A Precis of Fugal Form
William Renwick


Fugal form is problematic.  Fugue is often described as a process rather than a form, because there are many different forms that a fugue could take.  Apparently the only necessary qualifications for a piece of music to be designated as a fugue are (1) that it is based upon one or more repeated melodic ideas (subjects), and (2) that it present at least one exposition of subject (and answer) statements, and (3) that it continue beyond its exposition, into a complete musical expression: a fugal exposition by itself is insufficient to constitute a fugue.   Yet fugues exhibit formal principles of many kinds.  Indeed, the combination of several underlying formal principles may often be found in fugues.  This will be evident in many of the analyses presented in this journal.  The most important formal principles are listed below.


I.   Principal Formal Notions in Fugue

Motet Form

Fugue evolved during the 17th century from the canzona, fantasy and ricercar, which themselves originate in the Renaissance motet.  Thus the original formal concept of the genre was based on text: the motet form.  Motet form in its simplest terms links independent contrapuntal sections together.  Each section is characterized by an original motive and a single phrase of text.  The overall form of the work is therefore determined above all by the text.  The formal plan in simplest terms looks like A, B, C, D, etc.


Many early fantasies, canzonas, and ricercars continue to follow this pattern, even though the instrumental texture precludes the use of text.  However, as the 17th century progresses, we see increasing efforts to unify the form.  These efforts result in fugue as the form is well defined by 1700.  


Transitional varieties would include the “variation fugue” where succeeding points of imitation are based on varied forms of the initial motive.   These are found in the music of Frescobaldi, Froberger, and Roberday, for example, and continue in Bach’s Fugue in E major (WTC II).  Here we have the idea of A, A’, A’’, A’’’ etc. 


We can also view the development of fugue as a form from the organ verset.  The verset is a brief organ interlude between (or substituting for) verses of a hymn or canticle.  A simple verset in polyphonic style would essentially be a single point of imitation.  These can be found in the works of Pasquini, Murschhauser and Pachelbel.  We can easily imagine an how extension of this basic idea would introduce succeeding points of imitation that expand the form, and in due course add modulations to provide variety.  This heritage provides a basis for the simple baroque organ fugues.  Fine examples of this idea are found in the Langloz Manuscript, for example.1     The plan, again, would look like A, A’, A’’, etc., where each section is essentially a point of imitation.



Ideas of counterpoint—invertible counterpoint and stretto—provide the basis for fugues planned around the notion of thematic combinations; these are typically organized through a fugue from simple to complex.  The form is usually based on a progression of ideas, usually culminating in a final and most complex presentation of themes.  The combination of themes provides a convenient basis for large architectonic plans.   Out of these notions grow such phenomena as the double and triple fugue, the fugue based on stretto, and the fugue based on rectus et inversus.


Narrative and Rhetoric

Narrative and rhetoric are typically of little consequence in small fugues, but increasingly come into play as ways of organizing larger fugues.  Narrative typically deals with the idea that a thread of argument (a musical plot or drama) can be seen to run through the course of a fugue.  Rhetoric suggests the notions of presentation, discussion, and resolution of themes or ideas, or transformation.  Gregory Butler and Daniel Harrison have addressed these concepts, both historically and analytically, in journal articles.2


Binary Form

On rare occasions a fugue will exhibit characteristics associated with binary dance forms.  In particular, one will find examples in which the ending of the second half of a fugue is a transposition or re-composition of the ending of the first half.  This is known in formal terms as symmetrical binary.  Sometimes one finds that the composer has maintained an analogy between the parts of the two sections, such that the entire second section can be understood as a re-composition of the first section.   This technique creates a balanced fugal form.  Bach’s Fugue in E minor (WTC I), is an example of a perfectly balanced binary form.  Contrapuntally, the form is based on the idea of inversion of section 1 to form the basis of section 2.


Three-Part Form

Many theorists have suggested that fugue naturally falls into three parts: an opening exposition, a central “developmental” section, and a closing section.  To accurately determine the relevance of this idea for a given fugue, the analyst must determine the principle sections of the piece and then determine the relations between them.  Ultimately, a closing section needs to be identified as different from a middle section.  One way this may be done is through a return to the tonic key and introduction of the subject in the tonic.  Bach’s organ fugue in B minor, BWV 544, develops a very clear three-part form through its plan of themes and its use of the pedals in the first and third sections.


Ternary Form

True ternary form requires a contrasting middle section as well as a similarity or identity between outer, framing sections.  Due to the underlying developmental or transformational quality which is most typical of fugues, we find that examples of true ternary form are exceedingly rare and always of great interest.  Examples are found in the Prelude and Fugue in C minor, BWV 537, and Prelude and Fugue in E minor BWV 548 (for organ) by J. S. Bach. 3


Rondo Form

A fugue that is systematically based upon an alternation of expositions and episodic interludes may be perceived as exhibiting a rondo structure.  In the sense that a fugue is understood as a series of points of imitation that are more or less equivalent, this may be a valid concept.  At the same time, there are fugues whose rondo-like features are merely a symptom of more significant structural impulses.


Choral Fugue

Choral fugues usually differ from instrumental fugues in several important ways.  Above all, the music is constrained by the text, as well as by the tonal and registral limits of the ensemble.  Many choral fugues by Bach are little more than extended points of imitation, or permutations of thematic statements.  Occasionally a more fully worked choral fugue can be found; Handel’s fugue “And with his stripes we are healed” from The Messiah is a good example.  Choral fugues typically appear within a larger context, such as the cantata, oratorio or mass, and hence need to be understood in such terms.  They therefore often have less fully developed forms in terms of key, episode, and texture; instead functioning as sections within multi-movements forms.  This is particularly true where the text forms a narrative that links separate movements together.


Plan of Entries

A systematic plan of entries can be one of the principal design elements in the outer form of a fugue.  The degree to which the plan reflects notions of hierarchy, symmetry, and balance should be considered.  See for example Handel’s Fugue in F Major. 4


Points of Imitation

A point of imitation consists of two or more entries of the theme(s), perhaps followed by an episode and concluded by a cadence.  The point of imitation is the basic building block of the motet form.  Points of imitation often function as the basic components of the several sections of a fugue.  Therefore, the form of a fugue can be considered as a series of points of imitation.



Musical tension can be developed through register, texture, harmony, chromaticism, motivic complexity, dynamics, rhythm, or a combination of factors.  Musical tension often underlies our experience of the sections of a fugue and of the fugue as a whole.  Most typically a fugue will exhibit a curve of tension through each section, as well as an overarching curve of tension through the entire work.  There is often an identifiable point of climax (see below), typically shortly before the final cadence.   This curve of tension parallels the concept of dramatic tension that is understood in literary theory.



The notion of transformation—that somehow the music—and the listener’s experience of it—are changed through the course of the fugue can provide a sense of drama.   Transformation is evident in great romantic works, such as Beethoven’s fifth symphony, where the C tragic minor gives way to a triumphant C major.  Similar transformations can occur in fugue.  For example, the soft chromatic subject of Liszt’s Prelude and Fugue on BACH is transformed into a triumphant tutti presentation at the end, and contextualized in a solid diatonic framework.


II  Factors That Influence the Perception of Form in Fugue


Fugues can be most interesting from a formal point of view when several different formal factors are combined in a single piece.  For example, one might infuse a basic three-part form with qualities of narrative that develop into a climax in the closing section.  The following list outlines the most important features that affect our perception of form.



Cadence is amongst the most powerful features that signify division of music into sections.  Cadence articulates the end of something.  In many well-delineated and highly organized fugues, cadence provides the most powerful means of formal articulation.  In fugue, cadences are typically elided or overlapped in order to provide continuity and forward motion to the work.



Climax is often a feature of fugues.  Climax naturally comes about through the developmental quality of the genre.  Features that contribute to climax often include register, harmony, chromaticism, dissonance, motivic complexity, and pedal point.



Coda is an optional feature in fugue.  Once the main tonal events of a fugue have been completed, a coda will provide some sort of summary or addition that completes the motivic or rhetorical ideas.  It is enlightening to discover the compositional reasons why a composer may have chosen to include or to omit a coda from a particular work.   Bach’s fugue in C Major (WTC I), is a good example of a coda.  The lower voice holds a pedal C, signifying that this is the end, while the upper voices complete motivic statements and fill out the registers.


Counter exposition

The decision whether to include a counter exposition in a fugue is a very interesting one.  Essentially, the counter exposition, if it is to contribute to the form, must present a new context.  This may be in the form of a new contrapuntal combination, such as inversion, or a new texture.  The counter exposition, as the term perhaps implies, would be considered part of the opening or expository part of the fugue, since it is typically presents material rather than developing it.



Development is often a valid notion in fugue.  One can often see how the middle section of a fugue uses the exposition materials in new and diverse ways, and at the same time introduces variety of keys, textures and registers.  Whether the development ought to be considered a formal division or simply an overarching compositional concept depends on the particular piece.



Dialectic is often a useful concept in understanding fugal form.  In its most typical use, two different themes that are presented separately would be combined in the final section.  In Bach’s WTC-II Fugue in B-flat Minor, the first section (rectus) represents the thesis, the second section (inversus) represents the antithesis, and the final section (rectus et inversus) represents the synthesis.



Episode refers to music in which the subject is not present.  The briefest episodes have no formal significance; they simply prepare cadences or link sections together in the most direct manner, but provide no real content to the work.   Larger episodes are included in fugues for a variety of reasons.  They can effect changes of register or key, or provide relief from the subject.   Episodes may also take on larger formal roles in the design of fugue, particularly when they develop recognizable (often sequential) material, and most prominently when they are repeated or varied as part of a larger plan.   They may establish themselves as contrasting “B” material in relation to intervening points of imitation, and may lead to something like a rondo form.  In considering the various sections of a fugue, one may consider whether a given episode “belongs to” the foregoing section, or to the following section, or if it is a connector between sections.



A significant question for the form of fugue is whether the end of the exposition coincides with a formal division or not.  It is certainly attractive for the inner and outer forms to align in this manner, but it is by no means necessary.


Fundamental Structure

Schenker posits a fundamental structure as an underlying notion of any musical form, including fugue.  Fundamental structure represents the “inner form,” the voice-leading structure that controls the tonal and harmonic aspects of the music.  In many cases the fundamental structure, that is the final descent, occupies only the closing measures of a fugue, bringing into question the relevance of fundamental structure as a guiding force in the form of the work.


Growth and Limitation

Growth and limitation refers to the way that various musical factors contribute to a sense of continuation and expansion or of closure and ending in a fugue.  What factors suggest to the listener that a given section is expanding or coming to a conclusion?  When and why does the listener sense that the beginning is coming to an end and the “middle” is commencing?


Inner Form/Outer Form

Inner form represents the tonal and harmonic aspects of the work, while outer form represents the design in motivic terms.  In fugue, the question of the interrelation of these two concepts is very interesting.



Permutation in a general sense is the idea that somehow the composer is working through a complete (or nearly complete) set of variations or inversions on a given theme or group of themes. 



Proportion is a natural consideration in fugal form.  It is an issue of balance.  Depending upon the principal factors that govern the form, proportion may or may not be a significant issue.  For example, in a balanced binary, the resulting proportion of the two sections is one of equivalence.  In a dramatic work, the proportions may diminish as the fugue progresses in order to impart tension and urgency to the music.



Repetition is worked out in unique ways in fugue as compared to other musical forms.  In rare instances literal repetition occurs.  More often, transposed repetition, varied repetition and inverted repetition provide a sense of continuity and development.



Ritornello is a possible but unlikely concept in fugal design.  In ritornello forms, the ritornello is subordinate material as compared with the principal sections.  In fugues, on the other hand, the repeated material—the subject—is the principal content of the piece. One finds concerto movements in fugal style by Handel, where a fugal exposition serves as the ritornello.


William Renwick, The Langloz Manuscript (Oxford, Oxford University Press, 2001).

2[Back]Gregory Butler, “Fugue and Rhetoric”, Journal of Music Theory XXIV/1 (Spring, 1980), 19-109.  Daniel Harrison, “Rhetoric and Fugue: An Analytical Application”, Music Theory Spectrum, XII/1 (Spring, 1990), 1-42.

3[Back]Apparently Hugo Riemann was responsible for promoting the notion that all fugues are in ternary form.  See Ebenezer Prout, Fugue (London: Augeneer, 1890), p. xx.   It would seem that this error stems from basing formal perception simply upon the notion of harmonic progression, and then to conclude that every fugue begins and ends on the tonic, but in the middle moves elsewhere.  However, this is a feature of virtually all tonal music, including one-part, binary, and ternary forms, as well as sonata movements.

4[Back]William Renwick, “Hidden Fugal Paths: A Schenkerian View of Handel’s F-Major Fugue (Suite 1)”,   Music Analysis XIV/1 (March 1995), 46-67.


Copyright 2003 by William Renwick