The fugue is the highest achievement of contrapuntal composition. This lesson dissects its anatomy: subject (the main theme), answer (the imitation at the fifth), countersubject (the persistent companion), and exposition (the opening ritual of entries).
The Fugue: Definition and Significance
A fugue (from Latin fuga, "flight") is a polyphonic composition in which a single theme — the subject — is introduced in one voice, then imitated in each additional voice in turn, and thereafter developed through a series of entries and episodes. The fugue is not a strict form with fixed structural lengths (unlike the sonata or rondo) but a technique — a set of procedures for developing polyphonic texture from a single melodic idea. It is the highest and most demanding achievement of contrapuntal composition, requiring command of every technique studied in the species exercises plus the architectural sense to organise them into a coherent whole.
Bach's Well-Tempered Clavier (48 preludes and fugues in all 24 major and minor keys, published in two books, 1722 and 1742) and his Art of Fugue (BWV 1080, c. 1740-1750) are the supreme examples of the form. Every music theory textbook uses Bach fugues as the primary teaching material. The reason: Bach's fugues are not only technically perfect (their voice leading is a model of craft) but also musically extraordinary — each one is distinct in character, emotional range, and motivic invention. The C major fugue from Book I is serene; the C minor is energetic; the F minor is plaintive; the D minor is dramatic; each is unmistakably itself.
The Subject
The fugue subject is the main melodic idea from which the entire fugue is derived. It is typically 1-4 measures long, begins on either the tonic note (scale degree 1) or the dominant note (scale degree 5), and has a distinctive rhythmic and melodic profile that will remain recognisable through all its subsequent transformations. A well-designed fugue subject has the following qualities:
- A clear opening gesture, often a leap or a characteristic rhythm that makes the subject immediately identifiable. The leap of a perfect fourth at the opening of Bach's C minor fugue, BWV 847, is instantly memorable.
- A sense of melodic direction — the subject should move toward a goal, either by ascending to a peak or descending to a low point, rather than meandering.
- An implied harmonic content that establishes the key. The subject should outline tonic and dominant harmonies at minimum, so that the listener perceives the key from the subject alone.
- A memorable identity that can be recognised even when fragmented, inverted, or stretched. The subject must function as a thematic kernel that supports development without losing its character.
- A length suitable for the contrapuntal architecture. Too short a subject (only one measure) leaves little material for development; too long (over four measures) makes the entries cumbersome and the texture confusing.
The subject typically ends on a note that allows a smooth handoff to the answer. Its final pitch must harmonise with the answer's opening pitch — since both are heard simultaneously after the second voice enters.
The Answer
The answer is the second voice's response to the subject, appearing a perfect fifth higher (or a fourth lower) than the subject. The answer is said to be "tonal" when it modifies one or two notes to preserve the tonic-dominant relationship (avoiding modulation), or "real" when it transposes the subject exactly up a fifth without modification. Most fugue subjects use tonal answers because the exact transposition of a tonal subject would shift some pitches outside the home key.
The rule for tonal answers (sometimes called the "tonal answer principle"): notes in the subject that function as the tonic (scale degree 1) are answered by the dominant (scale degree 5), and notes that function as the dominant (scale degree 5) are answered by the tonic (scale degree 1). All other scale degrees are transposed normally up a fifth. The effect is that the answer feels "in the dominant key" without actually modulating away from the home key — the tonic-dominant axis is preserved.
Bach uses tonal answers in most of his fugues. The C minor fugue BWV 847 has a tonal answer: the subject's opening C is answered not by G (a real fifth above) but by G modified so that the leap of the fourth from G in the answer parallels the leap from C in the subject, preserving the harmonic identity of the gesture.
The Countersubject
Many fugues use a countersubject: a melody that accompanies the subject or answer whenever they appear, forming a consistent two-voice texture. The countersubject is typically written in invertible counterpoint with the subject (so it can appear above or below the subject interchangeably). It typically begins where the subject ends and runs through the remainder of the exposition. The countersubject provides harmonic contrast to the subject — if the subject uses stepwise motion, the countersubject may use leaps; if the subject uses half notes, the countersubject may use quarter notes.
Not every fugue has a countersubject. Some fugues use free counterpoint above and below the subject, with no fixed melodic accompaniment. Bach's WTC Book I Fugue in D major (BWV 850) is largely without a strict countersubject; the WTC Book I Fugue in C minor (BWV 847) has a clearly defined countersubject that appears in every subject entry. A "double fugue" has two subjects that may appear together or separately; a "triple fugue" has three subjects (Bach's C-sharp minor fugue from WTC Book I, BWV 849, is the usual example).
Subject Design in Practice
When designing a fugue subject, the student should consider: which scale degrees does the subject emphasise? Does it imply a clear tonic-dominant relationship? Will the tonal answer fit comfortably, or will the answer require awkward modifications? Does the subject end on a note that can lead smoothly into the countersubject or into the next subject entry? Is the rhythmic profile distinctive enough to remain audible when buried in the middle of a four-voice texture? Practical experience writing subjects — and then attempting to harmonise them with countersubjects and answer them tonally — is the only way to develop these intuitions.
Sources and Further Reading
- Gauldin. A Practical Approach to 18th-Century Counterpoint. Waveland Press. Chapters 10-12.
- Kennan. Counterpoint. Prentice-Hall. Chapters on Fugue.
- Open Music Theory — Fugue (openmusictheory.net, CC BY-SA 4.0).
- Walker, Paul. Theories of Fugue from the Age of Josquin to the Age of Bach. University of Rochester Press, 2000.
- IMSLP — Bach Well-Tempered Clavier, Book I, all fugues (free score, imslp.org).