The Art of Fugue

Types of Fugues, Part 1

 

Simple Fugues | Stretto Fugues | Double and Triple Fugues

SIMPLE FUGUES
The point of the first four pieces is to state and develop the principal theme using the most simple methods of variation.

Contrapunctus I: Main theme
The principal theme is pronounced and worked out in a simple fugue without the use of any technical devices - an understated opening to this Grand Tour of the fugue.

Contrapunctus I: Main theme
Listen - Main theme	Listen - Main theme answer

 

 

Contrapunctus II: Main theme, rhythmically varied
The principal theme is altered slightly by the use of dotted rhythms at the end of the theme, giving the piece a sense of urgency or energy.

Contrapunctus II: Main theme with rhythmic variation
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Contrapunctus III: Main theme inverted
The principal theme is turned upside down (inverted) so that its notes move in the opposite direction (up or down) of the original. Chromatic notes allow the harmonies to shift in unpredictable ways, giving the movement a searching, yearning quality.

Contrapunctus III: Inverted Main Theme
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Contrapunctus IV: Main theme inverted differently
The main subject is inverted in a new way, beginning on the dominant note A (fifth note in the scale of D minor) rather than the tonic, or main note, D. The piece is highly virtuosic, combining both the rhythmic and harmonic elements of the previous two movements into one work. Listen for the recurring cuckoo motif.

Contrapunctus IV: New Inversion
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STRETTO FUGUES
In this set of fugues (V, VI, VII), Bach focuses on overlapping the voices rather than altering the principal theme. This is accomplish by stretto technique, meaning that the secondary voice (answer) enters before the subject is completely finished. The result is added intensity and complexity. The three stretto fugues are also counter fugues - the answering voice is an inversion of the principal voice.

Contrapunctus V: Varied main theme with its inversion
Bach takes up a variant of a theme from Contrapunctus III and tries to show how many times the subject can be used to make a counterpoint for itself. He manages to do this in 11 different ways by varying the distance between the first note of the subject and the entry of the answer - from one to six beats - and even ends with a “hyperstretto” where there is no separation. Listen for a fanfare-like element.

Contrapunctus V: Varied main theme and its inversion
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Contrapunctus VI: In French style with upright/inverted themes, plus diminution
This fugue introduces the technique of diminution, which means that the value of the notes is halved: half notes become quarter notes, whole notes become half notes. As a result the theme moves twice as fast. (The opposite technique, augmentation, lengthens the note values and slows the theme.) In this movement the normal and diminished (fast) versions of the theme overlap. Bach also gives this movement a special twist using a dotted rhythm and rushing 16th notes - a characteristic of the French overture style (hence the name “Stylo Francese”). Listen for the tension between the slower theme in the lower voice and the stylized, worldly French elements surrounding it.

Contrapunctus VI: French-style variation
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Contrapunctus VII: Up and down, augmentation and diminution
The purpose of this stretto fugue is to show how the movement’s main theme can accompany itself in altered note values by means of augmentation and diminution (i.e. faster and slower versions). Listen for the slowest version of the theme as it climbs from the lowest voice to the highest voice over the course of the movement.

Contrapunctus VII: augmented and diminished - 4 versions
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DOUBLE & TRIPLE FUGUES
In the first seven movements the fugues are constructed around modifications of the principal theme. In the following fugues (VIII-XI) a number of counter-themes are introduced - a double fugue has two main themes, a triple fugue has three.

Contrapunctus VIII: Two new themes, plus main theme varied
The first triple fugue starts with a new theme (Theme I), which is first developed on its own and then in a double fugue with a second new theme (Theme II). Theme III (a variant of the Art of Fugue theme) is then introduced, and combined with Themes I and II in a triple fugue.

Contrapunctus VIII: Three themes
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Contrapunctus IX: New theme and main theme
This scherzo-like double fugue begins with an entirely new theme, although the principal Art of Fugue theme also appears in the middle of the piece in its normal (upright) form. The movement also employs double counterpoint, meaning that the upper and lower voices change places. Here they exchange at both the octave and at the 12th interval (octave plus five).
(See Tim Smith’s guide to double counterpoint at the Anatomy of a Fugue Web site)

Contrapunctus IX: New theme
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Contrapunctus X: Inversion of varied main theme, plus new theme upright and inverted
Another double fugue beginning, like Contrapunctus IX, with a new counter-theme. The main Art of Fugue theme enters later (again like IX), but this time in its inversion. Double counterpoint (where the voices exchange registers) is again employed, but this time at the interval of the tenth. This piece has a gentle, wistful feeling - a lull before the stormy Contrapunctus XI.

Contrapunctus X: New counter-theme
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Contrapunctus XI: Six themes
The second triple fugue uses the three subjects from Contrapunctus VIII but in both their upright and inverted forms. Bach also weaves in his name in the third subject - B flat-A-C-B natural - that is, in German notation,“BACH.” This turbulent movement is the most dramatic of the entire work and one of Bach’s boldest expositions of his harmonic powers.

Contrapunctus XI: Inversion of third theme from Contrapunctus VIII
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Types of Fugues, Part II | Art of Fugue home page.