Following are excerpts from Composing a Simple Fugue.^©

Note: A comprehensive glossary is included with the fugue guide.

Roman numerals refer to the Pachelbel Magnificat fugue tone, and arabic to the specific fugue for that tone. eg. VI/3=sixth tone, third fugue.

Writing the Subject

Melodic Characteristics

A good fugue subject is terse, has a distinct contour and harmonic outline. Alternative harmonizations are possible and desirable. The quicker the tempo, the longer the subject can be. At a slow tempo, a listener is hard pressed to grasp a long, rambling theme. For short fugues, a subject of one to three bars is typical. (cf. II/10, VII/7 for extremes of length.)

Composers often change the last note or few notes of the subject or answer in order to complete a harmony (VIII/8 pt.3 b.27 tenor), accommodate stretto (VIII/8 pt.1 b.14, alto), or to avoid a perfect authentic cadence (III/10 bb.6,16 soprano).

Most subjects lie within an octave (VIII/13 - Note the pains taken to avoid part crossings in this instance involving a subject of an octave range.) The narrower the range, the less the potential for problems of part crossing and overstepping of range when the theme becomes the answer.

Large leaps are infrequent and very active passages, such as arpeggios, are unusual. The violinistic character of VII/3's subject is atypical. Some subjects are chromatic (I/19, VII/7). Sequential subjects (VI/9) are possible, but may limit or preclude the sequences characteristic of episodes, since contrast between expositions and episodes will be diminished unless the sequence reverses direction in the episode. A subject may be echoic (II/2).

A long initial note poses a problem if there is to be a countersubject. We'll examine one solution when we discuss answering the subject. Some subjects may contain short pauses or hockets (V/5). Fugues in compound triple meters are known as gigue fugues (I/5, II/10).

Very often, a subject with a high linear density (i.e. one with many notes per beat, such as one in C running mostly in sixteenth notes) can be reduced to a very simple melodic skeleton (i.e. the running notes form diminution of a simpler theme. Note how in IV/4, the first bar could be reduced to quarter notes founded on the first note of each group of four sixteenths. The quarter note movement could continue in the next bar with a d and b.)

The juxtaposition of low and high linear density themes can be the basis for a double fugue -- one formed from the subjects and answers of two independent fugues that are then superimposed upon one another (VI/1). A livelier fugue results from a higher linear density.

Meter

In duple meters, the subject may start on any part of the bar, and the answer may start either at the corresponding point in the bar of its entry, or one beat further along in a bar of alla breve, or two beats further along in C or 4/2. An exception occurs if the initial note of the theme is shortened; we'll discuss this further when we consider the answer.

In triple meters, the answer must start on the same beat as the subject. Points of entry in compound triple meters are made as they would be in the simple meters from which they are derived. The subject should end on a strong beat.

Initial Note

Most subjects start on the first or fifth scale degree. The third is possible, but rare. Although it is seldom an issue in simple fugues, we should mention that if the dominant key is implied at the outset, the answer will be in the subdominant.

Also rare in simple fugues are subjects that modulate to the dominant. They may require either a tonal answer to return to the tonic before the next entry (V/3), or a codetta for the same purpose (VIII/13 b.6). Keep codettas short and as direct as possible. The subject should finish well below the opening of an answer by a higher voice or well above the opening of an answer by a lower voice.

Conjunction

The answer's entry usually overlaps the subject's conclusion such that the last note of the subject coincides with the first note of the answer (I/2). It may, however, enter on the beat following the subject's end (I/3). If a dissonance or perfect fourth results from overlapping, insert a codetta (I/1- codetta is the single eighth note e) or try bringing the answer in somewhat ahead of the end of the subject (VII/7).

Another solution in this situation is to recast the end of the subject such that a satisfactory conjunction is formed. Note for example how Pachelbel has ended the subject in VII/6 b.2 on the mediant rather than the tonic in order avoid a conjunction on a perfect fourth.

Other Melodic Characteristics

The opening of the subject should allow the tonality to establish itself, yet also induce rhythmic momentum. For this reason, the dactyl on a single note (I/13), or on notes of the tonic chord (VIII/3), was a favourite opening motive, particularly among early baroque fugue composers. Here, the melodic rhythm moves, but the harmonic rhythm is static.

Another common motive is a group of three eighths or sixteenths starting off the beat (cf. VIII/10, I/6, VI/1 pt.2) Many initial motives are based on ascending or descending fourths or fifths (q.v. esp. Tone I fugues) or triadic outlines (IV/5, VIII/3). On the whole, subjects tend to start slowly, accelerate towards the middle, and relent as they close. One particularly odd subject actually decelerates from the outset (VIII/6)!

Although subjects often have stereotypical qualities, a wide variety of characteristics is nonetheless present in the genre as a whole. Some display homogeneity of motive (I/17, VIII/5), while in others, two or three distinct melodic and rhythmic patterns are present (III/6). Some move in long notes, others in a rapid succession of short notes. Various ratios of disjunct to conjunct motion occur. Syncopation is possible (III/1). Composers may use the opening of a chorale or other prius factus tune if it meets the above criteria, either as is, or with some modification.

Stretto

To use stretto, construct a theme that will work in whole or in part in canon at the octave and/or the fifth. Relatively few of the Magnificat Fugues employ stretto and all instances are fifth-related (i.e. subject/answer); Experiment with subject or answer stretto on the downbeat of b.24 in I/11. Fifth-related (i.e. subject with answer) stretto is possible on the second half of b.23.

In some cases, other canonic techniques may be possible -- canon in contrary motion, for instance. For variety, write themes that work canonically at two or more intervals of linear displacement (I/4 cf. bb.1-2; 25-6). False stretto occurs if the leading voice aborts the theme and resorts to free counterpoint when the following voice enters (I/13 b.5).

Internal Cadences

Employ internal perfect authentic cadences cautiously. They may impede the flow and should occur only at the end of the fugue, at the end of the fugue proper if a coda is present (IV/1 b.25), at the end of an episode if it overlaps a running start to an exposition (I/15 bb.17-8), or vice versa (VIII/11 bb.10-1). In V/1, b.2, the ending of the subject on doh without a codetta or an overlap of subject and answer creates loss of momentum. This instance is exceptional.

Perfect authentic cadences may be avoided with a suspension (I/12 pt.1 bb.14-5), or by a melodic turn that produces an imperfect authentic cadence instead (V/5 bb.10-1). Subjects that do not end on doh will obviate this problem (IV/8). A V4/3 - I cadence often replaces the perfect authentic cadence.

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