More Than Its Parts

“I cannot believe that the author of Die Kunst der Fuge has composed what most musicians perceive: piano pieces, based merely on the external and superficial characteristics of succeeding entrances of a theme. At least, if such were the case, he would not have called them fugues, but perhaps suites, inventions, partitas, etc.”

Arnold Schönberg

Fugue, and its component parts, are resistant to classification and quantification in terms of musical form. While there is a general expectation for the appearance of endemic structural events (e.g. expositions and episodes, etc.), linear developmental techniques (e.g. diminution, augmentation, inversion, retrograde, and fragmentation), and common-practice harmonic boundaries (i.e. the tonic and dominant relationship), persistent theoretical and compositional models relegate fugue as being the result of a “procedure”, “process”, or as a “texture” rather than as an embodiment of the characteristics associated with form. Paul Walker crystallizes this issue in his entry for “Fugue” in The New Grove Dictionary of Music and Musicians:

“Since the early 19th century, genre designations have been defined largely if not exclusively by their formal structures. Formal structure, however, is not in the end a defining characteristic of fugue. As a result, there has been prolonged argument about whether fugue is a form at all (and, by extension, whether it is a genre) as well as whether any particular formal model should be considered necessary.”

Despite the absence of a universal formal model, an acute listener is often suspicious of the fugal experience as it is occurring, due largely to the proprietary return of thematic material. The notion that fugue is indefinable—yet unmistakable—raises interesting questions about music cognition, and perception in general. For example, is the sum total result of applied musical “procedures” (the composition) something more than the “external and superficial characteristics” of the procedures themselves? If this is true, than by what cognitive means does the listener step outside of the “procedural system” that went into creating the piece, in order to perceive the resultant contrapuntal fabric as fugue?

A Part Apart

Most of the compositional devices employed in fugue are also found in other contrapuntal genres, supporting the position that fugue may be best described as a unique combination of procedures, rather than as a kind of form. The following is a chart of six features shared between fugue and six other contrapuntal genres, and a brief comment on their relationships.

Fugue is essentially a repetition ‘form’, but the feature that separates it most from other repetition-genres is the way ‘A’ material returns (especially in the case of a tonal answer). Tangent to this, resolutions in fugue are heavily rendered in service of the melodic material. Even material that is designated as free counterpoint is still providing a service to the subject in the form of preparing a return. The following are some examples of compositional devices shared between fugue and other contrapuntal genres.

In a fugue, the subject and countersubject are often constructed in such a way that their inversions are suitable material for development, and can sometimes be paired with their own inversions. From the second book of the Well-Tempered Clavier, the subject of the fugue in B-flat minor is inverted about halfway through the piece:

Inversion is frequently found in dance movements, such as the Gigue in the third English Suite:

Perhaps the most erudite of contrapuntal devices, retrograde is a striking if seldom-employed treatment of privileged melodic material. The retrograde canon from the Musical Offering by Bach is a tour de force of mirror-image composition. Ultimately, retrograde is a more noticeable treat for the eyes than the ears as it may take repeated listenings to notice a passage in retrograde without the benefit of a score. Aspects of symmetry arise when retrograde is present, and as such, it became a favorite technique among serial composers.

Often found within episodes, canonic passages unify fragmentary material in fugue, and may be contextualized further as a sequence. The first episode of Contrapunctus I from the Art of Fugue features a two-part canon between the soprano and tenor (m. 17-20):

Similar imitative restrictions can be found in other contrapuntal genres. This example is from the Goldberg Variations—a two-part canon at the second between the upper voices:

The technique of stretto is most often associated with fugue, though it applies to any instance of overlapping thematic material. A notable example of stretto in fugue is the first fugue from the first book of the Well-Tempered Clavier. This example, from the Art of Fugue, is an ingenious overlapping of thematic material: the subject appears in diminution, in stretto, and in inversion as well:

Stretto is not exclusive to fugue. The following example is an overlapping of thematic material from the Toccata in G major:

Despite the common features endemic to Baroque contrapuntal genres, fugue is singular in their intensity, proportion, and distribution. But since there is little in the way of a standardized format—save perhaps that there is an exposition—fugue continues to resist definition as a form.

But perhaps comfort—if not wonder—can be found in the maxim “every fugue conceals a secret flight.”

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