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The Art of the Fugue

Expended version of a review of The Art of Fugue by Joseph Kerman
for the London Review of Books, 2006

Counterpoint, the art of combining two or more independent melodic lines, is the prime distinguishing feature of Western music. Music began with monody - unaccompanied melody - and with rhythmic patterns beaten out on sticks and drums. The majority of the world's folk music is monodic. Often percussion underlines the rhythm, and sometimes a drone is added, an unchanging note in the bass, which keeps the tune in touch with the earth as it makes its aerial flights: this is a feature of some of the most sophisticated non-Western musics, for instance Classical Indian. Indonesian music uses heterophony - different versions of the same melodic line sounding together. Imitation is occasionally found in other non-Western musics. But European counterpoint is something else altogether. Counterpoint is a conversation; it acknowledges the presence and participation of the other. Two independent voices may be played by the same musician, on a keyboard for instance, but they are more often given to two players, who must listen to each other. It is significant that counterpoint grew to maturity in Europe where the concept of democracy was born.

By no means all European music is predominantly contrapuntal; much of it is melody with harmony, and this kind of music has the widest popular appeal. Even a complex piece such as a Beethoven symphony will almost always have a main melodic line that you can sing or whistle your way through. But try whistling a Bach fugue. After the first few bars where the main subject is announced unaccompanied, the music divides into two parts, then three, then possibly four, or even five or six. The contrapuntal discourse is continued throughout the duration of the piece. How can you hear all these lines at once? Most of us probably don't. The experience of listening to a fugue is stimulating yet at the same time forbidding. This is the most intellectual music that has been devised. But it is also capable of expressing emotion on the highest level, and where intellect and emotion are in perfect balance, the result can be sublime. To give three supreme examples: the B minor fugue in Book 1 of Bach's '48', the six-part ricercare from the same composer's Musical Offering, and the opening fugue of Beethoven's C sharp minor Quartet, op.131.

In the preface to his new book on Bach's keyboard fugues, Joseph Kerman quotes Charles Rosen's perceptive comments:

"The 'pure' fugue, the meditative fugue, is basically a keyboard work for Bach ... Only the performer at the keyboard is in a position to appreciate the movement of the voices, their blending and their separation, their interaction and their contrasts. A fugue of Bach can be fully understood only by the one who plays it, not only heard but felt through the muscles and nerves." [p.xvii]

Rosen is surely right, and in the same way a string quartet is best understood by a player taking an active part in the instrumental conversation. Mere listeners, however, should not despair. It is possible, with practice, to learn to hear contrapuntal music, especially if you can read music and follow a score. Then you will see as well as hear how, for instance, in the first fugue of the '48' - one of the 16 fugues that Kerman analyses in some detail - the first seven notes of the subject are inverted - turned upside-down - in two overlapping sequences as the second voice comes in with the subject a fifth higher, as prescribed by the rules of fugue. This little piece of clever craftsmanship - one of many in the course of this fugue - is, on rehearing and in contemplation, much more than that; it becomes a mystery - the uncanny power of counterpoint to suggest the unfathomable.

Fugue developed out of canon or round, music making strict use of the device of imitation, and exhilarating to perform, as anyone who has sung 'Frčre Jacques' or 'London's Burning' will know. Canon is a ubiquitous compositional resource: it can even be found in rock music - for instance the Beatles' 'She Said Se Said', and the fade-out endings of a number of Beach Boys' songs. Fugue is a freer form than canon, but there is a general scheme that most fugues adhere to. First, an exposition: the voices enter with the subject one by one, in a four-voice fugue in soprano, alto, tenor and bass registers (in any order). As the second voice enters the first voice continues with an accompanying 'countersubject', which must fit the subject whether it is played below it, or above. Additional countersubjects may be invented for further entries of the subject. Devising memorable countersubjects is a test of compositional prowess, one at which Bach especially excelled. A development follows where both themes appear in new keys (if it is a tonal fugue) and combinations. Then a return to the home key; finally a 'stretto' where the subject entries overlap, typically over a sustained note in the bass emphasizing the main tonality.

Kerman's book, which usefully includes a CD containing scores of all the fugues discussed and recordings of some of these played on piano, harpsichord, clavichord and organ by Davitt Moroney and Karen Rosenak, concentrates on analytical detail and does not attempt to put Bach in the wider context of fugal writing throughout musical history. He assumes a fair amount of prior knowledge, including understanding the vocabulary of harmony; but musically literate readers will find their appreciation of these fugues greatly enhanced by the insights that Kerman brings from a lifetime's study as he examines the music with scrupulous care, bar by bar. His prose is technical but never dry. Reading his commentary on the B major fugue from Book II of the '48', for instance, made me think anew about the way the subject rises, falls, and rises again to a higher note, and how this contour is mirrored in the progress of the fugue, so that the highest note reached, a B, which occurs three times but only on its third appearance is entrusted to the subject, feels there like the climax of great aspiration. It descends from this high point:

"With the greatest dignity and calm. With no harmonic undercutting and no tumble of faster notes ... The soprano response feels like a slow, deep bow ... touched with something like regret, though feelings are blurred by another suspended note ... Even as the fugue quietly gives up aspirations for the heights, it moots confident new possibilities, even now, for breadth."

Eloquently precise. Music like this attains such expressive perfection that I for one am reduced to bathos in attempting to describe my reactions to it. Kerman is undaunted. He concludes his book by asking himself what he has tried to do, questioning the very practice of writing about music, and gently justifying it: 'Talk mediates, differentiates, elucidates, and consoles; we use words, however imprecisely, to talk about love and death because talk, it seems, we must. We also use and surely must use words to talk about music.' [p.147]

The art of fugue had only been practised for a hundred years or so when Bach brought it to perfection, an achievement insufficiently appreciated by his contemporaries, some of whom thought the whole thing out of date. The new classical style which swept through Europe in the mid-18th century, and whose first practitioners included Bach's sons, was one centered more on accompanied melody than polyphony. But fugue did not die out with Bach; there was soon to be a revival of interest, and in fact there has been virtually no major composer since Bach who has not written at least one notable example of a fugue. There are exceptions: Chopin's forms admitted Bachian counterpoint, but not the fugue, which must have seemed alien to his Romantic, poetic sensibility. (It had not appeared so to his more Classically-oriented contemporaries Mendelssohn and Schumann; Schumann's sparkling fugal conclusion to his Piano Quintet, for instance, comes as a delightful bonne bouche.) Chopin was the most modern, least antiquarian of all the early Romantics: adapting the sonata was the furthest he was prepared to go in accommodating himself to the recent past; otherwise he transformed contemporary dance idioms (such as the mazurka) or invented new forms (such as the Ballade), in which the fantastic flowers of his melodies could find space to open and bloom. Wagner, in some ways the inheritor of Chopin's erotically-charged Romanticism, learned the art of fugue from Theodor Weinlig, a successor to Bach as Cantor of St Thomas's, Leipzig, and there is a fugue in the finale of the symphony he wrote when he was twenty. His mastery of Bachian counterpoint in Die Meistersinger is flawless, above all in the wonderful fugato ensemble at the end of Act Two; but, as with Chopin, there was no place for a full-blown fugue in his mature music. Nor in Sibelius, who nonetheless showed sufficient mastery of counterpoint - and in particular the Palestrinean counterpoint of the openings of his Sixth and Seventh Symphonies - to demonstrate that he too could have written an interestingly individual fugue had he chosen to do so. Even Debussy, who was primarily a harmonist, might at least have begun to think about fugue if he had lived to experience the neo-classical revival of the 1920s and been able to pursue the more linear style he was developing in his last chamber sonatas.

The revival of the fugue after Bach gets properly under way with Haydn's finale fugues in the last two of his op.20 string quartets. Haydn may not have known Bach's fugues, but both Mozart and Beethoven revered Bach - and Handel - and both made transcriptions of fugues from the '48'. Mozart transcribed three for string trio to which he added preludes of his own; Beethoven made a string quartet version of the C sharp minor fugue from Book 1, whose influence can be heard in his own great C sharp minor fugue in the op.131 Quartet. Mozart's own fugues sometimes seem to want to outdo Bach in sheer cleverness, as in the Adagio and Fugue, K546, where the tense fugue subject drives relentlessly through the music, as insistently memorable in inversion as it is the right way up. In the finale of the 'Jupiter' Symphony, Mozart dazzles the listener as he nonchalantly shows off every contrapuntal trick in the book. Here is the spirit of Apollo: pure delight in the form. With Beethoven, for whom the fugue became more and more important as he ventured into new areas of artistic aspiration at the end of his life, Apollo is joined by Dionysus in the duality that Nietzsche thought essential to the highest art. Dionysus prevails in the most extraordinary fugue of all, the 'Grosse Fuge' that Beethoven originally conceived as the finale of the B flat Quartet, op.130, but later detached to form a self-sufficient piece. As the opening Allegro charges along with manic exuberance, there is a feeling of exploring completely uncharted territory, like pioneers in the Australian outback. Huge vistas are glimpsed but are tantalizingly out of reach. The pace is relentless, the dynamics always forte. Then suddenly it stops, and a new fugue begins, slow and full of intense lyrical emotion. And then a third: a rough-edged, unbuttoned dance which sometimes loses all sense of key. So Beethoven has contrived to encompass all the elements of the symphony within the texture of the fugue. This music will always sound 'modern' because it is stretching the limits of the possible; it is still fiendishly difficult to play. No fugue since has ever been quite so adventurous on every level.

Many Romantic composers would have been wise to heed Schumann's warning: 'The emptiest head thinks it can hide its weakness behind a fugue; but a true fugue is the affair of a great master.' Liszt's fugues, for instance, tend to show up his deficiencies as a contrapuntist. His chromatic harmony sounds laboured, and he quickly runs out of steam. The whole philosophy of Romanticism, after all, was opposed to that of the baroque: the individual, revolutionary voice, whose natural expression was heightened melody, in contrast with the voice of the community still grounded in political stability and religion, and symbolised by polyphony. The majority of later 19th-century fugues are choral, and are descended from Handel rather than Bach, a routine part of the ubiquitous oratorio which was the pious Victorian counterpart to Wagner's unleashing of erotic feeling in his operas. Most of them are dutifully dull, but the best composers, such as Brahms in the German Requiem, or Elgar in The Dream of Gerontius, overcame pedantry with intellectual passion. The choral fugue that opens Berlioz's Grande Messe des Morts is compellingly unorthodox, the subject making a dramatic downward swoop on the words 'Requiem aeternam' while the countersubject sets the same words to a tremulous descending chromatic scale; at one point each entry of the subject surges in a tone higher than its predecessor, producing great cumulative power. Berlioz too found a fresh and colourful use for fugato to portray the brawling Montagues and Capulets at the start of his Roméo et Juliette. Mahler, as a student at the Vienna Conservatoire, neglected his counterpoint studies and failed his examination, and this seems to have spurred him on later to become an ardent student of Bach and eventually the most accomplished contrapuntist of all the Romantics. The influence of Bach may be heard as early as the Second Symphony, and is all-pervasive in the finale of the Fifth. It reaches its climax in the central double fugue in the first movement of the Eighth Symphony, where Mahler also almost matches the striving intensity of Beethoven's Missa Solemnis.

The 19th-century vocal fugue reaches its apogee in the fugal finale of Verdi's Falstaff, the last operatic music he wrote. Verdi had already composed a remarkable and innovative fugue. 'a light hearted Grosse Fuge', as Julian Budden has described it, in his E minor String Quartet, his only mature piece of chamber music. In introducing the fugue to the operatic ensemble, he was bringing to fruition what Mozart had hinted at in the final ensemble of Don Giovanni. At the end of Falstaff all the characters assemble on stage to pronounce their verdict on life: 'Tutto nel mondo č burla'. It is a compositional triumph: a last summoning up of all Verdi's powers in an effusion of contrapuntal jest.

In the 20th century the instrumental fugue made an impressive return. At the start of the century we find Bartók modelling the fugal first movement of his First String Quartet on Beethoven's op.131, and Schoenberg in his own First Quartet also taking up the challenge of Beethoven's late quartets - the first two composers to do so since Schubert and Mendelssohn made their tentative response; even Brahms had been daunted. Bartók went on to incorporate a fugue into the Allegro movement of his Third Quartet in a very Beethovenian way, and to write a measured fugue of masterful order and precision as the opening movement of his Music for Strings, Percussion and Celesta. The neo-classical movement after the First World War brought the fugue back into fashion. Busoni, who had already found his own way to an independent kind of neo-classicism, had in 1910 completed Bach's unfinished fugue from The Art of Fugue in his Fantasia Contrappuntistica, with masterly daring. Ives, another independent, working in isolation in New England, delighted in contrasting the wildest musical experiments with the orthodox harmony and counterpoint he had learned as a student at Yale. In his Fourth Symphony, he follows the polytonal second movement, probably the most revolutionary music he ever wrote, with a fugue based on the hymn 'From Greenland's Icy Mountains', whose orderly calm is only momentarily threatened by dissonance. Stravinsky, not a natural contrapuntist, absorbed himself in Bachian counterpoint in his neo-classical period and wrote an affecting, chromatic fugue in his Symphony of Psalms. Later in the 1930s he made an assiduous study of Beethoven's late fugues which bore fruit in the fugal finale of his Concerto for Two Pianos. Tippett, after studying at the Royal College of Music, decided to study Bachian fugue privately a few years later with R.O.Morris, an outstanding teacher of counterpoint. Tippett took the composition of fugue very seriously and it accorded with his belief at the time that a composer should go back to Beethoven to heal some of the wounds that modernism had inflicted. Several fine examples in Tippett's string quartets show evidence of Beethovenian labours. His friend and rival Britten had studied 16th-century counterpoint at the Royal College with John Ireland: it was one of the few disciplines he had not learned already from Frank Bridge. In his young maturity, Britten threw off several brilliant fugues with apparent ease; in particular the concluding fugue of the Young Person's Guide to the Orchestra is an example of the kind of carefree cleverness for which, absurdly, he was criticised at the time. Hindemith's many fugues tend towards earnest academicism, in contrast to Shostakovich's fresh and expressive set of 24 Preludes and Fugues in all the keys, composed in 1950-1, a deliberate homage to Bach's '48' and a impeccable answer to the avant-garde of the time who were pronouncing that such things were no longer possible.

The nearest the fugue came to a modernist gesture was probably Ernst Toch's 1930 Fuga aus der Geographie. This is a four-part spoken fugue, whose rhythms follow the natural rhythms of the carefully-chosen words. The subject, given to the tenors and needing Savoy Opera dexterity to deliver, is:

  • Ratibor! und der Fluss Mississippi und der Stadt Honolulu und der See Titicaca
  • der Popocatopetl liegt nicht in Canada sondern in Mexico Mexico Mexico

... at which point the second voice comes in, and the standard fugal procedures are worked through. Toch's fugue has a distant cousin in the 'Sirens' chapter of Ulysses, where Joyce - who might have wished to be a composer rather than a novelist, had he been able - attempts to use some of the techniques of fugue in a striking display of sonorous prose. He sets out his thematic material in an introduction - 'Bronze by gold', etc. - and then develops it into rounded, musical sentences: 'Shrill, with deep laughter, after, gold after bronze, they urged each each to peal after peal, ringing in changes, bronzegold, goldbronze, shrilldeep, to laughter after laughter.' There is an illusion of counterpoint in the juxtaposition of overheard conversation, snatches of songs, and onomatopoeic sounds. At the same period, musical modernism could initially accommodate the fugue (in Berg's Wozzeck for instance). Schoenberg wrote (in 1936): 'In its highest form . . . nothing would claim a place in a fugue unless it were derived, at least indirectly, from the theme', hinting at a connection with his 12-note method of composition; and indeed, 12-note fugues are quite feasible, though Schoenberg himself avoided them. It may be argued, however, that in denying the tonal basis on which the fugue had always relied, a great deal of its strength is lost. In turning against Schoenberg and the continuing emphasis on melody in his interpretation of the method, the post-war European avant-garde also renounced all traditional devices of counterpoint, rules of harmony, and regular rhythm, deeming them obsolete in their quest for a new-found language. Instead, Boulez and Stockhausen pursued the ideal of the sonic 'moment' in a floating world free from measured time. This most extreme phase of post-war modernism has long since passed, and the majority of composers nowadays are trying, in various ways, to reinstate what was temporarily discarded. Few composers today, however, are writing fugues, and it has to be asked if fugue can still make a valid contribution to contemporary musical language.

My own answer would be yes, and I can point to several examples of contemporary fugue that, in my view, demonstrate its continuing vitality. Their composers will probably not become household names, but then I would hardly expect the art of fugue ever to be modish and popular when the art of serious contemporary music itself has become an unfashionable minority interest. Before I'm tempted to lament any further the reluctance of many to engage with the difficult and the complex in music today, despite its undiminished intrinsic power to move the emotions, I had better name my fuguists: first, the Scottish composer Alistair Hinton, who in the huge finale of his nearly three-hour String Quintet (1969-77), included a 20-minute fugue, or rather three continuous fugues, modelled on the Grosse Fuge and rivalling it in its scope and emotional intensity, if not quite achieving its transcendental vision. Hinton's first fugue, in similar dotted rhythms, has the fierce energy of Beethoven's opening fugue; his second fugue, in total contrast calm and sweet-toned and sounding like a piece from the Renaissance, begins and ends with a canon whose theme becomes a fugue subject in its central section; the third employs subjects and countersubjects from the first two fugues together with new themes of its own, and combines all together in the most learned (yet never pedantic) style, with the themes played backwards and in inversion, all the time gradually generating another volcanic eruption of Beethovenian energy. In the spirit of his friend Kaikhosru Sorabji, who wrote many gargantuan fugues in his still hardly known keyboard works, Hinton has continued to include large-scale fugues in his own pieces, including the Variations and Fugue on a Theme of Grieg and Sequentia Claviensis, both for piano.

My second fugue composer is the Moravian, Pavel Novák, who has been working for the past 17 years on another vast project, a set of 24 Preludes and Fugues for piano based on the Old and New Testaments (twelve for each part). The second set is still to be completed; the first has so far only had one complete performance, by William Howard, for whom the work is being written. Novák has a radically unorthodox attitude to fugue: the first fugue, evoking the creation of heaven and earth, has only one voice, and no counterpoint; the sixth fugue is built on a one-note theme and employs only seven notes altogether. The music grows into greater complexity as the world grows with it. A fugue without counterpoint might seem a contradiction in terms, but Novák somehow contrives to give substance to his omissions. The background to his music is rich and firmly-rooted enough to enable him at times merely to sketch in the foreground. It is impossible to know yet what the cumulative effect of the whole work will be, but what he has composed so far constitutes one of the most impressive piano works of recent times.

Shostakovich's fugues had brought a new sense of spacious calm into the fugue: they are fugues for the unchanging landscape of Russia. The immense canon that opens Górecki's Third Symphony (if anyone has paid enough attention to this carelessly heard piece to notice that it is a canon), beginning in the double basses, growing to encompass the whole string section, and again receding, has the same sense of space and of gradual, unhurried movement, like a slow journey across some featureless plain. Canon is well suited to Górecki's pared-down musical language; fugue perhaps would be too active for him. In Howard Skempton's recent and remarkably beautiful string quartet, Tendrils, the texture is one of continuous canon. While the mood is one of sustained contemplation, there is much more contrast than in Górecki. Skempton's Shostakovich-like chromaticism keeps the music in a continuous state of mild tension, which the abrupt resolution into E flat at the end does not altogether dispel. Skempton may now be ready to write a contemplative fugue; he certainly doesn't think it impossible.

At this point I should declare an interest. I had used canonic devices in my own music for many years, but it was not until 1998 that I felt able to introduce a fugue, a contemplative one somewhat indebted to Beethoven, into my Eighth String Quartet. It seemed to work. The following year, at a concert in London, I heard my violinist friend Peter Sheppard Skćrved play Bach's G minor solo Sonata, which contains an elaborate three-part fugue. I wondered if it was possible to write a four-part fugue for solo violin, something that as far as I knew no-one had attempted, for the obvious reason that four-part counterpoint on a violin is virtually impossible. I wrote a few bars and sent them to Peter, who to my surprise pronounced them playable. So I finished the piece, in a neo-Bachian E minor, and thought of it as a one-off technical exercise until Peter persuaded me to write more. I wrote another four-part fugue, in A minor but highly chromatic and almost atonal; then, over period of nine months, carried on writing them occasionally until I had 15, cast in the more practical keys. Only five of them are four-part fugues, and even in these there is little continuous four-part writing, which would be almost intolerable for the listener, let alone the player. There are two two-part fugues and the rest are in three parts. I amused myself with the kinds of games that fugal writing seems to encourage: my first two-part fugue has a ten-note theme derived from the keys of all the fugues in my series in the order they appear (major and minor counted as one) and it modulates in turn through all these keys before returning to its home C minor. One fugue was entirely pizzicato. Another was based on a blackbird's song. I was learning a new skill, like a painter learning how to etch. Because I hadn't been to a music college, I had never learned the art of fugue formally. Perhaps those who have to go through what at the time may seem merely an academic chore cannot associate it afterwards with living music. I'm grateful to have discovered the sheer pleasure of fugue by myself, without any prejudices.

Even if counterpoint is presently neglected, it will not die out: it is too rich a resource. In his exemplary little book, Counterpoint, Edmund Rubbra, no mean practitioner himself of the art of fugue, wrote: 'The history of Western music is the history of the form-compelling power of counterpoint.' That is justification enough for its survival. Throughout Western music's history, composers who have possessed what Rubbra defined as 'an intuitive grasp of the essential spirit of fugue' have been able to renew this most intriguing and demanding of all contrapuntal forms, and there seems no valid reason why, if composers can learn to master it, the art of fugue should not continue to evolve in the future; in Rubbra's words, 'an evolution that never destroys the basic nature of the form'.