The Fugue (from Latin Fuga "escape") is a musical composition principle polyphonic polyphony. The fugue is characterized by a special arrangement of imitations at the beginning of the composition: a musical theme is repeated in different voices at different times, each beginning at different pitches (usually alternating on the root note and the fifth ).
A fugue can be an independent composition. Fugues were often composed with a preceding prelude . However, joints and joint-like structures are also used within works of other shapes, e.g. B. in cantatas , masses , concerts , symphonies or overtures .
Origin of the term
The term fugue was used for the canon as early as the 14th century , and later also generally for imitations. Even among composers of the Franco-Flemish school , Fuga or ad fugam referred to canonical compositions, although the first structures laid out in the later sense of the fugue appear in the polyphony of the 16th century. Only in the course of the 17th century were such pieces referred to as joints .
A special feature of the joint is its complex processing of themes. A fugue begins with the exposition of the voices : the first voice presents the - mostly short and concise - topic . This topic use is also referred to as Dux (Latin dux "leader"). This is followed by a second voice, which now presents the topic as comes (lat. Comes "companion"), mostly shifted to the upper fifth (or lower fourth).
If the fifth tone appears exposed above the fundamental tone in the Dux theme, this is usually modified to a fourth in the Comes (tonal answer) in order to guarantee the identity of the key . This technique goes back to the arrangement of the modes . Otherwise the topic will be transposed according to the interval ("real").
Further votes can be added according to this principle until the full number of votes (usually 3 or 4, less often 5 or more) is reached.
If the first voice brings motivically or thematically significant material during the second use of the topic, which is taken up again later (in some cases even as a new topic), one speaks of a counter-subject . The counter-subject must form a double counterpoint with the subject in order to appear both above and below the subject without violating the voicing rules.
All sections in which the subject - in different voices - will be carried forward, hot -throughs (not to be confused with the implementation of the sonata movement) or theme-phase , with the start of the joint, so the exposure is already the first implementation is. The other thematic assignments or implementations can u. a. are also in the parallel key of the root key as well as the upper and lower fifth key. From the 19th century, the theme appeared in even more distant keys.
There are different types of joints. In most cases, the themes are linked by interludes , which are generally used for modulation and often consist of sequences . Other fugues have no interludes at all (e.g. C major, WK I, BWV 846). The fugue in C sharp minor by JS Bach (WK I, BWV 849), which contains three themes, is a special case here . These are introduced one after the other and continuously brought closer together in the further course , so that, in addition to the lack of interludes , there is hardly any room for non-topic material at all. For the formal structure in such cases it is less the key of each entry than the underlying cadence order that is decisive - in other words: which steps of the basic key are reached by a recognizable cadence?
Before the end of a fugue, an organ point - on the dominant or the tonic - is sometimes inserted, be it as a signal for the coming end or as a development of the same. A well-known example of this is the fugue in C minor (WK I) cited here or the G minor fugue from the sonata for solo violin ( BWV 1001) by JS Bach.
This three-part fugue by Johann Sebastian Bach begins with a typical exposition that extends to the beginning of bar 9. The alto part begins first, followed by the soprano in bar 3 and the bass in bar 7.
The theme extends over two bars. As is usual with fugues, it appears at the beginning only to introduce yourself, in the key of C minor.
The answer to the theme (called Comes in Latin ) represents an exact transposition of the theme to the major quint key of G minor, with one exception: the fourth note is C, not D, as would actually be expected. This small change is necessary in order to be able to maintain the basic key beyond the 2nd theme start. In this case, one speaks of a tonal answer (in contrast to the real answer , in which a topic appears without change in the upper fifth key).
In measure 5, the two voices have finally reached the upper quint key of G minor. However, so that the third part can begin with the theme, it must be modulated back to the original key of C minor. This happens in the two-bar codetta of bars 5 and 6. The composer makes use of the characteristic opening motif of the theme in the soprano, while the alto uses the counter-subject (or counterpoint ) he introduced in bar 3 . However, the tone steps typical for this counter-subject appear reversed; i.e. not descending, but ascending. In addition, the ascent takes place three times in a row at the next higher note level : it is a sequence . In bar 7 the basic key of C minor is reached again, and the bass can begin with the theme.
While the bass leads the theme, the counter-subject can be heard in the soprano. The alto introduces a second counter-subject, which will appear several times in different voices in the further course of the fugue, establishing the threefold counterpoint.
Due to their simple, almost homophonic leadership, soprano and alto take on accompanying functions from bar 8. At this point the chamber music, less complex-polyphonic character of this fugue becomes particularly clear.
At the beginning of bar 9, the introduction of the theme in the bass is completed, and with it the exposition: Each of the three voices has carried out the theme in full.
History and meaning
The principle of imitation between different voices of a piece of music has been known since the late Middle Ages. As a preliminary stage to the fugue, the canon was first maintained. Around 1600 the terms Fantasia , Canzona , Capriccio , Ricercar and Tiento denote similar forms of instrumental pieces (mostly for keyboard instruments), which may be regarded as forerunners of the fugue. The fugue principle is also gradually finding its way into the motet .
In the high baroque era , the fugue was emancipated as an independent (partial) form. Lutenists and guitarists, such as the Spaniard Gaspar Sanz , also composed fugues in the 17th century. In the French Overture the second part is a fugue, in the North German Organ School the fugue becomes the final counterpart of a preceding prelude , a toccata or other forms.
Probably the most famous composer of Fugen was Johann Sebastian Bach; In his works (e.g. Well-Tempered Clavier , The Art of Fugue ) he tried out all the possibilities of the fugue, so that many later composers also dealt with Bach on the subject of the fugue. In 1753/54, a few years after Bach's death, Friedrich Wilhelm Marpurg's treatise on the fugue was published , which was used well into the 19th century as a music-theoretical guide for learning the fugue technique.
After the baroque period, the fugue was considered a historical and therefore outdated form, but it was never abandoned. Later composers repeatedly grappled with their principles, whereby it was always clear that the results always meant a reference to the past. Writing a fugue was also seen as proof of special compositional skills.
Neighboring skirt master of joint composition (selection)
Composers who devoted themselves to the fugue after the Baroque era included:
Joseph Haydn :
- Finale of the string quartets opus 20 No. 2, 5 & 6
Wolfgang Amadeus Mozart :
- Adagio and Fugue in C minor, K. 546
- Fugues for piano for 2 and 4 hands
- Finale of the string quartet in G major KV 364
- Final movement of the Symphony No. 41 in C major KV 551 "Jupiter's Symphony"
- Anton Reicha : 36 fugues op.36
- Ludwig van Beethoven :
- August Alexander Klengel : 48 Canons and Fugues, Volume I and Volume II
- Simon Sechter : musical diary with approx. 4000 fugues
Franz Schubert :
- Fugue in E minor op. Posth. 152 D 952
- Fantasia in F minor D 940 for piano four hands, in the finale there is a large fugue
- Franz Lachner : Introduction and Fugue in D minor op.62
- Samuel Wesley : Fugue in B flat minor (for Felix Mendelssohn Bartholdy)
Felix Mendelssohn Bartholdy :
- Three Preludes and Fugues op.37 (1836/37)
- Three Fugues (1839)
Robert Schumann :
- Six fugues on the name BACH op. 60 (1845)
- Four Fugues, Op. 72 (1845)
- Seven Piano Pieces in Fugette Form, Op. 126 (1853)
Friedrich Kiel :
- Six fugues op.2 (1850)
- Four two-part fugues op.10 (1856)
- Variations and Fugue in F minor op.17 (1860)
- Seven fugues or op.
- Fughetta FH..g o. Op.
Franz Liszt :
- Fantasy and fugue on the chorale Ad nos, ad salutarem undam (1850)
- Prelude and fugue in the name of BACH (1855, rev. 1870)
Giuseppe Verdi :
- Finale of the String Quartet in E minor (1873)
- Prélude, choral et fugue in B minor for piano FWV 21 (1884)
- Prélude, fugue et variation in B minor for organ FWV 30 (1862)
Johannes Brahms :
- Fugue in A flat minor WoO8
- Prelude and Fugue in A minor WoO 9
- Prelude and Fugue in G minor WoO 10
- Variations and Fugue on a Theme by Handel op.24 (1861)
- Anton Bruckner :
Felix Draeseke :
- 3rd movement of the symphonic poem Frithjof WoO 7
- 6 fugues op.15 (1876)
- 11 four-part fugues WoO 37
Georges Bizet :
- Six fugues and a collection of fugues and exercises (WD 60–66)
- Fugue Fiat misericordia tua (from the Te Deum )
- Robert Kahn : 53 fugues and fugues in the diary in tones (manuscript)
Max Reger :
- Variations and Fugue on a Theme (from the Singspiel Der Ärndtekranz ) by Johann Adam Hiller op.100 (1907)
- Variations and Fugue on a Theme by Wolfgang Amadeus Mozart op.132 (1914)
- Variations and fugue on a theme by Johann Sebastian Bach op.81 (1904)
- Variations and Fugue on a Theme by Ludwig van Beethoven op.86 for 2 pianos (1904)
- Introduction, Passacaglia and Fugue op.96 for 2 pianos (1906)
- Variations and Fugue on a Theme by Georg Philipp Telemann op.134 (1914)
- Fantasy and Fugue on BACH op.46 (1900)
- Symphonic Fantasy and Fugue op.57 (1901)
- Variations and Fugue in F sharp minor op.73 (1903)
- Introduction, Passacaglia and Fugue in E minor, Op. 127 (1913)
- Fantasy and Fugue in D minor op.135b (1915)
- Johann Nepomuk David : 12 organ fugues through all keys Wk 66 a. a.
Franz Schmidt :
- Variations and fugue on a separate theme in D major (King's Fanfares from Fredigundis ) (1916/1924)
- Fantasy and Fugue in D major (1924)
- Prelude and Fugue in E flat major (1924)
- Fugue in F major (1927)
- Prelude and Fugue in C major (1924)
- Four Little Preludes and Fugues (1928)
- Prelude and Fugue in A major (1934)
- Toccata and Fugue in A flat major (1935)
- Siegelfuge (organ) from the book with seven seals (1935–1937)
- 6. Seal (organ) from the book with seven seals (1935–1937)
- Alban Berg : Wozzeck, 3rd act, 1st scene, Marie with the child, variations and fugue on a theme (1925)
- Hans Gál : 24 fugues op.108
- Paul Hindemith : Ludus tonalis fugue collection for piano
- Georgi Muschel : 24 Preludes and Fugues
- Dmitri Dmitrijewitsch Schostakowitsch : 24 Preludes and Fugues for piano op.87 (1951)
- Rodion Konstantinowitsch Schchedrin : 24 Preludes and Fugues for Piano (1964)
- Olivier Messiaen : Par lui tout a été fait (No. 5 from Vingt Regards sur L'Enfant Jesus )
- Benjamin Britten: Closing part (Fugue: Allegro Molto) from The Young Person's Guide to the Orchestra op.34 (1945)
Astor Piazzolla mixed classical fugue technique and Argentine tango into a new unit. Fugues can also be found in jazz, e.g. B. in Love Me or Leave Me by Nina Simone or Passacaglia & Fugue by Don Ellis .
One speaks of a permutation fugue when there are always several constant counterpoint themes on the subject. The composer then only exchanges the voices for each other in the next topic phase. This is popular in vowel sentences; Example: Opening choir of the cantata Himmelskönig, welcome from J. S. Bach.
A double fugue is a fugue with two themes and one or two counter-subjects that can be presented and processed one after the other or at the same time. Examples: Johann Sebastian Bach : Well-Tempered Clavier, Part II, G sharp minor fugue ; Contrapunctus IX and X from the Art of Fugue .
A special case is the use of the term double fugue by Johann Mattheson . In his 1739 publication "The Perfect Capell Master", he calls double fugues all fugues in which double counterpoint is used. In doing so, he calls for "double fugues with three subjects", a type of fugue that Bach used not only in the art of the fugue, but also in earlier works. Examples of this are the fugue for Passacaglia in C minor BWV 582, in which two counter-subjects are added to the theme (subject), and the three-part Sinfonia in F minor BWV 895. If three themes are treated in double counterpoint, one speaks of in modern terminology sixfold counterpoint.
The triple fugue is a fugue with three themes. These are in turn set up in separate expositions and then combined with one another. Examples: J. S. Bach, Well-Tempered Clavier, Part II, Fugue in F sharp minor , Art of the Fugue , Contrapunctus 8 and 11, the organ fugue in E flat major BWV 552 which concludes the third part of the piano practice.
The quadruple fugue is a fugue with four themes. The fragmentary final fugue of Bach's cycle “ The Art of Fugue ” is often cited as an example, but it breaks off after the introduction of the third theme and its combination with the preceding ones. Since the basic theme of the work would also fit in, a planned quadruple fugue is likely, but has not been handed down in this form.
This is a fugue in which the theme in the Comes first goes to the fifth, but then the dux does not follow the tonic again, but rises a fifth again. This technique developed with the need for modulation in Romanticism. Example: Johannes Brahms , “Why is the light given to the laborious?”, From: Two Motets , op. 74. Here the fugue theme, which begins in D minor, is answered in A minor for real. This answer is again answered in real terms in E minor. This again in B minor and the last one in F sharp minor. The fugue theme rises four times in a row by a fifth in this motet. The first movement from Béla Bartók's “ Music for String Instruments, Percussion and Celesta ” is also designed in the shape of a fan or pyramid . The first appearance of the theme is answered first in the upper fifth, then in the lower fifth, followed by the second upper fifth, the second lower fifth, etc. In the whole piece, transpositions of the theme occur on every chromatic level. After six inserts, the theme sounds in the tritone of the original note, i.e. H. in a constructively important interval for Bartók. This commitment is also the dynamic climax of the piece.
In a mirror fugue , the entire contrapuntal movement can be reversed as a mirror image. All downward movements become upward movements, the highest voice becomes the lowest, etc. Fugues of this kind are extremely rare; Bach brings three examples in the art of the fugue (Contrapunctus 16, 17, 18), in each of which the entire movement is repeated in (tonal, i.e. not one hundred percent 'exact') reflection.
It is a contrafuge when the comes is the reverse of the dux , usually in such a way that the tonic and dominant correspond to each other. Contra joints can be found, for example, in JS Bach's Art of Fugue , Contrapunctus 5, 6, 7 and 14.
The Fughetta or Fugette is a joint of a smaller scale, without broad implementation and already the topic of lighter, graziöserer attitude.
A fugato is a fugue-like section in a sonata, a symphony , a concert, etc. It is not about leading the theme through all the voices, it should just look like a fugue. Often these fugati are only a few bars long. Examples are most of the final movements in Bach's harpsichord suites and partitas or in the Brandenburg Concerts Nos. 2 and 5, as well as the fast middle parts of his French overtures in the first movements of the orchestral suites . Handel skillfully uses the fugato technique in his Messiah's Hallelujah chorus . Mozart developed a. a. in the last movement of his Jupiter symphony an extremely effective fugato. Also in the 9th Symphony of Beethoven and the 5th Symphony of Bruckner known fugati are included. In Shostakovich's 4th Symphony , a fugato forms the climax of the first movement.
- Michael Beiche: Fuga / Fugue. In: Concise dictionary of musical terminology . Vol. 3, ed. by Hans Heinrich Eggebrecht and Albrecht Riethmüller , editor Markus Bandur, Steiner, Stuttgart 1990 ( digitized version ).
- Carl Dahlhaus : On the history of the permutation fugue. In: Bach-Jahrbuch 46, 1959, pp. 95–110.
- Zsolt Gárdonyi : Counterpoint - shown on the joint technique J. S. Bachs , Wolfenbüttel 1991
- Markus Grassl: Fugue. In: Oesterreichisches Musiklexikon . Online edition, Vienna 2002 ff., ISBN 3-7001-3077-5 ; Print edition: Volume 1, Verlag der Österreichischen Akademie der Wissenschaften, Vienna 2002, ISBN 3-7001-3043-0 .
- Siegmar Keil: Investigations into joint technique in Robert Schumann's instrumental works , Hamburg 1973.
- Rudolf Reuter: Johann Sebastian Bach's organ and piano fugue. (= Diss. Westfälische Landesuniversität Münster 1948). Open Access available via ViFaMusik
- Celan Project: The Fugue.
- All fugues from the well-tempered piano including analysis and interactive operation (sound + notes) ( Flash or Shockwave )
- Lehrklaenge (online course for music theory): The fugue
- Free teaching units on fugue for general schools (p. 9 and p. 23 in the OpenBook Johann Sebastian Bach, each with sound files)
- Jerry Willard (Ed.): The complete works of Gaspar Sanz. 2 volumes, Amsco Publications, New York 2006 (translation of the original manuscript by Marko Miletich), ISBN 978-082561-695-2 , Volume 1, pp. 94-97.
- Matthias Schmidt: Permutation. In: Oesterreichisches Musiklexikon . Online edition, Vienna 2002 ff., ISBN 3-7001-3077-5 ; Print edition: Volume 4, Verlag der Österreichischen Akademie der Wissenschaften, Vienna 2005, ISBN 3-7001-3046-5 .
- Lexicon entry on counterfugue . In: Meyers Großes Konversations-Lexikon. Volume 7, Leipzig 1907, p. 455.