A Fugue in Ternary Form by J.S. Bach (BWV 998)
David R. Walker

NOTE: Because my original essay has been submitted for publication I will present only the major points of my analysis here.


General Comments


The fugue from J. S. Bach’s Prelude, Fugue and Allegro (BWV 998) is one of only three fugues that Bach wrote in ternary form, and is the only one with a literal repetition of the opening.1 The unusual repetition of so large a section seems to be the impetus for the strong use of narrative and rhetorical devices in this piece. In particular, the gradual motion away from the subject and its omission at key points makes the repetition of the opening material seem a necessity. Renwick points out that the contrapuntal plan for a fugue is typically organized from simple to complex; this fugue reverses that order, so that the most complex counterpoint occurs in the framing A sections, while the B section is concerned with the gradual disintegration of material from the subject.


Little is known of the history of BWV 998.  A manuscript copy is in a private collection in Tokyo. Christoph Wolff2 dates BWV 998 as 1740-1745; this would place its composition during same time as Bach’s original work on the Art of Fugue, and would date the fugue from Bach’s most mature period.




The general structural plan of the fugue is a standard ternary A-B-A plan (fig. 1a). The A part is a single section, while the B is divided into three sub-sections (fig. 1b).









Figure 1a. Overall formal structure.













Figure 1b. Form with sub-sections of B section.


Section A begins with a 3-voice exposition – the only exposition in the piece – and gradually widens the range until reaching the lowest note of the piece (Ab1) in m. 20. After this follows a cadence which ends the A section in m. 29. The exposition follows a simple Subject (I) – Answer (V) – Subject (I) plan in the three voices, Alto-Tenor-Bass (named for their approximate range).


Section B provides the contrast that is necessary for a true ternary form. The flowing arpeggiation that begins in m. 29 is a strong contrast to the linear style of the A section. Over the course of the B section, the subject is heard less and less frequently, with four statements in B1, only one in B2, and none in B3.


The return to the A section is masked by a brilliant elision beginning in m. 75 during which the initial subject entry emerges from the middle voice. With the entry of the answer in m. 77 the repetition becomes exact.



The subject is simple, almost banal on first hearing. Beginning with a double neighbour-note idea (the head motive Eb-D-Eb-F), its most important features are the upper neighbour motion (Eb-F-Eb) and the ascending fourth (the tail motive) Bb-C-D-Eb. This subject works well both as a melody or a bass voice. The two prominent motives contain thirds which are used motivically throughout the fugue. As the fugue progresses, these simple motives combine easily into varied forms, most frequently linking the head of the subject or answer with its opposite’s tail (i.e. the head of the subject with the tail of the answer or vice versa).



The answer in this fugue is unusual in that it lacks the characteristic neighbour note of the subject. This acquires an important structural role in the B section. Renwick (personal communication, 2003) considers this answer to be “almost like a ‘subject’ whose ‘answer’ is the actual subject of the fugue.” 

A section


In the A section the exposition comprises mm. 1-9. While there is no counter-subject, the counterpoint to the answer introduces an 8th note figure which reverses the direction of the 4th motive of the subject. Further diminution of this figure begins in m. 10 and leads to a sequence of entries in m. 11. Three entries (answer, answer, subject) appear in the bass outlining a IV-V-I progression in the tonic. Accompanying this sequence is an important new motive, which begins in the uppermost (alto) voice and also appears in the tenor: a three-8th note figure beginning on an upbeat, with that note retained as a suspension onto the following beat, which is resolved on the next 8th note (fig. 2).

Figure 2. Suspension motive.


After this sequence another sequence using the ‘suspension motive’ continues the expansion of range. This reaches the lowest pitch of the piece on the sub-dominant of m. 20 and begins an extended cadential motion that includes an entry of the answer in the alto in m. 21 and a ‘split’ entry in m. 23. This entry begins with the head of the answer in a middle voice (the texture becoming temporarily four voices) and ends with the tail of the subject in the bass. Two sequences lead to the tonic cadence in m. 29 which ends the A section.


B section


This section introduces a new texture, into which subject motives are then woven. The B section starts with an arpeggiated figure that establishes contrast immediately, even though it remains in the tonic key. The upper voice of the arpeggio figure outlines first the neighbour note motion (mm. 29-30) and then the ascending 4th – both motives from the subject. The actual neighbour note that begins the section is Bb-C-Bb, the very motion that was ‘missing’ from the answer.  The arpeggiated neighbour note and 4th figures are followed by a statement of the subject that leads from the tonic to the dominant (mm. 29-33), where the pattern is repeated, ending with a subject entry that returns to the tonic (mm. 33-37).


The same pattern of four measure phrases ending with a subject statement continues in mm. 37-45. Two rising fourths in bass and alto (mm. 37-39) continue on to a subject entry leading to IV in m. 41. Here a cadential figure enters which leads to a statement of the subject in the relative minor. This statement in VI is the furthest remove from the tonic and a major structural point as its C (alto m. 45) forms a large scale neighbour note motion between the Bb that begins the B section in m. 28 and its return in m. 63.


The important cadence of m. 45 ends sub-section B1. The next sub-section begins immediately, using the rising fourths in the outside voices from mm. 37-39. This leads to a sequence on the head of the answer which moves to a cadence on iii at m. 51. This initiates a sequence of descending steps from G to F (m. 53) to a cadence on Eb (m. 55). This tonic cadence does not demarcate a sub-section, and the following sequence returns to F-G-Ab (m. 61) before leading to a tonic cadence at m. 63 which does end sub-section B2.


This sub-section is similar to the rest of the B section in that it uses no complex contrapuntal devices such as stretto or inversion. The omission of the subject is much more evident here, with only the single entry leading to the cadence on m. 63. This sub-section uses the most remote versions of motives from the A section, although even in the arpeggios of mm. 55-61 there remain vestiges in the 3rd motives at the top and bottom of each arpeggio.


The final sub-section begins (m. 63) with a return to the arpeggiated tonic chords that began the B section  in m. 29. However, at m. 65 when we would expect to hear the subject (cf. m. 31) the suspension motive appears in its place (its first appearance in the B section). This is a sort of ‘double omission’ where the motive that replaces the subject is one that usually appears in counterpoint to it. This omission occurs at both points where the subject occurred earlier, and this creates a strong expectation for the return of the subject. Another indication that mm. 63-71 is a variation of mm. 29-37 is that its motion from I-V (mm. 63-67) is answered by a ‘real’ motion from V-ii rather than a return to I. This leads to a return of the cadential figure from m. 41 which leads into the cadence on V in m. 75.



The cadence on V in m. 75 is not the end of the section, but rather it begins the re-transition to the A section. The initial statement of the subject is ‘disguised’ beginning as the 7th of the dominant chord (tenor voice m. 75) in the middle voice, it becomes the upper voice as the alto drops out on beat 3 of m. 75. The rhythmic placement of the subject combines with the harmony to stress the neighbour tones D and F as part of the dominant harmony, which the rising line Bb-C-D-Eb is worked into the running 16th note line of the upper voice, obscuring its outline. Arguably we only realize the return to the beginning at the start of the answer in m. 77.


A section


The literal repeat of the A section makes sense for several reasons. There has not been a full exposition since m. 9, and there have been few entries of the subject in the B section (with only one between mm. 45-75). At the same time, motives from the A section have been varied until they are almost unrecognizable. As a final step, the start of the B section is repeated, creating an expectation to hear the subject that is overtly denied even as we are reminded that the subject should be present. The return of the A section is satisfying both motivically and texturally.




Bach’s use of a unique form for this fugue seems to indicate a desire to experiment. This same desire may have led to the unusual sequence of movements, i.e. a prelude and fugue with an additional allegro. Even though this is Bach’s only ternary fugue with a literal repetition of the A section, it is a brilliant solution to the inherent problem of repeating a large section without becoming obvious or pedantic. Bach’s strategy is to saturate the A section with the subject while providing only one exposition, then gradually moving completely away from the subject in the B section so that the listener at some level notices its absence. The return of the A section is then both fresh and satisfying. The forward momentum of this section is such that it carries the fugue along to a rewarding conclusion, despite the use of music that we have already heard. Context provides new meaning to the repeated A section, and it is the B section that creates that context.



1[Back]Renwick, William. Analyzing Fugue: A Schenkerian Approach. (Stuyvesant, NY: Pendragon Press, c1995).

2[Back]Wolff, Christoph. "J. S. Bach" in New Grove Dictionary of Music and Musicians. (New York: Grove, 2001).

Copyright 2003 by David R. Walker