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74-506: In its most common contemporary usage, it refers to an early kind of fugue , particularly one of a serious character in which the subject uses long note values . However, the term has a considerably more varied historical usage. Among the best-known ricercars are the two for harpsichord contained in Bach 's The Musical Offering and Domenico Gabrielli 's set of seven for solo cello . The latter set contains what are considered to be some of

148-661: A coda . Because of the composer's prerogative to decide most structural elements, the fugue is closer to a style of composition rather than a structural form. The form evolved during the 18th century from several earlier types of contrapuntal compositions, such as imitative ricercars , capriccios , canzonas , and fantasias . The Baroque composer Johann Sebastian Bach (1685–1750), well known for his fugues, shaped his own works after those of Jan Pieterszoon Sweelinck (1562–1621), Johann Jakob Froberger (1616–1667), Johann Pachelbel (1653–1706), Girolamo Frescobaldi (1583–1643), Dieterich Buxtehude (c. 1637–1707) and others. With

222-548: A development , and a final entry that contains the return of the subject in the fugue's tonic key. Fugues can also have episodes, which are parts of the fugue where new material often based on the subject is heard; a stretto (plural stretti), when the fugue's subject overlaps itself in different voices, or a recapitulation . A popular compositional technique in the Baroque era , the fugue was fundamental in showing mastery of harmony and tonality as it presented counterpoint . In

296-620: A distantly related key (or distant key ). In music harmony , there are six of them: four of them share all the pitches except one with a key with which it is being compared, one of them share all the pitches, and one shares the same tonic . Such keys are the most commonly used destinations or transpositions in a modulation , because of their strong structural links with the home key. Distant keys may be reached sequentially through closely related keys by chain modulation , for example, C to G to D. For example, "One principle that every composer of Haydn 's day [ Classical music era ] kept in mind

370-476: A tritone would produce F ♯ , G ♯ , A ♯ , C ♯ , D ♯ , which shares no common tones with the original scale. Thus the scale a fifth higher is very closely related, while the scale a tritone higher is not. Other modulations may be placed in order from closest to most distant depending upon the number of common tones. According to another view in modern music, notably in Bartók ,

444-476: A common tonic produces closely related keys, the other scales being the six other modes. This usage can be found in several of the Mikrokosmos piano pieces. When modulation causes the new key to traverse the bottom of the circle of fifths this may give rise to a theoretical key , containing eight (or more) sharps or flats in its notated key signature; in such a case, notational conventions require recasting

518-488: A demonstration of compositional expertise. Jan Pieterszoon Sweelinck , Girolamo Frescobaldi , Johann Jakob Froberger and Dieterich Buxtehude all wrote fugues. Fugues were incorporated into a variety of musical genres , and are found in most of George Frideric Handel 's oratorios . Keyboard suites from this time often conclude with a fugal gigue . Domenico Scarlatti has only a few fugues among his corpus of over 500 harpsichord sonatas. The French overture featured

592-401: A few notes near the beginning). When the answer is an exact transposition of the subject into the new key, the answer is classified as a real answer ; alternatively, if the intervals of the subject are altered in any way, the answer is a tonal answer . When the subject begins with a prominent dominant note, or when there is a prominent dominant note very close to the beginning of the subject,

666-512: A fugue, the subject may be altered by inversion, retrograde (where the subject is heard back-to-front), diminution (the reduction of the subject's rhythmic values by a certain factor), augmentation (the enlargement of the subject's rhythmic values by a certain factor), or any combination thereof. The excerpt below, bars 7–12 of J.S. Bach's Fugue No. 2 in C minor, BWV 847, from the Well-Tempered Clavier , Book 1 illustrates

740-432: A minor key, the closely related keys are the parallel major, mediant or relative major, the subdominant, the minor dominant, the submediant, and the subtonic . In the key of A minor , when we translate them to keys, we get: Another view of closely related keys is that there are six closely related keys, based on the tonic and the remaining triads of the diatonic scale , excluding the dissonant diminished triads. Four of

814-399: A predominantly homophonic piece, with occasional runs and passagework, not unlike a toccata, found from the late fifteenth to the mid-sixteenth century, after which time this type of piece came to be called a toccata; and from the second half of the sixteenth century onward, a sectional work in which each section begins imitatively , usually in a variation form . The second type of ricercar,

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888-538: A quick fugal section after a slow introduction. The second movement of a sonata da chiesa , as written by Arcangelo Corelli and others, was usually fugal. The Baroque period also saw a rise in the importance of music theory . Some fugues during the Baroque period were pieces designed to teach contrapuntal technique to students. The most influential text was Johann Joseph Fux's Gradus Ad Parnassum ("Steps to Parnassus "), which appeared in 1725. This work laid out

962-473: A set of five transcriptions for string quartet, K. 405 (1782), of fugues from Bach's Well-Tempered Clavier , introducing them with preludes of his own. In a letter to his sister Nannerl Mozart , dated in Vienna on 20 April 1782, Mozart recognizes that he had not written anything in this form, but moved by his wife's interest he composed one piece, which is sent with the letter. He begs her not to let anybody see

1036-483: A set of twenty-five variations and a concluding fugue, all based on a theme from George Frideric Handel's Harpsichord Suite No. 1 in B♭ major , HWV 434. Franz Liszt 's Piano Sonata in B minor (1853) contains a powerful fugue, demanding incisive virtuosity from its player: Closely related key In music , a closely related key (or close key ) is one sharing many common tones with an original key , as opposed to

1110-403: A tonal answer is usually necessary. To prevent an undermining of the fugue's key , this note is transposed up a fourth to the tonic rather than up a fifth to the supertonic . For the same reason, it is possible for the answer of such a subject to be in the subdominant key. During the answer, the voice in which the subject was previously heard accompanies with new material. If this new material

1184-518: A triple fugue for organ.) A counter-fugue is a fugue in which the first answer is presented as the subject in inversion (upside down), and the inverted subject continues to feature prominently throughout the fugue. Examples include Contrapunctus V through Contrapunctus VII , from Bach's The Art of Fugue . During the Baroque period, counter-fugues were sometimes called by the Latin name fuga contraria . German composer Johann Mattheson coined

1258-573: Is (are) presented simultaneously with the subject in the exposition (e.g. as in Kyrie Eleison of Mozart's Requiem in D minor or the fugue of Bach's Passacaglia and Fugue in C minor, BWV 582 ), and (b) a fugue in which all subjects have their own expositions at some point, and they are not combined until later (see for example, the three-subject Fugue No. 14 in F ♯ minor from Bach's Well-Tempered Clavier Book 2 , or more famously, Bach's "St. Anne" Fugue in E ♭ major, BWV 552 ,

1332-533: Is a contrapuntal , polyphonic compositional technique in two or more voices , built on a subject (a musical theme) that is introduced at the beginning in imitation (repetition at different pitches), which recurs frequently throughout the course of the composition. It is not to be confused with a fuguing tune , which is a style of song popularized by and mostly limited to early American (i.e. shape note or " Sacred Harp ") music and West Gallery music . A fugue usually has three main sections: an exposition ,

1406-409: Is a collection of fugues (and four canons ) on a single theme that is gradually transformed as the cycle progresses. Bach also wrote smaller single fugues and put fugal sections or movements into many of his more general works. J.S. Bach's influence extended forward through his son C.P.E. Bach and through the theorist Friedrich Wilhelm Marpurg (1718–1795) whose Abhandlung von der Fuge ("Treatise on

1480-565: Is a fugue, and there are fugal passages in the last movements of his Piano Sonatas in A major, Op. 101 and A ♭ major Op. 110 . According to Charles Rosen , "With the finale of 110, Beethoven re-conceived the significance of the most traditional elements of fugue writing." Fugal passages are also found in the Missa Solemnis and all movements of the Ninth Symphony , except the third. A massive, dissonant fugue forms

1554-461: Is absent. The subject concludes on the quarter note (or crotchet) B ♭ of the third beat of the second bar, which harmonizes the opening G of the tonal answer. The later codettas may be considerably longer, and often serve to develop the material heard in the subject/answer and countersubject and possibly introduce ideas heard in the second countersubject or free counterpoint that follows. They may also be present to delay, and therefore heighten

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1628-461: Is customary in the exposition to alternate entrances of the subject (S) with entrances of the answer (A). However, this order is occasionally varied. For example, the exposition from J.S. Bach's Well-Tempered Clavier, Book 1 Fugue No. 1 in C Major, BWV 846 uses a SAAS (subject-answer-answer-subject) exposition. A brief codetta is often heard connecting the various statements of the subject and answer, smoothly connecting each and often facilitating

1702-495: Is followed by an entry in the dominant of the relative major or minor when the fugue's subject requires a tonal answer. In the fugues of earlier composers (notably Buxtehude and Pachelbel ), middle entries in keys other than the tonic and dominant tend to be the exception, and non-modulation the norm. One famous example of such non-modulating fugue occurs in Buxtehude's Praeludium (Fugue and Chaconne) in C, BuxWV 137. When there

1776-401: Is no entrance of the subject and answer material, the composer can develop the subject by altering it. This is called a counter-exposition , which often uses the inversion of the subject, although the term is sometimes used synonymously with middle entry and may also describe the exposition of completely new subjects, such as those encountered in double fugues . In any of the entries within

1850-460: Is not strict, and the setting less formal. See for example, variation 24 of Beethoven 's Diabelli Variations Op. 120 . The term fuga was used as far back as the Middle Ages , but was initially used to refer to any kind of imitative counterpoint, including canons , which are now thought of as distinct from fugues. Prior to the 16th century, fugue was originally a genre. It was not until

1924-462: Is reused in later statements of the subject, it is called a countersubject ; if this accompanying material is only heard once, it is simply referred to as free counterpoint . The countersubject is written in invertible counterpoint at the octave or fifteenth (two octaves). The distinction is made between the use of free counterpoint and regular countersubjects accompanying the fugue subject/answer, because in order for it to be heard accompanying

1998-451: Is usually based upon some musical idea heard in the exposition. Each episode has the primary function of transitioning into a new key for the next entry of the subject, and may also provide release from the strictness of form required by the exposition. André Gedalge , a teacher of Maurice Ravel , stated that the episode of the fugue is generally based on a series of imitations of the subject that have been fragmented. Further entries of

2072-408: Is written according to certain rules. The composer has more freedom once the exposition ends, though a logical key structure is usually followed. Further entries of the subject will occur throughout the fugue, repeating the accompanying material at the same time, and often accompanying key changes. The various entries may or may not be separated by episodes or occur in stretto . A fugue begins with

2146-641: The Eroica Symphony (1805). Beethoven incorporated fugues in his sonatas, and reshaped the episode's purpose and compositional technique for later generations of composers. Nevertheless, fugues did not take on a truly central role in Beethoven's work until his late period. The finale of Beethoven's Hammerklavier Sonata contains a fugue, which was practically unperformed until the late 19th century, due to its tremendous technical difficulty and length. The last movement of his Cello Sonata, Op. 102 No. 2

2220-532: The Middle Ages , the term was widely used to denote any works in canonic style; however, by the Renaissance , it had come to denote specifically imitative works. Since the 17th century, the term fugue has described what is commonly regarded as the most fully developed procedure of imitative counterpoint. Most fugues open with a short main theme, called the subject, which then sounds successively in each voice . When each voice has completed its entry of

2294-520: The 16th century and is derived from the French word fugue or the Italian fuga . This in turn comes from the Latin fuga , which is itself related to both fugere ("to flee") and fugare ("to chase"). The adjectival form is fugal . Variants include fughetta ("a small fugue") and fugato (a passage in fugal style within another work that is not a fugue). A fugue begins with the exposition and

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2368-415: The 16th century that fugal technique as it is understood today began to be seen in pieces, both instrumental and vocal. Fugal writing is found in works such as fantasias , ricercares and canzonas . "Fugue" as a theoretical term first occurred in 1330 when Jacobus of Liege wrote about the fuga in his Speculum musicae . The fugue arose from the technique of "imitation", where the same musical material

2442-594: The Baroque style. These included a fugue in C minor, K. 426, for two pianos (1783). Later, Mozart incorporated fugal writing into his opera Die Zauberflöte and the finale of his Symphony No. 41 . The parts of the Requiem he completed also contain several fugues (most notably the Kyrie, and the three fugues in the Domine Jesu; he also left behind a sketch for an Amen fugue which, some believe , would have come at

2516-527: The Classical era. Haydn's most famous fugues can be found in his "Sun" Quartets (op. 20, 1772), of which three have fugal finales. This was a practice that Haydn repeated only once later in his quartet-writing career, with the finale of his String Quartet, Op. 50 No. 4 (1787). Some of the earliest examples of Haydn's use of counterpoint, however, are in three symphonies ( No. 3 , No. 13 , and No. 40 ) that date from 1762 to 1763. The earliest fugues, in both

2590-698: The Salzburg Cathedral, the young Mozart composed ambitious fugues and contrapuntal passages in Catholic choral works such as Mass in C minor, K. 139 "Waisenhaus" (1768), Mass in C major, K. 66 "Dominicus" (1769), Mass in C major, K. 167 "in honorem Sanctissimae Trinitatis" (1773), Mass in C major, K. 262 "Missa longa" (1775), Mass in C major, K. 337 "Solemnis" (1780), various litanies, and vespers. Leopold admonished his son openly in 1777 that he not forget to make public demonstration of his abilities in "fugue, canon, and contrapunctus". Later in life,

2664-402: The application of most of the characteristics described above. The fugue is for keyboard and in three voices, with regular countersubjects. This excerpt opens at last entry of the exposition: the subject is sounding in the bass, the first countersubject in the treble, while the middle-voice is stating a second version of the second countersubject, which concludes with the characteristic rhythm of

2738-408: The basis for writing motets as well. Palestrina's imitative motets differed from fugues in that each phrase of the text had a different subject which was introduced and worked out separately, whereas a fugue continued working with the same subject or subjects throughout the entire length of the piece. It was in the Baroque period that the writing of fugues became central to composition, in part as

2812-609: The choruses of his mature oratorios The Creation and The Seasons , as well as several of his later symphonies, including No. 88 , No. 95 , and No. 101 ; and the late string quartets, Opus 71 no. 3 and (especially) Opus 76 no. 6. The young Wolfgang Amadeus Mozart studied counterpoint with Padre Martini in Bologna. Under the employment of Archbishop Colloredo , and the musical influence of his predecessors and colleagues such as Johann Ernst Eberlin , Anton Cajetan Adlgasser , Michael Haydn , and his own father, Leopold Mozart at

2886-405: The countersubjects and/or other free contrapuntal accompaniments. Middle entries tend to occur at keys other than the tonic. These are often closely related keys such as the relative dominant and subdominant , although the key structure of fugues varies greatly. In the fugues of J.S. Bach, the first middle entry occurs most often in the relative major or minor of the work's overall key, and

2960-522: The decline of sophisticated styles at the end of the baroque period , the fugue's central role waned, eventually giving way as sonata form and the symphony orchestra rose to a more prominent position. Nevertheless, composers continued to write and study fugues; they appear in the works of Wolfgang Amadeus Mozart (1756–1791) and Ludwig van Beethoven (1770–1827), as well as modern composers such as Dmitri Shostakovich (1906–1975) and Paul Hindemith (1895–1963). The English term fugue originated in

3034-404: The earliest pieces for solo cello ever written. In the sixteenth century, the word ricercar could refer to several types of compositions. Terminology was flexible, even lax then: whether a composer called an instrumental piece a toccata , a canzona , a fantasia , or a ricercar was clearly not a matter of strict taxonomy but a rather arbitrary decision. Yet ricercars fall into two general types:

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3108-526: The end of the Sequentia). Ludwig van Beethoven was familiar with fugal writing from childhood, as an important part of his training was playing from The Well-Tempered Clavier . During his early career in Vienna , Beethoven attracted notice for his performance of these fugues. There are fugal sections in Beethoven's early piano sonatas, and fugal writing is to be found in the second and fourth movements of

3182-413: The entry of one of the voices may not be heard until considerably later. For example, in J.S. Bach's Fugue in C minor for Organ, BWV 549, the subject entrance in the lowest voice (played by the organ pedals), is not heard until near the end of the fugue. Further entries of the subject may follow the initial exposition either immediately or separated by episodes. Episodic material is always modulatory and

3256-429: The exposition of its subject in one of the voices alone in the tonic key. After the statement of the subject, a second voice enters and states the subject with the subject transposed to another key (almost always the dominant or subdominant , with the latter being less common), which is known as the answer . To enable a natural harmonic progression, the answer may also be altered slightly (usually by changing one or

3330-459: The extraordinary profundity of this fugue ." By the beginning of the Romantic era , fugue writing had become specifically attached to the norms and styles of the Baroque. Felix Mendelssohn wrote many fugues inspired by his study of the music of Johann Sebastian Bach . Johannes Brahms' Variations and Fugue on a Theme by Handel , Op. 24, is a work for solo piano written in 1861. It consists of

3404-406: The final entry of the subject is considered to be the final coda and is normally cadential . A simple fugue has only one subject, and does not utilize invertible counterpoint . A double fugue has two subjects that are often developed simultaneously. Similarly, a triple fugue has three subjects. There are two kinds of double (triple) fugue: (a) a fugue in which the second (third) subject

3478-694: The finale of his String Quartet, Op. 130 (1825); the latter was later published separately as Op. 133, the Große Fuge ("Great Fugue"). However, it is the fugue that opens Beethoven's String Quartet in C ♯ minor, Op. 131 that several commentators regard as one of the composer's greatest achievements. Joseph Kerman (1966, p. 330) calls it "this most moving of all fugues". J. W. N. Sullivan (1927, p. 235) hears it as "the most superhuman piece of music that Beethoven has ever written." Philip Radcliffe (1965, p. 149) says "[a] bare description of its formal outline can give but little idea of

3552-440: The five differ by one accidental, one has the same key signature, and one uses the parallel modal form. In the key of C major , these would be: D minor , E minor , F major , G major , A minor , and C minor . Despite being three sharps or flats away from the original key in the circle of fifths, parallel keys are also considered as closely related keys as the tonal center is the same, and this makes this key have an affinity with

3626-421: The fugue and manifests the hope to write five more and then present them to Baron van Swieten. Regarding the piece, he said "I have taken particular care to write andante maestoso upon it, so that it should not be played fast – for if a fugue is not played slowly the ear cannot clearly distinguish the new subject as it is introduced and the effect is missed". Mozart then set to writing fugues on his own, mimicking

3700-460: The fugue", 1753) was largely based on J.S. Bach's work. During the Classical era , the fugue was no longer a central or even fully natural mode of musical composition. Nevertheless, both Haydn and Mozart had periods of their careers in which they in some sense "rediscovered" fugal writing and used it frequently in their work. Joseph Haydn was the leader of fugal composition and technique in

3774-502: The harpsichord in The Well-Tempered Clavier , which many composers and theorists look at as the greatest model of fugue. The Well-Tempered Clavier comprises two volumes written in different times of Bach's life, each comprising 24 prelude and fugue pairs, one for each major and minor key. Bach is also known for his organ fugues, which are usually preceded by a prelude or toccata . The Art of Fugue , BWV 1080 ,

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3848-451: The imitative, contrapuntal type, was to prove the more important historically, and eventually developed into the fugue. Marco Dall'Aquila (c. 1480–after 1538) was known for polyphonic ricercars. Examples of both types of ricercars can be found in the works of Girolamo Frescobaldi , e.g. in his Fiori musicali . Fugue In classical music , a fugue ( / f juː ɡ / , from Latin fuga , meaning "flight" or "escape" )

3922-407: The impact of the subject proper. The counter-exposition is a second exposition. However, there are only two entries, and the entries occur in reverse order. The counter-exposition in a fugue is separated from the exposition by an episode and is in the same key as the original exposition. Sometimes counter-expositions or the middle entries take place in stretto , whereby one voice responds with

3996-436: The impact of, the reentry of the subject in another voice. Finally, they may be modulatory passages to return the fugue to the tonic. The exposition usually concludes when all voices have given a statement of the subject or answer. In some fugues, especially those with an odd number of voices, the exposition will end with a redundant entry, or an extra presentation of the theme in a voice which has already entered. Furthermore,

4070-411: The initial subject, continues by stating two or more themes (or countersubjects), which must be conceived in correct invertible counterpoint . (In other words, the subject and countersubjects must be capable of being played both above and below all the other themes without creating any unacceptable dissonances.) Each voice takes this pattern and states all the subjects/themes in the same order (and repeats

4144-400: The inversion of a perfect fifth results in a perfect fourth, which, unlike the perfect fifth, is considered a dissonance, requiring proper preparation and resolution. The countersubject, if sounding at the same time as the answer, is transposed to the pitch of the answer. Each voice then responds with its own subject or answer, and further countersubjects or free counterpoint may be heard. It

4218-500: The major impetus to fugal writing for Mozart was the influence of Baron Gottfried van Swieten in Vienna around 1782. Van Swieten, during diplomatic service in Berlin, had taken the opportunity to collect as many manuscripts by Bach and Handel as he could, and he invited Mozart to study his collection and encouraged him to transcribe various works for other combinations of instruments. Mozart was evidently fascinated by these works and wrote

4292-408: The material when all the themes have been stated, sometimes after a rest). There is usually very little non-structural/thematic material. During the course of a permutation fugue, it is quite uncommon, actually, for every single possible voice-combination (or "permutation") of the themes to be heard. This limitation exists in consequence of sheer proportionality: the more voices in a fugue, the greater

4366-412: The modulation between the tonic and the key of the answer. The codetta, like other parts of the exposition, may be reused throughout the remainder of the fugue. The first answer must occur as soon after the initial statement of the subject as possible; therefore, the first codetta is often absent or very short. In the example shown above of J.S. Bach's Fugue No. 16 in G minor, BWV 861 , the first codetta

4440-414: The number of possible permutations. In consequence, composers exercise editorial judgment as to the most musical of permutations and processes leading thereto. One example of permutation fugue can be seen in the eighth and final chorus of J.S. Bach's cantata, Himmelskönig, sei willkommen , BWV 182 . Permutation fugues differ from conventional fugue in that there are no connecting episodes, nor statement of

4514-469: The opening exposition takes place in stretto form is known as a close fugue or stretto fugue (see for example, the Gratias agimus tibi and Dona nobis pacem choruses from J.S. Bach's Mass in B minor ). The closing section of a fugue often includes one or two counter-expositions, and possibly a stretto, in the tonic ; sometimes over a tonic or dominant pedal note . Any material that follows

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4588-486: The original key. In modern music, the closeness of a relation between any two keys or sets of pitches may be determined by the number of tones they share in common, which allows one to consider modulations not occurring in standard major-minor tonality. For example, in music based on the pentatonic scale containing pitches C, D, E, G, and A, modulating a fifth higher gives the collection of pitches G, A, B, D, and E, having four of five tones in common. However, modulating up

4662-410: The second bar in the second system, and the first middle entry. Here, Bach has altered the second countersubject to accommodate the change of mode . At any point in the fugue there may be "false entries" of the subject, which include the start of the subject but are not completed. False entries are often abbreviated to the head of the subject, and anticipate the "true" entry of the subject, heightening

4736-483: The subject in more than one instance, the countersubject must be capable of sounding correctly when played above or below the subject, and must be conceived, therefore, in invertible (double) counterpoint. In tonal music, invertible contrapuntal lines must be written according to certain rules, because several intervallic combinations, while acceptable in one orientation, are not permissible when inverted. As an example, perfect fifths are contrapuntally acceptable, while

4810-404: The subject, and is always used together with the first version of the second countersubject. Following this an episode modulates from the tonic to the relative major by means of sequence , in the form of an accompanied canon at the fourth. Arrival in E ♭ major is marked by a quasi perfect cadence across the bar line, from the last quarter note beat of the first bar to the first beat of

4884-430: The subject, or middle entries, occur throughout the fugue. The development must state the subject or answer at least once in its entirety, and may also be heard in combination with any countersubjects from the exposition, new countersubjects, free counterpoint, or any of these in combination. It is uncommon for the subject to enter alone in a single voice in the middle entries; rather, it is usually heard with at least one of

4958-408: The subject, the exposition is complete. This is often followed by a connecting passage, or episode , developed from previously heard material; further "entries" of the subject are then heard in related keys . Episodes (if applicable) and entries are usually alternated until the final entry of the subject, at which point the music has returned to the opening key, or tonic , which is often followed by

5032-441: The subject/answer before the first voice has completed its entry of the subject/answer, usually increasing the intensity of the music. Only one entry of the subject must be heard in its completion in a stretto . However, a stretto in which the subject/answer is heard in completion in all voices is known as stretto maestrale or grand stretto . Strettos may also occur by inversion, augmentation and diminution. A fugue in which

5106-468: The symphonies and in the Baryton trios , exhibit the influence of Joseph Fux's treatise on counterpoint, Gradus ad Parnassum (1725), which Haydn studied carefully. Haydn's second fugal period occurred after he heard, and was greatly inspired by, the oratorios of Handel during his visits to London (1791–1793, 1794–1795). Haydn then studied Handel's techniques and incorporated Handelian fugal writing into

5180-456: The term gegenfuge to refer to a counter-fugue construct in his Der vollkommene Capellmeister (1739), and some German-language texts use that name to refer to a counter-fugue. Permutation fugue describes a type of composition (or technique of composition) in which elements of fugue and strict canon are combined. Each voice enters in succession with the subject, each entry alternating between tonic and dominant, and each voice, having stated

5254-433: The terms of "species" of counterpoint , and offered a series of exercises to learn fugue writing. Fux's work was largely based on the practice of Palestrina 's modal fugues. Mozart studied from this book, and it remained influential into the nineteenth century. Haydn , for example, taught counterpoint from his own summary of Fux and thought of it as the basis for formal structure. Bach's most famous fugues are those for

5328-405: The themes in related keys. So for example, the fugue of Bach's Passacaglia and Fugue in C minor, BWV 582 is not purely a permutation fugue, as it does have episodes between permutation expositions. Invertible counterpoint is essential to permutation fugues but is not found in simple fugues. A fughetta is a short fugue that has the same characteristics as a fugue. Often the contrapuntal writing

5402-439: Was over-all unity of tonality . No piece dared wander too far from its tonic key, and no piece in a four-movement form dared to present a tonality not closely related to the key of the whole series." For example, the first movement of Mozart's Piano Sonata No. 7 , K. 309, modulates only to closely related keys (the dominant, supertonic, and submediant). Given a major key tonic (I), the related keys are: Specifically: In

5476-503: Was repeated starting on a different note. Gioseffo Zarlino , a composer, author, and theorist in the Renaissance , was one of the first to distinguish between the two types of imitative counterpoint: fugues and canons (which he called imitations). Originally, this was to aid improvisation , but by the 1550s, it was considered a technique of composition. The composer Giovanni Pierluigi da Palestrina (1525?–1594) wrote masses using modal counterpoint and imitation, and fugal writing became

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