Data
- Bach's last great collection, written in the last ten years of his life (an autograph manuscript from the early 1740s, then revisions from 1747) and left unfinished at his death in 1750.
- Published in 1751, second edition in 1752 with a preface by Marpurg.
- Fourteen fugues (Contrapunctus) and four canons, all in D minor and all derived from a single subject.
- Written in open score (one staff per voice), with no indication of instrument; the keyboard is today the most accepted destination.
The subject
D A F D C# D E F (then a stepwise tail): arpeggio of the D minor triad, leading tone, rise. In Contrapunctus 1 the subject enters in the alto; the soprano answers with a tonal answer (A D C A G# A B C), then bass and tenor enter; the exposition closes at bar 17.
The plan of the collection
| Group | Pieces | Principle |
|---|---|---|
| Simple fugues | Contrapunctus 1–4 | subject direct (1, 2) and inverted (3, 4) |
| Counter-fugues | 5–7 | subject direct against inverted, diminution (6, in French style), augmentation and diminution (7) |
| Double and triple fugues | 8–11 | 8 triple in three voices; 9 double at the twelfth; 10 double at the tenth; 11 triple on the subjects of 8 inverted |
| Mirror fugues | 12–13 | rectus and inversus form (12 in four voices, 13 in three) |
| Canons | 4 | by augmentation and contrary motion, at the octave, the tenth, the twelfth |
| Unfinished fugue | Contrapunctus 14 | three subjects, the third on the motif B–A–C–H |
The transformations of the subject
- Rhythmic: dotted values (Contrapunctus 2, 6), variants in triplets or with passing notes.
- Melodic: inversion, chromaticism (Contrapunctus 3), ornaments.
- Contrapuntal: stretto, augmentation, diminution, double counterpoint at the tenth and twelfth, mirror.
The Fugue on 3 subjects
Preserved in a separate manuscript, it breaks off at bar 239. The third subject begins with B–A–C–H (Bb A C B). A note by Carl Philipp Emanuel Bach links the interruption to his father's death, but the manuscript is autograph and scholars date it to an earlier period, when Bach was still writing with his own hand. Many musicians have proposed completions with a fourth subject, the main theme of the collection (among others Tovey, Moroney, Walcha); Busoni drew from it the Fantasia contrappuntistica.
What it teaches
- A single subject is enough for an entire cycle if you know the devices.
- Each group isolates one technique: like a treatise in music, from the simple fugue to the mirror fugue.
- Complexity grows gradually, as in Fux's species.
How to study it
- Learn the subject by heart and recognize it in all the rhythmic variants.
- Analyze the expositions of Contrapuncti 1–4 and compare the order of the voices (1: alto, soprano, bass, tenor; 2: bass, tenor, alto, soprano; 3: tenor, alto, soprano, bass; 4: soprano, alto, tenor, bass).
- In Contrapuncti 5–7 mark in different colors the subject direct, inverted, augmented, diminished.
- In Contrapuncti 9 and 10 find the point where the two subjects combine and check the interval of inversion.
- Play Contrapunctus 12 in both forms and compare the cadences.
Typical mistakes
- Considering the work only as an abstract exercise: many fugues have very different expressive characters.
- Thinking that the order of the print is surely the one Bach intended: the sources diverge.
- Ignoring the canons, which are part of the design.
Modern application
- Film scores and series: a single motif transformed into many characters (inverted for the antagonist, augmented for the finale, dotted for the march) is the principle of the leitmotif applied with contrapuntal means.
- Production: working on a single idea with rhythmic variations and inversions is an excellent exercise for writing a coherent album or soundtrack.
- Choirs and ensembles: the work is performed by string quartets, wind ensembles, organ, piano; arranging a Contrapunctus for four voices is an effective orchestration exercise.
Related topics
Double and triple fugues, counter-fugue and mirror fugue, invertible counterpoint at the tenth and twelfth, types of canon, tonal answer.