Bach's Die Kunst der Fuge (The Art of the Fugue) was an academic exercise. Are there other compositions out there that could be described as "academic exercises"?
Die Kunst der Fuge was, to an extent, a didactic work (as were Musikalisches Opfer and WTC 1 & II), but not an academic exercise - there's a difference. To Bach's work, you can certainly add Hindemith's Ludus Tonalis, Shostakovich's 24 Preludes and Fugues, Luigi Dallapiccola's Quaderno musicale di Annalibera and Sonatina canonica su Capricci di Niccolò Paganini, and any number of sets of preludes and/or études. (Chopin's set of Preludes was directly inspired by the 48.) To ttw's études by Chopin and Liszt, you can certainly add sets of études by composers like Scriabin, Szymanowski and Ligeti.
And then there are the 6 books of Bartók's Mikrokosmos...
...and the list goes on. All of these sets or pieces have, to a greater or lesser extent, express didactic purpose; none are academic exercises in the sense of the composer getting practice in certain kinds of writing, as all of these were written by composers at the height of their powers to demonstrate the expressive possibilities of the technical problems they were illustrating (even in a progression of piano exercises like Mikrokosmos).
Depends of course on what's considered an "academic exercise". In addition to the above, I would include Johannes Ockegem's Missa Prolationum, which is a fugue, but one in which two or three of the voices have the motive at different tempi. It's a staggeringly complex compositional problem to compose a motive that works out this way. A very academic, but also very beautiful, piece of music.
I might have to disagree with you that it was "solely an academic exercise," but here are some other possibilities:
- Bach's Musical Offering, where King Frederick II gave Bach a particularly nasty fugue subject and eventually asked him to improvise a six-voice fugue based upon it. In a huff, Bach went home, wrote it, and sent it back to him. The book Evening in the Palace of Reason is a terrific account of this whole sequence. (Speaking of books, Gödel, Escher, Bach mentions Die Kunst der Fuge.)
- Hindemith's Ludus Tonalis could be considered an "academic exercise" most clearly showing his own theory of music; it's sort of the 20th-century version of Bach's Well-Tempered Clavier. Note that the first and last pieces are exact retrograde inversionss of each other; the final piece is just the first piece played backwards and upside down.