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 2-part contrapuntalpieces, and 15 sinfonias, which are 3-part contrapuntal pieces. They were originally written as musical exercises for his students. Bach titled the collection: The two groups of pieces are both arranged in order of ascending key, each group covering eight major and seven minor keys.