with a theme or “subject” that is successively introduced by each of the voices, every voice being an independent and equal line. As the second and following voices state the subject, the voices that have previously done so utter complementary material, typically called a “counter-subject.” When all the voices have spoken—in Bach fugues between two and seven, most often three or four—the so-called exposition is completed. What follows is a slight relaxation of the preceding rigor, in which the subject is given a rest and other, related material, still in strict counterpoint, acts as an “episode” before the next iterations of the subject, now usually in a different key.
The whole process can be terse or expansive. The piece can be lengthened by various devices, all of which point up the skill required in the composition of the original subject: it can be turned upside down, stretched into longer note-values, or compressed into shorter ones. It can even be played backwards, though this particular stunt makes the subject unrecognizable to the unalerted ear; it is called a cancrizan—crabs in music, like those in Hamlet, being thought to walk backwards. Tension can be ratcheted up by the use of stretto, a technique whereby the subject is successively introduced at shorter time intervals than in the exposition. The ending may be prolonged by a brief coda.
Bach’s greatest fugues, some of which last for several minutes, are so ingenious that it feels as if they could go on forever—and one wishes they would. The final achievement of a hard-won resolution is almost overwhelmingly exhilarating, all the more because the elements of drama and contrast that form such a large part of the music of a later period are here strictly controlled; in their place is a narrative intensity that makes the listener attend to every note.
Although fugues are usually whole pieces, as with Bach’s or Shostakovich’s Preludes and Fugues, fugal writing is sometimes embedded within larger structures, such as the movements of a classical sonata or concerto. Here, the composer imitates the easily recognizable beginning of a fugue, but after a time the music dissolves back into the elements of a later style. For this reason, and because of the variety of different treatments to which it may be subjected, fugue has been referred to as a procedure or texture rather than a form. There are many examples of so-called fugato writing in Beethoven, for instance in the finale of his Third Piano Concerto, or the funeral march of the “Eroica” Symphony. Mozart had worked the same technique into the finale of his “Jupiter” Symphony, where it makes a somehow inevitable appearance in a movement that lays claim to be the most astonishing and inventive orchestral movement of all. The adolescent Mendelssohn concludes his String Octet, tongue firmly in cheek, with a learned and rapid fugue subject at which all eight instruments must labor before gladly abandoning the task in favor of a deliberately contrasting unison.
After the Baroque period, fugues proper were usually confined to choral music and special occasions, but there are exceptions. Haydn, the inventor of the string quartet, saw how well fugues could work in that medium, composing fugal finales for three of his set of six groundbreaking Op. 20 quartets. The musicologist Donald Tovey writes that these provide a hint of the volcano to come—a reference to Beethoven, who in his late period produced occasional but colossal fugues of an unsurpassed heat and energy, following, as so often, in the footsteps of his teacher by setting them as last movements. Tovey compares the presence of a fugue in a classical sonata with a playwright inserting a trial scene into a play: while the scene proceeds in accordance with its own internal rules, nothing else can happen and nothing else matters. In the right hands, however, such scenes can be the most exciting of all.
The piano virtuoso Alkan wrote a Grande Sonate portraying four ages of man; the second movement, rather ludicrously subtitled “Quasi-Faust,” contains an eight-part fugue, no less, based on a subject from Book II of Bach’s Well-Tempered Clavier. Wagner and Verdi may not be composers one associates with the form, but the riot in Act II of Meistersinger and the final chorus of Falstaff are both fugues. In the twentieth century, Bartok and Hindemith joined Shostakovich as names with whom the fugue is associated.
As with music in general, however, so in the case of fugue it is to Bach that one returns. Many will be familiar with the “forty-eight”—two books of Preludes and Fugues written in all the major and minor keys. Fewer will know the astonishing series of pieces known as The Musical Offering. These have their origins in a visit paid by Bach in 1747 to Frederick the Great at Potsdam, where his son Carl Philip Emanuel was an increasingly restless court musician. The king (possibly with help from the younger composer) had prepared a severe, chromatic theme on which he invited the old man to improvise a three-part fugue on the spot. Bach obliged, but the king then asked him to compose a fugue in six voices. For this, Bach replied, he would need time; but he did it, and we have the result today. It is the culmination of Das musikalische Opfer, and almost the last word in that exalted music of the spheres, which links together the notes on the page, the planets’ obedience to mathematical laws, and Bach’s worship of the ultimate ground of being, on whom he thought that these and all other glories depended.
To listen to almost any piece by Bach is the aural equivalent of looking into a kaleidoscope directed heavenward, where patterns of inexhaustible beauty form and reform, and human senses never tire of the notes’ unceasing refrain—proclaiming as they sing, in the words of Joseph Addison’s hymn, “the Hand that made us is divine.” Small wonder that the Romanian writer Emil Cioran said that “without Bach God would be a completely second-rate figure,” and again that “God’s creation would be a total failure were it not for the music of Bach.”
Even by his standards, there is one composition of Bach’s that sits above the rest. The musical forces for which it was composed remain a mystery, and it can therefore be played on many different instruments or on one; even so, it is rarely performed. This is The Art of Fugue, a work largely written in 1742, though it occupied Bach intermittently thereafter until his death, and which has been said to make even other masterpieces of his appear relatively superficial by comparison. With one exception, it fits perfectly on the keyboard, for which it may therefore have been intended, but many specialists in Bach do not attempt it (or do so armed with sheet music, since among its many challenges is the feat of memory that playing it entails). In not performing the work, they are actually behaving consistently with the composer’s intentions: it is doubtful that Bach envisaged a public rendition of any of the constituents of The Art of Fugue, let alone all of them, since the piece was meant for pedagogic purposes.
All the fourteen fugues and four canons in The Art of Fugue derive in some way from a single theme or “motto” in D minor, but, following an initial treatment that almost wilfully eschews the usual devices, their ingenuity and increasing complexity amount to one of the great intellectual and artistic achievements of Western civilization, an absorbing Glass Bead Game of esoteric abstraction that will never disclose all its secrets. The theme is so contrived that it can be played simultaneously with itself in double or half time or upside down (in double or half time); all these shapes fit together to make musical sense. The internet is studded with partial explanations of individual fugues—each known as a contrapunctus—but the student’s true reward comes from examining the score.
A few examples of Bach’s genius will convey the absorbing nature of the whole. In Contrapunctus VIII, Bach begins a long fugue with an angular theme that has no relation to the motto. About a quarter of the way through, a second subject is heard, also new. With these two tunes the composer appears to the listener to have departed from his hitherto monothematic ground plan. However, at the halfway point a yet further subject is discreetly given, which we slowly come to recognize as a variant of the original motto in inversion. Needless to say, the conjuring trick at the end is to show that all three apparently disparate themes fit together simultaneously. So it emerges that another feature of the motto is that it readily combines with subjects that appear to have no musical connection with it.
Even this is only an intermediate revelation, for in the serene, four-part Contrapunctus XI, perhaps the culminating feat of intellect in The Art of Fugue, these same three subjects are turned upside down, presented in a different order—and then combined with the subjects the “right” way up, as they appeared in Contrapunctus VIII. It is perhaps worth emphasizing the point that this mental prestidigitation in no way detracts from and even enhances the otherworld beauty of the music.
Then there is Contrapunctus XIII, sometimes called a “mirror fugue.” The fugue subject (recognizably related to the motto, though now transformed into a lively gallop) works equally well either way up, and Bach exhibits plenty of humorous ingenuity in setting these two versions against each other. But that is only the beginning, for it emerges that the whole fugue is designed on the same principle: it is possible in effect to turn the pages round and play the entire piece upside-down, though the reflection is not exact, because Bach turns the voices inside-out as well, giving the treble line to the bass, the alto to the treble, and so on.
Contrapunctus XIII is the only piece in The Art of Fugue that cannot be executed by a single keyboard player. So delighted was Bach by this irrepressible pair of twins—the rectus and the inversus—that he arranged a version for two claviers and, finding himself thus with four hands available to play a three-part fugue, he proceeded to compose a free fourth part for the spare hand. His achievement in fitting this extra voice within the straitjacket of the existing scheme has been described as the most astonishing tour de force of the whole work.
Naturally, the ear cannot hear all this unless the listener has become very familiar with the material. But it does not matter. As Tovey wrote in his Companion to The Art of Fugue about Contrapunctus XI: “To complain that we cannot attend to all three themes at once is like arguing that no picture ought to be larger than a postage stamp because that is as large an area as the eye’s centre of clear vision can comprise.” (If Tovey himself could not attain a synoptic grasp of all the detail, we may regard ourselves as absolved from the task with consciences unblemished. The great violinist Joseph Joachim said that he was able to “discuss music with Brahms and the Schumanns, but not with that young Englishman Tovey . . . he knows too much . . . after an hour with Donald, I feel as if my head were on fire. I have never seen his equal for knowledge and memory.”)
The long final contrapunctus is incomplete. It too comprises three subjects, the third a fugal treatment of the notes represented by Bach’s own name in German (which uses the letter B for our B flat and denotes B natural with an H). His death came before he had time to combine all three subjects with a fourth—the original motto theme, of course, which would thus have set its seal for the last time on the whole work. One of the great silences in music comes when the contrapunctus breaks off abruptly at the point where Carl Philip Emanuel writes in the score that here the composer died (it is hard to resist the vivid if unhistorical image of the pen falling from Bach’s hand).
Some who should know better have ventured to “complete” this fugue. Sir András Schiff has said that this is as misguided as an attempt to take a hammer and chisel to Michelangelo’s Slaves. No less a figure than Edward Elgar held a different view, being so impressed by the completed Contrapunctus XIV in Tovey’s 1931 edition of The Art of Fugue that he allowed himself an ebullition of incongruous sentiment: “I have a feeling of pride and reflected glory that an Englishman should have done what no fellow-countryman of the mighty author has been able to do.”
It is not often that one has the opportunity to contradict Elgar and Tovey in a single sentence, and it may be thought rash to do so. Yet paradoxical as it may seem, to experience the stillness at the very moment when Bach’s music passes from the measures of time into measureless eternity is to come as close to the greatest of all composers as it is possible to get. It is also to realise that all classical music (unlike other music) emerges from, is sustained by, and returns again to silence, and that this relationship is the deep truth which lies at its core.
