Two-part invention (Bach)

What it is

The Two-Part Inventions BWV 772–786 are 15 short keyboard pieces that J. S. Bach wrote for the education of his son Wilhelm Friedemann (first versions in the Clavier-Büchlein of 1720) and collected in a fair copy in 1723 together with the 15 three-part Sinfonias. In the preface Bach says they serve to learn to play cleanly in two and three parts, but above all to have good ideas ("inventiones") and develop them, and to acquire a singing style of playing. "Invention" in rhetorical language means finding the idea: the whole piece is the development of a single motif.

The 15 keys

C major, C minor, D major, D minor, Eb major, E major, E minor, F major, F minor, G major, G minor, A major, A minor, Bb major, B minor: in ascending order, skipping the keys with too many accidentals for the temperament and for a beginner.

The typical structure (Invention No. 1 in C major, BWV 772)

1. Exposition (mm. 1–2): the sixteenth-note motif (C–D–E–F–D–E–C, then a leap) enters in the right hand; the left imitates it an octave lower after half a bar, while the right repeats the motif on the dominant (G). In the second bar the roles alternate.
2. Development toward the dominant (mm. 3–6): the motif appears in inversion (contrary motion) and in a descending sequence; the cadence in G major arrives in m. 7.
3. Second section (mm. 7–14): the hands swap roles (invertible counterpoint), the motif is developed in G and leads to a cadence in A minor (the relative minor) in m. 15.
4. Third section (mm. 15–22): sequences that bring back the tonic, final cadence in C major.

The tonal path I → V → vi → I is the same as in many Baroque arias and concerto movements.

The techniques you learn

• Imitation at the octave or the fifth between the hands.
• Inversion (the motif turned upside down), rhythmic augmentation and diminution.
• Sequence: the cell repeated on different scale degrees, often by descending fifths.
• Invertible counterpoint: what the right hand plays returns in the left.
• Complementary rhythm: when one hand moves in sixteenth notes the other holds eighth notes or long notes.
• Intermediate cadences that articulate the piece into sections.

Other inventions to study

• No. 4 in D minor BWV 775: 3/8, scalar and arpeggiated motif, long sequences.
• No. 8 in F major BWV 779: close canon at the octave one bar apart, ascending arpeggio.
• No. 13 in A minor BWV 784: broken arpeggios that outline the harmony, very close to the style of the Alberti bass before the fact.

Analyzing them step by step

1. Isolate the motif (often half a bar or a bar) and write it out separately.
2. Mark its appearances with different colors: original, inversion, fragment, sequence.
3. Find the cadences and the keys they reach: they divide the piece into sections.
4. Annotate the functions (I, V, vi…) at least once per bar.
5. Observe when the hands swap material.

Exercise for a producer

Write a quick 12-bar invention in C major:

• mm. 1–2 motif of 8 sixteenth notes in the right hand, imitation in the left half a bar later;
• mm. 3–6 sequence of the motif and inversion, cadence in G in m. 6;
• mm. 7–10 hand swap, cadence in A minor;
• mm. 11–12 return to C.

Play it with a harpsichord or an electric piano (Wurli V or Stage-73 V) and then re-orchestrate it for a synth pluck + bass: the idea of "one motif that generates everything" is the same as in a good techno riff or a synthwave arpeggio.

Related topics

Motif and motivic development, Canon and imitation, Invertible counterpoint at the octave, Harmonic sequences, Fugue.