Fugue - Knowledge

29: 1956: 989: 712: 769: 1898: 1762: 1079: 4732: 1026: 4753: 1743:, 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 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 801:

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.

1320:. (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 the material when all the themes have been stated, sometimes after a rest). 2185:': the many voicedness of small intervals at small distances in time from one another is a kind of conjuring trick. At the micro level of the individual lines, and there are dozens and dozens of them in this music...there's an astonishing detail and finesse, but the overall macro effect is a huge overwhelming and singular experience. 2428:. This is unlike later forms such as the sonata, which clearly prescribes which keys are explored (typically the tonic and dominant in an ABA form). Then, many modern fugues dispense with traditional tonal harmonic scaffolding altogether, and either use serial (pitch-oriented) rules, or (as the Kyrie/Christe in 2181:

allow us access to the labyrinth through listening in to individual lines… He creates instead a vastly dense texture of voices in his choir and orchestra, a huge stratified slab of terrifying visionary power. Yet this is music that's made with a fine craft and detail of a Swiss clock maker. Ligeti's so-called '

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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, the

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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

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Further entries of 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

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the composer, having completed the initial imitative entrances, take the passage which has served as accompaniment to the theme and make it the basis for new imitative treatment, so that "he will always have material with which to compose without having to stop and reflect". This formulation of the

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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 the Baroque style. These included a fugue in C minor, K. 426,

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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

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middle-voice is stating a second version of the second countersubject, which concludes with the characteristic rhythm of 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

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takes the logic of the fugal idea and creates something that's meticulously built on precise contrapuntal principles of imitation and fugality, but he expands them into a different region of musical experience. Ligeti doesn't want us to hear individual entries of the subject or any subject, or to

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It expresses the Creation of All Things: space, time, stars, planets – and the Countenance (or rather, the Thought) of God behind the flames and the seething – impossible even to speak of it, I have not attempted to describe it ... Instead, I have sheltered behind the form of the Fugue.

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The fugue is the most complex of contrapuntal forms. In Ratz's words, "fugal technique significantly burdens the shaping of musical ideas, and it was given only to the greatest geniuses, such as Bach and Beethoven, to breathe life into such an unwieldy form and make it the bearer of the highest

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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 the subject in more than one instance, the countersubject must be capable of

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and 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

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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

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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 the inversion of a perfect fifth

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voices in a fugue, the greater 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,

1040:. This passage is bars 6/7, at the end of the codetta before the first entry of the third voice, the bass, in the exposition. The false entry occurs in the alto, and consists of the head of the subject only, marked in red. It anticipates the true entry of the subject, marked in blue, by one 961:

illustrates 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

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concerto. Stravinsky recognized the compositional techniques of Bach, and in the second movement of his Symphony of Psalms (1930), he lays out a fugue that is much like that of the Baroque era. It employs a double fugue with two distinct subjects, the first beginning in C and the second in

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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 the impact of the subject proper.

1386:, which are now thought of as distinct from fugues. Prior to the 16th century, fugue was originally a genre. It was not until 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 817:

is often heard connecting the various statements of the subject and answer, smoothly connecting each and often facilitating 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.

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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 is (are) presented simultaneously with the subject in the exposition (e.g. as in

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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.

2172:(multiple simultaneous subdivisions of the measure), blurring everything both harmonically and rhythmically so as to create an aural aggregate, thus highlighting the theoretical/aesthetic question of the next section as to whether fugue is a form or a texture. According to 1728:(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, the major impetus to fugal writing for Mozart was the influence of Baron 1101: 1315:

are combined. Each voice enters in succession with the subject, each entry alternating between tonic and dominant, and each voice, having stated the initial subject, continues by stating two or more themes (or countersubjects), which must be conceived in correct

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This is related to the idea that restrictions create freedom for the composer, by directing their efforts. He also points out that fugal writing has its roots in improvisation, and was, during the Renaissance, practiced as an improvisatory art. Writing in 1555,

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and 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.

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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.

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begins with a fugal exposition. The exposition ends with a chorale, the melody of which is then used as a second fugal exposition at the beginning of the development. The recapitulation features both fugal subjects concurrently. The finale of Mahler's

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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.

700:. To enable a natural harmonic progression, the answer may also be altered slightly (usually by changing one or 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 733: 2336:, at the point where Kevin, accidentally left at home by his family, and realizing he is about to be attacked by a pair of bumbling burglars, begins to plan his elaborate defenses. Another fugue occurs at a similar point in the 1992 sequel film, 1008: 2405:

are more commonly explored in fugal development, the overall structure of a fugue does not limit its harmonic structure. For example, a fugue may not even explore the dominant, one of the most closely related keys to the tonic. Bach's Fugue in

1576:) 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 2014:

Twentieth-century composers brought fugue back to its position of prominence, realizing its uses in full instrumental works, its importance in development and introductory sections, and the developmental capabilities of fugal composition.

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across the bar line, from the last quarter note beat of the first bar to the first beat of the second bar in the second system, and the first middle entry. Here, Bach has altered the second countersubject to accommodate the change of

913:), 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. 2453:

points out that "counterpoint itself, since time out of mind, has been associated in the thinking of musicians with the profound and the serious" and argues that "there seems to be some rational justification for their doing so."

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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, a tonal answer is usually necessary. To prevent an undermining of the fugue's

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counterpoint that follows. They may also be present to delay, and therefore heighten the impact of, the reentry of the subject in another voice. Finally, they may be modulatory passages to return the fugue to the tonic.

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who died in 1746. The subject, including an eighth note rest, is seen in the alto voice, starting on beat 1 bar 1 and ending on beat 1 bar 3, which is where the answer would usually be expected to begin. As this is a

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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

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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 the countersubjects and/or other free contrapuntal accompaniments.

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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

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argues that the formal organization of a fugue involves not only the arrangement of its theme and episodes, but also its harmonic structure. In particular, the exposition and coda tend to emphasize the

1811:, 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 the 4640: 905:

of the work's overall key, and 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

2398:, whereas the episodes usually explore more distant tonalities. Ratz stressed, however, that this is the core, underlying form ("Urform") of the fugue, from which individual fugues may deviate. 1098: 821:

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

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of all Bartók's works – a fugue that unfolds like a fan to a point of maximum intensity and then closes, returning to the mysterious atmosphere of the opening." The second movement of Bartók's

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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.

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It 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

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of Handel during his visits to London (1791–1793, 1794–1795). Haydn then studied Handel's techniques and incorporated Handelian fugal writing into the choruses of his mature oratorios

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During the answer, the voice in which the subject was previously heard accompanies with new material. If this new material is reused in later statements of the subject, it is called a

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quotes Beethoven's monumental "Große Fuge" for string quartet and employs Arnold Schoenberg's twelve tone technique, all in the context of a jazz infused Broadway show stopper.

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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

1099: 1938:, Op. 24, is a work for solo piano written in 1861. It consists of a set of twenty-five variations and a concluding fugue, all based on a theme from George Frideric Handel's 1231:), 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 1334:

Permutation fugues differ from conventional fugue in that there are no connecting episodes, nor statement of the themes in related keys. So for example, the fugue of Bach's

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is a short fugue that has the same characteristics as a fugue. Often the contrapuntal writing is not strict, and the setting less formal. See for example, variation 24 of

2109:, starting at rehearsal mark 63, is a gigantic fugue in which the 20-bar subject (and tonal answer) consist entirely of semiquavers, played at the speed of quaver = 168. 1775: 731: 1075:

whereby one voice responds with the subject/answer before the first voice has completed its entry of the subject/answer, usually increasing the intensity of the music.

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has a composition called "Fugue State", which incorporates a fugue-like section between Theo Katzman (guitar), Joe Dart (bass), and Woody Goss (Wurlitzer keyboard).

1423:, 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 4528: 2467:

basic rule for fugal improvisation anticipates later sixteenth-century discussions which deal with the improvisational technique at the keyboard more extensively.

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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

1620:(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 196:. 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 1828: 728:, Book 1. The first note of the subject, D (in red), is a prominent dominant note, demanding that the first note of the answer (in blue) sound as the tonic, G. 4647: 4115: 1817:(1805). Beethoven incorporated fugues in his sonatas, and reshaped the episode's purpose and compositional technique for later generations of composers. 204:. 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. 4407:

Einführung in die Musikalische Formenlehre: Über Formprinzipien in den Inventionen J. S. Bachs und ihre Bedeutung für die Kompositionstechnik Beethovens

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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

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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

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Introduction to Musical Form: On the Principles of Form in J. S. Bach's Inventions and their Import for Beethoven's Compositional Technique

2194: 1894:(1965, p. 149) says " bare description of its formal outline can give but little idea of the extraordinary profundity of this fugue ." 1721: 854:

Further entries of the subject may follow the initial exposition either immediately or separated by episodes. Episodic material is always

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was evidently fascinated by these works and wrote a set of five transcriptions for string quartet, K. 405 (1782), of fugues from Bach's

1514:. Some fugues during the Baroque period were pieces designed to teach contrapuntal technique to students. The most influential text was 2046:(1986, pp. 346–47) regards as "certainly the finest and most characteristic example of Bartók's subtle style... probably the most 2038: 1725: 1713: 1335: 1228: 107:(repetition at different pitches), which recurs frequently throughout the course of the composition. It is not to be confused with a 4554: 1616:

Joseph Haydn was the leader of fugal composition and technique in the Classical era. Haydn's most famous fugues can be found in his

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When there is no entrance of the subject and answer material, the composer can develop the subject by altering it. This is called a

897:, although the key structure of fugues varies greatly. In the fugues of J.S. Bach, the first middle entry occurs most often in the 1325: 793:

sounding correctly when played above or below the subject, and must be conceived, therefore, in invertible (double) counterpoint.

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at the Salzburg Cathedral, the young Mozart composed ambitious fugues and contrapuntal passages in Catholic choral works such as

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Fugues (or fughettas/fugatos) have been incorporated into genres outside Western classical music. Several examples exist within

1413:. The fugue arose from the technique of "imitation", where the same musical material was repeated starting on a different note. 1820:

Nevertheless, fugues did not take on a truly central role in Beethoven's work until his late period. The finale of Beethoven's

4413:] (first edition with supplementary volume). Vienna: Österreichischer Bundesverlag für Unterricht, Wissenschaft und Kunst. 2117: 867:, stated that the episode of the fugue is generally based on a series of imitations of the subject that have been fragmented. 3994: 3967: 3834:. Translated by Thomas Irvine (this chapter). Cambridge, Massachusetts: Harvard University Department of Music. p. 236. 3639: 3570: 3532: 3486: 3447: 3414: 3371: 3319: 3228: 3116: 3070: 2977: 2878: 2838: 2793: 2723: 2670: 2592: 2098: 822: 719: 2902:, eleventh edition, revised, ed. Catherine Soanes and Angus Stevenson (Oxford and New York: Oxford University Press, 2006). 2495:, eleventh edition, revised, ed. Catherine Soanes and Angus Stevenson (Oxford and New York: Oxford University Press, 2006). 1608:

had periods of their careers in which they in some sense "rediscovered" fugal writing and used it frequently in their work.

1095:, the answer already takes place in the tenor voice, on the third quarter note of the first bar, therefore coming in "early" 259:

rose to a more prominent position. Nevertheless, composers continued to write and study fugues; they appear in the works of

4633: 2055: 2083: 2064:(Czech: Švanda dudák), written in 1926, an opera in two acts (five scenes), with music by Jaromír Weinberger, includes a 4525: 1849:, "With the finale of 110, Beethoven re-conceived the significance of the most traditional elements of fugue writing." 114: 2051: 1148: 4578: 4509: 4453: 4384: 4337: 4142: 3839: 2962: 2655: 2527: 1873: 1863: 4568: 3437: 3060: 2967: 2904: 2497: 1971: 1543:, for example, taught counterpoint from his own summary of Fux and thought of it as the basis for formal structure. 207:

The form evolved during the 18th century from several earlier types of contrapuntal compositions, such as imitative

4547: 3476: 2660: 1532: 1428: 2268:, the characters Nicely-Nicely, Benny, and Rusty sing simultaneously about hot tips they each have in an upcoming 4783: 1949: 1836: 1832: 1821: 1621: 1617: 1452:

that the writing of fugues became central to composition, in part as a demonstration of compositional expertise.

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may also occur by inversion, augmentation and diminution. A fugue in which the opening exposition takes place in

1087: 4573: 2093:. Techniques such as stretto, sequencing, and the use of subject incipits are frequently heard in the movement. 1270:(upside down), and the inverted subject continues to feature prominently throughout the fugue. Examples include 4562: 2643: 2338: 2211: 1633: 2320:

included an atonal or twelve-tone fugue, for flute trumpet and string quartet, in his score for the 1953 film

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The closing section of a fugue often includes one or two counter-expositions, and possibly a stretto, in the

3158: 2156:'s second movement, the Kyrie, in which each part (SMATB) is subdivided in four-voice "bundles" that make a 2142:) have nothing to do with the academic fugue. Like those great models, this one is an anti-scholastic fugue. 1531:, and offered a series of exercises to learn fugue writing. Fux's work was largely based on the practice of 2006:

features a "fugue-like" passage early in the movement, though this is not actually an example of a fugue.

1600:, the fugue was no longer a central or even fully natural mode of musical composition. Nevertheless, both 3621: 3514: 3396: 3353: 3301: 3210: 3098: 2860: 2820: 2775: 2705: 2574: 177:

has described what is commonly regarded as the most fully developed procedure of imitative counterpoint.

1624:(1787). Some of the earliest examples of Haydn's use of counterpoint, however, are in three symphonies ( 4743: 4620: 4609: 4347: 2386:

A widespread view of the fugue is that it is not a musical form but rather a technique of composition.

2355: 1859: 1854: 1813: 4595: 2745: 1890:(1927, p. 235) hears it as "the most superhuman piece of music that Beethoven has ever written." 1801:

was familiar with fugal writing from childhood, as an important part of his training was playing from

4537: 4364: 4082: 3712: 2548: 2295: 2102: 1998: 1803: 1581: 1577: 1548: 1453: 750:. For the same reason, it is possible for the answer of such a subject to be in the subdominant key. 228: 180:

Most fugues open with a short main theme, called the subject, which then sounds successively in each

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describes a type of composition (or technique of composition) in which elements of fugue and strict

942:(the enlargement of the subject's rhythmic values by a certain factor), or any combination thereof. 4778: 1755: 1689: 1673: 1597: 3820: 3591: 2647: 2349:, includes a fugue as the climax of his score (a classical theme with variations, and fugue) for 2003: 1697: 1669: 1665: 1629: 1605: 1536: 1317: 1221: 1200: 789: 781: 260: 813:

Fugue No. 1 in C Major, BWV 846 uses a SAAS (subject-answer-answer-subject) exposition. A brief

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Analyses of J. S. Bach's Fugue for Solo Violin in C major, BWV 1005 (tutorial video with score)

2161: 2024: 1625: 1476: 1461: 232: 192:, developed from previously heard material; further "entries" of the subject are then heard in 143: 20: 3984: 3957: 3599: 1997:

also included them in their respective symphonies. The exposition of the finale of Bruckner's

3562: 1928: 1735: 1729: 1637: 1238: 1034: 1030: 997: 993: 955: 951: 809: 805: 724: 716: 224: 43: 2437: 3827: 3631: 3524: 3473:, fourth edition, ed. Michael Kennedy (Oxford and New York: Oxford University Press, 1996) 3406: 3363: 3311: 3220: 3108: 2870: 2830: 2785: 2715: 2584: 2246: 2138: 1798: 1693: 1653: 1528: 1457: 1351: 939: 264: 240: 38: 28: 8: 4614: 4551: 3897: 2402: 2279:", the dance sequence following the song "Cool" is structured as a fugue. Interestingly, 2250: 2094: 1923:, fugue writing had become specifically attached to the norms and styles of the Baroque. 1659: 1519: 1465: 1355: 1174:. Any material that follows the final entry of the subject is considered to be the final 931: 906: 886: 876: 704:; alternatively, if the intervals of the subject are altered in any way, the answer is a 268: 244: 193: 134: 92: 4076:

Eric Drott, "Lines, Masses, Micropolyphony: Ligeti's Kyrie and the 'Crisis of the Figure

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is a fugue, and there are fugal passages in the last movements of his Piano Sonatas in

1492: 855: 679: 329: 256: 150:, the fugue was fundamental in showing mastery of harmony and tonality as it presented 130: 126: 1750: 1647:

Haydn's second fugal period occurred after he heard, and was greatly inspired by, the

1636:) that date from 1762 to 1763. The earliest fugues, in both the symphonies and in the 247:(c. 1637–1707) and others. With the decline of sophisticated styles at the end of the 4696: 4505: 4459: 4449: 4423: 4390: 4380: 4333: 4326: 4309: 4292: 4148: 4138: 4131: 4009: 3990: 3963: 3926: 3835: 3635: 3566: 3555: 3528: 3482: 3443: 3410: 3367: 3315: 3224: 3112: 3066: 2973: 2958: 2874: 2834: 2789: 2719: 2666: 2651: 2588: 2523: 2280: 1955: 1924: 1887: 1515: 1504: 1420: 1284:. During the Baroque period, counter-fugues were sometimes called by the Latin name 1267: 922: 777: 761: 212: 170: 104: 4448:. Eastman studies in music. Vol. 13. Rochester: University of Rochester Press. 3550: 2449:

thoughts." In presenting Bach's fugues as among the greatest of contrapuntal works,

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A fugue begins with the exposition of its subject in one of the voices alone in the

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featured a quick fugal section after a slow introduction. The second movement of a

1416: 1387: 1382:, but was initially used to refer to any kind of imitative counterpoint, including 1289: 1280: 1224: 963: 773: 664: 236: 220: 60: 4280: 3821:"On ancient languages: the historical idiom in the music of Wolfgang Amadé Mozart" 2599:‎ for discussion of the changing use of the term throughout Western music history. 2429: 2215:, a full-scale fugue set to a text that cleverly explicates its own musical form. 2146: 1300:(1739), and some German-language texts use that name to refer to a counter-fugue. 860: 4773: 4711: 4681: 4558: 4542: 4532: 2276: 2075: 1986: 1952:(1853) contains a powerful fugue, demanding incisive virtuosity from its player: 1882:

that several commentators regard as one of the composer's greatest achievements.

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studied from this book, and it remained influential into the nineteenth century.

1496: 1179: 1155: 977: 930:. In any of the entries within a fugue, the subject may be altered by inversion, 894: 849: 746:, this note is transposed up a fourth to the tonic rather than up a fifth to the 693: 100: 50: 4067:. Translator not indicated. Erato Disques S.A. 4509-91705-2, 1993. Compact Disc. 759:; if this accompanying material is only heard once, it is simply referred to as 4686: 4372: 3245:

Bach, Johann Sebastian (1997). "Fuge Nr. 2". In Heinemann, Ernst-Günter (ed.).

2417: 2346: 2261: 2232: 2182: 1990: 1976: 1966: 1920: 1748:

for two pianos (1783). Later, Mozart incorporated fugal writing into his opera

1740: 1705: 1427:, but by the 1550s, it was considered a technique of composition. The composer 1379: 902: 898: 755: 272: 4603: 4166: 3267:. Cambridge, Massachusetts, and London: Harvard University Press. p. 178. 1960: 1908: 1676:; and the late string quartets, Opus 71 no. 3 and (especially) Opus 76 no. 6. 4767: 4721: 4706: 4676: 4671: 4625: 4487: 3910: 3892: 3816: 3617: 3510: 3392: 3349: 3297: 3206: 3094: 2856: 2816: 2771: 2701: 2570: 2360: 2327: 2317: 2265: 2236: 2199: 2157: 2043: 2019: 1994: 1883: 1846: 1701: 1685: 1573: 1552:, which many composers and theorists look at as the greatest model of fugue. 1484: 1472: 1449: 1424: 1383: 1312: 1167: 1116:

in which the subject/answer is heard in completion in all voices is known as

967: 864: 711: 685: 656: 248: 197: 162: 138: 96: 4463: 4152: 4099: 2522:. Vol. 2 (3rd ed.). Dubuque: Wm. C. Brown Publishers. p. 45. 1868: 1495:

has only a few fugues among his corpus of over 500 harpsichord sonatas. The

227:(1685–1750), well known for his fugues, shaped his own works after those of 4716: 4656: 4427: 4394: 2364: 2350: 2303: 2269: 2132: 1601: 1540: 1511: 1435:

counterpoint and imitation, and fugal writing became the basis for writing

1432: 1175: 1041: 982: 890: 885:

Middle entries tend to occur at keys other than the tonic. These are often

826: 689: 201: 181: 151: 137:, and a final entry that contains the return of the subject in the fugue's 109: 85: 4313: 4296: 2957:, ed. Alison Latham (Oxford and New York: Oxford University Press, 2002). 4116:"Listening to Britten – the Young Person's Guide to the Orchestra, Op.34" 4103: 4095: 3057:, ed. Alison Latham (Oxford and New York: Oxford University Press, 2002) 2425: 2206: 2173: 1945: 1790:

fugue which, some believe, would have come at the end of the Sequentia).

1171: 743: 252: 166: 158: 122: 4402: 4328:

Music Alone: Philosophical Reflections on the Purely Musical Experience

4321: 2740: 2450: 2421: 2390: 2332: 2169: 2165: 1862:, except the third. A massive, dissonant fugue forms the finale of his 1739:, introducing them with preludes of his own. In a letter to his sister 1692:, and the musical influence of his predecessors and colleagues such as 1588:("Treatise on the fugue", 1753) was largely based on J.S. Bach's work. 935: 747: 147: 118: 4500: 988: 938:(the reduction of the subject's rhythmic values by a certain factor), 4660: 2395: 2029: 1524: 910: 768: 89: 16:

Contrapuntal musical form based on a subject that recurs in imitation

1266:

is a fugue in which the first answer is presented as the subject in

319:(a passage in fugal style within another work that is not a fugue). 4701: 2310: 1897: 1648: 1480: 1391: 1108:

Only one entry of the subject must be heard in its completion in a

797: 287:

originated in the 16th century and is derived from the French word

208: 33: 2202:

theme is triumphantly cited at the end, making it a choral fugue.

1866:(1825); the latter was later published separately as Op. 133, the 1640:, exhibit the influence of Joseph Fux's treatise on counterpoint, 1068:

Sometimes counter-expositions or the middle entries take place in

346:

Example of key and entry structure in a three-voice Baroque fugue

4731: 4171: 1872:("Great Fugue"). However, it is the fugue that opens Beethoven's 1761: 1562: 1395: 1251: 1078: 1070: 1063: 814: 216: 2032:(200, p. 88) describes as having "a subtle glint of jazz". 188:

is complete. This is often followed by a connecting passage, or

113:, which is a style of song popularized by and mostly limited to 3475:

Kennedy, Michael; Kennedy, Joyce Bourne; Bourne, Joyce (2007).

2700:

Walker, Paul (2001). "Fugue, §1: A classic fugue analysed". In

2659:

Kennedy, Michael; Kennedy, Joyce Bourne; Bourne, Joyce (2007).

1886:(1966, p. 330) calls it "this most moving of all fugues". 1808: 4588: 4308:. Washington, D.C.: The Catholic University of America Press. 1025: 184:. When each voice has completed its entry of the subject, the 2168:(running) parts overlaid onto skipping intervals, and use of 1488: 1436: 1217: 78: 4446:

Theories of Fugue from the Age of Josquin to the Age of Bach

2440:

works), use panchromatic, or even denser, harmonic spectra.

1718:

Mass in C major, K. 167 "in honorem Sanctissimae Trinitatis"

1684:

The young Wolfgang Amadeus Mozart studied counterpoint with

1527:"), which appeared in 1725. This work laid out the terms of 825:, the first codetta is absent. The subject concludes on the 696:, with the latter being less common), which is known as the 334:

changes. The various entries may or may not be separated by

66: 2224: 1787: 1765:

Fugal passage from the finale of Mozart's Symphony No. 41 (

1546:

Bach's most famous fugues are those for the harpsichord in

251:, the fugue's central role waned, eventually giving way as 4025:

Howat, R. (2000) "Ravel and the Piano" in Mawer, D. (ed.)

1401:"Fugue" as a theoretical term first occurred in 1330 when 1227:

or the fugue of Bach's Passacaglia and Fugue in C minor,

103:(a musical theme) that is introduced at the beginning in 69: 4605:

Visualization of Bach's "Little" Fugue in G minor, organ

2815:

Walker, Paul (2001). "Fugue, §6: Late 18th century". In

1927:

wrote many fugues inspired by his study of the music of

1510:

The Baroque period also saw a rise in the importance of

4291:]. trans. A. Levin. Mattapan: Gamut Music Company. 3093:

Drabkin, William (2001). "Invertible Counterpoint". In

2078:

also incorporated fugues into his works, including the

4167:"Fugue for Tinhorns - Guys and Dolls (1955) - YouTube" 1664:

as well as several of his later symphonies, including

4741: 4492:

The Art of Fugue: Bach Fugues for Keyboard, 1715–1750

3348:

Walker, Paul (2001). "Fugue, §5: The golden age". In

2121:(1944) wrote of the sixth piece of that collection, " 1979:

included a whimsical example at the end of his opera

63: 3474: 3434:, Ed. Alison Latham, Oxford University Press, 2002, 3276: 3274: 2658: 3156:Paul Walker, "Fugue, §1: A Classic Fugue Analysed" 3025: 3023: 2855:Walker, Paul (2001). "Fugue, §8: 20th century". In 1206: 4325: 4130: 3799: 3797: 3554: 3263:(1996). "Figments of the Organicist Imagination". 3177: 3175: 2607: 2605: 2101:is the composer's homage to Bach's two volumes of 161:, the term was widely used to denote any works in 4133:Wondrous Strange: The Life and Art of Glenn Gould 3742:. New York: Oxford University Press. p. 243. 3678: 3676: 3271: 2330:includes a fugue in his score for the 1990 film, 267:(1770–1827), as well as modern composers such as 4765: 4482:. New York/London: Free Press/Collier-Macmillan. 3020: 2160:. The melodic material in this fugue is totally 1989:contained two (originally three) choral fugues. 1244:, or more famously, Bach's "St. Anne" Fugue in E 780:(dissonant) and therefore cannot be employed in 3962:. University of California Press. p. 223. 3794: 3627:The New Grove Dictionary of Music and Musicians 3520:The New Grove Dictionary of Music and Musicians 3402:The New Grove Dictionary of Music and Musicians 3359:The New Grove Dictionary of Music and Musicians 3307:The New Grove Dictionary of Music and Musicians 3216:The New Grove Dictionary of Music and Musicians 3172: 3104:The New Grove Dictionary of Music and Musicians 3014:Contrapuntal Technique in the Sixteenth Century 2866:The New Grove Dictionary of Music and Musicians 2826:The New Grove Dictionary of Music and Musicians 2781:The New Grove Dictionary of Music and Musicians 2711:The New Grove Dictionary of Music and Musicians 2602: 2580:The New Grove Dictionary of Music and Musicians 2359:, based on the 1953 novel by British novelist, 4655: 4205:. London: Oxford University Press. p. 17. 4086:49, no. 1 (Winter 2011): 4–46. Citation on 10. 3673: 3585: 3205:Walker, Paul (2001). "Counter-exposition". In 3016:. London: Oxford University Press. p. 47. 2953:G. M. Tucker and Andrew V. Jones, "Fugue", in 2905:"Oxford Reference Online, subscription access" 2498:"Oxford Reference Online, subscription access" 1369: 1086:fugue in a quotation from Fugue in C major by 129:. A fugue usually has three main sections: an 4641: 4203:Essays in Music Analysis Volume I: Symphonies 3959:The Great Composers: Reviews and Bombardments 3815: 3616:Walker, Paul (2001). "Permutation Fugue". In 3291: 3289: 2546:(Cambridge: Harvard University Press, 2003), 2443: 2136:and the fugue from Beethoven's Opus 106 (the 1296:to refer to a counter-fugue construct in his 3858:. New York: Dorset Press. 1986. p. 195. 3478:Oxford Reference Online, subscription access 3439:Oxford Reference Online, subscription access 3062:Oxford Reference Online, subscription access 2969:Oxford Reference Online, subscription access 2765: 2763: 2662:Oxford Reference Online, subscription access 2363:, as well as several times in his score for 934:(where the subject is heard back-to-front), 3737: 2483: 2481: 1487:from this time often conclude with a fugal 1471:Fugues were incorporated into a variety of 1199:has only one subject, and does not utilize 1146: 146:. A popular compositional technique in the 4648: 4634: 4420:Fugue and Invention in Theory and Practice 4377:Classic Music: Expression, Form, and Style 3286: 2949: 2947: 2945: 2943: 2941: 2939: 2937: 2935: 2933: 2381: 2218: 2054:is a fugue, and the first movement of his 1907:minor, Op. 131, opening fugal exposition. 1419:, a composer, author, and theorist in the 1033:Fugue No. 2 in C minor, BWV 847, from the 996:Fugue No. 2 in C minor, BWV 847, from the 954:Fugue No. 2 in C minor, BWV 847, from the 4499: 3557:The Art of Fugue & A Musical Offering 3509:Walker, Paul (2001). "Counter-fugue". In 2760: 2695: 2693: 2691: 2689: 2195:The Young Person's Guide to the Orchestra 2039:Music for Strings, Percussion and Celesta 1936:Variations and Fugue on a Theme by Handel 1336:Passacaglia and Fugue in C minor, BWV 582 1161: 4379:. London: Collier Macmillan Publishers. 3989:. Oxford University Press. p. 340. 3586:Paul M. Walker (2001). "Counter-fugue". 3391:Walker, Paul (2001). "Double Fugue". In 2478: 1954: 1896: 1760: 1077: 1024: 987: 767: 710: 173:works. Since the 17th century, the term 27: 4417: 4279: 4128: 3706: 3611: 3609: 3600:10.1093/gmo/9781561592630.article.06689 3335: 3296:Walker, Paul (2001). "Stretto (i)". In 3280: 3259: 3193: 3181: 3144: 3132: 3092: 3041: 3029: 2999: 2930: 2924: 2623: 2517: 1644:(1725), which Haydn studied carefully. 945: 4766: 4443: 4434: 4371: 4303: 4190:. London: Plumbago Books. p. 167. 4185: 4051: 3982: 3880: 3868: 3803: 3788: 3764: 3752: 3725: 3682: 3667: 3655: 3615: 3508: 3471:The Concise Oxford Dictionary of Music 3435: 3390: 3347: 3295: 3204: 3058: 3011: 2965: 2854: 2814: 2810: 2808: 2806: 2769: 2699: 2686: 2640:The Concise Oxford Dictionary of Music 2611: 2568: 1572:, is a collection of fugues (and four 4629: 4200: 4137:. New York: Oxford University Press. 2900:The Concise Oxford English Dictionary 2634: 2632: 2493:The Concise Oxford English Dictionary 2345:The jazz composer and film composer, 2205:Canadian pianist and musical thinker 1969:included several fugues in his opera 1852:Fugal passages are also found in the 1722:Mass in C major, K. 262 "Missa longa" 1170:; sometimes over a tonic or dominant 1048: 784:, without preparation and resolution. 307:("to chase"). The adjectival form is 169:, it had come to denote specifically 84:, meaning "flight" or "escape") is a 4439:. New York: Broude Brothers Limited. 4401: 4358: 4346: 4332:. Ithaca: Cornell University Press. 4320: 4263: 4251: 4239: 4233: 4227: 4215: 3955: 3776: 3694: 3606: 3548: 3386: 3384: 3244: 2056:Sonata for Two Pianos and Percussion 2042:(1936) opens with a slow fugue that 1710:Mass in C minor, K. 139 "Waisenhaus" 1688:in Bologna. Under the employment of 1303: 295:. This in turn comes from the Latin 4548:Fugues of the Well-Tempered Clavier 3709:Music in the Age of the Renaissance 3341: 2803: 2290:, such as the central movement of " 2149:wrote a five-part double fugue for 2125:" ("By Him were all things made"): 1940:Harpsichord Suite No. 1 in B♭ major 13: 4494:. University of California Press. 4471: 4354:. London: Oxford University Press. 3265:Bach and the Patterns of Invention 2629: 2192:used a fugue in the final part of 1726:Mass in C major, K. 337 "Solemnis" 1714:Mass in C major, K. 66 "Dominicus" 322: 299:, which is itself related to both 14: 4795: 4519: 3381: 2770:Walker, Paul (2001). "Fugue". In 2569:Walker, Paul (2001). "Fugue". In 2286:A few examples also exist within 2231:, composed by the Welsh composer 1959:Liszt Piano Sonata fugue subject 788:The countersubject is written in 4751: 4730: 4065:Vingt Regards sur l'Enfant Jésus 4027:The Cambridge Companion to Ravel 3983:Budden, Julian (December 2015). 3832:The Century of Bach & Mozart 2118:Vingt regards sur l'enfant-Jésus 1770: 1591: 1431:(1525?–1594) wrote masses using 1429:Giovanni Pierluigi da Palestrina 1257: 1207:Double (triple, quadruple) fugue 1096: 1016: 1004: 966:, in the form of an accompanied 950:The excerpt below, bars 7–12 of 823:Fugue No. 16 in G minor, BWV 861 729: 720:Fugue No. 16 in G minor, BWV 861 59: 4437:The Origin of Permutation Fugue 4304:Graves, William L. Jr. (1962). 4257: 4245: 4221: 4209: 4194: 4179: 4159: 4122: 4108: 4089: 4070: 4057: 4045: 4032: 4019: 4016:, trans. Wicker. Amadeus Press. 4003: 3976: 3949: 3936: 3920: 3904: 3886: 3874: 3862: 3848: 3809: 3782: 3770: 3758: 3746: 3731: 3719: 3700: 3688: 3661: 3649: 3579: 3549:Bach, Johann Sebastian (1992). 3542: 3502: 3463: 3424: 3329: 3253: 3238: 3198: 3187: 3150: 3138: 3126: 3086: 3047: 3035: 3005: 2993: 2918: 2888: 2848: 2544:The Harvard Dictionary of Music 2105:. In the first movement of his 2009: 1914: 1507:and others, was usually fugal. 1190: 1088:Johann Caspar Ferdinand Fischer 200:, which is often followed by a 4201:Tovey, Donald Francis (1962). 2733: 2617: 2562: 2536: 2511: 2462:, for example, suggests that: 2339:Home Alone 2: Lost in New York 2309:On their EP of the same name, 1972:Die Meistersinger von Nürnberg 1443: 870: 1: 4029:. Cambridge University Press. 4014:Gustav Mahler: The Symphonies 3432:The Oxford Companion to Music 3247:Das Wohltemperierte Klavier I 3055:The Oxford Companion to Music 2955:The Oxford Companion to Music 2471: 2376: 2212:So You Want to Write a Fugue? 1807:. During his early career in 1298:Der vollkommene Capellmeister 1254:, a triple fugue for organ.) 1029:Example of a false answer in 810:Well-Tempered Clavier, Book 1 715:Example of a tonal answer in 673: 4583:with accompanying recordings 4422:. Palo Alto: Pacific Books. 2520:Music in Theory and Practice 2260:" from the Broadway musical 1793: 1622:String Quartet, Op. 50 No. 4 1378:was used as far back as the 1327:Himmelskönig, sei willkommen 278: 7: 4480:Fugue: History and Practice 3944:Beethoven's String Quartets 3738:Schulenberg, David (2001). 3707:Perkins, Leeman L. (1999). 3481:. Oxford University Press. 3442:. Oxford University Press. 3065:. Oxford University Press. 2972:. Oxford University Press. 2665:. Oxford University Press. 1829:Cello Sonata, Op. 102 No. 2 1475:, and are found in most of 1370:Middle Ages and Renaissance 1341: 976:major is marked by a quasi 970:at the fourth. Arrival in E 32:The six-part fugue in the " 10: 4800: 4444:Walker, Paul Mark (2000). 4365:W. W. Norton & Company 4273: 3713:W. W. Norton & Company 3249:. Munich: G. Henle Verlag. 3053:"Invertible Counterpoint" 2444:Perceptions and aesthetics 2389:The Austrian musicologist 2296:Emerson, Lake & Palmer 2072:based on the Polka theme. 1364: 1154:choruses from J.S. Bach's 1061: 1057: 927: 874: 847: 843: 677: 18: 4728: 4667: 4579:Analyses of J. S. Bach's 4538:The Well-Tempered Clavier 4478:Horsley, Imogene (1966). 4418:Verrall, John W. (1966). 4083:Perspectives of New Music 3917:. Oxford University Press 3830:; Sean Gallagher (eds.). 3561:. Courier Dover. p. 2412:major from Book 1 of the 2103:The Well-Tempered Clavier 1858:and all movements of the 1804:The Well-Tempered Clavier 1679: 1582:Friedrich Wilhelm Marpurg 1580:and through the theorist 1554:The Well-Tempered Clavier 1549:The Well-Tempered Clavier 1529:"species" of counterpoint 1454:Jan Pieterszoon Sweelinck 532: 504: 484: 455: 429: 369: 357: 352: 229:Jan Pieterszoon Sweelinck 4557:25 February 2019 at the 4531:7 September 2006 at the 3901:, p. 501. London, Faber. 3630:(2nd ed.). London: 3523:(2nd ed.). London: 3405:(2nd ed.). London: 3362:(2nd ed.). London: 3310:(2nd ed.). London: 3219:(2nd ed.). London: 3107:(2nd ed.). London: 2869:(2nd ed.). London: 2829:(2nd ed.). London: 2784:(2nd ed.). London: 2714:(2nd ed.). London: 2583:(2nd ed.). London: 1919:By the beginning of the 1611: 1185: 327:A fugue begins with the 4596:The American Cyclopædia 4306:Twentieth Century Fugue 4129:Bazzana, Kevin (2004). 3933:. London, Jonathan Cape 3592:Oxford University Press 3436:Latham, Alison (2011). 3059:Latham, Alison (2011). 2966:Latham, Alison (2011). 2746:Encyclopædia Britannica 2648:Oxford University Press 2518:Benward, Bruce (1985). 2382:Musical form or texture 2219:Outside classical music 2176:, in this work, Ligeti 2123:Par Lui tout a été fait 2068:followed by a powerful 2028:(1917) is a fugue that 2018:The second movement of 1985:and his setting of the 1950:Piano Sonata in B minor 1901:Beethoven, Quartet in C 1864:String Quartet, Op. 130 1698:Anton Cajetan Adlgasser 1586:Abhandlung von der Fuge 1318:invertible counterpoint 1201:invertible counterpoint 920:, which often uses the 790:invertible counterpoint 782:invertible counterpoint 370:Final entries in tonic 261:Wolfgang Amadeus Mozart 223:. The Baroque composer 165:style; however, by the 93:compositional technique 4784:Classical music styles 3956:Shaw, Bernard (1978). 3915:The Beethoven Quartets 3012:Morris, R. O. (1958). 2646:(Oxford and New York: 2642:, fourth edition, ed. 2469: 2187: 2144: 2099:24 Preludes and Fugues 2052:Sonata for Solo Violin 2025:Le Tombeau de Couperin 1963: 1911: 1779: 1754:and the finale of his 1704:, and his own father, 1477:George Frideric Handel 1462:Johann Jakob Froberger 1162:Final entries and coda 1147: 1140:(see for example, the 1105: 1045: 1013: 785: 738: 315:("a small fugue") and 233:Johann Jakob Froberger 46: 21:Fugue (disambiguation) 4581:Well-Tempered Clavier 4574:Fugues and fugue sets 4435:Walker, Paul (1992). 4359:Mann, Alfred (1965). 4188:Film Music and Beyond 4186:Keller, Hans (2006). 4098:. (26 November 2017) 3946:. London, Hutchinson. 3942:Radcliffe, P. (1965) 2464: 2414:Well Tempered Clavier 2178: 2127: 2062:Schwanda the Bagpiper 1958: 1929:Johann Sebastian Bach 1900: 1764: 1736:Well-Tempered Clavier 1730:Gottfried van Swieten 1240:Well-Tempered Clavier 1081: 1036:Well-Tempered Clavier 1028: 999:Well-Tempered Clavier 991: 957:Well-Tempered Clavier 875:Further information: 848:Further information: 771: 725:Well-Tempered Clavier 714: 678:Further information: 225:Johann Sebastian Bach 44:Johann Sebastian Bach 31: 3828:Thomas Forrest Kelly 3740:Music of the Baroque 3632:Macmillan Publishers 3525:Macmillan Publishers 3407:Macmillan Publishers 3364:Macmillan Publishers 3312:Macmillan Publishers 3221:Macmillan Publishers 3159:"Grove Music Online" 3109:Macmillan Publishers 2871:Macmillan Publishers 2831:Macmillan Publishers 2786:Macmillan Publishers 2716:Macmillan Publishers 2585:Macmillan Publishers 2249:and recorded by the 2139:Hammerklavier sonata 2115:, writing about his 1799:Ludwig van Beethoven 1694:Johann Ernst Eberlin 1690:Archbishop Colloredo 1458:Girolamo Frescobaldi 946:Example and analysis 887:closely related keys 265:Ludwig van Beethoven 241:Girolamo Frescobaldi 39:The Musical Offering 19:For other uses, see 4550:(viewable in Adobe 3898:The Classical Style 2251:Modern Jazz Quartet 2095:Dmitri Shostakovich 2058:contains a fugato. 1874:String Quartet in C 1642:Gradus ad Parnassum 1520:Gradus Ad Parnassum 1516:Johann Joseph Fux's 1466:Dieterich Buxtehude 1357:Diabelli Variations 1142:Gratias agimus tibi 1132:form is known as a 992:Visual analysis of 877:Musical development 347: 311:. Variants include 269:Dmitri Shostakovich 245:Dieterich Buxtehude 4373:Ratner, Leonard G. 4361:The Study of Fugue 4352:The Study of Fugue 4285:Traité de la fugue 4118:. 18 October 2013. 4038:Boulez, P. (1986) 4010:Floros, Constantin 3927:Sullivan, J. W. N. 3715:. pp. 880–81. 3588:Grove Music Online 2438:Witold Lutosławski 2326:The film composer 2292:The Endless Enigma 2258:Fugue for Tinhorns 2080:Symphony of Psalms 1964: 1912: 1780: 1584:(1718–1795) whose 1493:Domenico Scarlatti 1468:all wrote fugues. 1288:. German composer 1237:minor from Bach's 1225:Requiem in D minor 1106: 1049:Counter-exposition 1046: 1014: 918:counter-exposition 786: 772:The interval of a 739: 680:Exposition (music) 651:= countersubject; 345: 257:symphony orchestra 127:West Gallery music 47: 4739: 4738: 4501:10.1525/luminos.1 4289:Treatise on Fugue 4012:. (1997, p. 135) 3996:978-0-19-027398-9 3969:978-0-520-03266-8 3856:Letters of Mozart 3641:978-1-56159-239-5 3572:978-0-486-27006-7 3534:978-1-56159-239-5 3488:978-0-19-920383-3 3449:978-0-19-957903-7 3416:978-1-56159-239-5 3373:978-1-56159-239-5 3321:978-1-56159-239-5 3261:Dreyfus, Laurence 3230:978-1-56159-239-5 3118:978-1-56159-239-5 3072:978-0-19-957903-7 2979:978-0-19-957903-7 2880:978-1-56159-239-5 2840:978-1-56159-239-5 2795:978-1-56159-239-5 2725:978-1-56159-239-5 2672:978-0-19-920383-3 2594:978-1-56159-239-5 2549:"credo Reference" 2401:Although certain 2322:Graham Sutherland 2281:Leonard Bernstein 2229:Bach goes to Town 1934:Johannes Brahms' 1925:Felix Mendelssohn 1888:J. W. N. Sullivan 1782:The parts of the 1776: 1535:'s modal fugues. 1505:Arcangelo Corelli 1309:Permutation fugue 1304:Permutation fugue 1276:Contrapunctus VII 1118:stretto maestrale 1102: 1010: 891:relative dominant 762:free counterpoint 735: 667: 634: 633: 519: 499: 470: 444: 391: 283:The English term 42:, in the hand of 4791: 4756: 4755: 4754: 4747: 4734: 4650: 4643: 4636: 4627: 4626: 4617: 4606: 4600: 4592: 4569:Theory on fugues 4515: 4503: 4483: 4467: 4440: 4431: 4414: 4398: 4368: 4355: 4343: 4331: 4317: 4300: 4267: 4261: 4255: 4249: 4243: 4237: 4231: 4225: 4219: 4213: 4207: 4206: 4198: 4192: 4191: 4183: 4177: 4176: 4163: 4157: 4156: 4136: 4126: 4120: 4119: 4112: 4106: 4100:"Chasing a Fugue 4093: 4087: 4079: 4074: 4068: 4061: 4055: 4049: 4043: 4042:. London, Faber. 4036: 4030: 4023: 4017: 4007: 4001: 4000: 3980: 3974: 3973: 3953: 3947: 3940: 3934: 3924: 3918: 3908: 3902: 3890: 3884: 3878: 3872: 3866: 3860: 3859: 3852: 3846: 3845: 3825: 3813: 3807: 3801: 3792: 3786: 3780: 3774: 3768: 3762: 3756: 3750: 3744: 3743: 3735: 3729: 3723: 3717: 3716: 3704: 3698: 3692: 3686: 3680: 3671: 3665: 3659: 3653: 3647: 3645: 3613: 3604: 3603: 3583: 3577: 3576: 3560: 3546: 3540: 3538: 3506: 3500: 3499: 3497: 3495: 3469:"Double Fugue", 3467: 3461: 3460: 3458: 3456: 3428: 3422: 3420: 3388: 3379: 3377: 3345: 3339: 3333: 3327: 3325: 3293: 3284: 3278: 3269: 3268: 3257: 3251: 3250: 3242: 3236: 3234: 3202: 3196: 3191: 3185: 3179: 3170: 3169: 3167: 3165: 3154: 3148: 3147:, pp. 71–72 3142: 3136: 3130: 3124: 3122: 3090: 3084: 3083: 3081: 3079: 3051: 3045: 3039: 3033: 3027: 3018: 3017: 3009: 3003: 2997: 2991: 2990: 2988: 2986: 2951: 2928: 2922: 2916: 2915: 2913: 2911: 2892: 2886: 2884: 2852: 2846: 2844: 2812: 2801: 2799: 2767: 2758: 2757: 2755: 2753: 2737: 2731: 2729: 2697: 2684: 2683: 2681: 2679: 2636: 2627: 2621: 2615: 2609: 2600: 2598: 2566: 2560: 2559: 2557: 2555: 2540: 2534: 2533: 2515: 2509: 2508: 2506: 2504: 2485: 2460:Nicola Vicentino 2411: 2410: 2288:progressive rock 2235:and recorded by 2190:Benjamin Britten 2113:Olivier Messiaen 2092: 2091: 1906: 1905: 1892:Philip Radcliffe 1879: 1878: 1842: 1841: 1833:A major, Op. 101 1778: 1777: 1745:andante maestoso 1568:The Art of Fugue 1503:, as written by 1501:sonata da chiesa 1417:Gioseffo Zarlino 1411:Speculum musicae 1405:wrote about the 1403:Jacobus of Liege 1292:coined the term 1290:Johann Mattheson 1281:The Art of Fugue 1249: 1248: 1236: 1235: 1178:and is normally 1152: 1149:Dona nobis pacem 1104: 1103: 1012: 1011: 975: 974: 834: 833: 737: 736: 639: 505: 485: 456: 430: 397:Relative maj/min 389: 348: 344: 303:("to flee") and 271:(1906–1975) and 263:(1756–1791) and 237:Johann Pachelbel 76: 75: 72: 71: 68: 65: 4799: 4798: 4794: 4793: 4792: 4790: 4789: 4788: 4779:Polyphonic form 4764: 4763: 4762: 4758:Classical music 4752: 4750: 4742: 4740: 4735: 4726: 4682:English cadence 4663: 4654: 4615: 4604: 4587: 4559:Wayback Machine 4543:Mutopia Project 4535:, J. S. Bach's 4533:Wayback Machine 4522: 4512: 4486: 4477: 4474: 4472:Further reading 4456: 4387: 4340: 4276: 4271: 4270: 4262: 4258: 4250: 4246: 4238: 4234: 4226: 4222: 4214: 4210: 4199: 4195: 4184: 4180: 4165: 4164: 4160: 4145: 4127: 4123: 4114: 4113: 4109: 4094: 4090: 4077: 4075: 4071: 4062: 4058: 4050: 4046: 4037: 4033: 4024: 4020: 4008: 4004: 3997: 3981: 3977: 3970: 3954: 3950: 3941: 3937: 3925: 3921: 3909: 3905: 3891: 3887: 3879: 3875: 3867: 3863: 3854: 3853: 3849: 3842: 3823: 3814: 3810: 3802: 3795: 3787: 3783: 3775: 3771: 3763: 3759: 3751: 3747: 3736: 3732: 3724: 3720: 3705: 3701: 3693: 3689: 3685:, pp. 9–10 3681: 3674: 3666: 3662: 3654: 3650: 3642: 3614: 3607: 3584: 3580: 3573: 3551:Dörffel, Alfred 3547: 3543: 3535: 3507: 3503: 3493: 3491: 3489: 3468: 3464: 3454: 3452: 3450: 3430:"double fugue" 3429: 3425: 3417: 3389: 3382: 3374: 3346: 3342: 3334: 3330: 3322: 3294: 3287: 3279: 3272: 3258: 3254: 3243: 3239: 3231: 3203: 3199: 3192: 3188: 3180: 3173: 3163: 3161: 3157: 3155: 3151: 3143: 3139: 3131: 3127: 3119: 3091: 3087: 3077: 3075: 3073: 3052: 3048: 3040: 3036: 3028: 3021: 3010: 3006: 2998: 2994: 2984: 2982: 2980: 2952: 2931: 2923: 2919: 2909: 2907: 2903: 2893: 2889: 2881: 2853: 2849: 2841: 2813: 2804: 2796: 2768: 2761: 2751: 2749: 2741:"Fugue | music" 2739: 2738: 2734: 2726: 2698: 2687: 2677: 2675: 2673: 2644:Michael Kennedy 2637: 2630: 2622: 2618: 2610: 2603: 2595: 2567: 2563: 2553: 2551: 2547: 2541: 2537: 2530: 2516: 2512: 2502: 2500: 2496: 2486: 2479: 2474: 2446: 2408: 2407: 2384: 2379: 2277:West Side Story 2221: 2183:micro-polyphony 2107:Fourth Symphony 2089: 2088: 2076:Igor Stravinsky 2022:'s piano suite 2012: 1961:Link to passage 1917: 1903: 1902: 1876: 1875: 1845:. According to 1839: 1838: 1814:Eroica Symphony 1796: 1771: 1756:Symphony No. 41 1751:Die Zauberflöte 1682: 1614: 1594: 1497:French overture 1446: 1372: 1367: 1344: 1306: 1272:Contrapunctus V 1260: 1246: 1245: 1233: 1232: 1209: 1193: 1188: 1164: 1156:Mass in B minor 1097: 1066: 1060: 1051: 1019: 1005: 978:perfect cadence 972: 971: 948: 879: 873: 863:, a teacher of 852: 850:Section (music) 846: 831: 830: 829:(or crotchet) B 730: 682: 676: 627: 621: 612: 606: 588: 579: 573: 564: 558: 541: 539: 537: 535: 529: 525: 517: 515: 513: 511: 509: 507: 497: 495: 493: 491: 489: 487: 482: 476: 468: 466: 464: 462: 460: 458: 450: 442: 440: 438: 436: 434: 432: 427: 390:redundant entry 364: 358:First mid-entry 325: 323:Musical outline 291:or the Italian 281: 95:in two or more 62: 58: 51:classical music 24: 17: 12: 11: 5: 4797: 4787: 4786: 4781: 4776: 4761: 4760: 4737: 4736: 4729: 4727: 4725: 4724: 4719: 4714: 4709: 4704: 4699: 4694: 4689: 4687:False relation 4684: 4679: 4674: 4668: 4665: 4664: 4653: 4652: 4645: 4638: 4630: 4624: 4623: 4612: 4601: 4585: 4576: 4571: 4566: 4545: 4521: 4520:External links 4518: 4517: 4516: 4510: 4488:Kerman, Joseph 4484: 4473: 4470: 4469: 4468: 4454: 4441: 4432: 4415: 4399: 4385: 4369: 4356: 4344: 4338: 4318: 4301: 4281:Gedalge, André 4275: 4272: 4269: 4268: 4256: 4244: 4232: 4220: 4208: 4193: 4178: 4158: 4143: 4121: 4107: 4088: 4069: 4056: 4044: 4031: 4018: 4002: 3995: 3975: 3968: 3948: 3935: 3919: 3911:Kerman, Joseph 3903: 3893:Rosen, Charles 3885: 3873: 3861: 3847: 3840: 3808: 3793: 3781: 3769: 3757: 3745: 3730: 3718: 3699: 3687: 3672: 3660: 3648: 3640: 3618:Sadie, Stanley 3605: 3578: 3571: 3541: 3533: 3511:Sadie, Stanley 3501: 3487: 3462: 3448: 3423: 3415: 3393:Sadie, Stanley 3380: 3372: 3350:Sadie, Stanley 3340: 3328: 3320: 3298:Sadie, Stanley 3285: 3270: 3252: 3237: 3229: 3207:Sadie, Stanley 3197: 3186: 3171: 3149: 3137: 3125: 3117: 3095:Sadie, Stanley 3085: 3071: 3046: 3034: 3019: 3004: 2992: 2978: 2929: 2917: 2887: 2879: 2857:Sadie, Stanley 2847: 2839: 2817:Sadie, Stanley 2802: 2794: 2772:Sadie, Stanley 2759: 2732: 2724: 2702:Sadie, Stanley 2685: 2671: 2628: 2616: 2601: 2593: 2571:Sadie, Stanley 2561: 2535: 2528: 2510: 2476: 2475: 2473: 2470: 2445: 2442: 2418:relative minor 2383: 2380: 2378: 2375: 2356:The Go-Between 2347:Michel Legrand 2262:Guys and Dolls 2233:Alec Templeton 2220: 2217: 2084:Dumbarton Oaks 2011: 2008: 2004:Symphony No. 5 1999:Symphony No. 5 1991:Anton Bruckner 1977:Giuseppe Verdi 1967:Richard Wagner 1916: 1913: 1880:minor, Op. 131 1860:Ninth Symphony 1855:Missa Solemnis 1795: 1792: 1741:Nannerl Mozart 1706:Leopold Mozart 1681: 1678: 1618:"Sun" Quartets 1613: 1610: 1593: 1590: 1473:musical genres 1450:Baroque period 1448:It was in the 1445: 1442: 1371: 1368: 1366: 1363: 1343: 1340: 1305: 1302: 1286:fuga contraria 1278:, from Bach's 1259: 1256: 1208: 1205: 1192: 1189: 1187: 1184: 1163: 1160: 1062:Main article: 1059: 1056: 1050: 1047: 1018: 1015: 947: 944: 899:relative major 872: 869: 845: 842: 756:countersubject 675: 672: 671: 670: 669: 668: 632: 631: 628: 625: 622: 619: 616: 613: 610: 607: 604: 601: 598: 596: 594: 590: 589: 586: 583: 580: 577: 574: 571: 568: 565: 562: 559: 556: 553: 550: 548: 544: 543: 531: 526: 523: 520: 503: 500: 483: 480: 477: 474: 471: 454: 451: 448: 445: 428: 425: 422: 419: 415: 414: 411: 408: 406: 403: 401: 398: 395: 393: 386: 383: 381: 378: 375: 372: 371: 368: 366: 361: 359: 356: 354: 351: 324: 321: 280: 277: 273:Paul Hindemith 249:baroque period 144:recapitulation 115:early American 15: 9: 6: 4: 3: 2: 4796: 4785: 4782: 4780: 4777: 4775: 4772: 4771: 4769: 4759: 4749: 4748: 4745: 4733: 4723: 4722:Voice leading 4720: 4718: 4715: 4713: 4710: 4708: 4705: 4703: 4700: 4698: 4695: 4693: 4690: 4688: 4685: 4683: 4680: 4678: 4675: 4673: 4670: 4669: 4666: 4662: 4658: 4651: 4646: 4644: 4639: 4637: 4632: 4631: 4628: 4622: 4618: 4613: 4611: 4607: 4602: 4598: 4597: 4591: 4590:"Fugue" 4586: 4584: 4582: 4577: 4575: 4572: 4570: 4567: 4564: 4560: 4556: 4553: 4549: 4546: 4544: 4540: 4539: 4534: 4530: 4527: 4524: 4523: 4513: 4511:9780520962590 4507: 4502: 4497: 4493: 4489: 4485: 4481: 4476: 4475: 4465: 4461: 4457: 4455:9781580461504 4451: 4447: 4442: 4438: 4433: 4429: 4425: 4421: 4416: 4412: 4408: 4404: 4400: 4396: 4392: 4388: 4386:9780028720203 4382: 4378: 4374: 4370: 4366: 4362: 4357: 4353: 4349: 4345: 4341: 4339:0-8014-2331-7 4335: 4330: 4329: 4323: 4319: 4315: 4311: 4307: 4302: 4298: 4294: 4290: 4286: 4282: 4278: 4277: 4265: 4260: 4254:, p. 210 4253: 4248: 4242:, p. 206 4241: 4236: 4230:, p. 259 4229: 4224: 4217: 4212: 4204: 4197: 4189: 4182: 4174: 4173: 4168: 4162: 4154: 4150: 4146: 4144:0-19-517440-2 4140: 4135: 4134: 4125: 4117: 4111: 4105: 4101: 4097: 4092: 4085: 4084: 4073: 4066: 4060: 4053: 4048: 4041: 4035: 4028: 4022: 4015: 4011: 4006: 3998: 3992: 3988: 3987: 3979: 3971: 3965: 3961: 3960: 3952: 3945: 3939: 3932: 3928: 3923: 3916: 3912: 3907: 3900: 3899: 3894: 3889: 3882: 3877: 3871:, p. 266 3870: 3865: 3857: 3851: 3843: 3841:9780964031739 3837: 3833: 3829: 3822: 3818: 3817:Ulrich Konrad 3812: 3805: 3800: 3798: 3790: 3785: 3778: 3773: 3767:, p. 317 3766: 3761: 3755:, p. 316 3754: 3749: 3741: 3734: 3728:, p. 165 3727: 3722: 3714: 3710: 3703: 3696: 3691: 3684: 3679: 3677: 3669: 3664: 3657: 3652: 3643: 3637: 3633: 3629: 3628: 3623: 3622:Tyrrell, John 3619: 3612: 3610: 3601: 3597: 3593: 3589: 3582: 3574: 3568: 3564: 3559: 3558: 3552: 3545: 3536: 3530: 3526: 3522: 3521: 3516: 3515:Tyrrell, John 3512: 3505: 3490: 3484: 3480: 3479: 3472: 3466: 3451: 3445: 3441: 3440: 3433: 3427: 3418: 3412: 3408: 3404: 3403: 3398: 3397:Tyrrell, John 3394: 3387: 3385: 3375: 3369: 3365: 3361: 3360: 3355: 3354:Tyrrell, John 3351: 3344: 3337: 3332: 3323: 3317: 3313: 3309: 3308: 3303: 3302:Tyrrell, John 3299: 3292: 3290: 3283:, p. 108 3282: 3277: 3275: 3266: 3262: 3256: 3248: 3241: 3232: 3226: 3222: 3218: 3217: 3212: 3211:Tyrrell, John 3208: 3201: 3195: 3190: 3183: 3178: 3176: 3160: 3153: 3146: 3141: 3134: 3129: 3120: 3114: 3110: 3106: 3105: 3100: 3099:Tyrrell, John 3096: 3089: 3074: 3068: 3064: 3063: 3056: 3050: 3043: 3038: 3031: 3026: 3024: 3015: 3008: 3001: 2996: 2981: 2975: 2971: 2970: 2964: 2963:0-19-866212-2 2960: 2956: 2950: 2948: 2946: 2944: 2942: 2940: 2938: 2936: 2934: 2926: 2921: 2906: 2901: 2897: 2891: 2882: 2876: 2872: 2868: 2867: 2862: 2861:Tyrrell, John 2858: 2851: 2842: 2836: 2832: 2828: 2827: 2822: 2821:Tyrrell, John 2818: 2811: 2809: 2807: 2797: 2791: 2787: 2783: 2782: 2777: 2776:Tyrrell, John 2773: 2766: 2764: 2748: 2747: 2742: 2736: 2727: 2721: 2717: 2713: 2712: 2707: 2706:Tyrrell, John 2703: 2696: 2694: 2692: 2690: 2674: 2668: 2664: 2663: 2657: 2656:0-19-280037-X 2653: 2649: 2645: 2641: 2635: 2633: 2625: 2620: 2614:, p. 263 2613: 2608: 2606: 2596: 2590: 2586: 2582: 2581: 2576: 2575:Tyrrell, John 2572: 2565: 2550: 2545: 2539: 2531: 2529:0-697-03633-2 2525: 2521: 2514: 2499: 2494: 2490: 2484: 2482: 2477: 2468: 2463: 2461: 2455: 2452: 2441: 2439: 2435: 2431: 2430:György Ligeti 2427: 2423: 2419: 2416:explores the 2415: 2404: 2399: 2397: 2392: 2387: 2374: 2372: 2371: 2367:'s 1970 film 2366: 2362: 2358: 2357: 2353:'s 1972 film 2352: 2348: 2343: 2341: 2340: 2335: 2334: 2329: 2328:John Williams 2324: 2323: 2319: 2318:Matyas Seiber 2316:The composer 2314: 2312: 2307: 2305: 2301: 2300:On Reflection 2297: 2293: 2289: 2284: 2282: 2278: 2273: 2271: 2267: 2266:Frank Loesser 2264:, written by 2263: 2259: 2254: 2252: 2248: 2244: 2243: 2239:in 1938, and 2238: 2237:Benny Goodman 2234: 2230: 2226: 2216: 2214: 2213: 2208: 2203: 2201: 2200:Henry Purcell 2197: 2196: 2191: 2186: 2184: 2177: 2175: 2171: 2167: 2163: 2159: 2155: 2154: 2148: 2147:György Ligeti 2143: 2141: 2140: 2135: 2134: 2126: 2124: 2120: 2119: 2114: 2110: 2108: 2104: 2100: 2096: 2085: 2081: 2077: 2073: 2071: 2067: 2063: 2059: 2057: 2053: 2049: 2045: 2044:Pierre Boulez 2041: 2040: 2035: 2031: 2027: 2026: 2021: 2020:Maurice Ravel 2016: 2007: 2005: 2000: 1996: 1995:Gustav Mahler 1992: 1988: 1984: 1983: 1978: 1974: 1973: 1968: 1962: 1957: 1953: 1951: 1947: 1943: 1941: 1937: 1932: 1930: 1926: 1922: 1910: 1899: 1895: 1893: 1889: 1885: 1884:Joseph Kerman 1881: 1871: 1870: 1865: 1861: 1857: 1856: 1850: 1848: 1847:Charles Rosen 1844: 1843:major Op. 110 1834: 1830: 1826: 1824: 1823:Hammerklavier 1818: 1816: 1815: 1810: 1806: 1805: 1800: 1791: 1789: 1785: 1768: 1763: 1759: 1757: 1753: 1752: 1746: 1742: 1738: 1737: 1731: 1727: 1723: 1719: 1715: 1711: 1707: 1703: 1702:Michael Haydn 1699: 1695: 1691: 1687: 1686:Padre Martini 1677: 1675: 1671: 1667: 1663: 1661: 1656: 1655: 1650: 1645: 1643: 1639: 1638:Baryton trios 1635: 1631: 1627: 1623: 1619: 1609: 1607: 1603: 1599: 1598:Classical era 1592:Classical era 1589: 1587: 1583: 1579: 1575: 1571: 1569: 1564: 1560: 1555: 1551: 1550: 1544: 1542: 1538: 1534: 1530: 1526: 1522: 1521: 1517: 1513: 1508: 1506: 1502: 1498: 1494: 1490: 1486: 1482: 1478: 1474: 1469: 1467: 1463: 1459: 1455: 1451: 1441: 1438: 1434: 1430: 1426: 1425:improvisation 1422: 1418: 1414: 1412: 1408: 1404: 1399: 1397: 1393: 1389: 1385: 1381: 1377: 1362: 1360: 1358: 1353: 1349: 1339: 1337: 1332: 1330: 1328: 1321: 1319: 1314: 1310: 1301: 1299: 1295: 1291: 1287: 1283: 1282: 1277: 1273: 1269: 1265: 1264:counter-fugue 1258:Counter-fugue 1255: 1253: 1243: 1241: 1230: 1226: 1223: 1219: 1218:Kyrie Eleison 1214: 1204: 1202: 1198: 1183: 1181: 1177: 1173: 1169: 1159: 1157: 1153: 1151: 1150: 1143: 1139: 1138:stretto fugue 1135: 1131: 1127: 1123: 1122:grand stretto 1119: 1115: 1112:. However, a 1111: 1094: 1089: 1085: 1080: 1076: 1074: 1072: 1065: 1055: 1043: 1039: 1037: 1032: 1027: 1023: 1017:False entries 1002: 1000: 995: 990: 986: 984: 979: 969: 965: 960: 958: 953: 943: 941: 937: 933: 929: 928:double fugues 925: 924: 919: 914: 912: 908: 904: 900: 896: 892: 888: 883: 878: 868: 866: 865:Maurice Ravel 862: 861:André Gedalge 857: 851: 841: 837: 828: 824: 819: 816: 812: 811: 807: 802: 799: 794: 791: 783: 779: 776:inverts to a 775: 770: 766: 764: 763: 758: 757: 751: 749: 745: 727: 726: 721: 718: 713: 709: 707: 703: 699: 695: 691: 687: 681: 666: 662: 658: 654: 650: 646: 642: 638: 637: 636: 635: 629: 623: 617: 614: 608: 602: 599: 597: 595: 592: 591: 584: 581: 575: 569: 566: 560: 554: 551: 549: 546: 545: 542: 527: 521: 501: 478: 472: 452: 446: 423: 420: 417: 416: 412: 409: 407: 404: 402: 399: 396: 394: 387: 384: 382: 379: 376: 374: 373: 367: 362: 360: 355: 350: 349: 343: 341: 337: 332: 331: 320: 318: 314: 310: 306: 302: 298: 294: 290: 286: 276: 275:(1895–1963). 274: 270: 266: 262: 258: 254: 250: 246: 243:(1583–1643), 242: 239:(1653–1706), 238: 235:(1616–1667), 234: 231:(1562–1621), 230: 226: 222: 218: 214: 210: 205: 203: 199: 195: 191: 187: 183: 178: 176: 172: 168: 164: 160: 155: 153: 149: 145: 140: 136: 132: 128: 125:") music and 124: 120: 116: 112: 111: 106: 102: 99:, built on a 98: 94: 91: 87: 83: 80: 74: 56: 52: 45: 41: 40: 35: 30: 26: 22: 4691: 4657:Counterpoint 4594: 4580: 4536: 4491: 4479: 4445: 4436: 4419: 4410: 4406: 4376: 4363:. New York: 4360: 4351: 4348:Mann, Alfred 4327: 4305: 4288: 4284: 4266:, p. 16 4259: 4247: 4235: 4223: 4211: 4202: 4196: 4187: 4181: 4170: 4161: 4132: 4124: 4110: 4096:Service, Tom 4091: 4081: 4072: 4064: 4059: 4054:, p. 67 4047: 4040:Orientations 4039: 4034: 4026: 4021: 4013: 4005: 3985: 3978: 3958: 3951: 3943: 3938: 3930: 3922: 3914: 3906: 3896: 3888: 3883:, p. 65 3876: 3864: 3855: 3850: 3831: 3811: 3806:, p. 64 3784: 3779:, p. 53 3772: 3760: 3748: 3739: 3733: 3721: 3711:. New York: 3708: 3702: 3690: 3663: 3658:, p. 56 3651: 3625: 3587: 3581: 3556: 3544: 3518: 3504: 3492:. Retrieved 3477: 3470: 3465: 3453:. Retrieved 3438: 3431: 3426: 3400: 3357: 3343: 3338:, p. 77 3336:Verrall 1966 3331: 3305: 3281:Gedalge 1964 3264: 3255: 3246: 3240: 3214: 3200: 3194:Gedalge 1964 3189: 3184:, p. 33 3182:Verrall 1966 3162:. Retrieved 3152: 3145:Gedalge 1964 3140: 3135:, p. 61 3133:Gedalge 1964 3128: 3102: 3088: 3076:. 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