Bach Fugue Bwv 862 Analysis Essay

Well-Tempered Clavier:
Index of Contrapuntal Operations,
Learning Objects, and Concepts
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Technical note: The fugues of Book 1 (left column) have been migrated to Flash, and Book 2 is 2/3 done.

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Contrapuntal Operations


Book I
No. 1: C
No. 2: cm
No. 3: C#
No. 4: c#m
No. 5: D
No. 6: dm
No. 7: Eb
No. 8: d#/ebm
No. 9: E
No. 10: em
No. 11: F
No. 12: fm
No. 13: F#
No. 14: f#m
No. 15: G
No. 16: gm (a)
No. 17: Ab
No. 18: g#m
No. 19: A
No. 20: am
No. 21: Bb
No. 22: bbm
No. 23: B
No. 24: bm



Book II
No. 1: C Flash
No. 2: cm Flash
No. 3: C# Flash
No. 4: c#m
No. 5: D Flash
No. 6: dm Flash
No. 7: Eb Flash
No. 8: d#m Flash
No. 9: E Flash
No. 11: F
No. 12: fm Flash
No. 13: F#
No. 14: f#m Flash
No. 15: G Flash
No. 16: gm Flash
No. 17: Ab
No. 18: g#m
No. 19: A Flash
No. 20: am Flash
No. 21: Bb Flash
No. 22: bbm Flash
No. 23: B
No. 24: bm Flash

     Style
verset
demonst.
moderno
passion
demonst.
dance
antico
ricercar
moderno
canon
dance
verset
moderno
antico
concerto
verset
verset
verset
verset
competit.
character
antico
verset?
passion



Style
character
verset
verset
dance
verset
improv.
ricercar
canzona
antico
partimento
dance
galant
passion
partimento
moderno
verset
verset
chorale
fughetta
dance
moderno
moderno
dance

 Voices
4
3
3
5
4
3
3
3
3
2
3
4
3
4
3
3
4
4
3
4
3
5
4
4



 Voices
3
4
3
3
4
3
4
4
4
3
3
3
3
3
4
4
3
3
3
3
4
4
3
  Subject
  Entries

24
8
12
31
11
17
9
36
10
9
13
10
8
9
14
17
15
12
14
38
8
22
12
13


  Subject
  Entries

8
23
45
15
25
9
11
16
38
7
9
11
30
6
17
15
12
10
8
11
24
14
9
 Tonal/
 Real

either
tonal
tonal
real
tonal
real
tonal
tonal
real
real
tonal
tonal
tonal
real
real
tonal
tonal
tonal
tonal
real
tonal
tonal
tonal
tonal


 Tonal/
 Real

tonal
tonal
tonal
real
either
real
tonal
real
either
tonal
tonal
real
tonal
tonal
tonal
tonal
real
real
tonal
tonal
real
tonal
tonal

    Stretti
extreme
-
-
moderate
moderate
moderate
-
extreme
-
-
moderate
-
-
-
moderate
moderate
-
-
moderate
extreme
-
extreme
moderate
-



    Stretti
-
extreme
extreme
-
extreme
moderate
moderate
slight
extreme
-
-
-
-
-
moderate
slight
-
-
-
-
extreme
-
-
 Counter
 Subject

-
6
11
-
-
5
7
-
9
10
4
8
11
7
-
12
-
7
-
-
7
-
5
11


 Counter
 Subject

6
-
14
-
-
4
-
7
13
-
-
9
-
5
15
11
3
-
7
7
9
5
4
 2nd
 Ctr

-
*
-
-
-
-
-
-
-
-
-
*
-
-
-
-
-
*
-
-
*
-
-
-


 2nd
 Ctr

-
-
-
-
-
-
-
-
-
-
-
*
-
*
-
-
-
-
-
*
*
*
*
 Mel
 Inv

-
*
*
*
-
*
-
*
-
-
*
-
*
*
*
-
-
-
-
*
*
-
*
*


 Mel
 Inv

-
*
*
*
-
*
-
*
*
-
-
-
*
-
-
-
-
-
-
-
*
-
-
 Inv
 Ctpt

-
*
*
*
-
*
*
-
-
*
-
*
*
*
-
*
-
*
*
-
*
-
*
*


 Inv
 Ctpt

*
-
-
*
-
-
*
*
*
-
-
*
*
*
10/12
12
*
-
*
10/12
*
12
*

 Aug
-
-
-
-
*
-
-
*
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-



 Aug
-
*
*
-
-
-
-
-
-
-
-
*
-
-
-
-
-
-
-
-
-
-
-
 Double
 Triple

-
-
-
Triple
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Double
-
-
-
-
-


 Double
 Triple

-
-
-
Double
-
-
-
-
Triple
-
-
-
Triple
-
-
-
Double
-
-
-
-
Double
-

 BACH
-
-
-
*
-
-
-
-
-
-
-
-
-
-
-
-
-
*
-
-
-
*
-
*



 BACH
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
*
-
*
-
-
-
-
*

 Crown
-
-
-
*
-
-
-
-
-
-
-
-
-
*
-
-
-
-
-
-
-
-
-
-



 Crown
-
-
-
-
-
-
-
*
-
-
-
-
*
-
-
-
*
*
-
-
-
-
*




Learning Objects and Concepts

Book I
No. 1: C
Flash
Shockwave
Prelude: streaming audio link
Topics: stretto and expositional architecture (tonal/real)
Key concepts: Prelude and fugue thematically linked; stretto, subject, answer, false subject defined; subject accompanies itself and inherently develops in certain ways.
Interpretation: Korevaar performance notes
Questionnaire: Students can answer ten questions online: English, Español.
Translations:Português, Español
No. 2: cm
Flash
Shockwave
Topics: figural structure of subject, countersubject, invertible counterpoint, melodic inversion, sequence, palindrome
Key concepts: Subject represents an economy of means; two countersubjects require triple counterpoint; sequence likened to stairs, functions to connect related keys.
Interpretation: Korevaar performance notes
Questionnaire: Students can answer ten questions online: English, Español.
Translations:Português, Español
No. 3: C#
Flash
Shockwave
Topics: structure of subject, countersubject, melodic
inversion, sequence, enharmonicism, well-tempered, re-exposition
Key concepts: Disjunct subject outlines compound melody; countersubject melodically inverted; sequence likened to engine; enharmonics justified; well-tempered intonation defined; exposition repeated at conclusion of fugue; similarity of fugue to Italian concerto grosso.
Interpretation: Korevaar performance notes
Questionnaire: Students can answer ten questions online: [English, Español] (or these alternate ten in English).
Translations:Português, Español 
No. 4: c#m
Flash
Shockwave
Topics: Lutheranism, chiasmus, lamento, triple fugue, Bach symbols, retrogradation, melodic inversion, passion music
Key concepts: Shortest subject in WTC is chiastic; triple fugue is passion music with which artist identified by authorial inclusion; BACH motive/numbers/monogram
Interpretation: Korevaar performance notes
Questionnaire: Students can answer ten questions online: English, Español.
Translations:Português, Español
No. 5: D
Flash
Shockwave
Topics: structure of subject, French manier
Key concepts: Subject contains two motives, one of which is developed by augmentation; influence of French music; performance practice of dotted rhythms
Interpretation: Korevaar performance notes
Questionnaire: Students can answer ten questions online.
Translations:Português, Español
No. 6: dm
Flash
Shockwave
Topics: structure of subject/countersubject, melodic inversion,
rounded binary, Fortspinnung
Key concepts: Subject fragmented into three motives and undergoes inversion for 1st time in WTC; countersubject motivically related to subject; fugue likened to big bang; form is rounded binary
Interpretation: Korevaar performance notes
Questionnaire: Students can answer ten questions online.
Translations:Português, Español
No. 7: Eb
Flash
Shockwave
Prelude: streaming audio link
Topics: modulating subject, bridge passage, ritornello
Key concepts: Prelude is a double fugue; following fugue has unusual tonal relationship between subject and answer; bridge passage receives extraordinary development; ritornello principle is likened to boomerang.
Questionnaire: Students can answer ten questions online.
Translations:Português, Español
No. 8: d#/ebm
Flash
Shockwave
Topics: inversion, augmentation, Dostoevsky Brothers K.
Key concepts: Classic example of subject inversion and augmentation; fugue like polyphonic novel, Brothers Karamazov.
Interpretation: Korevaar performance notes
Questionnaire: Students can answer ten questions online.
Translations:Português, Español
No. 9: E
Flash
Shockwave
Topics: structure of subject/countersubject, melodic inversion, retrogradation, augmentation, DNA
Key concepts: Motives in subject/countersubject analyzed at figural level; unusual variation of countersubject; atomized figures undergo inversion, retrogradation, augmentation; generative tendency of fugue likened to DNA.
Questionnaire: Students can answer ten questions online.
Translations:Português, Español
No. 10: em
Flash
Shockwave
Topics: counterfugue, double counterpoint, canon, Möbius
Key concepts: Only two-voiced fugue is canon comprised of two parts (fugue/counterfugue) in double counterpoint; fugue likened to Möbius strip.
Questionnaire: Students can answer ten questions (or these alternate ten) online.
Translations:Português, Español
No. 11: F
Flash
Shockwave
Topics: structure of subject, counterexposition, canon, melodic inversion
Key concepts: Subject fragmented into three motives; counterexposition and developments repeat structures in new voice order; canonic episodes; fugue like building blocks.
Questionnaire: Students can answer ten questions online.
Translations:Português, Español
No. 12: fm
Flash
Shockwave
Topics: countersubject, chromaticism, wohltemperirt, triple counterpoint
Key concepts: Second most chromatic subject in Book I provides occasion to reference wohltemperirt, Werckmeister, Kircher, and Kirnberger.
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 13: F#
Flash
Shockwave
Topics: invention, false sequence
Key concepts: Episodes develop material not derived from the subject; like a fugue with three-part invention.
Interpretation: Korevaar performance notes.
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 14: f#m
Flash
Shockwave
Topics: countersubject, stile antico, chromaticism, melodic inversion
Key concepts: Chromatic subject is complemented by sighing countersubject in the inverse of the subject's arched shape; fugue is an amalgam of opposites, stile antico with moderno; discussion weaves themes from O'Brien on James Joyce, and Ciardi.
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 15: G
Flash
Shockwave
Topics: structure of subject, scale, proportionality
Key concepts: Rhythmic symmetry of the subject; scalar material developed by economical means; fugue likened to Palladio villa with ensuing discussion of geometric and harmonic means, Zarlino, and "music of the spheres."
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 16: gm (a)
Flash
Shockwave
Topics: structure of subject/countersubject, melodic inversion, double counterpoint
Key concepts: Countersubject is derived from the subject by melodic inversion and reordering of head/tail; fugue likened to fractal.
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 16: gm (b)Topics: Paul Celan, Imre Kertész, the Holocaust, Bach's funeral music
Key concepts: fugal purpose, character, and essence.  It is the fugue's essence to reveal the likeness of seemingly unlike things. This alternate study of the gm fugue, asks why Paul Celan titled his poem on the Holocaust a "fugue" (Todesfuge). It compares Celan's work with the axial fugue of BWV 106, which uses the same subject as the gm fugue of WTC Book I. An analogue is suggested of the Jewish- Christian experience, with lessons of the fugue and Holocaust applied to contemporary life. Features the paintings and poetry of Holocaust survivor, Tamara Deuel.
No. 17: Ab
Flash
Shockwave
Topics: Heinrich Schenker, prolongation, fundamental structure
Key concepts: Schenkerian analysis briefly explained and applied to fugue.
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 18: g#m
Flash
Shockwave
Topics: structure of subject, tritone, modulation, harmonic cycle, wohltemperirt, tonal functions
Key concepts: Subject's head exposes a melodic tritone above tonic, modulation to dominant results; subject's tail implies tritone between predominant and dominant; tonic- predominant-dominant-tonic cycle explained and related to the Canon super Fa Mi (BWV 1078); explanation of well-tempered intonation; includes Index of Harmonic Variations
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 19: A
Flash
Shockwave
Topics: double fugue, imbrications of motive, Dante, Milton
Key concepts: Double fugue's disjunct subject developed by imbrications of motives; stepwise 2nd subject flies; etymology of fugue considered in Divine Comedy and Paradise Lost.
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 20: am
Flash
Shockwave
Topics: melodic inversion, stretto, canon, counterexposition, design, Gerhardt Niedt, Lutheranism, Bach symbols, S.D.G. and J.N.J.
Key concepts: Longest fugue in WTC I has the most iterations of subject, half inverted; symbolism of 14 canonic stretti; fugue compared to kinetic sculpture; theological implications of purposefulness and design; Soli Deo Gloria after WTC I.
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 21: Bb
Flash
Shockwave
Topics: permutation fugue, countersubject, pattern & metapattern
Key concepts: Contrapuntal texture with two countersubjects inverted in a pattern with one anomaly; rotation of polyphonic voices; fugue likened to Amish quilt, poetry, and folk art.
Interpretation: Korevaar performance notes included.
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 22: bbm
Flash
Shockwave
Prelude: streaming audio link
Topics: hyperstretto, stile antico counterpoint, Fux
Key concepts: Second of two fugues for five voices in the stile antico; counterpoint likened to choreography by Balanchine; Fux Gradus; dramatic leap (9th), largest of any subject; 2nd of three instance of the BACH motive in WTC Book I.  Theories about the affective connotation of b-flat minor.
Questionnaire: Students can answer ten questions online.
Translation: Español
No. 23: B
Flash
Shockwave
Topics: melodic inversion, tonal and modal variation, invertible counterpoint, Affekt, Monet
Key concepts: Fugue is like Monet series paintings of poplars; techniques that unite composition and painting. Questionnaire: Students can answer ten questions online.
Translation: Español
No. 24: bm
Flash
Shockwave
Prelude: streaming audio link
Topics: chromaticism, Lutheranism, chiasmus, Cranach, passion music
Key concepts: Most chromatic of subjects in WTC employs twelve tones; outlines three crosses; 25 iterations of BACH motive; intertextual associations of passion music with Weimar painting by Lucas Cranach the Elder; motivic connotations of prelude.
Questionnaire: Students can answer ten questions online.
Translations:Português, Español

 

Book II Contents

No. 1: C
Flash
Shockwave

Topics: structure of subject/countersubject, sequence, Voyager spacecraft, Carl Sagan
Key concepts: subject has two parts each of which can accompany the other; countersubject continues motives of the subject's tail; ramifications of fugue's inclusion on Voyager's "golden record"; fugue as the product of design (as opposed to Sagan's evolutionary analogue).
Translation:Español

No. 1: C
Flash
Shockwave
Topics: structure of subject, stretto, augmentation, melodic inversion, retrogradation
Key concepts: Second half of subject retrogrades contour of first half; improvisatory character of fugue likened to migrating geese.
Translations:Español , 中文

No. 3: C#
Flash
Shockwave

Topics: Hofstadter's Gödel Escher Bach, Polanyi
Key concepts: Subject appears in contrary motion, augmentation, and diminution; fugue is used to illustrate Gödel's incompleteness theorem; extensive discussion of Gödel, Turing, and Polanyi; fugue subjected to Turing test and undecidable proposition discovered.
Translation:Español

No. 4: c#m

Topics: Metalanguage, Metacognition, Metaphor, and Metamorphosis
Key concepts: Exploration of an interpretive framework, essentially a linguistic methodology, for revealing relationships between unlike things: a butterfly, a fugue, and the novel Pale Fire by Vladimir Nabokov.  The author concludes that all three address the problem of mortality, with the novel and fugue employing a self-reflexive technique to view the "one" from the perspective of the the "other."
Questionnaire: Students can answer ten questions online.

No. 5: D
Flash
Shockwave
Topic: (Flash version) T. S. Eliot's Four Quartets
Topics: (Shockwave version) Stockhausen, Adorno, Cage, universals, nominalism
Key concepts: Subject borrows rhythm and melody from canzona; "naturally" lends itself to stretto; tail motive consumes 3/4 of fugue; plagal exposition; perception of exposition in the "right" key; tonal "perspective"; Bach's music realistic vs. nominalistic; modern commitment to nominalism exemplified in Cage and Adorno; conclusion of nominalism in Stockhausen and World Trade Center tragedy.
No. 6: dm
Flash
Shockwave
Topics: rhetoric, word painting
Key concepts: Bach's conception of fugue as rhetoric; fugal invention; Aristotle's topoi, Mattheson's loci topici; exposition equivalent to thesis; development involves antithesis; connotations of specific word paintings including the lamento;Affekt and the relationship of (Prout's) words to music.
Questionnaire: Students can answer ten questions online.
No. 7: Eb
Flash
Shockwave

Topics: Nietzsche, Wagner, philosophy, nihilism, St. Matthew Passion
Key concepts: Mendelssohn's revival of the St. Matthew Passion stimulates interest in Bach's music; Schumann and the Bach Gesellschaft; 19th century reception of Bach as "healing force"; compared with Wagner; Nietzsche's nihilism, friendship with Wagner, and 1878 criticism of Bach in Aphorism 149, Human, All-Too-Human.
Questionnaire: Students can answer ten questions online.
No. 8: d#m
Flash
Shockwave
Topics: Scheibe, Mattheson, rhetoric, word painting
Key concepts: Scheibe's criticism of Bach's music and Mattheson's challenge; Bach responds by demonstrating mastery of musical rhetorical techniques: gradation, paronomasia, peroration, tmesis, and antithesis; implications of canzona rhythm, suspiratio, and chiastic motives as word paintings; discussion of rhetorical "meaning"; fugue compared with BWV 4.
No. 9: E
Flash
Shockwave
Topics: wave theory, quantum mechanics
Key concept: fugue is like a wave Fugue has three subjects plus a countersubject; counterexposition treats subject and countersubject separately, in stretto; perceptual challenge of this type of fugue to maintain distinction between motives; fugue likened to waves of all kinds: ocean, sound, light, electromagnetic; review of quantum physics from Niels Bohr and Werner Heisenberg; Bohr contra Einstein debates; contemporary revolution in physics; Carver Mead's Collective Electrodynamics; fugue as evidentiary of design; the "Uncreated Wave"
No. 10: em Not yet available
No. 11: FTopics: Kenneth L. Pike, linguistics, tagmemics
Key concept: The fugue contains elements of a wave, particle, and field.  Meaning "happens" when people interact with other people and objects in their environment.  In the fugue (an object), meaning is found in the perception of relationships between its "units in context," what the linguist Kenneth Pike called a tagmeme.  In Pike's conception, these relationships involve qualities of slot, class, role, and cohesion.  In the fugue, these qualities are expressed in the subject's distribution, pitch-class content, scale-degree function within a key, and tonality as cohesive force.  Additionally, slot, class, role, and cohesion can be mapped, as a group, onto properties of contrast, variation, and distribution, producing what Pike called a tagmemic grid.  The tonal grid comprises then the fugue's tonal tagmeme, which interacts with its similarly structured motivic tagmeme and referential tagmeme, these latter receiving mention without substantive discussion. 
No. 12: fm
Flash
Shockwave
Topic: reconstruction of Bach's likeness by forensic anthropologists at the University of Dundee, Scotland
Key concept: surreal comparison of fugal composition and analysis to forensic reconstruction, with analogies to Lamarckian Darwinism. Critique of scientific methods vs. humanistic ways of understanding what is "authentic" and "real."
Questionnaire: Students can answer ten questions online.
No. 13: F#Topics: time, tempo, perception of time, definition of time
Key concepts: Fugal time is neither circular nor linear, but epochal and spiraled. Meaning in the fugue is dependent upon relationships between the past, present, and future. The intensity of conscious cognitive processing required in listening to a fugue protracts (and compresses) the passage of time: the fugal future is in its past, and its past is in its future.
No. 14: f#m
Flash
Shockwave
Topics: Lutheranism, chiasmus, lamento (Passus duriusculus), triple fugue, Bach symbols, melodic inversion, passion music
Key concepts: definitive triple fugue of the cycle; two of its subjects borrowed from earlier works in the WTC; each subject receives its own exposition, followed by development with subjects prior to it; third of three "passion fugues" contains many symbols, both of the composer and his faith.
Translation:Português
No. 15: G
Flash
Shockwave
Topics: absolute expressionism, modern art, Kandinsky, Schoenberg
Key concepts: Kandinsky's 1914 painting, Fuga, provides occasion to explore the aesthetic ideal of expressionism and the historical roots of modern art, both in reaction to impressionism and as a continuation of the western aesthetic. Bach's legacy to Schoenberg and Kandinsky can be found in the principle of affect coupled with motivic development and economy of means. The spiritual quest of each artist also finds "expression" in his unique style and medium.
No. 16: gm
Flash
Shockwave
Topics: Grand Canyon, geology, double counterpoint
Key concepts: The fugue's subject and countersubject are heard in its various "voices." This analysis is primarily concerned with how the composer notates fugal voices so that they can be aurally and visually distinguished from each other. Analogy is made to the sedimentary layers of Grand Canyon, Arizona, with many allusions to its geology and history. This particular fugue is famous for its double counterpoint at the octave, 10th, and 12th--structures that are illustrated and explained.
Questionnaire: Students can answer ten questions online.
No. 17: AbTopics: Salmon migration, ecosystems, counterpoint, potentiality vs. actuality
Key concepts: Counterpoint involves an interdependence of musical ideas that is likened to the relationship of species within ecosystems.  With this fugue, in particular, the sprightly subject seems to be intuitively at odds with the somber countersubject (a lament).  The purpose of the analysis is to show how one does not generate the other, but how they both emanate, harmonious and on equal footing, from a more fundamental thought.
Questionnaire: Students can answer ten questions online.
No. 18: g#mTopics: Bach's Bible, Calov, Frederick the Great, Musical Offering, Enlightenment
Key concept: Bach's commitment to the preaching purpose of music. The narrative begins with Bach in the Weimar jail, by some counts beginning his composition of the Well-Tempered Clavier, and ends with his 1747 encounter with Frederick the Great. The discussion is threaded with references to Bach's many underlinings and annotations in the Calov Bible. His Lutheran understanding of music's purpose is contrasted with the galant style preferred by Frederick, as well as the philosophical assumptions of Aufklärung and what would come to be known as the Enlightenment.
No. 19: A
Flash
Shockwave
Topics: Architecture, Christopher Alexander, Milton Babbitt
Key concepts: In the Shockwave version the topic is: Art = beauty, beauty = life, life = relationships. This aesthetic philosophy, articulated by Berkeley professor of architecture in The Nature of Order, is applied to the fugue and contrasted with Milton Babbitt's article, "Who Cares if You Listen?"
In the Flash version the topic is: the derivation of the fugue's subject from the chorale Allein Gott in der Höh and its implications.
No. 20: am
Flash
Shockwave
Topics: Humor in music, self-similar structures, matryoshka doll
Key concepts: Dr. Ledbetter offers three reasons why this fugue should be interpreted as parody. Nevertheless, there are some serious ideas here, mainly in the self-similar contours and rhythms of the subject's head and tail. The fugue likened to a Russian "babushka" doll.
No. 21: Bb
Flash
Shockwave
Topics: Invariance, Permutation, Syllogism, Plato and Meno's Square
Key concepts: The brilliance of Bach's fugues lies in his understanding of process and invention. Unlike "book fugues" that mimic form, Bach understood that the fugal complex must have the capacity to generate new material from old. In this fugue Bach interrupted a process of permutation. The analysis asks why, concluding with analogies from astronomy, philosophy, and the words of C. S. Lewis
No. 22: bbm
Flash
Shockwave
Topics: Schweitzer, Sartre, Nietzsche
Key concepts: This fugue, the most logocentric of the cycle, provides an opportunity to compare theistic and atheistic existentialism, as exemplified in the writings of Bach biographer/editor/performer, Albert Schweitzer, and his cousin, Jean-Paul Sartre. Thematically, the analysis focuses on the Stoic concept of logos and its etymological derivatives. The logos of Bach's counterpoint demands recognition as purposeful and meaningful, not merely a display of contrapuntal process.
Questionnaire:
Students can answer ten questions online.
No. 23: BTopics: Triads, Tonality, Trinitarianism
Key concepts: Bach's music is the way it is because other things are the way they are. The power of Bach's music is proportional to the power of those other things. This fugue gives opportunity to consider how Trinitarian dogma has shaped musical structure. There is a brief discussion of the changing attitudes toward musical meaning and purpose during Bach's lifetime. This is contextualized in the dispute between Buttstett (representing the cantoral tradition) and Mattheson (representing the Enlightenment view).
No. 24: bm
Flash
Shockwave

Topics: Dance, Relationship of the bm fugues
Key concepts: This fugue is a dance, a passepied. The analysis considers Bach's use of the passepied in BWV 22, BWV 49, and BWV 202, the "Wedding" Cantata, and concludes that, in his liturgical music, Bach associated the passepied with the Wedding Supper of the Lamb. Associations between the bm fugues of Books 1 & 2 are developed with the conclusion that the former represents the cross and the latter the crown. The pair are theorized to be Bach's musical expression of Hebrews 12:2 -- "Who for the joy set before him" [book 2] "endured the cross" [book 1]. The last 14 measures contain the WTC's only instance of Bach's cross and crown motives (descending and ascending chromatics) in simultaneity. This follows Bach's 2nd quotation of the gefangen ("captured") motive from the St. Matthew Passion: counterpoint that he had earlier quoted in the bm prelude and fugue of Book 1.

For the Westworld episode, see The Well-Tempered Clavier (Westworld).

The Well-Tempered Clavier, BWV 846–893, is a collection of two sets of preludes and fugues in all 24 major and minor keys, composed for solo keyboard by Johann Sebastian Bach. In the German of Bach's time Clavier (keyboard) was a generic name indicating a variety of keyboard instruments, most typically a harpsichord or clavichord – but not excluding an organ either.

The modern German spelling for the collection is Das wohltemperierte Klavier (WTK; German pronunciation:[das ˌvoːlˌtɛmpəˈʁiːɐ̯tə klaˈviːɐ̯]). Bach gave the title Das Wohltemperirte Clavier to a book of preludes and fugues in all 24 major and minor keys, dated 1722, composed "for the profit and use of musical youth desirous of learning, and especially for the pastime of those already skilled in this study". Some 20 years later Bach compiled a second book of the same kind, which became known as The Well-Tempered Clavier, Part Two (in German: Zweyter Theil, modern spelling: Zweiter Teil).

Modern editions usually refer to both parts as The Well-Tempered Clavier, Book I (WTC I) and The Well-Tempered Clavier, Book II (WTC II), respectively.[1] The collection is generally regarded as being among the most important works in the history of Western classical music.[2]

Composition history[edit]

Each set contains twenty-four pairs of prelude and fugue. The first pair is in C major, the second in C minor, the third in C♯ major, the fourth in C♯ minor, and so on. The rising chromatic pattern continues until every key has been represented, finishing with a B minor fugue. The first set was compiled in 1722 during Bach's appointment in Köthen; the second followed 20 years later in 1742 while he was in Leipzig.

Bach recycled some of the preludes and fugues from earlier sources: the 1720 Klavierbüchlein für Wilhelm Friedemann Bach, for instance, contains versions of eleven of the preludes of the first book of the Well-Tempered Clavier. The C♯ major prelude and fugue in book one was originally in C major – Bach added a key signature of seven sharps and adjusted some accidentals to convert it to the required key.

In Bach's own time no similar collections were published, except one by Johann Christian Schickhardt (1681–1762), whose Op. 30 L'alphabet de la musique, contained 24 sonatas in all keys for alto recorder or flute or violin and basso continuo.[3]

Precursors[edit]

Although the Well-Tempered Clavier was the first collection of fully worked keyboard pieces in all 24 keys, similar ideas had occurred earlier. Before the advent of modern tonality in the late 17th century, numerous composers produced collections of pieces in all seven modes: Johann Pachelbel's magnificat fugues (composed 1695–1706), Georg Muffat's Apparatus Musico-organisticus of 1690 and Johann Speth's Ars magna of 1693 for example. Furthermore, some two hundred years before Bach's time, equal temperament was realized on plucked string instruments, such as the lute and the theorbo, resulting in several collections of pieces in all keys (although the music was not yet tonal in the modern sense of the word):

One of the earliest keyboard composers to realize a collection of organ pieces in successive keys was Daniel Croner (de) (1656–1740), who compiled one such cycle of preludes in 1682.[8][9] His contemporary Johann Heinrich Kittel (1652–1682) also composed a cycle of 12 organ preludes in successive keys.[10]

J.C.F. Fischer's Ariadne musica neo-organoedum (published in 1702 and reissued 1715) is a set of 20 prelude-fugue pairs in ten major and nine minor keys and the Phrygian mode, plus five chorale-based ricercars. Bach knew the collection and borrowed some of the themes from Fischer for the Well-Tempered Clavier.[11] Other contemporary works include the treatise Exemplarische Organisten-Probe (1719) by Johann Mattheson (1681–1764), which included 48 figured bass exercises in all keys,[12]Partien auf das Clavier (1718) by Christoph Graupner (1683–1760) with eight suites in successive keys,[13] and Friedrich Suppig's Fantasia from Labyrinthus Musicus (1722), a long and formulaic sectional composition ranging through all 24 keys which was intended for an enharmonic keyboard with 31 notes per octave and pure major thirds.[12][14] Finally, a lost collection by Johann Pachelbel (1653–1706), Fugen und Praeambuln über die gewöhnlichsten Tonos figuratos (announced 1704), may have included prelude-fugue pairs in all keys or modes.[15]

It was long believed that Bach had taken the title The Well-Tempered Clavier from a similarly-named set of 24 Preludes and Fugues in all the keys, for which a manuscript dated 1689 was found in the library of the Brussels Conservatoire. It was later shown that this was the work of a composer who was not even born in 1689: Bernhard Christian Weber (1 December 1712 – 5 February 1758). It was in fact written in 1745–50, and in imitation of Bach's example.[16][17]

Well-Tempered tuning[edit]

See also: Musical temperament and Musical tuning § Tuning systems

Bach's title suggests that he had written for a (12-note) well-tempered tuning system in which all keys sounded in tune (also known as "circular temperament"). The opposing system in Bach's day was meantone temperament[citation needed] in which keys with many accidentals sound out of tune. (See also musical tuning.) Bach would have been familiar with different tuning systems, and in particular as an organist would have played instruments tuned to a meantone system.

It is sometimes assumed that by "well-tempered" Bach intended equal temperament, the standard modern keyboard tuning which became popular after Bach's death, but modern scholars suggest instead a form of well temperament.[18] There is debate whether Bach meant a range of similar temperaments, perhaps even altered slightly in practice from piece to piece, or a single specific "well-tempered" solution for all purposes.

Intended tuning[edit]

During much of the 20th century it was assumed that Bach wanted equal temperament, which had been described by theorists and musicians for at least a century before Bach's birth. Internal evidence for this may be seen in the fact that in Book 1 Bach paired the E♭ minor prelude (6 flats) with its enharmonic key of D♯ minor (6 sharps) for the fugue. This represents an equation of the most tonally remote enharmonic keys where the flat and sharp arms of the circle of fifths cross each other opposite to C major. Any performance of this pair would have required both of these enharmonic keys to sound identically tuned, thus implying equal temperament in the one pair, as the entire work implies as a whole. However, research has continued into various unequal systems contemporary with Bach's career. Accounts of Bach's own tuning practice are few and inexact. The three most cited sources are Forkel, Bach's first biographer; Friedrich Wilhelm Marpurg, who received information from Bach's sons and pupils; and Johann Kirnberger, one of those pupils.

Forkel reports that Bach tuned his own harpsichords and clavichords and found other people's tunings unsatisfactory; his own allowed him to play in all keys and to modulate into distant keys almost without the listeners noticing it. Marpurg and Kirnberger, in the course of a heated debate, appear to agree that Bach required all the major thirds to be sharper than pure—which is in any case virtually a prerequisite for any temperament to be good in all keys.[19]

Johann Georg Neidhardt, writing in 1724 and 1732, described a range of unequal and near-equal temperaments (as well as equal temperament itself), which can be successfully used to perform some of Bach's music, and were later praised by some of Bach's pupils and associates. J.S. Bach's son Carl Philipp Emanuel Bach himself published a rather vague tuning method which was close to but still not equal temperament: having only "most of" the fifths tempered, without saying which ones nor by how much.

Since 1950 there have been many other proposals and many performances of the work in different and unequal tunings, some derived from historical sources, some by modern authors. Whatever their provenances, these schemes all promote the existence of subtly different musical characters in different keys, due to the sizes of their intervals. However, they disagree as to which key receives which character:

  • Herbert Anton Kellner argued from the mid-1970s until his death that esoteric considerations such as the pattern of Bach's signet ring, numerology, and more could be used to determine the correct temperament. His result is somewhat similar to Werckmeister's most familiar "correct" temperament. Kellner's temperament, with seven pure fifths and five ​15comma fifths, has been widely adopted worldwide for the tuning of organs. It is especially effective as a moderate solution to play 17th-century music, shying away from tonalities that have more than two flats.
  • John Barnes analyzed the Well-Tempered Clavier 's major-key preludes statistically, observing that some major thirds are used more often than others. His results were broadly in agreement with Kellner's and Werckmeister's patterns. His own proposed temperament from that study is a ​16 comma variant of both Kellner (​15) and Werckmeister (​14), with the same general pattern tempering the naturals, and concluding with a tempered fifth B–F♯.
  • Mark Lindley, a researcher of historical temperaments, has written several surveys of temperament styles in the GermanBaroque tradition. In his publications he has recommended and devised many patterns close to those of Neidhardt, with subtler gradations of interval size. Since a 1985 article in which he addressed some issues in the Well-Tempered Clavier, Lindley's theories have focused more on Bach's organ music than the harpsichord or clavichord works.

Title page tuning interpretations[edit]

More recently there has been a series of proposals of temperaments derived from the handwritten pattern of loops on Bach's 1722 title page. These loops (though truncated by a later clipping of the page) can be seen at the top of the title page image at the beginning of the article.

  • Andreas Sparschuh, in the course of studying German Baroque organ tunings, assigned mathematical and acoustic meaning to the loops. Each loop, he argued, represents a fifth in the sequence for tuning the keyboard, starting from A. From this Sparschuh devised a recursive tuning algorithm resembling the Collatz conjecture in mathematics, subtracting one beat per second each time Bach's diagram has a non-empty loop. In 2006 he retracted his 1998 proposal based on A = 420 Hz, and replaced it with another at A = 410 Hz.
  • Michael Zapf in 2001 reinterpreted the loops as indicating the rate of beating of different fifths in a given range of the keyboard in terms of seconds-per-beat, with the tuning now starting on C.
  • John Charles Francis in 2004 performed a mathematical analysis of the loops using Mathematica under the assumption of beats per second. In 2004, he also distributed several temperaments derived from BWV 924.[20]
  • Bradley Lehman in 2004 proposed[21] a ​16 and ​112 comma layout derived from Bach's loops, which he published in 2005 in articles of three music journals. Reaction to this work has been both vigorous and mixed, with other writers producing further speculative schemes or variants.
  • Daniel Jencka in 2005 proposed[22] a variation of Lehman's layout where one of the ​16 commas is spread over three fifths (G♯–D♯–A♯/B♭), resulting in a ​118 comma division. Motivations for Jencka's approach involve an analysis of the possible logic behind the figures themselves and his belief that a wide fifth (B♭–F) found in Lehman's interpretation is unlikely in a well-temperament from the time.
  • Graziano Interbartolo and others in 2006 proposed[23] a tuning system deduced from the WTK title page. Their work was also published in a book: Bach 1722 – Il temperamento di Dio – Le scoperte e i significati del 'Wohltemperirte Clavier', p. 136 – Edizioni Bolla, Finale Ligure.

Nevertheless, some musicologists say it is insufficiently proven that Bach's looped drawing signifies anything reliable about a tuning method. Bach may have tuned differently per occasion, or per composition, throughout his career.

  • David Schulenberg, in his book The Keyboard Music of J. S. Bach, allows that Lehman's argument is "ingenious" but counters that it "lacks documentary support (if the swirls were so important, why did Bach's students not copy them accurately, if at all?")[24] and concludes that the swirls cannot "be unambiguously interpreted as a code for a particular temperament".[25]
  • Luigi Swich, in his article "Further thoughts on Bach's 1722 temperament",[26] more recently presents an alternative reading from that of Bradley Lehman and others of Johann Sebastian Bach's tuning method as derived from the title-page calligraphic drawing. It differs in significant details, resulting in a circulating but unequal temperament using ​15 Pythagorean-comma fifths that is effective through all 24 keys and, most important, tunable by ear without an electronic tuning device. It is based on the synchronicity between the fifth F–C and the third F–A (c. 3 beats per second) and between the fifth C–G and the third C–E (c. 2 beats per second). Such a system is reminiscent of Herbert Anton Kellner's 1977 temperament and even more, among the others, the temperament of the 1688 Arp Schnitger organ in Norden, St Ludgeri and the temperament later described by Carlo Gervasoni in his La scuola della musica (Piacenza, 1800). Such a system with all its major thirds more or less sharp is confirmed by Friedrich Wilhelm Marpurg's report about the way a famous student of Bach's, Johann Philipp Kirnberger, was taught to tune in his lessons with Bach. It allows all 24 keys to be played through without changing tuning nor unpleasant intervals, but with varying degrees of difference-the temperament being unequal, and the keys not all sounding the same. Compared to Werckmeister III, the other 24 keys-circulating temperament, Bach's tuning is much more differentiated with its 8 (instead of Werckmeister's 4) different kinds of major thirds. The manuscript Bach P415 in Berlin Staatsbibliothek is the only known copy of the WTC to show this drawing which represents, a bit cryptically in Bach's spirit, the purpose for which the masterpiece was written and its solution at the same time. Not surprisingly, since this is most probably the working copy that Johann Sebastian Bach used in his classes.

Content[edit]

See also: List of solo keyboard compositions by Johann Sebastian Bach § The Well-Tempered Clavier (846–893), and List of compositions by Johann Sebastian Bach § BGA14

Each Prelude is followed by a Fugue in the same key. In each book the first Prelude and Fugue is in C major, followed by a Prelude and Fugue in its parallel minor key (C minor). Then all keys, each major key followed by its parallel minor key, are followed through, each time moving up a half tone: C → C♯ → D → E♭ → E → F → F♯ → ... ending with ... → B♭ → B.

Book I[edit]

The first book of the Well-Tempered Clavier was composed in the early 1720s, with Bach's autograph dated 1722. Apart from the early versions of several preludes included in W. F. Bach's Klavierbüchlein (1720) there is an almost complete collection of "Prelude and Fughetta" versions predating the 1722 autograph, known from a later copy by an unidentified scribe.[27]

Title Page[edit]

The title page of the first book of the Well-Tempered Clavier reads:

Das Wohltemperirte Clavier oder Præludia, und Fugen durch alle Tone und Semitonia, so wohl tertiam majorem oder Ut Re Mi anlangend, als auch tertiam minorem oder Re Mi Fa betreffend. Zum Nutzen und Gebrauch der Lehrbegierigen Musicalischen Jugend, als auch derer in diesem studio schon habil seyenden besonderem Zeitvertreib auffgesetzet und verfertiget von Johann Sebastian Bach. p. t: Hochfürstlich Anhalt-Cöthenischen Capel-Meistern und Directore derer Camer Musiquen. Anno 1722.

In English:[28]

The well-tempered Clavier, or Preludes and Fugues through all the tones and semitones, both as regards the tertiam majorem or Ut Re Mi [i.e., major] and tertiam minorem or Re Mi Fa [i.e., minor]. For the profit and use of the studious musical young, and also for the special diversion of those who are already skilful in this study, composed and made by Johann Sebastian Bach, for the time being Capellmeister and Director of the Chamber-music of the Prince of Anhalt-Cothen. In the year 1722.

No. 1: Prelude and Fugue in C major, BWV 846[edit]

Further information: Prelude and Fugue in C major, BWV 846

Early version BWV 846a of the Prelude in Klavierbüchlein für Wilhelm Friedemann Bach (No. 14: "Praeludium 1"). The prelude is a seemingly simple progression of arpeggiated chords, one of the connotations of 'préluder' as the French lutenists used it: to test the tuning. Bach used both G♯ and A♭ into the harmonic meandering.

No. 2: Prelude and Fugue in C minor, BWV 847[edit]

Prelude and Fugue in C minor, BWV 847. Prelude also in WFB Klavierbüchlein, No. 15: Praeludium 2.

No. 3: Prelude and Fugue in C♯ major, BWV 848[edit]

Prelude and Fugue in C-sharp major, BWV 848. Prelude also in WFB Klavierbüchlein, No. 21: Praeludium [8].

No. 4: Prelude and Fugue in C♯ minor, BWV 849[edit]

Prelude and Fugue in C-sharp minor, BWV 849. Prelude also in WFB Klavierbüchlein, No. 22: Praeludium [9].

No. 5: Prelude and Fugue in D major, BWV 850[edit]

Prelude and Fugue in D major, BWV 850 (commons). Prelude also in WFB Klavierbüchlein, No. 17: Praeludium 4.

No. 6: Prelude and Fugue in D minor, BWV 851[edit]

Prelude and Fugue in D minor, BWV 851 (commons). Prelude also in WFB Klavierbüchlein, No. 16: Praeludium 3.

No. 7: Prelude and Fugue in E♭ major, BWV 852[edit]

Prelude and Fugue in E-flat major, BWV 852 (commons).

No. 8: Prelude in E♭ minor and Fugue in D♯ minor, BWV 853[edit]

Prelude in E-flat minor and Fugue in D-sharp minor, BWV 853 (commons). Prelude also in WFB Klavierbüchlein, No. 23: Praeludium [10]. The fugue was transposed from D minor to D♯ minor.

No. 9: Prelude and Fugue in E major, BWV 854[edit]

Prelude and Fugue in E major, BWV 854 (commons). Prelude also in WFB Klavierbüchlein, No. 19: Praeludium 6.

No. 10: Prelude and Fugue in E minor, BWV 855[edit]

Prelude and Fugue in E minor, BWV 855. Early version BWV 855a of the Prelude in Klavierbüchlein für Wilhelm Friedemann Bach (No. 18: "Praeludium 5").

No. 11: Prelude and Fugue in F major, BWV 856[edit]

Prelude and Fugue in F major, BWV 856 (commons). Prelude also in WFB Klavierbüchlein, No. 20: Praeludium 7.

No. 12: Prelude and Fugue in F minor, BWV 857[edit]

Prelude and Fugue in F minor, BWV 857 (commons). Prelude also in WFB Klavierbüchlein, No. 24: Praeludium [11].

No. 13: Prelude and Fugue in F♯ major, BWV 858[edit]

Prelude and Fugue in F-sharp major, BWV 858 (commons).

No. 14: Prelude and Fugue in F♯ minor, BWV 859[edit]

Prelude and Fugue in F-sharp minor, BWV 859 (commons).

No. 15: Prelude and Fugue in G major, BWV 860[edit]

Prelude and Fugue in G major, BWV 860 (commons).

No. 16: Prelude and Fugue in G minor, BWV 861[edit]

Prelude and Fugue in G minor, BWV 861.

No. 17: Prelude and Fugue in A♭ major, BWV 862[edit]

Prelude and Fugue in A-flat major, BWV 862 (commons).

No. 18: Prelude and Fugue in G♯ minor, BWV 863[edit]

Prelude and Fugue in G-sharp minor, BWV 863 (commons).

No. 19: Prelude and Fugue in A major, BWV 864[edit]

Prelude and Fugue in A major, BWV 864 (commons).

No. 20: Prelude and Fugue in A minor, BWV 865[edit]

Prelude and Fugue in A minor, BWV 865 (commons).

No. 21: Prelude and Fugue in B♭ major, BWV 866[edit]

Prelude and Fugue in B-flat major, BWV 866 (commons).

No. 22: Prelude and Fugue in B♭ minor, BWV 867[edit]

Prelude and Fugue in B-flat minor, BWV 867 (commons).

No. 23: Prelude and Fugue in B major, BWV 868[edit]

Prelude and Fugue in B major, BWV 868 (commons).

No. 24: Prelude and Fugue in B minor, BWV 869[edit]

Prelude and Fugue in B minor, BWV 869 (commons).

Book II[edit]

The two major primary sources for this collection of Preludes and Fugues are the "London Original" (LO) manuscript, dated between 1739 and 1742, with scribes including Bach, his wife Anna Magdalena and his oldest son Wilhelm Friedeman, which is the basis for Version A of WTC II,[29] and for Version B, that is the version published by the 19th-century Bach-Gesellschaft, a 1744 copy primarily written by Johann Christoph Altnickol (Bach's son-in-law), with some corrections by Bach, and later also by Altnickol and others.[30]

No. 1: Prelude and Fugue in C major, BWV 870[edit]

Prelude and Fugue in C major, BWV 870.

No. 2: Prelude and Fugue in C minor, BWV 871[edit]

Prelude and Fugue in C minor, BWV 871 (commons).

No. 3: Prelude and Fugue in C♯ major, BWV 872[edit]

Prelude and Fugue in C-sharp major, BWV 872 (commons).

No. 4: Prelude and Fugue in C♯ minor, BWV 873[edit]

Prelude and Fugue in C-sharp minor, BWV 873 (commons).

No. 5: Prelude and Fugue in D major, BWV 874[edit]

Prelude and Fugue in D major, BWV 874 (commons).

No. 6: Prelude and Fugue in D minor, BWV 875[edit]

Prelude and Fugue in D minor, BWV 875 (commons).

No. 7: Prelude and Fugue in E♭ major, BWV 876[edit]

Prelude and Fugue in E-flat major, BWV 876 (commons).

No. 8: Prelude and Fugue in D♯ minor, BWV 877[edit]

Prelude and Fugue in D-sharp minor, BWV 877 (commons).

No. 9: Prelude and Fugue in E major, BWV 878[edit]

Prelude and Fugue in E major, BWV 878 (commons).

No. 10: Prelude and Fugue in E minor, BWV 879[edit]

Prelude and Fugue in E minor, BWV 879 (commons).

No. 11: Prelude and Fugue in F major, BWV 880[edit]

Prelude and Fugue in F major, BWV 880 (commons).

No. 12: Prelude and Fugue in F minor, BWV 881[edit]

Prelude and Fugue in F minor, BWV 881. Prelude as a theme with variations. Fugue in three voices.

No. 13: Prelude and Fugue in F♯ major, BWV 882[edit]

Prelude and Fugue in F-sharp major, BWV 882 (commons).

No. 14: Prelude and Fugue in F♯ minor, BWV 883[edit]

Prelude and Fugue in F-sharp minor, BWV 883 (commons).

No. 15: Prelude and Fugue in G major, BWV 884[edit]

Prelude and Fugue in G major, BWV 884 (commons).

No. 16: Prelude and Fugue in G minor, BWV 885[edit]

Prelude and Fugue in G minor, BWV 885 (commons).

No. 17: Prelude and Fugue in A♭ major, BWV 886[edit]

Prelude and Fugue in A-flat major, BWV 886

Title page of Das Wohltemperierte Clavier, Book I (autograph)

Contents

  • 1Composition history
  • 2Content
    • 2.1Book I
      • 2.1.1Title Page
      • 2.1.2No. 1: Prelude and Fugue in C major, BWV 846
      • 2.1.3No. 2: Prelude and Fugue in C minor, BWV 847
      • 2.1.4No. 3: Prelude and Fugue in C♯ major, BWV 848
      • 2.1.5No. 4: Prelude and Fugue in C♯ minor, BWV 849
      • 2.1.6No. 5: Prelude and Fugue in D major, BWV 850
      • 2.1.7No. 6: Prelude and Fugue in D minor, BWV 851
      • 2.1.8No. 7: Prelude and Fugue in E♭ major, BWV 852
      • 2.1.9No. 8: Prelude in E♭ minor and Fugue in D♯ minor, BWV 853
      • 2.1.10No. 9: Prelude and Fugue in E major, BWV 854
      • 2.1.11No. 10: Prelude and Fugue in E minor, BWV 855
      • 2.1.12No. 11: Prelude and Fugue in F major, BWV 856
      • 2.1.13No. 12: Prelude and Fugue in F minor, BWV 857
      • 2.1.14No. 13: Prelude and Fugue in F♯ major, BWV 858
      • 2.1.15No. 14: Prelude and Fugue in F♯ minor, BWV 859
      • 2.1.16No. 15: Prelude and Fugue in G major, BWV 860
      • 2.1.17No. 16: Prelude and Fugue in G minor, BWV 861
      • 2.1.18No. 17: Prelude and Fugue in A♭ major, BWV 862
      • 2.1.19No. 18: Prelude and Fugue in G♯ minor, BWV 863
      • 2.1.20No. 19: Prelude and Fugue in A major, BWV 864
      • 2.1.21No. 20: Prelude and Fugue in A minor, BWV 865
      • 2.1.22No. 21: Prelude and Fugue in B♭ major, BWV 866
      • 2.1.23No. 22: Prelude and Fugue in B♭ minor, BWV 867
      • 2.1.24No. 23: Prelude and Fugue in B major, BWV 868
      • 2.1.25No. 24: Prelude and Fugue in B minor, BWV 869
    • 2.2Book II
      • 2.2.1No. 1: Prelude and Fugue in C major, BWV 870
      • 2.2.2No. 2: Prelude and Fugue in C minor, BWV 871
      • 2.2.3No. 3: Prelude and Fugue in C♯ major, BWV 872
      • 2.2.4No. 4: Prelude and Fugue in C♯ minor, BWV 873
      • 2.2.5No. 5: Prelude and Fugue in D major, BWV 874
      • 2.2.6No. 6: Prelude and Fugue in D minor, BWV 875
      • 2.2.7No. 7: Prelude and Fugue in E♭ major, BWV 876
      • 2.2.8No. 8: Prelude and Fugue in D♯ minor, BWV 877
      • 2.2.9No. 9: Prelude and Fugue in E major, BWV 878
      • 2.2.10No. 10: Prelude and Fugue in E minor, BWV 879
      • 2.2.11No. 11: Prelude and Fugue in F major, BWV 880
      • 2.2.12No. 12: Prelude and Fugue in F minor, BWV 881
      • 2.2.13No. 13: Prelude and Fugue in F♯ major, BWV 882
      • 2.2.14No. 14: Prelude and Fugue in F♯ minor, BWV 883
      • 2.2.15No. 15: Prelude and Fugue in G major, BWV 884
      • 2.2.16No. 16: Prelude and Fugue in G minor, BWV 885
      • 2.2.17No. 17: Prelude and Fugue in A♭ major, BWV 886
      • 2.2.18No. 18: Prelude and Fugue in G♯ minor, BWV 887
      • 2.2.19No. 19: Prelude and Fugue in A major, BWV 888
      • 2.2.20No. 20: Prelude and Fugue in A minor, BWV 889
      • 2.2.21No. 21: Prelude and Fugue in B♭ major, BWV 890
      • 2.2.22No. 22: Prelude and Fugue in B♭ minor, BWV 891
      • 2.2.23No. 23: Prelude and Fugue in B major, BWV 892
      • 2.2.24No. 24: Prelude and Fugue in B minor, BWV 893
  • 3Style
  • 4Reception
  • 5Recordings
  • 6References
  • 7Sources
  • 8External links
Bach's autograph of the 4th Fugue of Book I
Bach's autograph of Fugue No. 17 in A♭ major from the second part of Das Wohltemperierte Clavier
Top of Bach's title page for the 1st book of 'The Well-Tempered Clavier', 1722, showing handwritten loops which some have interpreted as tuning instructions.
Early version BWV 846a (1720) of the first prelude of the first book, as written down by Bach in his eldest son's notebook
Bach's autograph (1722) of the first prelude of Book I

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