J.S. Bach composed his 15 Three-Part Inventions (he actually called them Sinfonias) for keyboard at the same time as their 15 two-part counterparts. They first appear along with the Two-Part Inventions in the 1722 Clavier-Büchlein for Wilhelm Friedemann, Bach's then pre-teen son, and then reappear, slightly revised, in an 1723 volume which Bach prefaces with a detailed description of the 30 pieces' instructional purpose. An excerpt: "to play cleanly in two voices...[and] deal correctly with three obbligato voices...but, above all else, to acquire a true cantabile style of playing, and, with it, to get a good foretaste of the art of composition." And instructional these sinfonias are: many is the young piano student who, riding high and triumphant after conquering the Two-Part Inventions, has discovered by moving on to the Three-Part Sinfonias just how truly difficult is the task of mastering that true and beautiful "cantabile style" -- and, furthermore and fully in realization of Bach's purpose, as studies in counterpoint, miniature form, and efficient motivic invention they are without equal.
The Three-Part Sinfonias' value, however, like the value of the Two-Part Inventions, goes well beyond simple pedagogy; for, like the Art of the Fugue or the Well-Tempered Clavier, both of which are also superficially instructional in nature, the Sinfonia is as wonderful, beautiful and, frankly, difficult to the expert as it is to the student -- and there are not many exercise-books that can claim such.
The 15 sinfonias follow the same order of keys as the 15 inventions (an order similar in kind to that used in the Well-Tempered Clavier, though of course in the WTC there are more keys to explore). Fugal procedure is used very frequently throughout the sinfonias (the most striking case is No. 9 in F minor, a true triple fugue!), and even in the cases where the music unfolds in freer fashion, the opening gesture is invariably one of imitation between the top two voices. Bach chose to limit himself to two pages when composing the inventions and sinfonias so that the student would not need to turn pages, and so the pieces are all on the short side; but they are wealthy miniatures indeed.