The fugue is a contrapuntal genre popular since at least the 18th century.

This chapter sets out some key principles of the opening exposition section.

We introduce new terms including these (click on the term for the glossary entry):

Subject

Answer

Countersubject

Exposition

We also meet some fugue-specific variants of familiars terms, notably:

Voices

SATB

We now move on from imitative practices common in the 16th century to the fugue, which may be thought of as the 18th-century equivalent and successor to this tradition. Fugues can vary quite a bit, and thus "fugue" is a surprisingly difficult term to define satisfactorily. Fugues in general are contrapuntal compositions that are defined by the strict use of a certain number of independent voices; each voice enters one by one, stating the main theme (subject) of the fugue. In this chapter, we will treat fugue as a process and show how to construct (the first part of) a fugue from first principles. This chapter deals with the basics of writing a fugal exposition from a given subject according to the "high Baroque" technique of Bach, Handel, and their contemporaries.

Basic Definitions

First, let's define some of the terms we'll need.

Subject: A short tune that forms the melodic basis of a fugue, recurring throughout.

Answer: A transposition of the subject that is also sometimes slightly altered, as discussed below.

Countersubject: A melodic line that is sounded with (and complements) the subject/answer.

Exposition: The first part of a fugue, during which each of the voices enters with the subject or answer. Note that this is distinct from the use of the term “exposition” in sonata form; they both refer to a first section setting out the main material, but they otherwise differ.

Voices: The separate contrapuntal lines, which may be either instrumental or vocal. The number of voices does not necessarily correspond to the number of parts or musicians involved—a keyboard fugue for one player may have three, four, five, or six voices, and there are even some fugues for solo violin (which is quite a compositional feat!).

SATB: Although a fugue may not involve any singers, it is customary to refer to the lines in a four-voice texture with S (soprano), A (alto), T (tenor), and B (bass) from highest to lowest. The ranges do not need to match those of the vocal parts exactly.

Structure / Voice Entries

Basically, the fugal exposition works as shown in Example 1: one voice begins with the subject, then the next voices enters with the answer while the first continues with a countersubject, and so on.

Voice 1

Subject

Countersubject

Free counterpoint

Voice 2

Answer

Countersubject

Voice 3

Subject

Example 1. Hypothetical structure of voice entries at the beginning of a fugue.

Note that the voices are numbered according to the order in which they enter. While it is perfectly common for the voices to enter in order from highest to lowest or lowest to highest, this is not strictly necessary. However, when a new part enters, it should be the highest or lowest voice at that stage, so it is uncommon for an inner part (alto or tenor) to enter last. That leaves us plenty of options. For instance, the order of voice entries in a four-voice fugue could be:

In register order from highest to lowest (SATB), or vice versa (BTAS)

Starting in the middle with the alto: ASTB, ATSB, ATBS

Starting in the middle with the tenor: TBAS, TABS, TASB

Any further subjects/answers entering (beyond the total number of voices) are described as "redundant" entries.

Subject

When considering how to handle a subject, look at its structure and character.

The structure of a subject can often be thought of in three parts. Like many tonal phrases, the subject charts a course from a distinctive opening to a generic cadence:

Kopfmotiv (literally "head motive"): an opening gesture

Fortspinnung: prolongation that may include sequence and/or motor rhythm

Cadence

Types of character include:

Toccata style: this has a motor-rhythm feel, is often chromatic, and may have irregular rhythmic placement.

Ricercar: deriving from the plainsong/motet tradition, this is slow moving, has an antiquated feel, and makes extensive use of suspensions.

Answer

We distinguish between two types of answer: real for an exact transposition, and tonal for one that has been altered further.

A real answer simply transposes the original subject by perfect fifth/fourth. All generic intervallic relationships remain the same between the notes.

We need a tonal answer if the subject:

starts on sol (\hat5) or otherwise uses it prominently at the outset. In this case, we must adjust the transposed version such that sol (\hat5) is not transposed up to re (\hat2), but instead to do (\hat1).

includes any other V–I suggestion at start. Prominent dominant note in subject becomes tonic note in answer, so T → D progressions often become D → T and vice versa.

modulates. In this case, split the subject into two phrases, one in each key, and adapt accordingly. If the subject modulates at its end to the dominant, the answer must modulate back to the tonic.

In all cases, we seek to make minimal adjustment such that the subject and answer are still as alike as possible, and both make melodic sense.

Countersubject

Try working up a skeletal version of your countersubject first before fully fleshing it out. It's frustrating to dash off a lovely tune and then realize that it doesn't fit. Additionally, sketch the version that will go with the answer at the same time as the version that goes with the subject. It's just as frustrating to write a countersubject that works beautifully with the subject but which the answer makes harmonically nonsensical.

Indeed, countersubjects are melodies, but they only work if they make sense harmonically as well. To that effect, remember that your countersubject will first appear in a two-voice passage, so consider how best to outline clear larger harmonies (triads and sevenths) with only two voices.

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