The Inventions and Sinfonias, BWV 772–801, also known as the Two- and Three-Part Inventions, are a collection of thirty short keyboard compositions by Johann Sebastian Bach (1685–1750): 15 inventions, which are two-part contrapuntal pieces, and 15 sinfonias, which are three-part contrapuntal pieces. They were originally written as musical exercises for his students.
Bach titled the collection:
Honest method, by which the amateurs of the keyboard – especially, however, those desirous of learning – are shown a clear way not only (1) to learn to play cleanly in two parts, but also, after further progress, (2) to handle three obligate parts correctly and well; and along with this not only to obtain good inventions (ideas) but to develop the same well; above all, however, to achieve a cantabile style in playing and at the same time acquire a strong foretaste of composition.
The two groups of pieces are both arranged in order of ascending key, each group covering eight major and seven minor keys.
The inventions were composed in Köthen; the sinfonias, on the other hand, were probably not finished until the beginning of the Leipzig period.