Bach's two-part inventions are the pedagogical apex of two-voice counterpoint. This lesson guides the student through the process of writing an original invention, from subject design through complete composition.
The Two-Part Invention as Compositional Form
Bach's 15 Two-Part Inventions (BWV 772-786) were composed primarily as teaching pieces — Bach described them as pieces "showing clearly not only how to play both parts cleanly and in correct style, but also how to create a good singing tone, to develop taste in composition, and to achieve a good musical imagination." They are the ideal model for student contrapuntal composition because they are short enough to compose completely (most are 24-40 measures); built on simple imitative technique accessible to any student who has completed species counterpoint; and musically beautiful and satisfying, demonstrating that technical rigour and aesthetic pleasure are not opposed.
Bach composed the inventions for the education of his own children and students, and they were collected in a clavier book for his eldest son Wilhelm Friedemann in 1720, then revised and fair-copied in 1723. The 15 inventions traverse 15 different keys (avoiding only those with too many sharps or flats to be comfortable on the harpsichord of the period). Each is a compact masterpiece of two-voice writing, and the set as a whole forms a complete pedagogical curriculum in itself.
Subject Design
The first step in writing a two-part invention is designing the subject — the opening 1-2 bar melodic idea from which the invention will be derived. A good invention subject has the following qualities:
- A distinctive opening — usually a leap or a characteristic rhythm that makes the subject immediately recognisable. The rising arpeggio that opens Bach's Invention No. 8 (F major) is unmistakable; the rising-and-turning scale figure of Invention No. 4 (D minor) is equally distinctive.
- A clear tonal implication — the harmonised scale degrees should be unambiguous. The subject should outline tonic and dominant harmonies so that the listener perceives the key from the subject alone.
- A shape that works well in inversion — since the subject will be answered by imitation, possibly at the octave below, the subject must harmonise with itself in counterpoint when one statement is in progress while another is beginning.
- A length that allows meaningful development without becoming too long to fragment into motives. Most successful invention subjects are 1-2 measures of moderate motion (predominantly eighth notes or sixteenth notes).
- An internal motive that can be developed — typically a head motive (the first 2-4 notes) and a tail motive (the last 2-4 notes), each of which can appear independently in episodic material.
Structure of a Two-Part Invention
A typical two-part invention structure unfolds in six stages:
- Opening (measures 1-4): Both voices present the subject in imitation. Voice 1 enters with the subject; voice 2 answers (usually at the octave, sometimes at the fifth) one or two measures later. Voice 1 continues with free counterpoint or a countersubject while voice 2 states the subject.
- First episode (measures 5-10): Sequential development derived from subject material, modulating from the tonic toward a closely related key (usually the dominant in major keys, or the relative major in minor keys).
- Middle entry (measures 10-14): The subject returns in the new key, again with imitation between the two voices.
- Second episode (measures 14-20): Further sequential development, exploring additional keys (often the submediant or supertonic) and preparing the return to the home key.
- Return (measures 20-26): Subject in the home key, possibly with the voices exchanged from the original presentation (using invertible counterpoint).
- Closing (measures 26-end): Final cadence in the home key, possibly with stretto (overlapping subject entries) or a brief coda extending the final cadence.
This structure is not fixed — Bach's inventions vary considerably. The C major invention (BWV 772) is more loosely structured around continuous figuration; the F minor invention (BWV 780) is more rigorously formal with clear sectional divisions. But the alternation of subject entries (giving direction and formal articulation) with episodic sequences (providing harmonic development) is the invariable underlying logic.
Writing the Countersubject or Free Counterpoint
After the subject enters, voice 1 must continue with material that harmonises with voice 2's statement of the subject. There are two approaches:
Free counterpoint: Voice 1 invents new melodic material that simply harmonises well with the subject and follows good voice-leading principles. This is more flexible but provides less unity.
Countersubject: Voice 1 plays a fixed melody (the countersubject) that will accompany every statement of the subject throughout the invention. The countersubject must be written in invertible counterpoint with the subject so that it works above or below. This provides greater motivic unity at the cost of compositional flexibility.
Bach uses both approaches in different inventions. The C major (BWV 772) uses essentially free counterpoint with continuous figuration; the B-flat major (BWV 785) has a clearer countersubject that recurs throughout.
Practical Composition Guidelines
Step-by-step procedure for writing your own two-part invention:
- Design your subject. Test it by singing it; if you can sing it once and remember it, it has enough character.
- Write the answer (a transposition of the subject, beginning in the other voice at the octave or fifth) and ensure the two voices harmonise when the answer enters while voice 1 continues.
- Plan your key areas. In a C major invention, you will typically visit G major (dominant), A minor (relative minor), and possibly F major (subdominant) or D minor (supertonic) before returning home.
- Write the subject entries in each key area first. These are the structural pillars of the invention.
- Fill in the episodes between subject entries using sequential development of motivic material drawn from the subject.
- Revise for voice-leading errors (parallel perfect consonances, poor dissonance treatment) and musical quality (smooth melodic lines, clear phrase structure, satisfying overall arc).
- Play through the invention many times at the keyboard, noting which passages feel awkward to play or hear. Revise accordingly. A good invention should feel inevitable in performance.
Sources and Further Reading
- Gauldin. A Practical Approach to 18th-Century Counterpoint. Waveland Press. Chapter 14: Writing Inventions.
- Kennan. Counterpoint. Prentice-Hall. Chapter on Compositions.
- IMSLP — All 15 Bach Two-Part Inventions with scores (imslp.org).
- Open Music Theory — Writing Counterpoint (openmusictheory.net, CC BY-SA 4.0).
- Bach, J.S. Two-Part Inventions BWV 772-786 — study the scores while listening to multiple recordings.