Editing Fugue (section)

== Types ==

===Simple fugue===
A '''simple fugue''' has only one subject, and does not utilize [[Invertible Counterpoint|invertible counterpoint]].<ref name="sim" >{{Cite Grove |last=Walker |first=Paul |title=Fugue, §5: The golden age}}</ref>

===Double (triple, quadruple) fugue===
A '''double fugue''' has two subjects that are often developed simultaneously. Similarly, a triple fugue has three subjects.<ref name="x">{{Cite Grove |last=Walker |first=Paul |title=Double Fugue}}</ref><ref>"double fugue" ''The Oxford Companion to Music'', Ed. Alison Latham, Oxford University Press, 2002, {{cite book |url=http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t114.e2059|title=Oxford Reference Online, subscription access|isbn=978-0-19-957903-7|access-date=2007-03-29|last1=Latham|first1=Alison|year=2011|publisher=Oxford University Press }}</ref> 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 [[Kyrie|Kyrie Eleison]] of [[Wolfgang Amadeus Mozart|Mozart's]] [[Requiem (Mozart)|Requiem in D minor]] or the fugue of Bach's Passacaglia and Fugue in C minor, [[Passacaglia and Fugue in C minor, BWV 582|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{{music|sharp}} minor from Bach's [[Well-tempered Clavier|''Well-Tempered Clavier'' Book 2]], or more famously, Bach's "St. Anne" Fugue in E{{music|flat}} major, [[BWV 552]], a triple fugue for organ.)<ref name="x"/><ref>"Double Fugue", ''The Concise Oxford Dictionary of Music'', fourth edition, ed. Michael Kennedy (Oxford and New York: Oxford University Press, 1996) {{cite book |url=http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t76.e2780|title=Oxford Reference Online, subscription access|isbn=978-0-19-920383-3|access-date=2007-03-29|last1=Kennedy|first1=Michael|last2=Kennedy|first2=Joyce Bourne |year=2007|publisher=Oxford University Press }}</ref>

===Counter-fugue===
A '''counter-fugue''' is a fugue in which the first answer is presented as the subject in [[Melodic inversion|inversion]] (upside down), and the inverted subject continues to feature prominently throughout the fugue.<ref>{{Cite Grove |last=Walker |first=Paul |title=Counter-fugue}}</ref> Examples include ''Contrapunctus V'' through ''Contrapunctus VII'', from Bach's ''[[The Art of Fugue]]''.<ref>{{cite book | last = Bach | first = Johann Sebastian | editor-first = Alfred | editor-last = Dörffel | editor-link = Alfred Dörffel | title = The Art of Fugue & A Musical Offering | year = 1992 | publisher = Courier Dover | isbn=978-0-486-27006-7 | url = https://archive.org/details/artoffuguemusica00joha | url-access = registration | page = [https://archive.org/details/artoffuguemusica00joha/page/56 56]}}</ref> During the Baroque period, counter-fugues were sometimes called by the Latin name  ''fuga contraria''. German composer [[Johann Mattheson]] coined 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.<ref>{{Cite encyclopedia |author=Paul M. Walker|date=2001|entry=Counter-fugue|encyclopedia=Grove Music Online|publisher=[[Oxford University Press]] |doi=10.1093/gmo/9781561592630.article.06689}}</ref>

===Permutation fugue===
'''Permutation fugue''' describes a type of composition (or technique of composition) in which elements of fugue and strict [[Canon (music)|canon]] are combined.<ref name="perm">{{Cite Grove |last=Walker |first=Paul |title=Permutation Fugue}}</ref> 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 [[Invertible Counterpoint|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 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 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|''Himmelskönig, sei willkommen'', BWV 182]].

Permutation fugues differ from conventional fugue in that there are no connecting episodes, nor statement of the themes in related keys.<ref name="perm" /> 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.<ref>{{harvnb|Walker|1992|p=56}}</ref>

===Fughetta===
A '''fughetta''' 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 [[Ludwig van Beethoven|Beethoven]]'s [[Diabelli Variations|''Diabelli Variations'' Op. 120]].

===Mirror fugue===
A mirror fugue is a fugue, or rather two fugues, one of which is the mirror image of the other. It is as though a mirror were placed above or below an existing fugue, producing [[Inversion (interval)|inversions]] of each interval in each part, as well as inverting the position of the parts within the texture, so that, for example, the topmost part in one fugue is inverted to produce the lowest part in the other. This is well demonstrated by the two four-part fugues of Contrapunctus 12 in ''[[The Art of Fugue]]''.

The two three-part fugues of Contrapunctus 13 exhibit a similar relationship to each other, but this cannot strictly be called a mirror fugue, since the position of each inverted part is not itself inverted in the texture, SAB becoming not BAS, but BSA.<ref>Boyd, Malcolm. ''Oxford Composer Companions: J.S. Bach'', Oxford University Press, 1999, p. 296</ref>