The work consists of a
fantasia followed by a three-voice
fugue. The fantasia is organized through passagework,
arpeggiation,
chromatic voice leading, and
recitative-like writing; the fugue is organized through repeated entries of a chromatic subject and varied episodes. Several commentators treat the fantasia and fugue as different in form while also noting continuities between them, especially in chromatic procedure,
tonal instability, and keyboard
figuration.
Fantasia Analysts divide the fantasia in related but not identical ways.
Heinrich Schenker describes the fantasia as having two principal parts of comparable weight: a
prelude-like first part in bars 1–49 and a recitative-like second part in bars 49–79. also distinguishes a prelude and a recitative, while noting that each section borrows to some degree from the style of the other. In Schulenberg's account, the first half moves comparatively directly to the
dominant at bar 49, while the second half returns to the
tonic only after remote
modulations.
Richard D. P. Jones gives a more detailed four-part division: an opening passagework section ending with a half close in the tonic at bar 20; a second paragraph, bars 21–49, in which arpeggiated chords alternate with further passagework; an instrumental recitative, bars 49–74; and a
coda from bar 75.
Opening passagework, bars 1–20 The opening part of the fantasia is not built around a recurring theme in the manner of the fugue. Jones describes the fantasia as "quite athematic" and notes that in some earlier free keyboard pieces Bach introduced more definite thematic material as a counterweight to improvisatory freedom.
Joseph Kerman describes the opening as organized by rhythmic patterns rather than by free rhythmic disorder. In Kerman's account, after the two opening gestures, the passagework of bars 3–20 is shaped by patterns of three, five, six, and twelve sixteenth notes. Kerman also notes that Schenker's written-out arpeggio realizations for the later shorthand chords continue the same principle:
notation is used to suggest a varied performance rather than a mechanically regular one. Schenker contrasts the standard version of the opening with the early version, BWV 903a. In his discussion of bars 3–4, Schenker states that the early version is comparatively repetitive in its figuration, while the standard version avoids literal repetition through small alterations that introduce contrast and variety. For Schenker, the alteration at bar 4 is significant because it marks a departure from a more uniform figural pattern and helps define the later version's treatment of variation within passagework. Despite the rapid figuration, Schenker emphasizes the tonal control of the first part. Schenker notes that within bars 1–49 Bach reaches the dominant of
D minor seven times, in bars 4, 6, 8, 29, 30, 41, and 49. In Schenker's reading, these dominant arrivals divide the section and help preserve the main key amid the passagework and arpeggiation. Schulenberg makes a related point through voice leading. Schulenberg argues that ordinary harmonic labels are less useful here than an understanding of which notes function as chord tones and which function as anticipations, passing tones, suspensions, or
similar embellishing tones. His bass-line sketch for bars 1–49 treats the chromatic surface as an elaboration of underlying bass and voice-leading patterns. In that analysis, the sonorities that resemble
augmented-sixth chords in bars 7, 9, and 11, together with the
C-minor harmony at bar 12, arise through related chromatic voice leading. Compared with later parts of the fantasia, the opening paragraph remains closer to D minor, although chromatic writing is already present. Jones treats bars 1–20 as an extended passagework section ending with a half close in D minor. Schulenberg describes the first half of the fantasia as an arpeggiated prelude whose figuration ranges from regular broken-chord sequences to freer
cadenzas. Schulenberg singles out the C-minor harmony at bar 12 as a temporary displacement into a remote flat-side area that foreshadows later movement to remote tonal regions. Schenker identifies the C–E–G harmony at bar 12 as an unusual sonority that is absorbed into the broader motion toward the dominant of D minor.
Arpeggiated and modulatory passage, bars 21–49 The second paragraph, bars 21–49, introduces larger arpeggiated spans. Jones describes bars 21–49 as a section in which arpeggiated chords alternate with passagework. Schenker treats the arpeggiated passages as governed by voice leading, not merely as keyboard display. In his discussion of the passage beginning at bar 27, Schenker argues that arpeggiation should not be realized mechanically as simple ascent and descent through chord tones. Instead, Schenker treats Bach's written-out arpeggio practice as evidence that passing tones,
acciaccaturas, changes of direction, and registral choices can serve voice-leading purposes. The arpeggio section beginning at bar 33 introduces more remote tonal motion. Schenker emphasizes the harmonic connection between the first chord of bar 33 and the chord at bar 30, with bars 31–32 functioning as intervening
composed-out material. Schenker summarizes the harmonic motion of bars 33–42 as passing through D, B, E, A, F, D, E, A, and B. Schulenberg also treats bar 33 as a structural turning point. In Schulenberg's account, the steady bass descent from D to A that had governed the opening gives way at bar 33 to more irregular voice leading, including
diminished fourths and other intervals that do not fit a simple linear reduction. Schulenberg reads the passage as pointing first toward
G minor at bar 33, then toward
E minor at bar 34, and then toward
B minor at bar 38. The only sustained modulation in bars 33–45, according to Schulenberg, is the move at bar 45 to
A minor, the minor dominant.
Recitative, bars 49–74 The recitative begins at bar 49. Schenker gives a harmonic outline for bars 49–70 in which the dominant of D minor is followed by a succession of motions by third with chromatic alteration: A to D, then F to G, E to F/E, C to B/E, and G to C, before the return toward D minor through A–D–G and the approach to
cadence. In his broader tonal description, Schenker treats bars 50–62 as brief departures from the main key, followed by the return of D minor from bar 62: A, the dominant, is heard in bar 62; D minor follows at bar 63 with a chromatically raised third; the tonic degree is retained until bar 68; IV appears at bar 68; a regular half cadence follows at bar 70; and a full cadence arrives at bar 74. Schenker also identifies a concealed melodic line running through much of the recitative. Schenker reads this line as a chromatic descent through an
octave beginning on B. The line is most clearly heard, in Schenker's account, in the eighth notes associated with the chords that begin and end individual recitative statements. Kerman approaches the recitative through phrase structure. Kerman describes the recitative as built from repeated short, slow figures, mostly
upbeat–downbeat units: the downbeats usually descend by step, while the upbeats are varied by shorter note-patterns. Kerman counts about eleven such figures in the twenty-five bars of the recitative proper and eight more in the closing passage over the tonic pedal. The
enharmonic notation at bar 50 is central to both Schenker's and Schulenberg's accounts. Schenker argues that the succession B–A in bars 49–50 belongs to the chord A–C–E–G, understood as the seventh
degree in
B major/minor. In Schenker's reading, Bach moves from the A–C–E chord in bar 49 to D–F–A, then extends that harmony to include E and respells F as G, thereby preparing F as the dominant of B. Schulenberg describes the same passage as more coherent than the notation may first suggest: the dominant chord
tonicizing D in bar 50 is enharmonically equivalent to the one tonicizing
C minor in bar 61, and the intervening passage is essentially a sequence over a descending bass. Schulenberg therefore reads the opening of the recitative as a digression in C minor, or iii of the dominant, a remote relation to D minor. Jones similarly emphasizes that the recitative moves to the outer limits of the tonal system and back while remaining organized by planned harmonic motion.
Coda, bars 75–79 The
coda begins at bar 75 over a tonic
pedal. Schenker describes bars 75–79 as a chain of
diminished seventh chords descending by
semitone, interrupted at three points by simple
triads on IV, I, and IV. In Schenker's account, these triads lead to the final dominant–tonic close. Jones emphasizes that the coda is both highly chromatic and supported by the tonic: the treble descends chromatically through an octave, the accompanying chords also descend chromatically, and the coda is supported by the tonic pedal. Schulenberg likewise describes the coda as a chromatic descent through a full octave over a tonic pedal, with an underlying gesture that functions as a prolonged
plagal cadence. Schenker also treats the figuration of bars 76–79 as ordered in stages: the underlying arpeggiations begin with five ascending figures, change type at the sixth, and then move toward a more fully elaborated close.
Fugue The fugue is in three voices and has eleven subject entries. Schenker gives the entries as follows: Kerman likewise states that the eight-bar
subject appears eleven times in a 161-bar fugue. Schenker warns against treating the three keyboard lines as if they were fixed vocal parts such as
soprano,
alto,
tenor, and
bass; for an instrumental fugue, Schenker instead refers to the lines as upper, middle, and lower voices. Schenker divides the fugue into three large sections. The first section is the
exposition, comprising the first three entries: subject, answer, subject, in
D minor,
A minor, and D minor. It ends with a cadence to
F major at bar 35. Bars 35–41 form an episode leading to the second section. The second section begins with the fourth and fifth entries in A minor and D minor, then moves to the more distant sixth and seventh entries in
B minor and
E minor. Schenker treats the B-minor and E-minor entries as consistent with the middle section's modulatory function. Schenker regards the beginning of the third section as open to question, but prefers to begin the third section with the eighth entry at bar 107. The third section therefore includes the eighth through eleventh entries. Schenker explains this grouping through the relation of their keys: the
G-minor ninth entry functions as a
subdominant midpoint between D-minor entries and is then absorbed into the movement toward the final D-minor close. Jones describes the fugue as more formally defined than the fantasia. In Jones's account, the fugue has a clearly articulated subject, a sequential
headmotive, an
inversion halfway through the subject, a regular countersubject, a
reprise element associated with
concerto form, and a modulatory phase divided into sharp-side and flat-side regions. Schulenberg also emphasizes the tonal plan of the fugue. Schulenberg argues that if the fugue is called chromatic, the reason is not only the subject, since Bach wrote other fugues on chromatic subjects, but rather the fugue's movement to tonalities not normally expected in D minor, especially B minor and E minor. He locates these remote minor keys near the centre of the fugue, around bars 83–97.
Subject and answer The subject begins on the dominant rather than the tonic. Schenker reads the subject's chromaticism as grounded in a composed-out D-minor harmony: by taking the first quarter note of bar 1 and adding the first quarter notes of bars 4, 6, 7, and 8, Schenker obtains the descent A–G–F–E–D. In Schenker's reading, the subject's apparently diffuse chromaticism is therefore rooted in the D-minor chord. Schenker also notes that the subject begins on the dominant so that the subject can close on the tonic. Kerman accepts the importance of Schenker's analytical reduction of the subject but argues that it does not account for the subject's dynamic process. In Kerman's reading, the subject's main issue is not the amount of chromaticism but its tonal ambiguity. Heard by itself, the opening A–C suggests A minor rather than D minor; E–G in bars 3–4 then suggests E minor, the dominant of the dominant; the B at bar 5 cancels that sharp-side implication and turns the subject back toward a D-minor cadence. {{Image frame \relative c'' { \key d \minor \time 3/4 a4 bes b | c c8 b c4 | e,4 f fis | g4 g8 fis g a | bes4 a g | f4 g8 f e d | e4 a, cis | d4 } }} Kerman identifies the B at bar 5 as the subject's melodic and structural crux. In later entries, Kerman argues, this point generates unusual
canonic writing, helps trigger the breakdown of contrapuntal texture into thick chords, and supplies the basis for the large sequence in bars 135–140. Kerman also assigns rhythmic importance to this point: with the help of the dissonant
trill in the countersubject beginning at bar 13, the corresponding bar can take on the force of a downbeat against the usual accentual pattern. The answer at bar 9 raises the question of whether the answer should be tonal or real. Schenker explains that, since the subject begins on the dominant, the subject calls for a
tonal answer beginning on the tonic; at the same time, the subject's shape calls for a real answer preserving the intervallic relation, so that A would be answered by E, the dominant of A minor. Schenker reads Bach's solution as a compression of both possibilities: the answer begins with D but also includes E within the same quarter-note span through the
dotted rhythm. Jones likewise treats the answer as formally important, noting the
unprepared seventh at the answering entry in bar 9 and the inexact dotted opening rhythm, which later becomes the basis of an episodic sequence in bars 72–75. Schulenberg describes the same answer as replacing the original half-step A–B with D–F, while E functions as a passing tone.
Exposition and first episodes, bars 1–41 The exposition comprises the first three entries. At bar 1, the upper voice presents the subject in D minor. At bar 9, the middle voice gives the answer in A minor, while the upper voice continues with the first countersubject. Schenker treats bar 8, between the first subject and the answer, as an insertion required by contrapuntal and registral considerations: the first subject ends on D, the answer begins on D, and the upper voice must rise above the answer to function as counterpoint. Schenker adds that Bach gives this necessary insertion a role in the first countersubject by making its figure the basis of that countersubject. The first episode, bars 16–18, is based on the principal motive of the first countersubject. At the third entry, bars 19–26, the lower voice states the subject in D minor; the middle voice adheres to the first countersubject, and the upper voice introduces the second countersubject. The second episode, bars 26–41, modulates to F major, articulates the cadence, and prepares the second section. In Schenker's account, the length of the second episode separates the fourth entry from the third and prevents the fourth entry from sounding like an extra exposition entry. The second episode uses material derived from the first countersubject, and Schenker identifies a bass motion by fifths through the opening notes of successive bars, E–A–D–G–C.
Middle section and remote entries, bars 42–106 The fourth entry begins at bar 42 in A minor, in the middle voice. Schenker notes that the fourth entry is the first entry in which Bach varies the original form of the subject: the quarter notes corresponding to bars 5–6 of the theme appear in
diminution as eighth notes. Kerman treats the fourth entry as the start of a purposeful process in which the subject is gradually altered. In Kerman's reading, the melodic peak is softened by
appoggiatura eighth notes, and the cadence of the original subject is obscured. The third episode, bars 49–59, includes new material. Schenker reads bars 57–59 through a larger A–C–E triad, within which the bass motion on each eighth note expresses smaller chordal fragments. Kerman describes the third episode as a composite of two contrasting ideas: arpeggiated chords and continuous sixteenth-note figuration doubled in thirds or sixths. The fifth entry begins at bar 60 in D minor. Schenker observes that the fifth entry varies the theme more extensively than the fourth entry: the final bars of the subject are omitted, and the fifth and sixth bars of the theme are repeated in bars 66–67 in another voice. Schenker compares this internal repetition to a technique more typical of
homophonic continuity than of strict fugue. Kerman reads the fifth entry as altered in rhythm and harmony: the bass A at bar 60 shifts the accent from the subject's second bar to its first and makes the tonic entry less clear by emphasizing the dominant. The fourth episode, bars 68–75, prepares a half cadence on the dominant of D minor. Schenker treats bars 72–75 as a foreshadowing of the answer at bar 76. In Schenker's preferred reading, bar 72 begins with C rather than C, so that bars 72–73, bars 74–75, and bars 76–77 present related forms of the same figure, moving from simpler to more complex harmonic settings. Kerman describes bars 72–75 as resembling a false
stretto before the sixth entry, with a touch of diminution that helps destabilize the sixth entry. The sixth entry begins at bar 76, where the answer appears in B minor in the lower voice. Schenker notes that bars 5–7 of the subject, corresponding here to bars 80–82, are again fragmented through diminution, but differently from the diminutions in the fourth and fifth entries. Schenker also observes that the countersubjects are new, with only a trace of the first countersubject in bar 81. Kerman treats the sixth entry as another stage in the weakening of the subject's original shape: the entry is not strongly launched, its opening contour is blurred, and the sixth entry ends with a cadence in the remote key of B minor. The fifth episode, bars 83–89, is based on material from the first countersubject. Schenker identifies bars 83–86, including the bass figures in bars 85–86, as derived from that countersubject. At bar 85, Schenker insists on G rather than G, explaining the note as part of the chord E–G–B and as required by a chromatic line extending through bars 84–89. The seventh entry begins at bar 90 in E minor, in the upper voice. Schenker identifies a new countersubject in the middle voice and relates its sixteenth-note motion to the preceding episode. Schenker treats bar 94 as a prepared expansion of the three-voice texture into a denser sonority: the uninterrupted sixteenth notes in bars 87–93, the pedal beginning at bar 90, and the deletion of the last eighth note in the fourth bar of the subject all prepare the increase in density. Jones similarly singles out the E-minor entry at bar 90, where the three-part fugal texture expands at bar 94 into an eight-part
dominant-ninth chord; Jones notes that this sonority recurs climactically in bars 135–139 and 158. Kerman reads the passage as a climactic breakdown of subject, countersubject, harmony, and counterpoint. The sixth episode, bars 97–106, follows the E-minor entry. Schenker compares the sixth episode with the fourth episode. Kerman describes the sixth episode as a return of the arpeggiated texture associated with earlier episodes, serving to reduce the tension after the distant E-minor climax.
Return and closing section, bars 107–161 The eighth entry begins at bar 107 in D minor, with the answer in the middle voice. Schenker notes that the subject is stated only as far as its sixth measure and that the fifth and sixth measures are repeated, as in the fifth entry. Schenker identifies several further changes in the eighth entry: the leap of a sixth in the second measure is composed out, the third measure uses a dotted rhythm similar to that of the first measure, and the same dotted rhythm replaces the two eighth notes in the third quarter of the fourth measure. The seventh episode, bars 115–130, combines previously heard material with new material in bars 118–125. Schenker notes the two-voice texture in bars 120–121 and identifies a chromatic descent in the middle voice in bars 126–130. Kerman treats bars 115–130 as a relatively long passage centered on D minor and leading toward the final climax. The ninth entry begins at bar 131 in G minor. Schenker stresses that the subject appears in the middle voice for four measures, after which its fifth and sixth measures are transferred to the upper voice. Schenker explains this through exchange of voices. As in earlier shortened entries, the remaining bars of the subject are replaced by repetition of its fifth and sixth measures; in the ninth entry, however, the repeated material also modulates first to D minor at bar 137 and then to A minor within bar 139. Schenker therefore treats the repeated material as also forming the eighth episode. Kerman interprets the G-minor entry as a subdominant event that does not provide closure by itself. In Kerman's account, Bach uses the subject's crux and its associated marching figure, intensifies it with thick chords, and sequences it from the subdominant past the tonic toward the dominant, producing dominant-ninth sonorities at bars 135 and 139. The tenth entry begins at bar 140 with the subject in D minor in the lower voice. Kerman reads the tenth entry as the lowest bass entry, placed immediately after the large climactic sequence and coordinated with the pedal that began at bar 132. The ninth episode begins at bar 147 and recalls material from bars 118ff. The eleventh and final entry begins at bar 154, with the subject in D minor in the upper voice. Schenker notes the high register of the final entry and its contrast with the preceding low-register entry. Schenker also observes that, although the subject is stated only through its sixth measure, the second eighth note of the third quarter in the fourth measure of the subject is restored here, unlike in the earlier climactic entries, because the closing section requires a more intact restatement of the theme. Kerman describes the final entry as answering the preceding bass entry, with left-hand octaves below in bars 154–160; Kerman also treats the closing flourish as emphasizing the original rhythmic endpoint of the subject. Schenker adds that the free ending in bar 160 is still based on the closing notes of the subject. Schenker summarizes the fugue as a flexible application of fugal procedure. In Schenker's view, the first part establishes the subject and answer without alteration; later parts vary, abbreviate, embellish, or repeat the subject once its basic shape has been made clear. Schenker also argues that the episodes retain their freedom while being balanced with the entries, that the chosen three-voice texture is sometimes reduced or expanded, and that the first countersubject is followed flexibly rather than mechanically. Kerman makes a related but differently framed point: the fugue uses no major contrapuntal devices such as stretto,
inversion, or thematic combination, and even the countersubject appears irregularly; the structure of the fugue depends instead on the subject, its variants, its tonal implications, its episodes, and the gradual buildup of texture toward climaxes.
Relationship between the fantasia and fugue The formal relation between the fantasia and fugue has been described in different ways. Jones presents the fugue partly as a structural counterpart to the fantasia. Since the fantasia is largely athematic, the fugue supplies the definite thematic organization that the fantasia avoids, whether or not the fugue was part of the original conception. Jones contrasts the fantasia's free, pseudo-improvisatory writing with the fugue's articulated subject, countersubject, reprise elements, and organized modulatory regions. Jones also emphasizes continuity between the fantasia and fugue. The fugue's chromatic sequential headmotive, the tonal instability of the subject before its midpoint, the unprepared seventh at the first answer in bar 9, the inexact dotted answer, the later episodic use of that dotted rhythm in bars 72–75, and the eight-part dominant-ninth chord at bar 94 all make the fugue a continuation of the fantasia's chromatic and improvisatory procedures. Kerman similarly rejects the view that the fugue is merely a purely strict counterpart to the fantasia. Kerman argues that the steady motion of the fugue provides a large-scale rhythmic resolution to the irregular starts and stops of the fantasia, but he also describes the fugue as preserving an improvisatory quality through radical modulations, free figuration, instability of subject and countersubject, and homophonic outbursts. For Kerman, Bach translates some of the fantasia's freedom into fugal texture rather than simply opposing it. Schulenberg links the fantasia and fugue through tonal design. Schulenberg treats the fugue's remote B-minor and E-minor regions as analogous to the fantasia's movement beyond the ordinary tonal range of D minor. For Schulenberg, the fugue's chromatic character is justified less by the chromatic subject alone than by its movement to tonalities not normally encountered in D minor. This agrees broadly with Jones's and Kerman's view that the fugue continues important formal and tonal features of the fantasia, while retaining the distinct procedures of fugal writing. ==Reception and interpretation==