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 Praeambula and Fantasiae in the Klavierbüchlein für Wilhelm Friedemann Bach, a clavier-booklet for his eldest son, and later rewritten as musical exercises for his students.

Bach titled the collection:

Forthright instruction, wherewith lovers of the clavier, especially those desirous of learning, are shown in a clear way not only 1) to learn to play two voices clearly, but also after further progress 2) to deal correctly and well with three obbligato parts, moreover at the same time to obtain not only good ideas, but also to carry them out well, but most of all to achieve a cantabile style of playing, and thereby to acquire a strong foretaste of composition.^[1]

This section includes inline links to audio files. If you have trouble playing the files, see Wikipedia Media help.

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.^{[original research?]} The autograph fair copy is dated 1723.^[2]

Key	Invention		Sinfonia
C major		No. 1, BWV 772		No. 1, BWV 787
C minor		No. 2, BWV 773		No. 2, BWV 788
D major		No. 3, BWV 774		No. 3, BWV 789
D minor		No. 4, BWV 775		No. 4, BWV 790
E♭ major		No. 5, BWV 776		No. 5, BWV 791
E major		No. 6, BWV 777		No. 6, BWV 792
E minor		No. 7, BWV 778		No. 7, BWV 793
F major		No. 8, BWV 779		No. 8, BWV 794
F minor		No. 9, BWV 780		No. 9, BWV 795
G major		No. 10, BWV 781		No. 10, BWV 796
G minor		No. 11, BWV 782		No. 11, BWV 797
A major		No. 12, BWV 783		No. 12, BWV 798
A minor		No. 13, BWV 784		No. 13, BWV 799
B♭ major		No. 14, BWV 785		No. 14, BWV 800
B minor		No. 15, BWV 786		No. 15, BWV 801
	These (Inventions) are MIDI representations of Bach's music, and do not convey how a human pianist would perform them.		All Sinfonia performances above were played by Randolph Hokanson. Sinfonia No. 8 A version of Sinfonia No. 8 (BWV 794) for clarinet, oboe and cello Sinfonia No. 15 and another version of Sinfonia No. 15 (BWV 801).

Wikimedia Commons has media related to Inventions and Sinfonias.

• Inventions, Sinfonias: Scores at the International Music Score Library Project
• Bach's Inventions and Sinfonias, Mutopia Project
• Yo Tomita (1999). "The Inventions and Sinfonias – History and analysis of Bach's inventions". Archived from the original on 2012-01-20.
• Graphical motif extraction of the Inventions and Sinfonias Archived 2012-03-03 at the Wayback Machine