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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"?

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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.

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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.
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    Ludus Tonalis has the added interest point of having been illustrated by Hindemith himself directly on the printed score, assigning specific drawing motifs to the musical motifs (image examples here). So if we look at it from the perspective of a composition an exercise, we have visual clues to the musical approach. – José David Aug 7 '16 at 0:57
  • Interesting! I've seen these images, but I had no idea they were from Hindemith himself. Thanks for that! – Richard Aug 7 '16 at 0:58
  • On the same vein of Ludus Tonalis and also inspired by Bach's Well Tempered Klavier, there's also Shostakovitch's 20 Preludes and Fugues – José David Aug 7 '16 at 0:59
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    The Praeludium and Postludium of Ludus Tonalis are exact retrograde inversions of each other. – user16935 Aug 9 '16 at 8:37
  • My pleasure. Hindemith is a good call, though. Ludus Tonalis has everything: stretto fugue, binary fugue with the 2nd half inverting the first, a fugue using the inversion, retrograde and retrograde inversion of the subject, canon fugue, double fugue... Hindemith's facility with counterpoint was at least as great as Bach's. – user16935 Aug 9 '16 at 12:23
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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).

  • I guess it depends on what constitutes an "academic exercise". I doubt that there is a hard and fast definition thereof. – Scott Wallace Aug 9 '16 at 13:24
  • @ScottWallace, I kind of doubt it as well, which is the problem with this sort of question: we end up dealing with the OP's presuppositions. I thus tend to set the term as self-practice within a set of academic rules, so as to create a contrast with didactic work: the latter can comprise other goals and values, and break out of the mould; the point of the former is remain within the "rules". Even Kunst der Fuge, which deliberately calls to mind the generation of Cipriano de Rore, goes well beyond that generation's standard practice. – user16935 Aug 9 '16 at 13:55
  • Good information, regardless of definitions. Fwiw for me "academic" means made with the express (not necessarily exclusive) intention of demonstrating a theory. In that regard the tonal harmony focused works seem to fit quite well. I guess some didactic works too, if they thoroughly cover some theoretical base. It seems to me that works like Chopin's Preludes are more the exploration of an aesthetical concept, and so don't fit the definition too well (otherwise any artistic body of work with some degree of consistency would be "academical"). Anyway that's obviously just my opinion. – José David Aug 9 '16 at 14:49
  • @joseem, perhaps - that certainly covers Hindemith - but what theories do Bach's works purport to demonstrate? Rameau was the guy with the theories. :D – user16935 Aug 9 '16 at 15:11
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    @joseem, WTC championed re-entrant temperament, to be sure, but most of the pieces were written for other occasions and purposes (and we're not entirely sure which temperament he espoused). That takes care of WTC I & II, but neither Kunst der Fuge nor Musikalisches Opfer expose all the keys. – user16935 Aug 9 '16 at 16:20
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We could add Chopin's Etudes although these are not primarily contrapuntal. Likewise, Liszt's Transcendental Etudes.

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