Fugue

(from Lat. fuga: ‘flight’, ‘fleeing’; Fr. fugue; Ger. Fuge; It. fuga).

A term in continuous use among musicians since the 14th century, when it was introduced, along with its vernacular equivalents chace and caccia, to designate a piece of music based on canonic imitation (i.e. one voice ‘chasing’ another; the Latin fuga is related to both fugere: ‘to flee’ and fugare: ‘to chase’). Like ‘canon’, fugue has served since that time both as a genre designation for a piece of music and as the name of a compositional technique to be introduced into a piece of music. Imitative counterpoint in some fashion has been the single unifying factor in the history of fugue, but as compositional approaches to imitation changed so did the meanings and usages of the word ‘fugue’. Between 1400 and 1700 the word held a wide variety of meanings and was employed in a great many contexts, with the idea of fugue as a compositional technique predominating. By the early 18th century musicians had come to prefer its use as a genre designation, in which guise fugue has continued until the present. It is generally distinguished on the one hand from canon, which involves the strictest sort of imitative counterpoint, and on the other from mere imitation, which involves the least strict.

Despite the prominence of fugue in the history of Western art music and its virtually continuous cultivation in one form or another from the late Middle Ages until today, there exists no widespread agreement among present-day scholars on what its defining characteristics should be. Several factors contibute to this lack of consensus: (1) between the late Middle Ages and the late Baroque a great variety of genre designations – ricercare, canzona, capriccio, fantasia, fugue itself, even motet – came and went in which techniques of imitative counterpoint figured prominently. Thus the history of fugue cannot adequately be accounted for if only pieces called fugue are studied. (2) If all pieces called fugue were collected together and compared, no single common defining characteristic would be discovered beyond that of imitation in the broadest sense. (3) Since the early 19th century genre designations have been defined largely if not exclusively by their formal structures. Formal structure, however, is not in the end a defining characteristic of fugue. As a result, there has been prolonged argument about whether fugue is a form at all (and, by extension, whether it is a genre) as well as whether any particular formal model should be considered necessary (most often recommended in this context is a ternary model vaguely reminiscent of sonata form; see Dreyfus, 1993). (4) There has developed, beginning in the mid-17th century, a theoretical, textbook model for fugue, most often associated with Fux’s Gradus ad Parnassum and, thanks in large part to Cherubini, with the teaching of the Paris Conservatoire. The appropriateness of this model as a standard, and of its characteristics as necessary and sufficient for the genre, has been a topic of considerable debate. The most commonly recommended alternative to this model has been the fugues of J.S. Bach, especially those of Das wohltemperirte Clavier (the ‘48’). (5) Although it is generally agreed that a great deal of fine fugal composition appeared before Bach and Fux, reliance on post-1700 models has caused disagreement and uncertainty about how to define and evaluate fugal works composed before 1700.

The historical survey beginning in §2 below is preceded by a detailed analysis of the C minor fugue from book 1 of the ‘48’ as it is commonly presented by English speakers. This particular fugue is frequently cited as a paradigm, and it is through just such an analysis that over the years many musicians have encountered fugue for the first time. The analysis introduces the most important standard fugal terminology and demonstrates the kind of norm that many musicians consider essential to define the genre. The emphasis throughout the survey that follows will be on the changing nature and uses of fugal composition and the various meanings of the word as understood by musicians of each era.

1. A classic fugue analysed.

2. Medieval and Renaissance vocal music.

3. 16th-century instrumental music.

4. 17th century.

5. The golden age: early 18th century.

6. Late 18th century.

7. The romantic era.

8. 20th century.

BIBLIOGRAPHY

PAUL WALKER

Fugue

1. A classic fugue analysed.

The fugue in C minor from book 1 of Bach’s ‘48’ (ex.1) is now generally described by English speakers as follows.

The fugue is for three voices, which may be labelled soprano, alto and bass, and the independence and integrity of each are strictly maintained until the last two bars, when chords are introduced to lend fullness and finality. A single voice, the alto, begins the fugue by stating the ‘subject’. The subject is in the tonic key: it begins on the tonic note C, emphasizes the dominant note G (downbeat of bar 2) and ends on the mediant note (downbeat of bar 3). Once the subject has been stated in its entirety, the second voice (the soprano) enters with the same subject, but transposed to the key of the dominant. This second statement is termed the ‘answer’. Such a transposition often requires, as here, that the original intervals of the subject be altered in order to keep the answer close to the tonic key. More specifically, whereas tonic note is answered by dominant note (i.e. transposed up a 5th or down a 4th), dominant note is answered by tonic rather than by supertonic. In this particular answer, the second note is an exact intervallic reproduction, producing F and signalling the key of the dominant, G minor, but the fourth note is changed from D (supertonic) to C (tonic). All other intervals from the fifth note to the end of the answer are exact renderings of the subject’s intervals. An answer of this sort, in which intervals are altered to remain close to the tonic key, is called a ‘tonal answer’. Any answer in which no intervals of the subject are altered is called a ‘real answer’.

While voice 2 states the answer, voice 1 continues with counterpoint against it. This counterpoint may, as here, be material that returns frequently during the course of the piece, usually as counterpoint to the subject, or it may present material that never returns. Especially in the former case, this thematic material is called a ‘countersubject’. Both answer and countersubject conclude on the downbeat of bar 5, at which point both continue in counterpoint for two bars without stating either the subject or the countersubject in complete form. These two bars constitute what is often called a ‘codetta’. Although neither thematic unit is present in its entirety, the material in voice 2 is a melodic sequence based on the opening motif of the subject, and voice 1 contains scalar passages reminiscent (although in contrary motion) of the countersubject. The final voice enters with the subject (in its original, not its answer, form) at the beginning of bar 7, accompanied by voice 2 with the countersubject. Voice 1 states yet another countersubject, though one that is treated rather freely during the course of the fugue. All three – subject, countersubject 1 and countersubject 2 – end with the downbeat of bar 9.

The opening eight bars make up the fugue’s ‘exposition’. Standard requirements of a fugal exposition are that (1) the voices enter one by one with the subject, each waiting until the preceding voice has completed its statement before entering; (2) each voice enter with the subject, in either subject or answer form, only once (occasionally the first voice to enter may restate the subject at the end of the exposition); and (3) the entries alternate between subject and answer statements. Additional options are that (1) the first statement of the answer may be accompanied by a countersubject, which is then stated in turn by all voices (except the last) as accompaniment to the next statement of the subject; and (2) there may be a codetta between statements 1 and 2 and statement(s) 3 (and 4).

An exposition is the most strictly regulated portion of a fugue. The remainder is understood to be an alternation between sections in which the subject is stated in its complete form by one or more voices and sections in which it is not present in its complete form. The latter, called ‘episodes’, may or may not take any of their motivic material from the subject or countersubject. Complete statements of the subject may take place in keys other than the tonic, in which case episodes serve to modulate to and from those keys. Statements may also incorporate some learned contrapuntal device that alters the subject in some way but leaves it complete and recognizable. These devices include augmentation (the slowing down, generally by a factor of two, of the original note values), diminution (halving or quartering the note values), inversion (stating the subject upside down) and stretto (introducing a second statement before the first has finished). It is generally understood that the fugue will end with some sort of statement of the subject in the tonic key. Any material following that statement is termed a coda.

Beginning with bar 9, Bach’s C minor fugue proceeds as follows: there are four episodes (bars 9–10, 13–14, 17–19 and 22–6). Each takes its thematic material from the opening five-note motif of the subject and the scalar passages of quavers and semiquavers in the two countersubjects. These motifs are generally treated in melodic sequence. In addition, the first two episodes modulate to and from the key of the relative major, E. The complete statements of the subject that appear in between involve in each case subject and two countersubjects distributed among the three voices. In bars 11–12 (in E) the soprano carries the subject, in 15–16 the alto, in 20–21 the soprano again, and in 26–8 the bass. After a brief connecting passage the final statement of the subject, in its original form and at its original pitch, is stated by the soprano over a C pedal point in the bass and accompanied by a few full chords in the alto. The entire fugue appears in ex.1. Most elements of a ‘textbook’ fugue are present in Bach’s C minor fugue. One of its most attractive features is its thematic tightness, that is, the presence of material from the subject or one of the countersubjects in virtually any voice at any point in the fugue. Also present is a modulation to a related key with the subject stated in that key. What this particular fugue lacks is the use of any of the contrapuntal devices enumerated above.

Fugue

2. Medieval and Renaissance vocal music.

(i) 14th and 15th centuries.

The words ‘fuga’, ‘chace’ and ‘caccia’ all denote the chase or hunt, and in the 14th century all acquired the same musical meaning, namely a piece of music consisting either entirely or principally of two or more voices in canon. Canonic technique was, along with Stimmtausch, the earliest type of imitative counterpoint in Western music, and it may therefore fairly be said that the word ‘fugue’ has been associated with imitative techniques since their first formulation. By the 15th century, ‘chace’ and ‘caccia’ had largely fallen from use and ‘fugue’ became the term of choice for any piece in which all voices participated in the canonic performance of a single melodic line (see, for example, the fugues by Oswald von Wolkenstein).

As early as the mid-15th century, however, ‘fugue’ had begun to take on new meanings. As canonic technique came increasingly to be incorporated into pieces that also included non-canonic voices, musicians often continued to apply the word, though not to the piece as a whole; they reserved it instead for the canonic voices. Also at this time, musicians began to use ‘fugue’ to designate the compositional technique itself. Johannes Tinctoris, in his dictionary of musical terms written about 1472, defined it as ‘the sameness [idemtitas] of the voice parts in a composition. The notes and rests of the voice parts are identical in [rhythmic] value, name [i.e. hexachord syllable], shape and sometimes even location on the staff’. Here fugue is not a piece of music or group of voices governed by canonic technique; it is the technique itself, the quality of having made the voice parts identical. Perhaps the best-known use of the word in this sense is Josquin des Prez’s Missa ad fugam, or ‘mass by means of fugue’.

(ii) 16th century.

During the 15th century, as composers gradually abandoned the compositional process of writing one voice at a time above a cantus firmus in favour of the simultaneous composition of all voices a few bars at a time, the point of imitation began to replace canonic writing as the pre-eminent technique of imitative counterpoint. To write a motet or mass movement using this technique, the composer first created for each phrase of text a musical phrase that fitted its Latin declamation well. The piece then proceeded as a series of imitative sections, each devoted to its own textual/musical phrase which was treated in a manner similar to (if much freer than) the fugal exposition described in §1 above. These imitative sections, usually referred to today as ‘points of imitation’ but called ‘fugues’ by musicians of the time, might also alternate with occasional homophonic sections for contrast. A classic early example of a piece composed in this manner is Josquin’s four-voice Ave Maria … virgo serena. Musicians never adopted the word ‘fugue’ as a genre designation for such pieces, however. The first composers to import point-of-imitation technique into instrumental music – beginning with the Musica nova (1540²²) of Julio Segni, Willaert and others – chose instead the designation ‘ricercar’, a word meaning ‘to seek out’ or ‘to search’. Throughout the 16th century, only the strictly canonic piece might bear the genre designation ‘fugue’.

North of the Alps, composers of the post-Josquin generation, most notably Clemens non Papa and Nicolas Gombert, made point-of-imitation technique the cornerstone of their style. As described by the German theorist Gallus Dressler, an enthusiast for the music of Clemens, in his manuscript treatise Praecepta musicae poeticae dated 1563, a ‘fugue’ (i.e. point of imitation) that appeared at the beginning of a piece needed to be constructed in such a way that the mode of the composition was made clear at the outset. This meant that the melodic motion of the voices should emphasize the important modal notes of final, dominant, mediant and psalm tone tenor(s), and that the imitation should show a certain clarity of structure. As a result the opening ‘fugue’ of a 16th-century motet resembles in many respects the exposition of an 18th-century fugue: its voices are most likely to enter on final (tonic) and dominant, its theme is also likely to feature those notes prominently, and each voice is likely to wait until the previous one has completed its thematic statement before entering.

Dressler borrowed the tripartite division of beginning (exordium), middle (medium) and end (finis) from classical rhetoric to describe a composition’s overall structure, and indicated that ‘fugues’ appearing in the body of the piece (i.e. the medium) could be handled much more freely than the opening one (which Dressler defined as the exordium). This freedom extended to the allowing of thematic entrances on notes other than final and dominant, the greater altering of the theme from statement to statement, the incorporation into the theme of notes ‘outside the mode’, and considerable use of stretto. For the finis, however, the composition should close with a strong reaffirmation of the mode. Here again certain parallels can be drawn, this time between the structure of a motet and that of an 18th-century fugue: both begin and end ‘in the key’ (or mode) and with greater regularity but may wander (i.e. touch on other notes or keys) and behave more freely in the body of the composition. Most of the motets of Clemens and Gombert fit Dressler’s model well.

South of the Alps, meanwhile, Clemens’s and Gombert’s Netherlandish contemporary Adrian Willaert and his Italian pupil Gioseffo Zarlino took a different attitude towards imitative counterpoint and attempted instead to preserve Tinctoris’s 15th-century definition of fugue as exact imitation. In his Istitutioni harmoniche (1558) Zarlino subdivided imitative counterpoint into four categories, for which he coined the expressions fuga legata, fuga sciolta, imitatione legata and imitatione sciolta. Whereas musicians in the north had already begun to label all imitative counterpoint ‘fugue’, Zarlino insisted that the word be reserved exclusively for instances in which the following voice (which he called consequente) reproduced exactly all the intervals and rhythmic values of the preceding voice (guida). Imitatione should refer to instances when the consequente did not reproduce the guidaexactly. The adjectives legata and sciolta then distinguished further between, respectively, passages in which the consequentecontinued to imitate the guida from beginning to end of the piece, and those in which the imitation was broken off at some point. Zarlino also allowed for both fuga and imitatione in contrary motion, for which he offered the modifier per arsin et thesin (a Greek expression literally designating upbeats and downbeats).

Zarlino pointed out that fuga was possible only when the consequentewas a perfect interval from the guida. This requirement was a direct descendant of Tinctoris’s insistence that the solmization syllables of the two voices be identical, which restricted the imitation to the three hexachords. However, a perfect interval does not guarantee exactness of imitation. For instance, any imitative counterpoint written at the 4th or 5th can be melodically exact only so long as the voices remain within the bounds of their respective hexachords. Thus, if Zarlino’s distinction between exact and inexact replication is to be strictly maintained, it must be conceded that his technique of imitation can take place at any interval, perfect or imperfect.

Scholars are not in full agreement about whether Zarlino meant to allow for the technique of imitatione at a perfect interval, but in any case the theorist himself seems to have recognized a conflict between categories of imitative counterpoint based on the degree of exactness of replication and those based on imitation at perfect as opposed to imperfect intervals. To address this problem, Zarlino created a final category, which he called ‘part fugue and part imitation’ but admitted was often called fugue. The example he offered involves two voices that imitate each other canonically at the 5th. At only three places does the second voice answer inexactly, and in each case the inexactness consists of an F answered by a B natural rather than the B that would be required for precise replication.

Willaert’s music reflects Zarlino’s thinking closely in its penchant for introducing imitative counterpoint horizontally into a composition voice by voice. The point of imitation almost never serves as the building-block for Willaert’s mature works as it does for the works of Clemens and Gombert, whereas canon is frequently encountered (see, for example, Verbum supernum and Praeter rerum seriem from Musica nova, 1559). Nevertheless, despite Willaert’s prestige and the lasting influence of Zarlino’s writings, the wave of the future was not canon but the point of imitation, which allowed a much more flexible treatment of the words and thus fitted better with humanistic ideals about text expression and clarity of declamation. In the end, therefore, Zarlino’s role in the history of fugue is a peculiar one. On the one hand, the traditional idea of fugue as precision of imitation and its manifestation in canonic writing quickly faded. Yet, at the same time, the categories of imitative counterpoint which he invented lived on, though with very different meanings from those intended by their creator.

As the 16th century drew to its close, the rise of humanism, with its emphasis on clarity of text, caused many musicians, especially in Italy, to question altogether the suitability of fugal techniques in vocal music, since their use virtually ensured that different words were being sung simultaneously by the various parts. By the 1580s, when Vincenzo Galilei began to call for the abandonment of fugal writing, it was apparent that the most important and innovatory genre of music was the Italian madrigal, in which fugue played no significant role. Even such conservative composers as Palestrina and Lassus began, partly under the influence of Counter-Reformation concerns for textual clarity, to show much greater caution in introducing points of imitation into their motets, in contrast to its almost ubiquitous presence in the works of Clemens and Gombert. Introduce it they did, however. In fact, Lassus continued to be cited by German theorists writing about fugue throughout the first half of the 17th century, and in the 1660s Christoph Bernhard chose Palestrina’s offertories to illustrate his chapters on fugue. The first major composers of vocal music in the new Baroque style, however, all but abandoned fugal techniques for their seconda pratica music. (A piece such as Monteverdi’s Piagne e sospira, from the fourth book of madrigals, is a rare exception.) Fugue found no place in the new genres of opera, monody or cantata, nor, surprisingly, did it play a role in the early development of the oratorio. Even such a retrospective collection as Schütz’s Geistliche Chor-Music (1648) is of little significance in the history of imitative counterpoint. It was not until towards the end of the 17th century that fugue once again re-entered the sphere of vocal music in a significant way. By that time, a great deal had changed.

Fugue

3. 16th-century instrumental music.

Although histories of Western music tend to emphasize a sharp division in musical style about 1600, the history of fugal techniques in instrumental music cuts across this divide. A direct and continuous line of development can be traced from the ricercares of Segni’s Musica nova of 1540 to the fugues of Das wohltemperirte Clavier. Surprisingly, this development has been less well mapped out than one might expect. Perhaps the most troublesome of the several difficulties inherent in the study is the issue of genre and terminology. Very few of these pieces written before 1700 were designated as fugues, and other designations abound. The best way to approach this body of music and to tie all the compositions together is to consider fugue in its guise as a compositional technique.

From its inception the imitative ricercare seems to have carried connotations of learnedness – that is, it served either as compositional study or, in Newcomb’s phrase, as ‘intellectual chamber music’. Michael Praetorius, writing at the beginning of the next century, described its function as follows (his use of ‘fugue’ is discussed below, §4(i)):

Fugue: Ricercar
Fugues are nothing more than … repeated echoes of the same theme on different degrees [of the scale], succeeding each other through the use of rests… In Italy they are called ricercars. RICERCARE is the same thing as ‘to investigate’, ‘to look for’, ‘to seek out’, ‘to research diligently’ and ‘to examine thoroughly’. For in constructing a good fugue one must with special diligence and careful thought seek to bring together as many ways as possible in which the same [material] can be combined with itself, interwoven, duplicated, [used] in direct and contrary motion; [in short,] brought together in an orderly, artistic and graceful way and carried through to the end.

Because some collections were published in partbooks, some in open score, and a few in keyboard score, earlier scholars (e.g. Apel) attempted to uncover a stylist distinction between those collections intended for instrumental ensemble performance (i.e. in partbooks) and those intended for keyboard (in score or keyboard notation). More recently, Newcomb has argued against such a distinction and has noted instead consistency of style and purpose that cuts across the differences of format. Interest in the later classic fugue has also led scholars frequently to overemphasize the presence of monothematicism in these works. The 16th-century ricercare makes much better sense if understood as the instrumental counterpart to the motet in both seriousness of purpose and severity of contrapuntal style; indeed, it represents the first genre of purely instrumental music to challenge the sophistication of Flemish vocal polyphony.

Furthermore, because it had no text, the instrumental ricercare escaped the humanistic criticism levelled at vocal fugue, and composers felt free to embrace the genre and to continue to explore new possibilities. Most 16th-century ricercares proceed, like the imitative motet, as a series of points of imitation, each based on its own theme. Also reminiscent of the motet in these cases is a frequent emphasis on the opening point as the longest and most systematic. The two genres differ in several respects, however. To compensate for the ricercare’s lack of text, composers sought out a more purely musical solution to the problem of continuity and structural logic, for which they turned to techniques of thematic manipulation. A point may be quite long in comparison to its vocal counterpart, therefore, with many more thematic statements. A much less tidy compartmentalization of themes each to its own point is found, and considerably greater and more systematic use of the contrapuntal devices of augmentation, diminution, inversion and stretto is to be expected.

Adding to the impression of these ricercares as systematic pieces for study or the display of compositional skill is their frequent publication in collections devoted to the genre, usually by a single composer, and often organized with exactly one ricercare in each mode. Towards the end of the 20th century several such collections of 16th-century ricercares once thought lost were rediscovered, and a re-evaluation of the genre was undertaken by Newcomb, who identified two distinct ‘schools’ of ricercare composition in the 16th and early 17th centuries, the first centred in Venice, the second in Ferrara and, later, Naples. The most important composers in the first group are Willaert, Girolamo Cavazzoni, Buus, Padovano, Merulo and Andrea Gabrieli; the second includes Luzzaschi, Jacques Brunel, Macque, Mayone and Frescobaldi. Although these works differ in significant respects from the classic fugue of the 18th century, they certainly represent the oldest instrumental works to merit detailed study in a history of fugue.

Fugue

4. 17th century.

During the first half of the 17th century, fugue as a compositional technique might have seemed to many musicians to be well on its way to the historical scrap-heap as the most pre-eminent composers focussed increasingly on opera, cantata and oratorio. And yet Monteverdi had staked his defence of modern music on the premise that the old style and its technical basis remained valid and worthy of attention. Certainly the ricercare’s role as compositional study, and its absence of text, made it well suited for continued cultivation of the stile antico. In addition to its museum-piece status, however, fugue continued to evolve, especially in the hands of organists and violinists. By around mid-century most of the characteristics of the classic fugue as we recognize it today were in place, and as the century progressed to its conclusion they gradually reintegrated themselves into most genres of music and most parts of Europe.

(i) Fugue and genre in organ music, 1600–20.

(ii) Theory: terminology, structure.

(iii) Second half of the century.

Fugue, §4: 17th century

(i) Fugue and genre in organ music, 1600–20.

The imitative ricercare had been throughout the 16th century an Italian phenomenon, cultivated exclusively by composers – either Italian or northern – working in Italy. By the early years of the new century, however, this monopoly had come to an end as keyboard composers working in Germany and the Low Countries also began to produce fugal works characterized by rigorous handling of counterpoint, extended length, carefully controlled dissonance and strictly maintained part-writing. With the wider geographic cultivation of this genre came a variety of labels for such works. The most important Italian composer of such pieces in the early 17th century, Frescobaldi, used at various times the designations fantasia, ricercare, canzona and capriccio. Roughly speaking, these four can be grouped according to the nature of their thematic material into the slower and more ponderous (fantasia and ricercare) and the quicker and livelier (canzona and capriccio). The first important German composer to cultivate the serious fugue was Hassler (a pupil of Andrea Gabrieli), who, judging from surviving manuscripts, chose two designations, ricercare and fugue. In the Low Countries Sweelinck and Peeter Cornet preferred ‘fantasia’.

It is not certain how the various composers came to choose such a variety of titles for pieces that are more alike than different. Sweelinck presumably chose ‘fantasia’ under the influence of the English, who preferred that designation for most of their untexted pieces without vocal models. (Frescobaldi’s use of the term followed shortly after a visit he made to the Low Countries.) Praetorius’s definition of ricercare quoted above implies that ‘fugue’ was appropriated because of its connotations of seriousness and sophistication. ‘Fugue’ may have appealed also to the Germans because of its international character, as opposed to the very Italian ‘ricercare’. Frescobaldi’s use of ‘canzona’ and ‘capriccio’ introduces yet another layer into the terminological morass. In both of these cases, the kind of lively thematic material traditionally associated with the canzona alla francese is treated with the contrapuntal sophistication and length of the ricercare.

Probably the most significant compositional trend to emerge in serious fugal works at the beginning of the 17th century was an emphasis on monothematicism. Because monothematicism could easily lead to tediousness in a long work, however, composers sought to maintain interest by varying their treatment of the theme as the work progressed. Two approaches predominated. For the first a series of sections, neatly dovetailed to create a continuous flow from beginning to end, proceeds with either a new counter-theme or a new contrapuntal device applied to the principal theme in each new section. A classic example is Sweelinck’s Fantasia chromatica. See Table 1.

In the second category, best exemplified by many of Frescobaldi’s works, the sections are fewer but not dovetailed and the principal theme is rhythmically transformed from one to the next, usually including at some point a change of metre from duple to triple. Such pieces are sometimes referred to as ‘variation canzonas’ or ‘variation fugues’.

Both these types show many elements of the later classic fugue: severity of contrapuntal style, strictness of part-writing, greater regularity of exposition than in the old ricercare (about which more below), thematic hierarchy with a single principal theme, and emphasis on learned devices. Overall structure, however, differs considerably. Whereas the classic fugue proceeds as a series of well-defined sections alternating between episodes and self-contained groups of thematic statements, the early 17th-century ‘learned fugue’ proceeds as a kind of continuous unfolding of contrapuntal possibilities with only a few major cadences to mark off sections.

Certain German musicians of the early 17th century also began to designate contrapuntally free, short pieces fugues. These works traced their ancestry to the lively Parisian chansons of the previous century, instrumental intabulations and arrangements of which Italian composers had designated canzone alla francese. Both the chanson and the canzona often consisted of a short series of brief sections, each beginning with simple imitative entries but quickly lapsing into chords or melody-and-accompaniment texture. The Zarlinian rules of counterpoint were more often flouted than followed, and keyboard canzonas often showed in addition little regard for strictness of part-writing and frequent lapses into stock keyboard figuration. Bernhard Schmid the younger, in his Tabulatur Buch of 1607, included 12 pieces written by Andrea Gabrieli, Adriano Banchieri and other Italians that he described as ‘Fugues or, as the Italians name them, Canzone alla francese’. A similar tablature book was published in 1617 by Johann Woltz, who included in it 20 fugues from the pen of Simon Lohet, a Netherlander who had served as organist to the Württemberg court in Stuttgart until his death in 1611. Although modest in nearly every respect, Lohet’s are the first group of non-canonic pieces to be called fugues. It is characteristic of this experimental age that ‘fugue’ could serve as a genre designation for these simple, almost banal works while Hassler and Praetorius were reserving it for pieces of the most sophisticated, serious sort.

Fugue, §4: 17th century

(ii) Theory: terminology, structure.

Zarlino’s attempt to restrict the word’s meaning to imitative counterpoint in which the imitation is exact failed to take hold, despite later Italian theorists’ attempts to preserve his terminology. What these later writers did instead (inadvertently, it appears) was to keep Zarlino’s restriction of fugue to the perfect intervals but to suppress the ideal of exactness of imitation. Because the two are not always identical, the end result of their change of emphasis was that exact imitation came to be replaced by the relationship between fugue and mode. In other words, for early 17th-century theorists the technique of fugue took place at a perfect interval not in order that the intervals might remain identical but in order to emphasize final and dominant notes of the mode.

To this restriction was then added, by Girolamo Diruta in 1609, the theory of tonal answers. Both Zarlino and Dressler had insisted that modal clarity was important in the beginning of a work, Zarlino by insisting that the voices begin on final and dominant of the mode, Dressler by advising the composer to see to it that the thematic material emphasized those and other important modal notes. Diruta, a disciple of Zarlino, took these admonitions one step further and insisted that they be applied not only to the opening theme but to its answer as well. As a result, given that theme and answer were to begin on final and dominant (in either order) and were to emphasize important modal notes, and given that the octave was divided unevenly into a 5th and a 4th, then the answer had to be altered such that 5th was answered by 4th and 4th by 5th. The rather general advice of the mid-16th-century musicians had become by the early 17th century a specific, strict edict.

Progressive musicans of the time quickly adopted Diruta’s theory. Marco Scacchi, for instance, used it repeatedly in his Cribrum musicum of 1643 to fault Paul Siefert’s handling of the stile antico in a collection of psalm settings published in 1640. Siefert’s defence that he was simply doing what his teacher, Sweelinck, had taught him was probably true, given the freedom with which most 16th-century composers handled such imitation, but by the 1640s the majority of musicians considered tonal answers a virtual necessity to ensure modal clarity. Schütz’s early collection of double-choir psalms (published only a few years after his study with Giovanni Gabrieli) and his Geistliche Chor-Music of 1648 (possibly published as a practical response to the Scacchi–Siefert quarrel) contain numerous instances of opening tonal answers and not a single real answer.

Musicians in the north had never accepted Zarlino’s definitions of fugue and imitation, and continued instead to experiment with their own subdivisions of imitative counterpoint. They generally referred to all imitative counterpoint as fugue, which most writers divided into canonic (variously called fuga ligata, totalis or imaginaria) and non-canonic (fuga soluta, partialis or realis). Sethus Calvisius further subdivided the latter into fuga ejusdem modulationis and fuga diversae modulationis, or fugue of either similar or diverse melodic motion, which he understood to mean, respectively, imitative counterpoint in which the melodic contour of the theme was maintained (whether exactly or approximately) by the answering voices and that in which imitation was perceived to be present even though melodic contour was not maintained (his example was the opening of the Lassus motet Inclina Domine). Joachim Burmeister, by contrast, categorized the techniques of non-canonic imitation based on rhetorical terminology, although he seems to have fitted fugal techniques to his chosen rhetorical figures rather than subdividing fugal techniques first and then naming them. Those figures he chose to relate to fugue were metalepsis, for which he chose imitation with two themes; hypallagē, imitation in inversion; and apocopē, imitation of a very brief head-motif. Calvisius even went so far as to allow ‘fugue’ to designate virtually any repetition of musical material in a composition, including ostinato technique and the answering back and forth of polyphonic textures in double-choir music. Others were more restrictive. Burmeister, for instance, insisted that only if all voices of the texture participated in the imitation of a theme should the name ‘fugue’ be used.

None of these schemes for subdividing non-canonic imitation took firm root, however, and the Italian theory of fugue as imitative counterpoint handled according to proper treatment of the mode began to find wide acceptance. With this understanding of fugue as a basis, the south German writer Wolfgang Schonsleder distinguished in 1631 between ‘long [fugues] that are worked out’ and ‘short ones or imitations’, and he suggested as paradigms works by Palestrina and Frescobaldi for the former category and duets by Monteverdi for the latter. With this division of imitative techniques into canon, fugue and imitation, the essence of our understanding of these words is in place.

All the above definitions refer to fugue as a compositional technique involving imitative counterpoint. The word continued to be applied also to pieces of music, but here again there was no universal agreement. Musicians had of course inherited from the late Middle Ages the idea of fugue as canon, to which in the Renaissance they added fugue as a point of imitation. The former category proved surprisingly durable and was still being used by German school treatises as late as the early 18th century. (It is interesting to speculate whether Bach’s first encounter with the word was when he sang canons while a schoolboy in Ohrdruf.) Fugue as a single point of imitation also survived the Baroque. Praetorius, for instance, defined motet style as the alternation of ‘harmonies and fugues’ and the canzona as a textless piece ‘with brief fugues and artful fantasies’. Keyboard composers in the early 17th century (e.g. Lohet in south Germany and Heinrich Scheidemann in the north) sometimes wrote short pieces entitled ‘fugue’ that consisted of nothing more than a single point of imitation. Well into the 18th century French organists designated as fugues similarly brief imitative works, and Henry Purcell understood the word thus in his discussion of fugue published by Playford in 1694. Perhaps the last such use of the word can be traced to early 19th-century New England, where William Billings and his colleagues took up the form of the ‘Fuging tune’, which had first become popular in 18th-century English parish churches.

As already noted, German musicians at the beginning of the 17th century introduced ‘fugue’ as a genre designation for non-canonic pieces widely disparate in style and intent. One final meaning of the word turns up in Italy about 1600, where a few musicians used it to refer to the thematic material of an imitative piece (e.g. ‘Ricercar primo tono con tre fughe’). Perhaps the most famous composer to use the word in this way was Monteverdi, whose six-voice Missa da capella (1610) is composed with ten ‘fugues’, derived from Gombert’s motet In illo tempore, which are spelt out even before the piece begins.

The origin of the textbook fugue’s structural principles, until recently obscure, can now be traced with some certainty. In the early years of the 17th century the two most common models were the motet, with its series of points of imitation each based on a different theme, and the extended keyboard fugue, with its longer sections, few cadences, and almost continuous presence of the theme. What was lacking was a series of much shorter points of imitation (or, in modern terms, groups of thematic statements) all based on the same theme but set apart from each other in some way.

The earliest theoretical source to describe such a scheme is a manuscript treatise, Sequuntur regulae compositionis, surviving in several copies and now thought to be the work of Antonio Bertali, a north Italian violinist and Kapellmeister of the imperial court in Vienna from 1649 to 1669. Bertali’s text treats the study of counterpoint as a progression of species counterpoint leading to the writing of fugue, as does Fux’s classic Gradus ad Parnassum. Bertali’s treatise outlines for fugal composition the following structural plan: (1) once a theme has been selected, it should be assigned to an appropriate mode. (Note the inversion of the modern approach, which is to select the key first, then devise a theme for it.) (2) The opening point of imitation brings in the theme in systematic fashion in all voices (beginning on final and dominant of the mode), after which free counterpoint leads to the first cadence. (3) Successive points of imitation, all of course based on the same theme, should be distinguished in some fashion, for which the author recommends exchanging starting notes among the voices or switching the order of entry of the voices. (4) In the body of the composition, the theme may be brought in on notes other than final or dominant. (5) Stretto is particularly prized, but only in the middle or towards the end of the piece, since it generally requires thematic alteration and does not allow for careful treatment of mode. (6) The whole piece will generally consist of four or five such sections, with the theme presented prominently at the very end. Here, then, we find most elements of the modern fugue: carefully worked-out opening point of imitation (i.e. exposition), groups of thematic statements separated from each other (by free counterpoint), variety among the thematic groups, possible movement to closely related keys for later groups (described as ‘beginning the theme on other notes’), fondness for stretto and prominence of the theme at the end of the piece. Lacking only are the countersubject and the well-defined episode.

This model obtains, not in keyboard works of the period, but in pieces entitled canzona or sonata and composed by Bertali’s north Italian violinist colleagues. The fugues found in these works do not generally form the entire piece, but rather one section (often the first) of a multi-section work. One of the first composers of such pieces may be Tarquinio Merula, whose Primo libro delle canzoni of 1615 already includes several. Massimiliano Neri and Giovanni Legrenzi also wrote sonatas incorporating such fugues. The contibution of all these composers to the history of fugue merits further study.

Fugue, §4: 17th century

(iii) Second half of the century.

Much remains to be learnt about the history of fugal composition in the second half of the 17th century, and this lack of knowledge has led some scholars to attribute to Bach and Handel innovations in fugal writing with which they should not be credited. Only in the realm of keyboard music is there a relatively complete and well-rounded picture of the music of the time. There is, however, no questioning that, with respect to fugal composition, the years 1650–1700 witnessed the gradual but complete passing of the mantle from Italy to Germany, where it largely remained into the 20th century. Several factors contributed to this transfer: Italy’s gradual abandonment of interest in keyboard music and inexorable move towards paramountcy of opera; Germany’s continued fascination with counterpoint (even in the music of such early Baroque composers as Schütz); and the eagerness with which German musicians learnt from such Italian teachers as Frescobaldi and Bertali.

Perhaps the key figure in this transfer of fugal ‘authority’ from south to north was the Stuttgart-born Johann Jacob Froberger, who studied with Frescobaldi, worked for the Holy Roman Emperor in Vienna (at the same time as Bertali), and during the 1650s travelled widely to other parts of Germany, France and even England. The four autograph manuscripts of keyboard works that Froberger presented to the Emperor Ferdinand III in the years around 1650 include easily the best fugal compositions written at a time when most of Europe’s leading composers were absorbed with opera, cantata and oratorio. Froberger’s fugues follow closely the example of Frescobaldi and comprise the same four genre designations of ricercare, fantasia, canzona and capriccio, understood in the same way. Of even greater historical significance than the quality of these works may be Froberger’s role in awakening interest in fugal composition among composers north of the Alps. Inspired by Froberger’s example the Frenchman François Roberday published in 1660 a volume of Fugues, et caprices explicitly modelled after the composer’s variation fugues and even including one of Froberger’s own pieces. French composers did not follow Roberday’s lead, but in Germany Froberger’s influence bore spectacular fruit. Through his personal contacts with Schütz’s pupil Matthias Weckmann and others, he reawakened the interest of the Germans in large-scale fugal composition. In north Germany, where Weckmann spent most of his career, this led to significant experimentation with fugue and invertible counterpoint. In central Germany, where Froberger’s music circulated widely in manuscript, the interest in fugal writing led directly to Bach and Handel.

The unbroken tradition of serious fugal composition begun in the 1540s continued through this period and, indeed, well into the 18th century. Composers retained the two types developed by keyboard composers early in the 17th century – namely, Sweelinck and Hassler’s continuous piece in a single metre with contrapuntal devices, and the ‘variation fugue’ cultivated by Frescobaldi and Froberger. Italians who composed such extended fugal works include Fasolo, Battiferri, Fabrizio Fontana and Pasquini. Among the many German contributions one might mention as particularly significant the set of 12 ricercares compiled by Poglietti and keyboard fugues (variously designated) by Weckmann, J. Krieger and N.A. Strungk (a complete list is given in Riedel, 1979).

Also during this half-century fugue took on a much greater significance within the genre of toccata and its sometime equivalent, praeludium. Improvisation and freedom had traditionally been among the genre’s principal characteristics, but since the 16th century many keyboard works entitled toccata had included relatively freely imitative sections interspersed among the more improvisatory passage-work. Froberger also began to bring a contrapuntally freer version of the variation fugue into this genre, with the two or more fugal sections based on rhythmic variants of the same theme. Undoubtedly the best such pieces are the organ praeludia of Buxtehude. Although it was not the model he ultimately chose for most of his fugal writing, Bach himself wrote a few pieces incorporating fugue in this way (e.g. the E major Praeludium bwv566).

Probably the most important innovation in fugue during the period under discussion was developed in the north German cities of Hamburg and Lübeck by a circle of musicians that included Weckmann, Buxtehude, Reincken and Christoph Bernhard. In the 1660s and 70s these men discovered a common interest in the compositional potential of combining fugal writing (to which they had been awakened most probably by Froberger) with invertible counterpoint, about which they had learnt through Zarlino’s Istitutione harmoniche as taught by Sweelinck to their teachers Jacob Praetorius (ii) and Heinrich Scheidemann. This combination led to two significant and related innovations: the idea of countersubject and the so-called permutation fugue.

An incipient form of both phenomena can be seen in the fugue from the fifth suite of Reincken’s Hortus musicus (1688) for instrumental ensemble, whose structure is shown in Table 1 (where A represents the opening theme, B the second theme, ‘xxx’ free counterpoint, and dux and comes the two forms, subject and tonal answer, of theme A). Though tediously formulaic, Reincken’s fugue employs Bertali’s groups of thematic statements (five altogether), with variety from one to the next provided by the exchanging of starting notes (S I begins the first group with the dux form, but begins the second with the comes form). To this is added a second theme that accompanies every statement of the first theme except the opening one. If episodes were to be added between groups of thematic statements, and the scheme in general loosened up, the result would bring Reincken’s model very close to the classic 18th-century fugue.

If instead the formulaic nature of Reincken’s model were emphasized by the addition of further themes and the elimination of the free counterpoint, the resulting scheme would be close to that of the earliest Bach vocal fugues, called by modern scholars permutation fugues. The opening fugue from bwv182, Himmelskönig, sei willkommen, for instance, is constructed as shown in Table 2 (A, B, C and D refer to the themes, T and D to entries of theme A on tonic and dominant). The permutation fugue consists of fugue and canon in equal measure. Characteristic of the former is the presence of a fugal exposition, complete with tonal answer, properly spaced entries and strict alternation of tonic and dominant for entries. Characteristic of canon is the near absence of non-thematic material, in that each voice continues with the same material as every other once it has stated the opening theme complete, and returns to the opening theme once it has fully stated all themes. Although the first known piece to fit this description appears to have been composed by Johann Theile for instructional purposes and is found in his treatise Das Musikalisches Kunstbuch, Bach was among the first to employ the technique successfully in a musical context.

Fugue

5. The golden age: early 18th century.

C.P.E. Bach, writing to Forkel about his father in 1775, remarked: ‘Through his own study and reflection alone he became even in his youth a pure and strong fugue writer’. His models, according to Carl Philipp Emanuel, included Froberger, Kerll, Pachelbel, Frescobaldi, J.C.F. Fischer, Strungk, Buxtehude, Reincken, Bruhns and Böhm. Among the results of this study were the following: (1) although his earliest fugues bear a variety of designations, including Canzona (bwv588), Capriccio (bwv993), Praeludium (bwv566) and even Imitatio (from the Fantasia bwv563), Bach seems early on to have settled on fugue as the designation of choice for all pieces based on non-canonic imitation. This choice is not entirely expected; it may reflect the influence of Pachelbel, the teacher of Bach’s older brother (and first teacher) Johann Christoph and the only composer listed above who preferred that designation. (2) After some experimentation with other models for fugal writing, Bach settled for his keyboard or organ fugues on the model ultimately derived from Bertali, but including by this time frequent use of a countersubject and episodes and eventually incorporating tonal harmony and modulation to related keys. (3) Bach paired most of his keyboard fugues with preludes. Praetorius had described in 1619 the practice of improvising a toccata or prelude before a written-out fugal piece, and only towards the end of the 17th century did a few composers begin to attach written-out preludes to their fugues. Bach’s preference for this practice ensured that wherever his keyboard fugues have been admired the prelude and fugue has served as one of the most important genres to incorporate fugal writing. (4) For his earliest vocal fugues, Bach chose in place of this model the permutation fugue, which he probably encountered through the treatises of Theile.

The mature Bach employed fugue in his music for organ, for keyboard (harpsichord) and for voices. The harpsichord fugues are in general relatively brief and tight in construction; they would seem to have been intended primarily for study and teaching. Those for the organ are usually grander and more expansive; they would seem to have been intended for public performance. For his mature vocal fugues (e.g. in the B minor Mass) Bach eventually abandoned the permutation fugue model in favour of that of the keyboard fugues.

Like all masterly bodies of music, Bach’s fugues resist easy summary, generalization and classification. A few attempts have however been made to subdivide these works further. Kunze proposed that the fugues of Das wohltemperirte Clavier be categorized on the basis of musical style: fuga pathetica, with predominantly slow movement and expressive of a certain affect; ricercar-fugue, the ‘artful’ fugue reminiscent of the old ricercare; dance-fugue, based on certain dance idioms; Spielfuge, characterized by idiomatic instrumental writing; and choral- or motet-fugue, which brings together instrumental structure and vocal style. Stauffer has applied Kunze’s plan to the organ fugues, adopting two of the categories (dance-fugue and Spielfuge) but offering in place of the others the allabreve fugue (i.e. derived from the stile antico) and the art fugue (emphasizing learned devices). More recently Dreyfus has questioned the idea of categorization based on style and has proposed instead subdivisions derived from Mattheson’s Der vollkommene Capellmeister and based on the use of contrapuntal procedures: simple fugue, based on only one theme and without invertible counterpoint; double fugue, based on two or more themes treated invertibly; and counterfugue, involving the application of contrary motion, augmentation or diminution to one of the themes.

In contrast to the almost universal esteem accorded Bach’s fugues since at least the early 19th century, those of Handel have been somewhat neglected. Handel’s focus on opera and oratorio, and the relative paucity of keyboard music from his pen, result in a very small number of pieces designated ‘fugue’, the most prominent being the Six Fugues or Voluntarys for the Organ or Harpsichord issued by Walsh in 1735. Handel’s most important contributions to the genre are probably those in the choruses of his oratorios, which differ in only small ways from the keyboard fugues (two of the six keyboard fugues of 1735, for instance, ended up arranged as choruses in Israel in Egypt). In general, Handel’s treatment of fugue is freer and less rigorous than Bach’s: the part-writing (at least of the keyboard fugues) is often loosely handled, the counterpoint is sometimes allowed to relax into thematic statement accompanied by chordal texture, thematic statements are less recognizably grouped, episodes less clearly defined, thematic material less economically used. These characteristics have not universally been considered signs of inferiority: writing in 1789, Burney (History) called Handel ‘perhaps the only great Fuguist exempt from pedantry’. Marpurg in his treatise on fugue (1753–4) subdivided the genre into strict (fuga obligata) and free (fuga libera or soluta) which he associated, without expressing particular preference, with Bach and Handel respectively.

The third great figure of this era for the history of fugue is J.J. Fux, whose Gradus ad Parnassum (1725) remains a classic of fugal theory. The book is written, in Latin, as a dialogue between the author (as pupil) and Palestrina (as teacher); its goal, however, is the writing not of a stile antico motet but of late Baroque fugue, especially Fux’s preferred genre, the fugue with two themes. Fux is probably most famous today for his use of the pedagogical progression from species counterpoint to fugue, but he probably also deserves credit for popularizing the terms ‘subject’ and ‘countersubject’, which he used, in their Latin forms, for the two themes of a fugue. His model for fugal composition, like his use of species counterpoint, derives ultimately from Bertali, although Fux recommends a tripartite structure of only three groups of thematic statements. This model seems intended purely as a way of getting the student started; Fux’s own use of fugue in his music is considerably more imaginative than his somewhat formulaic plan would lead one to expect.

Fugue

6. Late 18th century.

The golden age of fugue was brilliant but short-lived. By the 1750s, during which decade both Bach and Handel died, Enlightenment ideals had brought fugue once again (as had humanistic ideals at the beginning of the Baroque) into disrepute, this time as pedantic and unnatural. Never again would the genre play the central role it had enjoyed in music of the early 18th century. At the same time, however, musicians continued to find fugue and counterpoint important for a composer’s training, just as they had a century and a half earlier, and fugue even made an occasional appearance in music in the new style. In the latter case, its most common role was that of finale, a role it had long played in the Mass, where ‘et in secula seculorum’ and ‘amen’ fugues were a well-established tradition. In addition, composers began to experiment with the insertion of brief fugal imitation, sometimes only a single point of imitation, into works in sonata form and other forms.

Fugue retained its prestige longest in Vienna, aided by the aura surrounding Fux’s bestselling treatise as well as the conservative musical tastes of the city’s Habsburg patrons. The technique figures relatively prominently in the works of most composers, both German and Italian, associated with the Viennese court and churches during the third quarter of the 18th century. G.J. Werner (Haydn’s predecessor at the Esterházy court), G.C. Wagenseil, M.G. Monn, F.L. Gassmann, Nicola Porpora (Haydn’s teacher) and F.X. Richter all incorporated fugues into their instrumental music for chamber ensemble and larger orchestra. Perhaps the most significant of all Viennese contributions to fugue was that of J.G. Albrechtsberger, Beethoven's teacher, who not only assigned fugue a prestigious role in his compositions but wrote one of the most admired counterpoint treatises of the day. Elsewhere interest in fugue waned rapidly. A handful of composers in northern Italy, most notably F.M. Veracini and CA. Campioni, continued to cultivate fugue under the influence of the Bologna theorist G.B. Martini. In Germany J.S. Bach’s fugal legacy was carried forward not primarily by his sons but by his students and admirers, in particular F.W. Marpurg and J.P. Kirnberger.

With the establishment of the so-called Viennese Classical style by Haydn, Mozart and Beethoven, however, fugue’s central role in music came to an end as sonata form and the symphony orchestra quickly rose to a position of dominance. Nevertheless, none of the three composers entirely abandoned fugue. Haydn’s study of the technique seems to have been accomplished on his own using primarily Fux’s Gradus ad Parnassum. In addition to a number of fugues in his masses, fugues serve as finales to several of his instrumental works, including three of the op.20 string quartets, the quartet op.50 no.4 and the symphonies nos.3, 40 and 70. These fugues are finely wrought works in the late Baroque style and suggest that Haydn would probably have been comfortable writing many more if his patrons had desired them. Mozart learnt fugal composition not through any treatise but through the study of other composers’ works: first Haydn and the earlier Viennese instrumental composers, then in 1782 J.S. Bach (the ‘48’) and Handel (probably the Six Fugues or Voluntarys, among other works), to both of which he was introduced by Baron von Swieten. As a result, we find in Mozart fugal finales to string quartets à la Haydn (k168, 173 and 387), as well as independent fugues or preludes and fugues in late Baroque manner, including the Prelude and Fugue for keyboard k394/383a and the Fugue for two pianos four hands k426, later arranged for string quartet as k546. Of course, fugal finales also appear in Mozart’s sacred music, including the C minor Mass k427/417a, and the Requiem. Mozart’s most important contribution to the history of fugue, and certainly his most innovatory, is probably the insertion of fugal imitation into works in sonata form. This category includes perhaps his two best-known instrumental movements incorporating fugal imitation: the finale of the ‘Jupiter’ Symphony and the overture to Die Zauberflöte.

As in so many facets of composition, Beethoven pushed back the boundaries of fugue while integrating it into the new style. He was introduced both to the ‘48’ (through his teacher in Bonn, Neefe) and to a systematic study of counterpoint and fugue (through his later teacher Albrechtsberger). Perhaps the most traditional are the fugal finales Beethoven included in the Missa solemnis; among his instrumental works, by contrast, scarcely a single fully worked-out, traditional fugue is to be found. Instead we find such offerings as the ‘Finale: alla fuga’ of his variation set op.35, on the theme of the last movement of the ‘Eroica’ Symphony. Here Beethoven’s fugal finale begins conventionally enough, but, in a manner reminiscent of Buxtehude’s praeludia, the counterpoint eventually begins to break down and is finally abandoned about two-thirds of the way through the movement. The composer acknowledged his freer approach to fugue in two of his most famous efforts, the finale to the Hammerklavier Sonata op.106, and the Grosse Fuge op.133 (originally conceived as the finale to op.130). He headed the first ‘Fuga … con alcune licenze’, the second ‘tantôt libre, tantôt recherchée’. Like Mozart, Beethoven also introduced fugal imitation into sonata form movements, for instance in place of the first theme group (in the finale of the string quartet op.59 no.3) or as a part of the development (in the opening movement of op.59 no.1).

Fugue emerged from its golden era accompanied by no particular consensus with regard to its rules, definitions or how it ought best to be handled. Musicians who wrote about fugue and counterpoint in the second half of the 18th century continued to focus on the styles and techniques of the late Baroque, but they brought to the task a variety of approaches. One of the most famous of these writers was G.B. Martini of Bologna, renowned as a teacher of counterpoint and sought out by Mozart and many others. In his Esemplare, o sia Saggio … de contrappunto of 1774–6, Martini subsumed all imitative counterpoint under the general heading fugue, which he subdivided into fuga reale (i.e. with a real answer), fuga del tuono (with a tonal answer) and fuga d’imitazione (freer sorts of imitation). He further subdivided the former into canonic (legata) and non-canonic (sciolta). Here we see fugal terminology at the crossroads: words and pairings traceable all the way back to Zarlino (fuga legata and sciolta) side by side with newly paired expressions central to our modern theory (real versus tonal answers). The tripartite division (with additional subdivision) obscures to some extent the more apt one of canon, fugue and imitation, and certainly shows Martini’s respect for traditional Italian terminology. In Austria Fux’s Gradus ad Parnassum continued to find favour among musicians. Beethoven’s teacher Albrechtsberger (Gründliche Anweisung zur Composition, 1790) was only the best-known of a number of Austrian pedagogues who, either directly or indirectly under Fux’s influence, likewise wrote texts on counterpoint and fugue.

Meanwhile the predominant influence on fugal theory in Germany remained J.S. Bach and his many pupils. Whereas Bach’s most progressive sons, Carl Philipp Emanuel and Johann Christian, showed in their compositions little interest in fugue, two members of the Bach circle with more conservative bent, F.W. Marpurg (Abhandlung von der Fuge, 1753–4) and J.P. Kirnberger (Die Kunst des reinen Satzes, 1771–9), made important contributions to its theory. Marpurg, author of the first full-length treatise to include ‘fugue’ in its title, divided imitative counterpoint as we do today into canon, fugue and imitation. He insisted that fugue was ‘actual, proper or regular’ only if it was constructed according to the rules; otherwise, it was ‘figurative, improper or irregular’. Five essential characteristics defined fugue, and these required proper handling for a piece to earn the designation ‘proper’: Führer (dux) and Gefährte (comes), Wiederschlag (i.e. regularity of opening imitation between dux and comes forms), Gegenharmonie (i.e. good counterpoint accompanying the theme) and Zwischenharmonie(episodes). Even when these five elements were handled in ‘proper’ fashion, Marpurg allowed for still further subdivision of proper fugue into strict (à la Bach) and free (à la Handel). Also worth mentioning is Marpurg’s borrowing from Mattheson of the word Durchführung(still used by German speakers today) to designate the fugue’s sections marked off by its episodes. One notices immediately in Marpurg’s use of ‘Harmonie’ the ever greater focus of the time on vertical sonority rather than horizontal part-writing.

Fugue

7. The romantic era.

In the early 19th century fugue became the subject of intense debate as musicians struggled to reconcile its myriad definitions and manifestations and to determine its role in contemporary composition. Nevertheless, it was the general consensus that fugue was the quintessential contrapuntal genre and as such was only with difficulty susceptible to integration into the modern style. One musician who did attempt to update the technique in light of post-Baroque compositional innovations was the Czech-born Antoine Reicha: contemporary and colleague of Beethoven, pupil of Haydn, Salieri and Albrechtsberger, and teacher of Berlioz, Liszt and Franck. In 1803 in Vienna Reicha dedicated a set of 36 fugues for piano to his teacher Haydn; for a new edition two years later he added an introduction entitled Über das neue Fugensystem defending their construction. In this introduction Reicha dismissed Martini’s three principal categories of fugue as irrelevant to contemporary composition and identified the following characteristics as necessary for a fugue: the leading of the theme through all voices, proper contrapuntal texture, derivation of all musical ideas from the theme alone, and the maintenance of a contrapuntal character throughout the piece. As might be expected from a composer interested in more adventurous Romantic harmony, Reicha rejected the traditional relationship between fugue and tonality, including the handling of the fugal answer and any restrictions on modulation during the course of the piece. In a later treatise, written after he had been appointed to the Paris Conservatoire, he also tried to bring the ubiquitous periodicity of Classical-style music into the fugue by describing its structure as a series of periods well delimited by phrases: these periods included an opening one called ‘exposition’ and, following an intervening episode, another called ‘counterexposition’. Reicha’s innovations were not widely accepted, however; Beethoven, who himself treated fugue relatively freely, expressed the probably common opinion that in Reicha’s collection of 36 fugues ‘the fugue is no longer a fugue’. Reicha’s colleagues at the Paris Conservatoire, Cherubini and Fétis, later expressed similar criticisms. When their ideals prevailed, the last serious attempt to update fugal theory died, and the teaching and writing of fugue became once and for all an act of homage to the past.

Writing about fugue meanwhile continued apace. Authors included Fétis (1824), Cherubini (1835), Weinlig (1845), E.F. Richter (1859), Riemann (1890–94), Prout (1891) and many others. Fugal theory came to focus increasingly on one of two strains: either fierce, partisan debate about what constituted a ‘proper’ fugue, principally for the purpose of evaluating music of the past, or the establishment of a rigid model to be followed to the letter by any student wishing to master the ideal fugue. The latter came eventually to be known as the school fugue or fugue d’école and to be associated most closely, as it still is today, with the Paris Conservatoire. André Gédalge’s Traité de la fugue (1901) offers the definitive outline of the school fugue. The model is laid out in great detail and is widely understood to bear no relationship at all to ‘real’ composition outside the academy.

Beethoven’s judgment concerning Reicha’s fugues and his ambivalence about the freedoms allowable in his own fugal composition mirror the widespread uncertainty of the time towards the question of fugue’s definition and essential characteristics. Marpurg had allowed for strict and free fugues, and some musicians of the early 19th century (e.g. Koch) simply expanded the latter to encompass such innovatory works as Mozart’s overture to Die Zauberflöte, in which fugal texture is by and large maintained but within a movement structured according to sonata form. Others (e.g. J.A. André) vigorously rejected such (as they saw it) terminological looseness. For André, the sine qua non of fugue was the opening fugal answer at the 5th. Other musicians since André have identified their own essential characteristics, including most commonly contrapuntal rigour or overall compositional structure (i.e. form). Most pieces designated ‘fugue’ by 19th-century composers have probably at some time been declared unworthy of the name for one or another reason; even Bach’s fugues themselves have occasionally been measured and found wanting.

Adding to the terminological confusion is the 19th-century introduction of the word fugato, an Italian past participle meaning ‘fugued’, which was occasionally used during the 16th and 17th centuries in the expression contrappunto fugato (literally ‘fugued counterpoint’, perhaps best rendered in English as ‘fugal counterpoint’). In 1760, however, Giorgio Antoniotto, an Italian-born musician living in England, published a treatise in English in which he introduced the word as a noun meaning imitative counterpoint that is not proper fugue (what earlier musicians had called simply ‘imitation’). Fugato subsequently came to be the term most commonly applied to brief passages of fugal imitation within non-fugal movements, as well as to any fugal piece (even if designated ‘fugue’ by its composer) that fails the test for proper fugue. In both of these senses, the word remains current today.

As fugal theory became more and more orientated towards the past (and, by extension, towards the analysis of earlier music), composers turned increasingly to the fugues of past composers, rather than to the theoretical pronouncements of their teachers, for inspiration. Chief among their models were the keyboard fugues of Bach, which, despite the disappearance of most of the rest of his works from public consciousness, had never really faded from the view of the musical cognoscenti. It is no accident that Schumann, Liszt and Reger all wrote fugues on the notes B–A–C–H, or that both Schubert and Beethoven showed their greatest interest in fugue late in life, as they searched for new ideas and models, rather than early in their careers, when their teachers’ precepts were fresh in their minds. In the end, only Chopin among all the major composers of the 19th century seems to have shown no interest whatsoever in counterpoint and fugue.

Perhaps the single exception to this new role of fugue as historical revival or archaeological relic was its traditional, well-established place as finale in sacred vocal music. Prominent examples from the century include, in addition to those of Beethoven’s masses, the final chorus of Mendelssohn’s Elijahand the end of the third movement (on the words ‘Der Gerechten Seelen sind in Gottes Hand’) of Brahms’s German Requiem. Berlioz, on the other hand, criticized this convention and chose to use fugue in more innovatory ways in his Requiem. Verdi introduced a brilliant spoof of the tradition by closing his final opera, Falstaff, with a fugue on the words ‘Tutto nel mondo è burla’ (the whole world is a joke). Meanwhile, the fugal finale in instrumental music, a much more recent tradition, faded in importance. Among its few post-Beethoven appearances one might name the Variations and Fugue on a Theme of Handel op.24 of Brahms and the fourth movement of Bruckner’s Symphony no.5.

With the decline of interest in sacred music generally and the instrumental fugal finale in particular, the writing of independent fugues, or preludes and fugues, came increasingly to attract composers’ attention, just as it had Mozart’s. Beethoven’s most contrapuntally rigorous fugue is probably the opening movement of the C minor Quartet op.131, Schubert’s the Fugue in E minor for piano four hands, written in the year before he died. Both Mendelssohn and Schumann showed keen interest in wrriting fugues, the former as an outgrowth of his interest in the revival of Bach’s music, the latter as a kind of artistic stimulus to his creative juices. Clara Schumann went so far as to refer to her husband’s Fugenpassion, and he enthusiastically instructed her using Cherubini’s counterpoint treatise. One can see in all of these compositions their creators’ attempts to rein in or adapt the current stylistic preference for beautiful, singing melody and adventurous harmony within a genre designed first and foremost for contrapuntal display and technical sophistication.

By the second half of the century fugue had found its most comfortable niche within the genre of prelude and fugue, and increasingly within the realm of organ music. These fugues might take the form of studies (e.g. the organ fugues of Brahms), showpieces (the preludes and fugues of Liszt), continued fascination with the Baroque (the works of Reger), or simply occasional essays (the Prélude, fugue et variation for organ op.18 of Franck). Of course fugue also retained its reputation for learnedness. In order to characterize Beckmesser’s pedantry Wagner introduced fugal counterpoint into Die Meistersinger (see bars 138–50 of the overture, reprised in association with Beckmesser in Act 3) and in La damnation de Faust Berlioz included a fugue in parody of German learnedness. Of all of these men probably the most consistently successful composer of fugue was Brahms, who also proved most capable of integrating past and present.

Fugue

8. 20th century.

The indissoluble bond between fugue and tonality, traceable back to Dressler and Clemens in the 16th century and strongly reaffirmed in the 19th, made the genre uncongenial to those 20th-century composers who had abandoned tonal harmony. A rare early use of fugue in atonal music occurs in ‘Der Mondfleck’ from Pierrot lunaire (1912), a movement that Schoenberg described as ‘fugue between piccolo and clarinet on the one hand, canon between violin and cello on the other’. Schoenberg’s understanding of the difference between the two techniques is clear: the canon carries through from beginning to end, whereas the fugue involves a theme, two bars long, which is stated several times in the two voices, with intervening free counterpoint, and to which the contrapuntal devices of inversion and stretto are applied. Nevertheless, as Schoenberg and Webern began to explore thematic transformation as yet another way to avoid the sensation of a recognizable tonality, fugue found itself all but excluded from 12-note music. The composers of the Second Viennese School favoured both counterpoint and classical forms, but canon, not fugue, was the preferred imitative technique. In fact, possibly the best-known fugue associated with these composers was not an original composition but Webern’s arrangement of the six-voice ricercare from Bach’s Musical Offering.

Perhaps the most significant atonal fugue from the first half of the century is the triple fugue in Act 2 scene ii, bars 286–365, of Berg’s Wozzeck (1917–22). Opera and fugue had traditionally had little to do with each other, but Berg exploited the technique brilliantly by assigning a fugue subject to each of the scene’s three characters and using various contrapuntal combinations to parallel the dramatic action. The fugue is laid out in several well-defined sections: exposition of theme 1, exposition of theme 2, combination of themes 1 and 2, transition based on theme 2, exposition of theme 3, combination of all three themes, and coda on themes 1 and 2. Even allowing for the absence of tonality (the first five thematic statements enter on F, F, E, D and G), the handling of the imitation itself is free and untraditional, much more so than Schoenberg’s in ‘Der Mondfleck’. Berg’s three expositions do not present their themes in the customary orderly fashion, integrity of voices is not maintained, and thematic alteration, although seldom drastic, is omnipresent.

The so-called neo-classicism of the 1920s and 30s brought fugue back into favour. Each of the movement’s adherents sought to put his own individual stamp on the tonal harmony he inherited, and that desire led to a variety of tonal plans for both the imitative entries and the fugue as a whole. Whereas Stravinsky, in the second-movement fugue of his Symphony of Psalms (1930), presented a regularly laid-out fugal exposition with entries alternating between tonic and dominant, Bartók chose, for the opening fugue of his Music for Strings, Percussion and Celesta (1936), to take successive entries around the circle of 5ths, with odd-numbered entries proceeding around the circle in one direction and even-numbered entries in the opposite direction. These early attempts at reinterpreting fugue in 20th-century terms led to further experiments, including later 12-note fugues by Schoenberg (the finale of his Variations on a Recitative op.40 (1941) for organ and the Genesis Prelude op.44 (1945) for orchestra and chorus without text). Also falling within the category of ‘neo-classical’ are two major collections of fugues inspired by the example of Bach’s ‘48’: Hindemith’s Ludus tonalis (1942) and Shostakovich’s 24 Preludes and Fugues (1950–51).

The principal compositional trends since World War II – total serialism, aleatory music and minimalism – have proved inhospitable to fugue. Accordingly, interest in fugue during the second half of the 20th century came to rest almost exclusively with composers seeking to emulate past compositional styles and scholars engaged in the study of the history of imitative counterpoint.

Fugue

BIBLIOGRAPHY

composition manuals

J.J. Fux: Gradus ad Parnassum (Vienna, 1725/R; Ger. trans., 1742/R; partial Eng. trans., 1943, as Steps to Parnassus, rev. 2/1965 as The Study of Counterpoint)

F.W. Marpurg: Abhandlung von der Fuge (Berlin, 1753–4/R); ed. S. Sechter (Vienna, 1843)

L.A. Sabbatini: Trattato sopra le fughe musicali (Venice, 1802/R)

A. Reicha: Über das neue Fugensystem (Vienna, 1805) [pubd as suppl. to Trente six fugues pour le piano-forté]

F.-J. Fétis: Traité du contre-point & de la fugue (Paris, 1824/R, enlarged 2/1846)

L. Cherubini, with J.Halévy: Cours de contrepoint et de fugue (Paris, 1835; Eng. trans., 1837)

C.T. Weinlig: Theoretisch-praktische Anleitung zur Fuge für den Selbstunterricht (Dresden, 1845, enlarged 2/1852)

E.F. Richter: Lehrbuch der Fuge (Leipzig, 1859, 9/1921)

H. Riemann: Katechismus der Fugen-Komposition (Leipzig, 1890–94, 2/1906 as Handbuch der Fugen-Komposition; Eng. trans., 1890)

E. Prout: Fugue (London, 1891/R)

E. Prout: Fugal Analysis (London, 1892)

T. Dubois: Traité de contrepoint et de fugue (Paris, 1901)

A. Gédalge: Traité de la fugue (Paris, 1901; Eng. trans., 1965)

C.H. Kitson: Studies in Fugue (London, 1909/R)

C.H. Kitson: The Elements of Fugal Construction (London, 1929/R)

G. Oldroyd: The Technique and Spirit of Fugue (London, 1948)

C. Nalden: Fugal Answer (Auckland and London, 1970)

R. Bullivant: Fugue (London, 1971)

S. Gissel: Die Chorfuge im strengen Satz: ein Lehrbuch der Chorfugenkomposition (Wilhelmshaven, 1987)

historical and analytical studies

J. Müller-Blattau: Grundzüge einer Geschichte der Fuge (Königsberg, 1923, 3/1963 as Geschichte der Fuge)

W. Neumann: J.S. Bachs Chorfuge (Leipzig, 1938, 2/1950)

A. Ghislanzoni: Storia della fuga (Milan, 1952)

A. Mann: The Study of Fugue (New Brunswick, NJ, 1958/R, 2/1965/R)

K. Trapp: Die Fuge in der deutschen Romantik von Schubert bis Reger (Frankfurt, 1958)

H.-B. Dietz: Die Chorfuge bei G.F. Händel (Tutzing, 1961)

H.J. Pauly: Die Fuge in den Orgelwerken Dietrich Buxtehudes (Regensburg, 1964)

I. Horsley: Fugue: History and Practice (New York, 1966)

W. Kirkendale: Fuge und Fugato in der Kammermusik des Rokoko und der Klassik (Tutzing, 1966; Eng. trans., enlarged, 1979)

D. Chittum: ‘The Triple Fugue in Berg's Wozzeck’, MR, xxviii (1967), 52–62

S. Kunze: ‘Anton Reichas “Entwurf einer phrasirten Fuge”’, AMw, xxv (1968), 289–307

S. Kunze: ‘Gattungen der Fuge in Bachs Wohltemperiertem Klavier’, Bach-Interpretationen, ed. M. Geck (Göttingen, 1969), 74–93

H. Serwer: ‘Marpurg versus Kirnberger: Theories of Fugal Composition’, JMT, xiv (1970), 206–36

J. Haar: ‘Zarlino’s Definition of Fugue and Imitation’, JAMS, xxiv (1971), 226–54

S. Keil: Untersuchungen zur Fugentechnik in Robert Schumanns Instrumentalschaffen (Hamburg, 1973)

J. Hirshberg: ‘Berlioz and the Fugue’, JMT, xviii (1974), 152–88

G. Butler: ‘Fugue and Rhetoric’, JMT, xxi (1977), 49–109

W. Kirkendale: ‘Ciceronians versus Aristotelians on the Ricercar as Exordium, from Bembo to Bach’, JAMS, xxxii (1979), 1–44

F.W. Riedel: ‘Die zyklische Fugen-Komposition von Froberger bis Albrechtsberger’,Die süddeutsch-österreichische Orgelmusik im 17. und 18. Jahrhundert: Innsbruck 1979, 154–67

D. Kämper: ‘Die Kanzone in der norddeutschen Orgelmusik des 17. Jahrhunderts’,Gattung und Werk in der Musikgeschichte Norddeutschlands und Skandinaviens: Kiel 1980, 62–78

G.G. Butler: ‘Der vollkommene Capellmeister as a Stimulus to J.S. Bach's Late Fugal Writing’, New Mattheson Studies, ed. G.J. Buelow and H.J. Marx (Cambridge, 1983), 293–305

J. Ladewig: ‘The Origins of Frescobaldi's Variation Canzonas Reappraised’,Frescobaldi Studies: Madison, WI, 1983, 235–68

A. Newcomb: ‘The Anonymous Ricercars of the Bourdenay Codex’, ibid., 97–123

T. Müller: ‘Die Fuge in Händels Instrumentalmusik’, Georg Friedrich Händel: Halle 1985, 125–8

P. Walker: ‘From Renaissance “Fuga” to Baroque Fugue: the Role of the “Sweelinck Theory Manuscripts”’, Schütz-Jb 1985–6, 93–104

U. Siegele: ‘Zu Bachs Fugenkomposition’, Bach Studien, ix (1986), 19–24

G.B. Stauffer: ‘Fugue Types in Bach's Free Organ Works’, J.S. Bach as Organist (Bloomington, IN, 1986), 133–56

S. Town: ‘Toward an Understanding of Fugue and Fugato in the Masses of Joseph Haydn’, JMR, vi (1986), 311–51

A. Newcomb: ‘When the “stile antico” was Young’, IMSCR XIV: Bologna 1987, iii, 175–81

V.E. Newes: ‘Chace, Caccia, Fuga: the Convergence of French and Italian Traditions’,MD, xli (1987), 27–57

P. Walker: Fugue in German Theory from Dressler to Mattheson (diss., SUNY, Buffalo, 1987)

R. Kramer: ‘Gradus ad Parnassum: Beethoven, Schubert, and the Romance of Counterpoint’,19CM, xi (1987–8), 107–20

R. Ormesher: Beethoven’s Instrumental Fugal Style: an Investigation of Tonal and Thematic Characteristics in the Late-Period Fugues (diss., U. of Sheffield, 1989)

P. Walker: ‘Die Entstehung der Permutationsfuge’, BJb 1989, 21–42; Eng. trans., enlarged, in The Creative Process, Studies in the History of Music, iii (New York, 1992), 51–91

M. Beiche: ‘Fuga/Fuge’ (1990), HMT

D. Harrison: ‘Rhetoric and Fugue: an Analytical Application’, Music Theory Spectrum, xii (1990), 1–42

D.A. Sheldon: ‘The Stretto Principle: Some Thoughts on Fugue as Form’, JM, viii (1990), 553–68

D. Teepe: Die Entwicklung der Fantasie für Tasteninstrumente im 16. und 17. Jahrhundert: eine gattungsgeschichtliche Studie (Kassel, 1990)

P. Walker: ‘Modality, Tonality, and Theories of Fugal Answer in the Late Renaissance and Baroque’, Church, Stage, and Studio: Music and its Contexts in Seventeenth-Century Germany (Ann Arbor, 1990), 361–88

P. Walker: ‘Zur Geschichte des Kontrasubjekts und zu seinem Gebrauch in den frühesten Klavier- und Orgelfugen Johann Sebastian Bachs’, Das Frühwerk Johann Sebastian Bachs: Rostock 1990, 48–69

D.R. Boomgaarden and R.B.Nelson: ‘Johann Baptist Samber's (1654–1717) Manuductio ad Organum: the First Modern Discussion of Fugue in German’,JMR, xi (1991), 93–126

F.W. Riedel: ‘Johann Sebastian Bachs Kunst der Fuge und die Fugenbücher der italienischen und österreichischen Organisten des 17. und 18. Jahrhunderts’,Von Isaac bis Bach:… Festschrift Martin Just, ed. F. Heidlberger, W. Osthoff and R. Wiesend (Kassel, 1991), 327–33

K.-J. Sachs: ‘Das Fugenkorpus des Simon Lohet in Johannes Woltz' Tabulaturbuch von 1617’, ibid., 155–68

P. Wollny: ‘Mozarts Fugen und der fugierte Stil in seinem Spätwerk’, MJb 1991, 86–92

W. Breig: ‘Formprobleme in Bachs frühen Orgelfugen’, BJb 1992, 7–21; Eng. trans. in A Bach Tribute: Essays in Honor of William H. Scheide, ed. P. Brainard and R. Robinson (Kassel and Chapel Hill, NC, 1993), 45–56

G. Croll: ‘Wolfgang Amadeus Mozarts Bach- und Händel-Studien 1782’, HJb 1992, 79–93

L. Dreyfus: ‘Matters of Kind: Genre and Subgenre in Bach's Well-Tempered Clavier, Book I’,A Bach Tribute: Essays in Honor of William H. Scheide, ed. P. Brainard and R. Robinson (Kassel and Chapel Hill, NC, 1993), 101–19

L.E. Grossman: Fugal Procedures in the Symphonies of Joseph Haydn (diss., Northwestern U., 1993)

M. Heinemann: ‘Liszts Fugen und Rejcha’, Musiktheorie, viii (1993), 241–7

I. Bent, ed.: Music Analysis in the Nineteenth Century, i: Fugue, Form and Style (Cambridge, 1994)

G.A. Krumbholz: Friedrich Wilhelm Marpurg's Abhandlung von der Fuge (1753–4) (diss., U. of Rochester, 1995)

W. Renwick: Analyzing Fugue: a Schenkerian Approach (Stuyvesant, NY, 1995)

P. Walker: ‘Rhetoric, the Ricercar, and J.S. Bach's Musical Offering’, Bach Studies, ii, ed. D.R. Melamed (Cambridge, 1995), 175–91

W. Kirkendale: ‘On the Rhetorical Interpretation of the Ricercar and J.S. Bach's Musical Offering’, Studi musicali, xxvi (1997), 331–76