Anatomy of the Fugue

8/11/2019 Anatomy of the Fugue

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Site 1996 Timothy A. Smith

Author Sojurn Courses

Anatomy of a Fugue

Visit the Fugues of the Well-Tempered Clavier (Flashor Shockwave), where all of thetechniques discussed on this page are illustrated in interactive hypermedia.

I. Definition of a Fugue

Polyphonic procedure involving a specified number of voices in which a motive

(subject) is exposed, in each voice, in an initial tonic/dominant relationship, then

developed by contrapuntal means.

II. "Form" of a Fugue

A fugue generally consists of a series of expositionsand developmentswith no

fixed number of either. At its simplest, a fugue might consist of one exposition

followed by optional development. A more complex fugue might follow the

exposition with a series of developments, or another exposition followed by one or

more developments. Fugues that are tonally centered will expose the subject

without venturing out of an initial tonic/dominant constellation. Because its

outline is so variable, it is preferable to speak of the fugue as a "process" rather

than "form" per se.

III. The fugal purpose, method, character, and essence

Before form, the fugue is metaphorical; itspurposeis to reveal connections

between seemingly unlike things. Its methodis to develop an idea in never

precisely the same way. Its characteris to demonstrate relationships, unveiled

both in terms of new ideas born of old, but also in counterpoint with the old. The

fugal essenceis experienced in discovery of the new to be of the stame "stuff" as

the old.


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IV. Parts of a Fugue

A. Main Idea of the Fugue and How It Is Stated

1. Subject:Melody that comprises the primary melodic/rhythmic material of

the fugue. Subjects typically have two parts: the "head" is calculated to

attract attention either by unusual rhythmic or intervallic emphasis, while the

"tail" is typically more conjunct, rhythmically uniform, and sometimesmodulatory. The head and/or tail itself may employ variation of one or two

smaller motives or figures...each comprised of a characteristic rhythm and/or

interval.

2. Answer:Subject imitation which immediately follows the first statement of

the subject: in a different voice and usually fifth higher. Answers are a

subclass of subjects which bear certain interval characteristics in relationship

to the subject as it was originally stated.

Tonal Answer:An answer that typically (though not always) stays in

the same key as the subject. To do this it is necessary for the intervals

of the subject to change somewhat. In a tonal answer "do" and "sol"

switch places: The position occupied by "do," in the subject, becomes

"sol" in the answer and vice versa.Analytical technique: Subjects

having many skips (disjunct) that focus upon the tonic and dominant

scale degrees lend themselves to a tonal answer.

Real Answer:An answer that is a transposition of the subject toanother key, usually the dominant.Analytical technique: Subjects

having mostly steps (conjunct) that don't focus upon "do" and "sol"

lend themselves to a real answer.

3. Countersubject:Substantive figure that sometimes recurs immediately

following the subject or answer (in the same voice). Countersubjects serve as

counterpoint to subjects (or answers) sounding simultaneously in a different

voice. Not every fugue will have a countersubject. Some fugues may have

more than one countersubject.

4. False Subject:Some people use the term "false subject" to describe an entry

of the subject (or answer) that begins but never finishes. This term should be

reserved for instances where the subject appears to enter, breaks off, then

follows immediately with a complete statement. Most other instances of

incomplete subjects are developmental and should be termed "imitation."

B. Main Sections of the Fugue


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1. Exposition:Portion(s) of the fugue consisting of subject(s) with at least one

answer, and possibly countersubject(s). To qualify as an exposition, the

subject(or answer) must appear in all voices and answers must be in the

proper relationship (tonalor real) to subjects. The exposition normally

concludes immediately after the subject (or answer) appears in the last voice.

Expositions may defer the cadence until after a codetta. Differentiation

between exposition subtypes is based upon the order in which voices enter

(as compared to the first exposition) and whether or not the subject haschanged.

Re-Exposition:An exposition, following the initial

exposition, in which the voices enter in the same order as

the first exposition.

Counterexposition:An exposition following the initial

exposition in which the voices enter in a different order than

they did in the first exposition, or the subject of the newexposition is a contrapuntal variation of the original.

Double Exposition:Exposition utilizing a brand new

subject (i.e. not contrapuntally derived from the first). If the

new subject is unique, then the fugue is a double fugue (or,

in the case of three subjects, triple fugue).

2. Developmental Episode:Section in which motives from the exposition are

treated in sequence, modulation, contrary motion, double counterpoint,

stretto, augmentation/diminution,pedal, etc. Episodes are generally

terminated by a cadence and may follow one after the other. Developmental

episodes characteristically begin by departing from the subject, to fragment

or vary it in some way, but gradually building up to a restatement of the

subject in at least one voice. These statements of the subject are typically not

in the tonic/dominant relationship of the exposition and are called "middle

entries" (or in GermanDurchfhrung). Episodes typically do not enunciate

the subject in all voices.

3. Coda or Codetta:Concluding segment of a section (codetta) or of the entirefugue (coda). Codas and codettas often sound as if they are something added

after the structural end of the section or work. The function of codettas is

often modulatory (to return the tonality to the key of the subject after an

answer at the dominant). Not all fugues have these.

V. Compositional Techniques of the Fugue

A. Tonal Variation


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1. Modulation:Repetition of a motive in another key. Bach typically arranges

his fugues around closely related keys (major and minor keys immediately

adjacent to each other on the circle of fifths).

2. Mutation (also called "change of mode"):Statement of the subject or

answer (or any other primary material) in the opposing mode. A subject first

stated in minor and later stated in major is said to have "mutated."

B. Contrapuntal Variation

1. Stretto:Entry of a motive in a second voice before the first voice has

finished its statement. Motive can mean subject, answer, countersubject, or

any other substantive melodic/rhythmic entity in imitation.

2. Augmentation/Diminution:Statement of a motive in rhythmic durations

that are proportionately doubled or halved.

3. Pedal Point:Suspension of one pitch, often the bass, in such a manner that it

is alternately consonant then dissonant with the chord progression. Fugues

often conclude with episodes of pedal point.

4. Retrograde:(rare) Statement of the motive's pitches in reverse order.

5. Melodic Inversion:(Contrary Motion) Statement of a motive where interval

directions have been made to move in the opposite direction of the original

motive. If the quality of the intervals is preserved the motion is said to be the

"mirror inversion."

6. Sequence:Repetition of a motive at another pitch level, usually up or down

a step. Each repetition is called a "leg." Sequences in which each leg itself

contains a sequential pattern are said to be nested. Bach's sequences tend to

be of this latter variety, with the overall sequence comprised of two or three

legs, each leg comprised of two subsidiary units. For example: study the

sequences in the mirror fugues ofArt of Fugue. Sequential episodes seldom

appear in fugal expositionsbut are frequent accouterments to developments.

7. Contrapuntal Inversion:(Double/Triple Counterpoint) Reappearance of a

pair of voices (double ctpt.) or trio of voices (triple ctpt.) in which registers

have been reassigned in such a way that the voices have crossed and the

interval relationship between voices is fundamentally altered.

a. Types of Contrapuntal Inversions:

At the Octave:Fourths become fifths, unisons become

octaves, etc. While parallel 4ths sound fine, they do not


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invert contrapuntally, and double ctpt. at the octave avoids

them. See the Canon per Augmentationem in contrario

Motufrom theArt of Fuguefor an example of double

counterpoint at the octave.

At the Tenth (8va+3rd):Parallel motion tends to be

avoided altogether. This is because intervals that parallel

acceptably in one texture (e.g. 3rds & 6ths) becomeunacceptable when inverted (8vas & 5ths). Study the Canon

alla Decimaof theArt of Fugue.

At the Twelfth (8va+5th):With the exception of 3rds

(which remain 3rds), acceptable parallels become

unacceptable when inverted at the 12th. Thus, in the Canon

alla Duodecimaof theArt of Fugue(which features this

type of double ctpt.) the composer uses many parallel thirds.

b. How to Calculate Type of Contrapuntal Inversion:

1. Determine interval that the lower voice has been moved UP

2. Determine interval that the higher voice has been moved

DOWN. Note: if the voices have not exchanged registers,

the higher voice becoming the lower and vice versa, then

contrapuntal inversion has not occurred.

3. If steps 1 and 2 are each octaves, then the doublecounterpoint is at the octave. Otherwise, add the results of

steps 1 and 2, then subtract 1.

c. How to Calculate What Intervals Become After Inversion:

1. Double counterpoint @8va: Subtract the interval (before

inversion) from 9 to get the interval after inversion. For

example: a 4th before inversion will become a 5th after

inversion.

2. Double counterpoint @10th: Subtract the interval (before



inversion.

3. Double counterpoint @12th: Subtract the interval (before



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inversion.

For Practice: Recognizing Contrapuntal Inversions

The following examples of contrapuntal inversion are designed to be played from the Musica

Antiqua Koln(Archiv 431 704-2) recording of the "Art of Fugue" BWV 1080. The firstsystem, in each example, is paired with the analogous measures, in double counterpoint,

several bars later. Answer the following questions:

1. In what direction and how far is each part moved in analogous sections?

2. What happens to vertical intervals between analogous sections?

3. What is the basic interval of contrapuntal inversion?

4. What types of motion (parallel, contrary, oblique) characterize each example?

Exchange of Registers (contrapuntal inversion) in

Canon per Augmentationem in contrario Motu


Canon alla Decima


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Canon alla Duodecima

If you are contemplating the analysis of a fugue, see How to Analyze a Fuguefor step-by-

step instructions.

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