---
title: Fugue Subjects and Answers
dek: A fugue's opening notes commit the piece to more than a tune. The subject's shape and the answer's adjustment decide what can happen next.
topic: counterpoint
tags: [fugue, subject, answer]
date: 2026-09-25
author: Yunus Emre Vurgun
level: advanced
related: [imitation-and-invertible-counterpoint, first-species-counterpoint, sonata-form]
---

Almost every description of fugue begins by warning that fugue is not a form. The warning is necessary and usually wasted, because the terms that follow (subject, answer, countersubject, exposition, episode) get used as if they named fixed compartments. They are better understood as the vocabulary a composer uses to solve a specific problem: how to state an idea, leave it, return to it, and make every return sound like a consequence rather than a repeat.

The subject is where that problem is decided. Before the second voice enters, the first eight notes have already fixed the key, the harmonic direction, the rhythmic character and the contours that later entries can be inverted against.

## The anatomy, as working vocabulary

The **subject** is the idea itself, stated alone by one voice. The **answer** is its reappearance in another voice, normally at the interval of a fifth or an octave. The **countersubject** is a line that accompanies the answer and is designed to combine with the subject thereafter. The **exposition** is the section in which each voice enters with the answer or subject in turn. An **episode** is a passage of transition and development built from figures extracted from the subject, usually moving to a new key and preparing the next entry. Later passages repeat the subject in related keys and are called middle entries, and a **stretto** compresses the entries so that each voice enters before the previous one has finished.

Only two of those terms have an unambiguous referent in the score: the subject and the exposition. "Countersubject" is an analyst's convenience, applied after the fact to whichever line happened to accompany the answer and proved useful later. Many fugues have no counted countersubject at all. And a fugal passage inside a larger movement, a fugato, uses the same texture without committing to a full exposition.

The one structural rule with real teeth is that the exposition must state each voice's entry in a clear order and establish the key. Everything after that is variation, and the variation is the point.

## Two answers, and why only one of them can be literal

The simplest answer is the **real answer**: the subject transposed literally, usually up a fifth. If the subject is the five notes C–D–E–F–G, the real answer is G–A–B–C–D, and nothing has been adjusted.

The complication arrives with subjects that emphasize the dominant in their opening. Take a subject that begins by leaping from the tonic up to the dominant, then steps down: C–G–F. Transposed literally up a fifth, the answer begins G–D–C, and the second note, D, is the supertonic of the key, which means the answer's opening outlines the dominant's own dominant rather than a stable dominant. The relationship between the two entries is wrong: instead of hearing the tonic answered by the dominant, the ear hears a dominant answered by something that wants to leave it.

The traditional correction is the **tonal answer**, and its rule is worth stating exactly: when the subject's opening emphasizes the dominant by leap, the answer mirrors the intervals, so that a leap of a fifth is answered by a leap of a fourth. The subject C–G–F becomes the answer G–C–B. The second note is now the tonic, the tonic-dominant axis is preserved, and the rest of the subject proceeds as before.

[keys bpm=110]C4 G4 F4 G4 D5 C5 G4 C5 B4[/keys]

The button plays three three-note heads in order: the subject, then a literal real answer, then the corrected tonal answer. The first and second differ only in the size of the opening leap; the second and third differ in the second note, and it is that single note that keeps the answer inside the key.

Real answers are not simply the lazy choice. A subject that begins on the tonic and moves by step, or that leaps up a fourth, is usually answered literally, because a literal transposition keeps the harmonic meaning intact. The decision is made by the subject's opening intervals, not by its length, and treatises have always disagreed about the hardest cases. In Bach's Well-Tempered Clavier both kinds appear throughout, sometimes within the same pair of pieces.

The practical guide is short enough to memorize:

| The subject's opening | Typical answer | Reason |
| --- | --- | --- |
| Steps away from the tonic (1–2–3) | real | A literal transposition keeps the tonic-dominant relationship intact |
| Leaps from 1 up to 5 | tonal | A fifth answered by a fourth keeps the dominant answered by the tonic |
| Arpeggiates the dominant triad | tonal | A literal answer would push the music toward the dominant's own dominant |
| Begins on the dominant itself | tonal | The answer enters on the tonic, a fourth above |

None of the four rows is a law. They describe which choice preserves the relationship the ear is tracking, and the ear is the final authority in the cases where a subject sits between two categories.

## What the subject has already decided

A subject is a melody and a harmonic plan at once. Its first three or four notes imply a chord, and that implication is the fugue's engine: entries are placed where the harmony they imply can be prepared, and episodes exist to move from one entry's key to the next entry's key.

Several properties matter more than the tune itself. The **head motive**, the first few intervals and their rhythm, is what listeners recognize when the subject returns after an episode, so it needs something distinctive: an unusual rhythm, a characteristic leap, a repeated note. A subject that opens with four stepwise notes at the same speed gives the ear nothing to hold, and the whole fugue will depend on its countersubject to be memorable.

The **harmonic profile** determines how much freedom the composer has. A subject that arpeggiates the tonic triad is easy to place and hard to make interesting; a subject whose opening implies a dominant or a seventh chord creates tension that later entries can resolve differently. Most well-made subjects sit between those extremes, stating the tonic clearly but ending in a way that leaves the phrase open.

The **range** is a practical constraint that beginners overlook. The answer is a fifth above the subject, so a subject that climbs to the top of a voice's range will push its answer out of it. This is why so many subjects begin in the lower middle of the voice and rise late.

Finally, the **tail** of the subject is often designed to become the countersubject. If the last few notes state a rhythm that can continue in counterpoint against the head, the fugue has a ready-made second idea without needing a separate invention.

## The countersubject's obligations

A countersubject is judged by what it can do when the subject returns, not by how it sounds on its own. It accompanies the answer in the exposition, and it must then work when the two lines trade places: the subject below with the countersubject above, and later the reverse, at whatever inversion interval the composer has chosen.

That requirement is exactly the interval arithmetic of invertible counterpoint. A countersubject invertible at the octave cannot use perfect fifths against the subject, because a fifth inverts to a fourth; invertible at the twelfth, it can use fifths but not sixths, since a sixth inverts to a seventh. Most fugue countersubjects are written as note-against-note or in deliberately complementary rhythm, so that the two lines never compete for the same metrical position.

[keys]C4+E4 D4+F4 E4+C5 D4+B4[/keys]

That is the shape to aim for: the upper line moving mostly in steps, the lower line turning against it, and every vertical interval a third or a sixth. Nothing in the example is a fifth or an octave, which is what makes it survive being turned over.

The deeper obligation is negative. A countersubject that merely fills out the harmony of the subject will survive inversion technically and sound like an accompaniment in both versions. The test is whether the line, played alone, is a line.

## Where the labels fail

Two habits cause most of the confusion around fugue. The first is assuming that every fugue has all the parts named above. Plenty of fugues begin with a subject and a countersubject that is never used again, or build their middle sections from new material rather than episodes, or dispense with stretto entirely. The vocabulary describes what a fugue is likely to contain, and the piece is the authority.

The second habit is treating the answer's type as a fact about the piece rather than about the subject. A tonal answer is not a lesser version of a real answer, and a real answer is not a sign of a less sophisticated subject. The question that decides it is narrow: does the subject's opening need to have its dominant emphasized, or would a literal transposition preserve the tonic-dominant relationship? When a subject begins on the dominant, or arpeggiates it, the answer usually employs the same adjustment in the other direction.

There is also a naming problem specific to the countersubject. Because it is identified retrospectively, two analysts can disagree about which line deserves the name, and both can be right about the counterpoint while differing about the label. This does not matter for analysis and matters a great deal for writing: if you are composing, you choose which line will return with the subject, and you write it accordingly.

## Writing one

Start with the head, not the whole subject. Compose three or four notes with a rhythm and an interval you would recognize if you heard them again after thirty seconds of other music, and check what chord they imply. Then extend to the length of a normal phrase, ending on a note that leaves the phrase open, and check that the answer at the fifth stays inside the voice's range.

Then answer it twice: literally, and with the opening interval adjusted if the head emphasizes the dominant. Sing or play both, and decide which one preserves the tonic-dominant relationship rather than merely transposing the notes. The [ear training studio](/tools/ear-training-studio/) is useful at this stage, because hearing a fourth where you expected a fifth is the whole skill in miniature.

Only then write the countersubject, and write it with the inversion in mind from the first note. Play the subject and countersubject together on the [virtual piano](/tools/virtual-piano/) in both arrangements before you decide which one you prefer. If the second arrangement collapses, the countersubject is not finished, however good the first arrangement sounded.