See Anatomy of a Fugue by Dr. Tim Smith for detailed definitions and explanations.

Many fugues have three phases: (1) exposition of subject material, (2) series of single entries of subject in various keys, and (3) a concluding section in the home key. The structure of a fugue is the result of process rather than the result of using a conventional template. The fugue is an example of form-from-polyphonic process, the use of motive in a rhythmic layered texture, thematic cohesion from the continuous repetition of thematic cells and their variants.

Rota and Rondellus (types of medieval round); caccia (It. chase); sixteenth and seventeenth century vocal motets, chansons, madrigals, masses--and instrumental fantasia, canzona, ricercar (Sweelinck, Frescobaldi, Froberger, Gabrieli). Bach's early fugues resemble those of Buxtehude, canzoni and ricercars.
a vivid thematic idea ranging in length from a few notes to several bars, closure is open-ended, harmonic reference is clear.
a few extra notes at the end of the subject entry to make a connection with subsequent material (accompanying counterpoint, countersubject). Links are not used consistently throughout a fugue, a feature which helps one to determine the contents of the subject.
Imitative reply of the subject, usually at the dominant. Real answer if the subject is transposed interval-for-interval, tonal answer if some of the intervals were changed to comply with the harmony, usually to favor larger scale tonic emphasis.
Subject-answer cycles in Exposition:
In the first section of fugue ("exposition"), subject-answer pattern emphasizes tonic-dominant harmonic cycles, every voice states subject or answer. An "a3" fugue might have S(I)-A(V)-S(I) in the exposition.
Episodes and Transitions:
Connecting passages in which the subject is not stated intact, connects one statement of the subject to the next. A "transitional episode" is one which modulates. An episode is any passage that does not include the whole subject. Episodes use motives and fragments from first part of fugue, often in sequences. In the middle section of the fugue, entries and episodes may alternate, a pairing of subject matter and motive development passages.The middle section of a fugue may contain no episodes and proceed from middle entry to middle entry sans linking episodic passages.
Episode (alternate definition)
means the same as "middle entry," the statement of the subject in the middle section of a fugue.
in some fugues, a counterpoint to the subject that is repeated in subsequent entries (not necessarily every entry).
Free counterpoint:
counterpoint not repeated in subsequent entries. Usually based on motives and fragments stated in first part of fugue.
Invertible counterpoint:
counterpoint that can change score position with the subject, countersubject or other counterpoint, often at more than one interval.
exposition entries that follow a short episode in the exposition
Subject variation:
See material on motive variation in general; fragmentation, inversion, retrograde, augmentation, diminution, ornamentation and other varied repetition techniques.
Tonal Range:
Various key plans created through subject entries. Integral to structure of fugue.
Entry, middle entry
statement of the entire subject in the middle section of the fugue.
overlapping of entries, sometimes using abbreviated subject, sometimes a constant feature, sometimes used at end as a closing stretto entry, total stretto, partial stretto, tight stretto
Pedal Point:
used as in other forms to provide tonal keel action, used to terminate and excursion through keys, used to reorient listener to home key, dominant or tonic pedals very popular. Pedals sometimes used in developmental sections to underscore each tonal center (can be dominant or tonic pedal in each key in a series of keys).
The final stage:
return to tonic and unadulterated subject, sometimes heralded by a cadential haitus. Good place for a stretto, pedal tones, tonicizing progressions. Coda (codetta), the final entry, sometimes following a deceptive cadence, often over a tonic pedal.
Multiple Fugue:
Double fugues, two subjects. Kyrie from Mozart's Requiem, second subject on the words "Christe eleison"
Usually a fugal passage within a larger, non-fugal form, such as fugal passages in development sections.
A "little fugues" such as a fugal variation. Distinction between the Fugato and the Fughetto is passage (-ato) versus whole section with its own closure (-etto).
Examples in Nineteenth and Twentieth Century literature
Symphony of Psalms, second movement
Chromatic Invention in Mikrokosmos
Various instance of contrapuntal process throughout Mikrokosmos, especially books 4, 5 and 6.
Concerto for Orchestra
Music for Strings, Percussion and Celeste
Prelude, Chorale and Fugue (piano)
Ludis Tonalis, Fuga Prima in C
Ludus Tonalis, no. 2 in G (in 5/8)
Ludus Tonalis, no. 3 in F
Ludus Tonalis, no. 9 in B flat
Sonata No. 2 for organ, third movment
Metamorphisis on a Theme of Carl Maria von Weber

Response to a question on Counter Subject:
an analytical outlook

As in all analysis of music, the determination of a counter subject has an element of interpretation to it. The term "counter subject" refers to a counterpoint that has more thematic significance than other counterpoints to a subject. To make this determination, the analyst must examine all entries of the subject to see is the counterpoint to the subject:

- has special thematic significance
- is attached the subject as a secondary subject idea
- is repeated consistently throughout the fugue -- or
- is used in only a part or parts of a fugue.

A final determination depends on the analyst's interpretation of context. It would be a lot easier if we could apply a kind of universal check list to fugues and other structural genres. Yet, since all the music we hear/see is human artifact, it is as unlikely that a check list would work to describe the personality of the composer as it would to describe the product of her/his imagination.

Thus, if one creates a musical law that says a composer must always repeat a counter subject throughout a fugue, there will always be exceptions that refute the law. If a composer did not use the counter subject all the way through the fugue, we could say that she/he had employed a counter subject-like idea and note where in the fugue it was use -- or not used. We might also assume that counter subjects tend to be used in a particular way but there will always be individual variance to the practice. We can see such variance in the corpus of even one composer, J. S. Bach for example. Perhaps we should look at music the way we look a chaos phenomenon in general; that is, we can see common pattern as well as individual variance, a kind of unpredictable and disorderly order. This may help us better understand and appreciate the creative imagination that produced the work.

I'd rather reserve a definitive study of counter subject and other elements of the fugue for a specialized, detailed and advanced course on contrapuntal process. This area is Dr. Smith's passion and you can learn a great deal more about it by visiting his site on the web. All I want here is a general concept of the "counter subject." We will move to new material next week (except for students who choose a fugue as a semester