Editing Fugue (section)

==Musical outline==
A fugue begins with the ''[[Exposition (music)|exposition]]'' 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,<ref>{{harvnb|Gedalge|1964|p=70}}</ref> and often accompanying key changes. The various entries may or may not be separated by ''episodes'' or occur in ''stretto''.

{|class="wikitable" style="text-align:center"
|+Example of key and entry structure in a three-voice Baroque fugue
|-
! !!colspan=5 style="background-color:#ABCDEF;"| Exposition !! !! colspan=2 style="background-color:#ABCDEF;"| First mid-entry !! !! style="background-color:#ABCDEF;"| Second<br>mid-entry !! !! colspan=2 style="background-color:#ABCDEF;"| Final entries in tonic
|-
! !! Tonic !! Dom. !! !! T !! (D-<small>redundant entry</small>) !! !! Relative maj/min !! Dom. of rel. !! !! Subdom. !! !! T !! T
|-
!Soprano
| S || CS<sub>1</sub> ||rowspan="3" style="background:#ffdead;"| <small>C<br />o<br />d<br />e<br />t<br />t<br />a</small>|| CS<sub>2</sub> || A || rowspan="3" style="background:#ffdead;"| <small>E<br />p<br />i<br />s<br />o<br />d<br />e</small>
|| CS<sub>1</sub> || CS<sub>2</sub> || rowspan="3" style="background:#ffdead;"| <small>E<br />p<br />i<br />s<br />o<br />d<br />e</small> || S || rowspan="3" style="background:#ffdead;"| <small>E<br />p<br />i<br />s<br />o<br />d<br />e</small> || CS<sub>1</sub> || Free<br>counterpoint ||rowspan="3" style="background:#ffaa2d"| '''C<br />o<br />d<br />a<br />'''
|-
!Alto
| || A || CS<sub>1</sub> || CS<sub>2</sub> || S || CS<sub>1</sub> || CS<sub>2</sub> || S || CS<sub>1</sub>
|-
!Bass
| || || S || CS<sub>1</sub> || CS<sub>2</sub> || A || CS<sub>1</sub> || CS<sub>2</sub> || S
|}
::<small>'''S''' = subject; '''A''' = answer; '''CS''' = countersubject; '''T''' = [[Tonic (music)|tonic]]; '''D''' = [[Dominant (music)|dominant]]</small>

===Exposition===<!--[[Call and response (music)]] links directly here.-->
{{Further|Exposition (music)}}

A fugue begins with the exposition of its subject in one of the voices alone in the [[tonic (music)|tonic]] key.<ref name = "oxfcomp">
G. M. Tucker and Andrew V. Jones, "Fugue", in ''The Oxford Companion to Music'', ed. Alison Latham (Oxford and New York: Oxford University Press, 2002). {{ISBN|0-19-866212-2}} {{cite book |url=http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t114.e2723|title=Oxford Reference Online, subscription access|isbn=978-0-19-957903-7|access-date=2007-03-16|last1=Latham|first1=Alison|year=2011|publisher=Oxford University Press }}</ref> 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 key|dominant]] or [[Subdominant key|subdominant]], with the latter being less common), which is known as the ''answer''.<ref>{{harvnb|Gedalge|1964|p=12}}</ref><ref>{{cite book | first = R. O. | last = Morris | title = Contrapuntal Technique in the Sixteenth Century | location = London | publisher = Oxford University Press | year = 1958 | page = 47 }}</ref> 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 ''real answer''; alternatively, if the intervals of the subject are altered in any way, the answer is a ''tonal answer''.<ref name = "oxfcomp" />

{{Image frame|content=<score sound="1">
\new PianoStaff <<
  \new Staff \fixed c' {
    \key g \minor
    R1 |
    r2 r8 \once \override NoteHead.color = #blue g bes d |
    cis4 d r8 e16 f g8 f16 e |
  }
  \new Staff {
    \clef bass
    \key g \minor
    r8 \once \override NoteHead.color = #red d' ees' g fis4 g |
    r8 a16 bes c'8 bes16 a bes4 g |
    r8 a16 g f8 g16 a bes8 g e cis' |
  }
>>
</score>|caption=Example of a tonal answer in [[Johann Sebastian Bach|J.S. Bach's]] [[Prelude and Fugue in G minor, BWV 861|Fugue No. 16 in G minor, BWV 861]], from the ''[[Well-Tempered Clavier]]'', 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.}}

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.<ref name="oxfcomp" /> To prevent an undermining of the fugue's [[key (music)|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.<ref name="Verrall-1966-p12">{{harvnb|Verrall|1966|p=12}}</ref>

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 ''[[countersubject]]''; if this accompanying material is only heard once, it is simply referred to as ''[[free counterpoint]]''.
[[File:Interval Inversion.jpg|thumb|400px|The interval of a [[Fifth (interval)|fifth]] inverts to a [[Fourth (interval)|fourth]] (dissonant) and therefore cannot be employed in [[invertible counterpoint]], without preparation and resolution.]]
The countersubject is written in [[invertible counterpoint]] at the octave or fifteenth (two octaves).<ref>{{harvnb|Gedalge|1964|p=59}}</ref> 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 sounding correctly when played above or below the subject, and must be conceived, therefore, in invertible (double) counterpoint.<ref name = "oxfcomp" /><ref>"Invertible Counterpoint" ''The Oxford Companion to Music'', ed. Alison Latham (Oxford and New York: Oxford University Press, 2002) {{cite book |url=http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t114.e3465|title=Oxford Reference Online, subscription access|isbn=978-0-19-957903-7|access-date=2007-03-16|last1=Latham|first1=Alison|year=2011|publisher=Oxford University Press }}</ref>

In [[tonality|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 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.<ref>{{Cite Grove |last=Drabkin |first=William |title=Invertible Counterpoint}}</ref> The countersubject, if sounding at the same time as the answer, is transposed to the pitch of the answer.<ref>{{harvnb|Gedalge|1964|p=61}}</ref> Each voice then responds with its own subject or answer, and further countersubjects or free counterpoint may be heard.

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 [[Johann Sebastian Bach|J.S. Bach's]] ''[[Well-Tempered Clavier|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 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.<ref>{{harvnb|Gedalge|1964|pp=71–72}}</ref>

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 [[Prelude and Fugue in G minor, BWV 861|Fugue No. 16 in G minor, BWV 861]], the first codetta is absent. The subject concludes on the [[quarter note]] (or crotchet) B{{music|flat}} 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 the impact of, the reentry of the subject in another voice. Finally, they may be modulatory passages to return the fugue to the tonic.<ref>Paul Walker, "Fugue, §1: A Classic Fugue Analysed" {{cite web |url=http://www.grovemusic.com/shared/views/article.html?section=music.51678.1 |title=Grove Music Online |website=www.grovemusic.com |access-date=2007-02-18}}</ref>

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.<ref name="oxfcomp" /> Furthermore, 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.

===Episode===
{{Further|Section (music)}}

Further entries of the subject may follow the initial exposition either immediately or separated by episodes.<ref name="oxfcomp" /> Episodic material is always [[Modulation (music)|modulatory]] and is usually based upon some musical idea heard in the exposition.<ref name="classic" /><ref name="oxfcomp" /> Each episode has the primary function of transitioning into a new key for the next entry of the subject,<ref name="oxfcomp" /> and may also provide release from the strictness of form required by the exposition.<ref name="Verrall 1966 33">{{harvnb|Verrall|1966|p=33}}</ref> [[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.<ref>{{harvnb|Gedalge|1964|p=}}</ref>

===Development<!--linked from 'Musical development'-->===
{{further|Musical development}}
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 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.

Middle entries tend to occur at keys other than the tonic. These are often [[closely related key]]s such as the [[Dominant key|relative dominant]] and [[Subdominant key|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 [[Relative minor|minor]] 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 [[Dieterich Buxtehude|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 is no entrance of the subject and answer material, the composer can develop the subject by altering it. This is called a ''counter-exposition'',<ref>{{Cite Grove |last=Walker |first=Paul |title=Counter-exposition}}</ref> which often uses the ''[[Melodic inversion|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 [[#Types|double fugues]]. In any of the entries within a fugue, the subject may be altered by inversion, [[Permutation (music)|retrograde]] (where the subject is heard back-to-front), [[diminution]] (the reduction of the subject's rhythmic values by a certain factor), [[augmentation (music)|augmentation]] (the enlargement of the subject's rhythmic values by a certain factor), or any combination thereof.<ref name="oxfcomp" />

===Example and analysis===
[[File:Wiki-fugue-analysis.jpg|thumb|400px|Visual analysis of [[Johann Sebastian Bach|J.S. Bach's]] Fugue No. 2 in C minor, BWV 847, from the [[Well-Tempered Clavier|''Well-Tempered Clavier'', Book 1]] (bars 7–12)[[File:Wiki fugue analysis audio.mid]]]]
The excerpt below, bars 7–12 of [[Johann Sebastian Bach|J.S. Bach's]] Fugue No. 2 in C minor, BWV 847, from the [[Well-Tempered Clavier|''Well-Tempered Clavier'', Book 1]] illustrates the application of most of the characteristics described above. The fugue is for keyboard and in three voices, with regular countersubjects.<ref name = "classic" /><ref>{{cite book | first = Johann Sebastian | last = Bach | chapter = Fuge Nr. 2 | title = Das Wohltemperierte Klavier I | editor-first = Ernst-Günter | editor-last = Heinemann | location = Munich | publisher = G. Henle Verlag | year = 1997 }}</ref> 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 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 (music)|sequence]], in the form of an accompanied [[Canon (music)|canon]] at the fourth.<ref name="Verrall 1966 33"/> Arrival in E{{music|flat}} 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 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 (music)|mode]].<ref>{{cite book | first = Laurence | last = Dreyfus|author-link=Laurence Dreyfus| chapter = Figments of the Organicist Imagination | title = Bach and the Patterns of Invention | location = Cambridge, Massachusetts, and London | publisher = Harvard University Press | year = 1996 | page = 178 }}</ref>

===False entries===
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.<ref name="Verrall-1966-p12"/>
{{Image frame|content=<score sound="1">
\layout {
  \context {
    \Voice
    \consists "Horizontal_bracket_engraver"
    \override TextScript.font-size = -2
  }
}
\new PianoStaff <<
  \new Staff \fixed c' {
    \key c \minor
    <<
      {
        bes8 g'16 f' g'8 b c' d'16 ees' f'4~ |
        8 ees'16 d' c' bes aes g f8 aes' g' f' |
      }
      \\
      {
        g16 a bes8~ 16 ees f g
        aes g f ees d8 \override NoteHead.color = #red c'16\startGroup_"false entry" b |
        c'4\stopGroup \revert NoteHead.color r r8 f' ees' d' |
      }
    >>
    \bar "||"
  }
  \new Staff {
    \clef bass
    \key c \minor
    R1 | r8 \override NoteHead.color = #blue c'16^"\"real\" entry" b c'8 \revert NoteHead.color g
    aes c'16 b c'8 d' |
  }
>>
</score>|align=center|caption=Example of a false answer in [[Johann Sebastian Bach|J.S. Bach's]] Fugue No. 2 in C minor, BWV 847, from the [[Well-Tempered Clavier|''Well-Tempered Clavier'', Book 1]]. 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 [[quarter note]].}}

===Counter-exposition===
The counter-exposition is a second exposition. However, there are only two entries, and the entries occur in reverse order.<ref name=Gedalge-1964-p108>{{harvnb|Gedalge|1964|p=108}}</ref> The counter-exposition in a fugue is separated from the exposition by an episode and is in the same key as the original exposition.<ref name=Gedalge-1964-p108/>

===Stretto===
{{main|Stretto}}
[[File:Fischer-fugue1.png|thumb|400px|Example of ''stretto'' fugue in a quotation from Fugue in C major by [[Johann Caspar Ferdinand Fischer]] 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 ''stretto'', the answer already takes place in the tenor voice, on the third quarter note of the first bar, therefore coming in "early"<br/>[[File:Fugue in C major by Johann Caspar Ferdinand Fischer.mid]]]]
Sometimes counter-expositions or the middle entries take place in ''[[stretto]],'' 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.<ref name="ReferenceA">{{Cite Grove |last=Walker |first=Paul |title=Stretto (i)}}</ref>

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''.<ref>{{harvnb|Verrall|1966|p=77}}</ref> ''Strettos'' may also occur by inversion, augmentation and diminution. A fugue in which 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 ''{{lang|la|[[Mass in B minor structure#Dona nobis pacem|Dona nobis pacem]]}}'' choruses from J.S. Bach's [[Mass in B minor]]).<ref name="ReferenceA"/>

===Final entries and coda===
The closing section of a fugue often includes one or two counter-expositions, and possibly a stretto, in the [[tonic (music)|tonic]]; sometimes over a tonic or dominant [[pedal point|pedal note]]. Any material that follows the final entry of the subject is considered to be the final [[Coda (music)|coda]] and is normally [[cadence (music)|cadential]].<ref name = "classic" />