TREATISE ON COUNTERPOINT AND FUGUE (PART 17. FUGUE)

PART XVII — Historical, Formal, and Conceptual Foundations of the Fugue

XVII.1 Conceptual definition of the fugue
XVII.2 Terminological origin and historical consolidation of the fugue
XVII.3 Difference between form, technique, and genre in the fugue
XVII.4 Essential constitutive elements of the fugue
XVII.5 Real answer and tonal answer in the fugue
XVII.6 Principle of independence and coherence in the fugue
XVII.7 Exposition and order of entries in the fugue
XVII.8 Episode as functional articulation in the fugue
XVII.9 Modulations and tonal plan in the fugue
XVII.10 Stretto and structural densification in the fugue
XVII.11 The fugue as the culmination of imitative counterpoint
XVII.12 The fugue’s historical pedagogical function
XVII.13 The fugue’s aesthetic and expressive value

Part XVII — Historical, Formal, and Conceptual Foundations of the Fugue

XVII.1 Conceptual definition of the fugue

The fugue is essentially a monothematic composition in an imitative contrapuntal texture among multiple voices. That is, it is built on a single principal theme (the subject), which is presented successively by different voices or melodic lines; these voices imitate the theme, generating a polyphonic web. Each voice has equal melodic and rhythmic importance, maintaining independence, yet all voices share and develop the same thematic material, which gives unity to the musical discourse. The fugue is considered the most mature manifestation of contrapuntal art, combining artistic freedom with a high degree of structural rigor in writing. Not all fugues follow a single mold—there is great variety in formal detail—but they share that basic principle of multi-voice imitation of the same theme.

In a typical fugue, three or four voices participate (for example, soprano, alto, tenor, and bass, if written for keyboard or choir), though there are also fugues for five or more voices, and even a few for two voices (the latter are rare, since counterpoint is more limited with only two voices). When fugal technique appears within a larger work (for instance, a symphony or a sonata), we speak of a fugal section or fugato; and when a fugue is composed on a reduced scale, it is often called a fughetta. In all cases, the conceptual essence of the fugue is imitative counterpoint: each voice “pursues” the preceding one by repeating the theme at different pitch levels (keys), interweaving like an ordered musical “chase.” In sum, the fugue is more a compositional procedure than a closed form, characterized by the exposition and development of a single theme through contrapuntal imitation in multiple voices.

XVII.2 Terminological origin and historical consolidation of the fugue

The word fugue comes from the Latin fugare, meaning “to flee,” or fuga in the sense of “escape.” This etymology metaphorically alludes to how the voices “flee” or pursue one another through imitation. In medieval music theory, the term fuga was already used, but in a generic way, to describe any writing in canon (strict imitation among voices). During the Renaissance, fuga came to refer more specifically to works based on free imitation (for example, certain motets or ricercars), without the strict canonic obligation. However, the modern concept of the fugue—as a fully developed monothematic piece with a subject and systematic answers—was not firmly established until the 17th century. It is in the early Baroque that the term acquires the specific meaning we use today.

Historically, the fugue consolidated out of earlier forms and techniques. Its direct antecedents are found in the instrumental ricercar and canzona of the 16th–17th centuries, which were polyphonic pieces of imitation (especially for keyboard or wind ensembles) considered proto-fugues. At the beginning of the 17th century, the term begins to be used in its current sense: for example, Samuel Scheidt employs fugal style in his Tabulatura Nova (1624), including pieces called fantasies or fugues that already show a subject and imitative counterpoint. Likewise, organists such as Froberger and Buxtehude incorporated fugal sections within toccatas and preludes, a practice that led to the combined form of prelude and fugue. An important milestone was the publication of Ariadne Musica (1702) by Johann Fischer, a collection of preludes and fugues in various keys that foreshadowed J. S. Bach’s monumental Well-Tempered Clavier (1722).

During the late Baroque the fugue reached its golden age. Johann Sebastian Bach is considered the greatest master of the fugue, bringing it to its apex in works such as The Art of Fugue (1749–1750). G. F. Handel also stood out in his use of fugues—especially choral fugues—within his Baroque oratorios. After the Baroque period, interest in the fugue resurged at different times: in late Classicism and early Romanticism, composers such as Mozart (e.g., the final fugue of the “Jupiter” Symphony), Beethoven (who incorporated notable fugues in his late piano sonatas and string quartets, as well as the famous Grosse Fuge Op. 133), and Mendelssohn (who reintroduced Bach’s music to the public) took up the fugue as a vehicle for study and a display of technical mastery. In the 20th century, in the midst of Neoclassicism, works such as Dmitri Shostakovich’s 24 Preludes and Fugues, Op. 87 demonstrated the continuing vitality of the genre, re-exploring it in a modern language. In short, the term fugue originated with the idea of “flight” or pursuit among voices, and its musical meaning was refined from designating any contrapuntal imitation in Renaissance polyphony to the highly structured conception that crystallized in the Baroque and endures to this day.

XVII.3 Difference between form, technique, and genre in the fugue

One of the classic debates in musicology is whether the fugue should be considered a musical form, a genre, or simply a compositional technique. Unlike closed forms such as sonata form or ternary form, the fugue has no strictly predetermined structure applicable to all cases; there is enormous variety in its realization, depending on the composer and the period. For this reason, many theorists and musicologists prefer not to label it a “musical form” in the strict sense, but rather a procedure or a particular contrapuntal texture. In the words of musicologist Alfred Mann, “there is no such thing as a fixed fugue-form in the usual meaning of the word form (that is, a predetermined structural scheme); rather, a fugue is not a piece made to fit a particular mold, but a compositional procedure, not a form.”

Nevertheless, in practical usage, the term fugue is also used to designate a historical genre of composition. That is, during the Baroque and later periods, many independent works were written with the title “Fugue” (for example, those in Bach’s Well-Tempered Clavier, or Buxtehude’s organ fugues), which allows us to speak of the fugue as an emblematic genre with general characteristics. In this generic sense, the fugue is understood as a monothematic piece, usually in a single movement, centered on contrapuntal imitation—distinguishing it from other genres.

In sum, these views can be reconciled by saying that the fugue is, above all, a style of composition or writing technique (fugal style), which has given rise to many repertoire works (thus granting it the status of a musical genre). It is not a “form” in the sense of a rigid template with obligatory sections, but it does have typical components and a characteristic kind of development. In fact, this fugal procedure can be inserted within larger forms (giving rise to fugal sections or fugatos within symphonies, masses, quartets, etc.), which reinforces the idea that we are dealing more with a technique than with an autonomous form. Even so, for pedagogical convenience one often describes a general structure of the fugue—with exposition, episodes, development, and a final return—while acknowledging that it is flexible. Ultimately, the fugue transcends the simple label of form: it is a complex contrapuntal compositional method, with both technical and aesthetic value, which can appear either as an autonomous genre or as part of other musical forms.

XVII.4 Essential constitutive elements of the fugue

Despite the diversity of possible fugues, there are essential elements that appear, to a greater or lesser degree, in most of them. These constitutive components include both thematic elements (particular musical motives) and structural sections of the work. The most important are listed and described below:

Subject: The principal melody on which the entire fugue is built. The subject is a brief but characteristic theme (ranging from a few measures to a longer phrase) that contains the melodic–rhythmic seed from which all the material of the work will be derived. It is generally stated alone at the beginning by one voice in the main key, and then reappears repeatedly throughout the fugue in different voices and keys. It is crucial that the subject have a distinctive profile and be able to combine with other lines; for this reason, it typically features clear intervals and a well-defined rhythm. All other imitative entries (answers) are based on this subject.

Answer: The restatement of the subject in another voice, usually transposed to the fifth above (or the fourth below) relative to the initial entry. If the answer is an exact copy of the subject moved to the new key (typically the dominant), it is called a real answer; if instead one or more intervals are slightly altered to fit the key better (see section XVII.5), it is called a tonal answer. During the exposition, subject and answer often alternate among the voices until all have presented the theme. Some fugues use an answer in the subdominant (a so-called plagal fugue), though this is less common. The answer continues the imitative dialogue by initiating the theme in a new tonal area while maintaining continuity of discourse.

Countersubject: A secondary theme that accompanies the subject (or the answer) consistently. The countersubject typically appears for the first time in the initial voice precisely when the second voice enters with the answer: the first voice does not remain inactive, but continues with a new contrapuntal melody that “counter”-sounds alongside the subject in the second voice. If that accompanying line is reused every time the subject appears in any voice, it is a fixed (or obligato) countersubject. A well-constructed countersubject complements the subject harmonically, melodically, and rhythmically, creating enriched counterpoint without overshadowing the subject. For example, it often moves in contrary motion to the subject (if the subject rises, the countersubject falls, etc.) and balances its rhythms (if the subject has longer notes, the countersubject may move more actively, and vice versa). A fugue may contain more than one countersubject (double, triple fugues, etc.; see below), which are layered over the subject. Not all fugues have a countersubject; some use free counterpoint instead—that is, accompanying lines that do not repeat identically at each entry, but vary or introduce new phrases derived from the subject.

Exposition: The opening section of the fugue, in which the subject and answer are presented in an orderly way in all participating voices. It typically begins with the subject in a single voice; then another voice enters with the answer (while the first may add a countersubject or free counterpoint), then a third voice repeats the original subject, and so on until all voices have entered. The exposition establishes the thematic material (the subject) and the basic entry scheme. It usually ends once all voices have entered with subject or answer. Sometimes an additional redundant entry (an extra repetition of the subject) is added to close the exposition firmly in the home key. It may also happen that a voice is temporarily omitted and its entry delayed (for instance, in some Bach organ fugues, the pedal voice waits until after the exposition). The exposition is fundamental because it introduces, for the first time, the elements that will later be transformed throughout the fugue.

Episodes: Episodes (or divertimenti) are transitional passages that separate successive entries of the subject. Episodes do not present the full subject or answer; instead, they develop motivic fragments derived from them (for example, a rhythmic or melodic figure taken from the subject or countersubject) in the form of sequences or other combinations. Their function is twofold: on the one hand, to avoid excessive literal repetition of the subject by providing thematic breathing space and contrast; on the other hand, to prepare—through modulation—the next entry of the subject in a new key. Episodes often employ invertible counterpoint (to recombine motives among voices) and frequently follow harmonic progressions. There is no fixed structure for an episode—they are freer sections—but they typically culminate in a cadence or harmonic preparation that leads logically to the next subject entry. Notably, entirely new material not derived from the subject is rare in episodes; fugue writing tends toward thematic economy, exploiting the same motives in different forms.

Development and final return: After the initial exposition, many fugues enter a middle development section, where the subject reappears several times in keys other than the original. In this section, modulating episodes alternate with new entries of the subject (or answers) in related keys. During development, contrapuntal devices may intensify: invertibility of voices, augmentation or diminution of the subject (lengthening or shortening its rhythmic values), melodic inversion (presenting the subject “upside down,” with ascending intervals becoming descending), and so forth. Eventually, the fugue typically returns to the main key for a final reappearance of the subject (sometimes called the final stretto or a recapitulation), in which the subject sounds again in the home key to close the work. Not all fugues have a formal “recapitulation” like sonata form, but it is common for the last complete subject entry to be in the tonic, restoring tonal balance.

Stretto: The stretto (Italian for “tight” or “narrow”) is a contrapuntal device in which entries of the subject overlap in time—that is, one voice begins the subject before the previous voice has finished stating it. This produces a faster accumulation of voices, increasing textural density. Strettos are often used near the end of a fugue to intensify the climax: the voices enter in very close imitation, sometimes all in rapid succession, creating great tension and a culminating effect. A stretto may be canonic (if the voices imitate the subject exactly) or freer (with small variations), and it may even be double or triple if two, three, or more voices form strettos simultaneously. Though common, strettos do not always appear; they depend on whether the subject lends itself to them and on the composer’s expressive choices. (See section XVII.10 for more.)

Double, triple fugue, etc.: These are fugues that contain more than one independent subject. For example, a double fugue has two distinct themes that may be presented successively and later combined with each other. In that case, the fugue includes essentially two separate expositions (one for each subject) and a section where both are superimposed contrapuntally. Bach provides famous examples of double and triple fugues (such as some in The Well-Tempered Clavier or the Grosse Fuge for string quartet), and in later periods Shostakovich also composed fugues with two subjects. These complex fugues expand the essential elements listed above—since there will be answers and countersubjects associated with each theme, etc.—but the basic concept remains imitation among voices.

Pedal point: A pedal point is a sustained note, usually in the lowest voice, over which the other voices continue the counterpoint. In fugues it is typical to find a dominant or tonic pedal toward the end of the work, acting as a stable harmonic foundation while the other voices may even create strong dissonances against that pedal note. The pedal prepares the final cadence: after the accumulated tension, the dissonances resolve and the fugue concludes, often with that pedal note fitting into the final tonic harmony. Although the pedal is not exclusive to fugue (it appears in other forms), it is a frequent feature in the concluding sections of Bach fugues and the later tradition, contributing a sense of support and solemnity.

It should be noted that “school fugues” (see section XVII.12) often follow the presence and order of these elements quite strictly: a clearly defined exposition, a modulating development with episodes and strettos, and a final return, within certain patterns. In real compositional practice, however, great masters took liberties: there are fugues without a countersubject, fugues without formal episodes (e.g., built almost entirely by chaining subject entries), fugues that begin with a duet rather than a single voice, and so on. Nevertheless, the concepts of subject, answer, countersubject, exposition, episode, and stretto provide a vocabulary for analyzing and understanding most classical fugues.

XVII.5 Real answer and tonal answer in the fugue

In the exposition of a fugue, after the subject has been presented in the initial voice, the second voice typically enters by reproducing the theme in another key. This imitative entry is called the answer. There are two types of answer: real and tonal. A real answer is one in which the subject is transferred exactly to the new key, preserving all intervals as they are, usually transposed to the fifth (the dominant) of the original key. For example, if the subject is in C major, a typical real answer would be in G major, with the same melody transposed to that pitch level. A tonal answer, by contrast, introduces small intervallic alterations into the subject as it is transposed, in order to avoid awkward tonal deviations and maintain harmonic coherence in the fugue.

When is a tonal answer needed? Usually when the subject, in its opening measures, places too much emphasis on the dominant of the key. If the fugue is in C major but the subject begins by strongly emphasizing G (the dominant of C major), or by moving toward it, then a literal transposition up a fifth would make the answer begin by emphasizing D (the dominant of the dominant), thus pulling momentarily toward D major. That would cause a premature modulation and weaken the sense of the tonal center. To avoid this, the composer “adapts” the answer: for instance, instead of transposing the subject from C to G (a perfect fifth), the composer might transpose it from C to F (a perfect fourth, the subdominant), so that the opening note sounds like the tonic of the new area. In other words, the tonal answer corrects certain intervals (usually the initial ones)—moving up a fourth instead of a fifth, or down a fifth instead of a fourth, etc.—so that the translated subject does not introduce an unintended tonal implication.

In a classic Bach example (BWV 861 in G minor), the subject begins on D (the dominant of G minor), and the answer enters not on D (which would sound like a new dominant), but on G, the tonic, thereby adjusting the initial interval. This slight modification ensures that the answer remains within the sphere of G minor rather than diverting the tonality toward C (the dominant of the dominant). The result is that the tonal answer sounds fully coherent with the subject, but without undesirable early modulations. Therefore, the use of a tonal answer is a fundamental device for preserving the fugue’s central key while maintaining imitation of the subject.

In summary: real answer = exact transposition of the subject (usually to the fifth); tonal answer = adjusted transposition of the subject (altering critical intervals) to preserve the tonal center. It should be added that these labels describe the subject–answer relationship in the initial exposition. Once the tonal answer is established (if it was needed), the rest of the fugue will typically alternate subject and answer according to that pattern (for example, in a fugue with a tonal answer in the exposition, later entries often continue to alternate: subject in tonic, “tonal” answer in dominant, subject in tonic, etc., with exceptions). The real/tonal distinction is especially relevant in tonal Baroque fugues; in atonal or dodecaphonic fugues, the concept no longer has traditional meaning, but in the tonal classical repertoire it remains an essential part of fugal technique.

XVII.6 Principle of independence and coherence in the fugue

A central characteristic of the fugue—and, more broadly, of all contrapuntal music—is the balance between the independence of the voices and the coherence of the whole. Each voice in a fugue behaves with considerable melodic and rhythmic autonomy: it has its own line that is interesting in itself, with its own melodic contour and defined rhythmic motives. This principle of independence means that no voice is merely a monotonous accompaniment to another; rather, all participate actively in the musical fabric. In the Baroque period it was often emphasized that “the independent interest of the different melodic lines in combination with one another is the basis of contrapuntal music.” The fugue pushes this ideal to the maximum: several melodies coexist simultaneously—interwoven, yet individualized.

Yet this independence occurs within an overarching coherence. The voices, though distinct in their discourse, are united by common bonds: first, they share the same thematic material (the subject and its derivatives), providing motivic unity; second, they fit together harmonically, producing an overall consonant result (aside from controlled dissonances) consistent with the established key. In this way, the listener perceives both the individual personality of each voice and the harmony of the whole. As theory puts it, “the ear grasps the individuality of each melodic line, its personality, while also perceiving the totality as a cohesive whole.” This cohesion is achieved because the voices, despite their different contours, cooperate contrapuntally: they imitate, converse, and converge in shared cadential points.

The principle of independence and coherence also implies certain technical requirements. For example, to maintain autonomy, each voice often occupies its own register (ambitus), so it is not obscured by another; rhythmically, it is desirable that the voices do not all move at the same time in identical note-values (which would yield homophony), but rather display differentiated rhythms that allow them to be distinguished. At the same time, to guarantee coherence, the vertical encounters among voices (simultaneities) must generate logical harmonic relations: explicit or implicit chords that sustain the tonal framework. In the fugue, unlike in a simple homophonic chorale, these harmonies are perceived more subtly, but they are present and essential for the superposition of melodies to make unified sense.

In short, the fugue embodies the polyphonic ideal in which unity and plurality coexist. Each voice is like an independent character in a musical conversation, but all the characters are discussing the same topic in the same tonal language. The result is music of great richness, in which one can simultaneously enjoy the virtues of each individual line (its melodic beauty, its rhythmic ingenuity) and the collective harmony that arises from their combination. This independence/coherence duality is one reason why the fugue has historically been considered one of the deepest and most intellectually rewarding kinds of music: it satisfies both rational analysis (through its internal order) and aesthetic listening (through the harmonic sum of its voices).

XVII.7 Exposition and order of entries in the fugue

The term exposition refers to the opening segment of the fugue in which all voices present the subject or the answer for the first time. The exposition establishes the order of entries and introduces the listener to the fundamental thematic material. The typical process is as follows: a first voice begins alone, stating the complete subject in the main key. When that initial melody ends (or sometimes slightly before it ends), a second voice enters with the answer, generally in the key of the dominant. While the second voice sings the answer, the first voice typically continues with counterpoint (which may become a countersubject if it is repeated later). Then a third voice enters with the subject again in the main key, and so on with the remaining voices, alternating subject and answer until all voices have entered. In a four-voice fugue, for example, one might have: Voice 1 — subject (in tonic); Voice 2 — answer (in dominant); Voice 3 — subject (back in tonic); Voice 4 — answer (back in dominant). This pattern is not rigid, but it is very common.

An interesting detail is the systematic alternation between subject and answer in the entries. This means that if the fugue begins with the subject in the highest voice, the next entry (the answer) may be in a lower voice, then the subject returns in another higher voice, and so on, creating a kind of back-and-forth. Indeed, a common strategy is to alternate which voices carry the subject and which carry the answer: for instance, in a four-voice fugue, if the soprano and tenor present the subject, then the alto and bass present the answer, or vice versa. This alternation balances the exposition by distributing subject/answer functions between higher and lower registers, and by avoiding, for example, having the subject always appear in the top voice.

Formally, the exposition concludes once all voices have presented the theme, either as subject or as answer. After that, there is often a brief structural or cadential pause (explicit or implied) marking the end of this first section. However, several noteworthy variations exist:

• Sometimes the composer inserts an additional subject entry immediately after all voices have entered; this extra repetition is called a redundant entry (or recurrent entry). It often appears in the initial voice (or another) to reaffirm the main key before moving on. For example, in a three-voice fugue, after subject–answer–subject, the subject might appear again in the first voice (redundantly) to close the exposition firmly in the tonic.
• It may happen that one voice does not enter during the exposition but later. A famous case is Bach’s Fugue in C major BWV 547 for organ, where the pedal (bass) voice remains absent during the exposition and enters only in the following section, presenting the subject after a deliberate delay. This strategic omission creates expectation and varies the opening texture.
• Between entries within the exposition there may be brief interludes called codettas or bridges. For instance, after the second voice’s answer, the composer may add a couple of modulating measures to adjust the tonality before the third voice enters. These codettas are small connective links within the exposition—not as developed as a full episode, but useful for smoothing the succession of entries. Not all fugues require them; if the tonal connection is natural, they may be omitted.
• As for the order of voices in the exposition, there is no fixed rule (it depends on the composer’s preference and the desired sonority). Bach sometimes begins with the top voice, sometimes with an inner voice, and sometimes even with the lowest voice. Some expositions follow an ascending order (bass → tenor → alto → soprano), others descending, and others interleaved. What matters is that each voice enters once. A balanced scheme is for the first and last voices to enter in contrasting registers (one high and one low, for example), framing the exposition timbrally.

After the exposition is complete, the fugue normally proceeds into a development section with episodes and new entries (as detailed in later sections). It should be noted, however, that in certain very brief fugues the exposition can be almost the entire fugue (for example, “perpetual” fugues in which the subject chains multiple entries without clearly differentiated sections). In most cases, however, the exposition plays a clear role of initial presentation before later elaborations.

XVII.8 Episode as functional articulation in the fugue

In the fugue, the episode serves as an articulating element between presentations of the subject, fulfilling clearly defined structural and expressive functions. Put simply, an episode is a transitional passage that separates two (or groups of) subject entries, especially when these occur in different keys. Its presence is fundamental for giving the fugue fluency and direction, avoiding an overly mechanical succession of subject after subject.

Functionally, the episode has two main purposes. First, it provides variety and contrast: by “breaking” the insistence on the complete theme, it allows freer development of motivic fragments, offering breathing space both for the composer and for the listener. This refreshes the ear and avoids the monotony that would result from hearing the subject in full again and again without relief. During the episode, the main theme may be fragmented, inverted, or partially sequenced, enriching the discourse without literal repetition. Second, the episode creates a logical and directional connection between sections: it typically includes modulations that prepare the key in which the subject will re-enter next. In other words, it acts as a modulating bridge: for instance, if the last subject entry was in G major and the next will be in E minor (the relative minor, say), a modulating episode will carry the music smoothly from G major to E minor.

How are episodes constructed? There is no mandatory standard form, but they are generally based on motives derived from the subject (or countersubject). It is common to take a brief rhythmic or melodic motive extracted from the theme and develop it through sequences (ascending or descending repetitions) at different pitch levels. Episodes also often employ invertible counterpoint, allowing motivic fragments to pass from one voice to another, generating imitation even within the episode. Some theorists use episode and divertimento interchangeably; others make a subtle distinction, calling divertimento an episode based specifically on sequential melodic progressions, while reserving episode as the more general term. In analysis practice, the two terms are often treated as equivalent, indicating that “subjectless” transitional section.

The crucial point is that, during an episode, the subject and answer do not appear in complete form. If the complete subject were to appear, the passage would cease to be an episode and would instead become a new entry (a partial exposition). Thus, in the episode we hear “free development” material: secondary motives, sequences, modulations, and sometimes cadences. Indeed, certain episodes also present intermediate cadences (small closures in passing keys) to divide the fugue into musical paragraphs. This can be observed in some fugues with more symmetrical structures, where an episode concludes clearly in the dominant or relative key before initiating a new section.

From a formal standpoint, episodes are key pieces of articulation: they give the fugue contour and dynamism. A typical fugue alternates exposition (subject entries) with episodes (transitions) repeatedly—Subject → Episode → Subject → Episode…—until the approach to the end, where a stretto and final cadence may appear. Without episodes, the fugue would be more rigid and less tonally directed; with them, it achieves a more narrative discourse, with tension and release. As some treatises note, episodes “open the possibility for partial motivic transformation and establish a directional impulse that, through modulation, prepares the entry of the theme in a new key.” In short, the episode is the functional link that joins the different appearances of the subject, ensuring both musical variety and structural cohesion in the fugue’s tonal journey.

XVII.9 Modulations and tonal plan in the fugue

One of the fundamental dimensions of a fugue is its tonal plan—that is, its route through different keys across the piece. Unlike simpler forms that remain largely within one key, the typical Baroque fugue explores several related keys before returning to the starting key. This is achieved through modulations embedded in episodes and in some thematic entries.

The most common tonal scheme in fugues of the tonal era (Baroque/Classical) is roughly as follows: the exposition establishes the tonic and often touches the dominant (through the answer in the dominant). Then, in the development section, the music modulates to nearby keys such as the relative (for instance, if the fugue is in C major, its relative minor is A minor; if it is in G minor, its relative major is B-flat major) and the subdominant, or a close neighbor of the subdominant. Finally, the return to the original tonic is prepared, where the final subject entry appears and the work typically ends. Concretely, a “typical” Baroque tonal plan can be sketched as:

• Fugue in a major key: Exposition in the main key (I) and dominant (V). Development: modulations to the relative minor (vi), to the subdominant (IV) or its relative, and sometimes to the dominant of the dominant (II) depending on the length of the fugue. Final return: back to the tonic (I) for closure.
• Fugue in a minor key: Exposition in the minor tonic (i) and its major dominant (V or V7). Development: modulations to the relative major (III), to the minor subdominant (iv) or to the major subdominant if the parallel major mode is invoked, and to other neighboring keys such as VII or II in minor. Final return: back to the minor tonic (i).

Naturally, the tonal plan varies depending on the piece. Some short fugues may restrict themselves to moving from I to V and back to I. Others, more extended, explore chains of keys, sometimes following the circle of fifths. Even in longer fugues, however, the visited keys tend to remain close or functionally related, preserving overall tonal cohesion.

The primary mechanism for these modulations is the modulating episode. An episode often begins in the key where the previous section ended and, through progressions, chromatic inflections, and cadences, moves toward the next target key. At the end of the episode, a cadence typically confirms the new key, at which point the subject reappears. When the subject enters in that new key, it commonly does so as an answer in the dominant of that key, maintaining the subject/answer logic within the new tonal area.

A representative pattern is provided by the French “school fugue,” which codifies a tonal route: the first divertimento modulates to the relative, followed by entries in the relative; the second divertimento modulates to the subdominant, followed by entries in the subdominant or its relative; the third divertimento modulates back to the tonic for the final return. This scheme reflects a common Baroque practice: Tonic → Relative → Subdominant → (back to) Tonic.

What matters is that the fugue, through its modulations, achieves a balance between tonal unity and variety. It remains long enough in the home key to affirm it (at the beginning and end), but in the middle it travels through neighboring keys, adding interest and allowing the subject to be heard under different harmonic “lights.” The return to the original key at the end is often perceived with special clarity and satisfaction, producing a sense of organic closure.

XVII.10 Stretto and structural densification in the fugue

The Italian term stretto (“tight,” “narrow”) refers to the close overlapping of subject entries. Its use in the fugue has a strongly marked structural and expressive effect: it produces a densification of the contrapuntal texture and raises musical tension. In a typical stretto, one voice begins the subject and, before it finishes, another voice enters with the subject, generating successive overlaps.

Structurally, stretto is often placed toward the end of the fugue as a climactic device: after the development, a major stretto may appear in which many (or all) voices participate in very close imitation. This increases harmonic density (more friction and controlled dissonance) and heightens dramatic intensity: the listener senses urgency—an accumulation of energy. Not every fugue ends with stretto, but it is a characteristic feature in many Bach fugues.

In Bach’s Fugue in B-flat minor BWV 867b, one can observe how the subject entries overlap tightly, densifying the texture and creating a peak of tension before the final cadence. After this climax, a pedal point (dominant or tonic) often appears to stabilize the harmony and prepare the close.

In sum, stretto contributes to structural densification: from a clear, spaced exposition the music advances toward an extreme concentration of thematic material, functioning as a rhetorical culmination of the fugue.

XVII.11 The fugue as the culmination of imitative counterpoint

Historically, the fugue has been viewed as the culmination of imitative counterpoint. Although the Renaissance developed imitation extensively in motets, masses, and ricercars, it was with the Baroque fugue that the imitative procedure reached its highest level of systematization and sophistication. In the Baroque, many composers regarded the fugue as the supreme expression of the musical reasoning of the age, since it combines thematic unity, independence of voices, and complex tonal control.

Bach carried this idea to an extreme in The Art of Fugue, where a single subject is subjected to exhaustive transformations (inversions, augmentations, double/triple fugues, canons), functioning almost like a practical treatise on contrapuntal art. This work has been understood both as a pedagogical compendium and as a demonstration of contrapuntal mastery.

In later eras, the fugue continued to symbolize “mastery”: Mozart and Beethoven adopted it as a means of aesthetic and intellectual culmination (e.g., in finales and sections of very high density), and in the 20th century Shostakovich and Hindemith reactivated it in neoclassical contexts. For this reason, the fugue continues to be considered the point at which imitative counterpoint reaches its most complex and complete expression.

XVII.12 The fugue’s historical pedagogical function

The fugue has played a central pedagogical role: mastering it was (and in many contexts still is) the definitive test of contrapuntal training. In 19th- and 20th-century conservatories, composing a “school fugue” was the culminating exercise in advanced counterpoint courses. The school fugue is defined as an academic composition practiced at the final stages of counterpoint study, rooted in French treatises of the 19th and 20th centuries (Gédalge, Dupré, Cherubini, Koechlin, etc.), in which rules are codified for the subject, the entries, the tonal plan, and the use of episodes and strettos.

Bach also contributed to the pedagogical dimension through The Well-Tempered Clavier (24 preludes and fugues in all keys), which served as a didactic model for keyboardists and composers. The Art of Fugue is likewise often interpreted as a pedagogical compendium on fugal composition. Even in the 20th century, the composition of fugue cycles (Shostakovich, Op. 87) underscores its role as a craft discipline and a laboratory of musical thought.

In sum, the fugue has historically been a formative instrument that integrates harmony, voice-leading, modulation, intervallic control, and formal planning into a single exercise of high rigor.

XVII.13 The fugue’s aesthetic and expressive value

Although the fugue is often associated with the “intellectual,” its aesthetic and expressive value is enormous. Aesthetically, the fugue offers architectural beauty: symmetries, recurrences, variations, and a balance between design and sonic flow. Expressively, the fugue is versatile: it can convey solemnity, jubilation, drama, introspection, conflict, and catharsis, depending on the subject, the tonal plan, the handling of episodes, and the use of devices such as stretto and pedal point.

Handel used fugal techniques with great freedom for dramatic effect in his oratorios; his choral fugues can be unpredictable and oriented toward rhetorical purpose more than toward a “textbook fugue.” In Beethoven, the fugue can function as a vehicle of tension and resolution, particularly in late works. In Schumann, fugal work on the name B–A–C–H was an intense effort aimed at dignifying the Bach model and producing a piece of great expressive ambition. In the 20th century, Shostakovich shows that the fugue can absorb modern languages without losing power.

Thus, the fugue remains an artistic language in which structure does not limit emotion: it organizes and amplifies it. That combination—internal rigor and expressive impact—explains its cultural and aesthetic vitality.