academic maybe, but it is one of the finest compositions of all time.

Monteverdi's famous Vespers of the BVM is thought to have been composed as a sort of resume project, hence the variety of genres, textures, and compositional techniques empolyed.

Rather than "academic exercises" I would propose the term "didactic" —that is, pieces written to demonstrate (or 'teach') particular elements of composition; certainly all the above mentioned works rise above the mere "academic exercise." (The phrase makes me think of music school, where we dutifully harmonized chorale melodies, and did our species counterpoint exercises etc... We were certainly not composing masterworks!)

Bach's Orgelbuchlein was written fairly early in hs career (mostly at Weimar) and so he may not yet have had his sons in mind. The title page reads (in translation):

Little Organ Book
In which a beginning organist receives given instruction as to performing a chorale in a multitude of ways while achieving mastery in the study of the pedal, since in the chorales contained herein the pedal is treated entirely obbligato.

In honour of our Lord alone
That my fellow man his skill may hone.

I love that!

I would also add Hindemith's Ludas Tonalis to the list, and Bartok's volumes of "Mikrokosmos."

Frescobaldi's Fiori Musicali (esp. the toccata [?] with the sung part!) would fall into this category, I think.

There are those who are wont to consign the admirably didactic, the gorgeous academic exercise, the exemplars of astonishing musical craftsmanship and aesthetic worth to what are, to their pitifully clouded minds, categories of 'art music', ivory towered elitism, appeal to but a select few, and so on.

'Art music' is, perhaps, the most ubiquitous current signifer for what certain chic types like to clobber as having no value except as 'art', meaning, of course, that, as 'art', it is of no value to those people who are considered by them to be 'real' people (as opposed to you and me, who, presumably, are not 'real'). They are astonishingly callous, indeed, it would seem, utterly senseless, to the real value of 'the artful' in the lives of the very people whom they think have no use for it. Theirs is the world of leaden utilitarianism, intellectual vacuity, and the rape of the emotions. The spirit in which these denizens refer to 'art music' (or, even worse, 'western art music') is not a complimentary one. It is fundamentally pejorative. Avoid the term, and give no quarter to those who like, with a certain silly air of authority, to bandy it about.

All music of any worth is 'artful', is 'art', is didactic, is an academic exercise. That which isn't is that which is, actually, worthless to the human person and his and her spiritual, mental, and emotional development and maturity. If it does not achieve that artfulness which is the mark of fine and deliberate craftsmanship, it is void of value to the human soul and poison to its intellect. If it does not teach (didactic), it, then, has nothing to say and is pointless utterly.

Most of the examples given in the comments above reveal astute judgment. I especially like the mention of the Fiori Musicali, the mentioned works of Tallis, and such. One might add the Couperin masses, and much of de Grigny's work. These are the flower of a French baroque tradition which had really sunk to academic lows. (One might even go so far as to suggest that Couperin's Messe pour les paroisses is the French Clavier-Ubung III - or, vice versa.) Mention should be made of the incredibly luscious contrapuntal skill revealed in Titelouze's hymns. Oh, and allow me to nominate certain examples of the pre-XVIIIth century English voluntary and fantasia (pronounced 'fan-ta-see-ah'), of which 'fancy' is an abbreviation, admirable in their contrapuntal intricacies.There is really no end. The compelling thing, of course, about Bach's Kunst, is that it may be the last of that genre of 'academic exercises', a genre with roots back into the late mediaeval era, which consciously set out exhaustively to treat of specific musical challenges. But then, Beethoven's Diabelli falls most surely into this category.

Whatever our choices may be, it is a certainty that music is not really music unless it is an 'academic exercise', unless it teaches, unless it rises to genuine artistry and aesthetic worth, unless it is, in a word, kunstlichen. All these should be requirements for any music that is offered to the Lord in his worship, on behalf of his wonderfully chosen people, who should expect to be aedified by what they hear in his very own house. And, let it be stressed that the music at liturgy is, like incense and other 'works of human hands', an offering to God of a thing of great worth (that 'treasure', in the recent council's words, 'greater than any other') which he has bestowed upon us.

Never 'sell' people short! Just yesterday I played for an opening voluntary at St Basil's Chapel, UST, the long, three-sectioned, G-Major canzona by Buxtehude. The silence was pregnant with the weighty air of appreciativeness. And, I played the middle section on nothing more than one quiet eight-foot flute. The acoustic is quite live, and one heard naught but the intense stillness of attentive awe and respect. This was an exercise in a genuinely didactic musical form and spiritual apprehension - one might say 'a spiritual music lesson', such as puts the music in its proper place of being a close, very close, cousin of the didactic mass lectionary. Indeed, all of us know how that Bach's music is often said to be the 'fifth gospel'. The same may be said of all music that is of academic (and, therefore, human) worth, for it most assuredly is a gift of God for the spiritual formation of the human being.

Then (and this will certainly be controversial), there are those musics which each of us have little regard for and wonder why the composer bothered to write. In this category, for me (and I can hear already the howls of dissent) would be the likes of Sheherezade or Bolero. (I wonder, too, at the master Messiaen's love affair with the likes of the onde Martinot!)

@M. Jackson Osborn: a beautifully articulated response, as always! I believe Ravel regretted writing Bolero...The piece is cursed I swear. Every performance I'm sadly forced to play of it has some kind of disastrous meltdown about halfway through-usually the trombone or bassoon solos. The last one was just this past spring, and the trombone entrance was so bad my eyes were burning from trying to hold back laughter.

I would vote for Ockeghem's Missa Prolationum and his Missa Cuiusvis Toni.

An obscure source once told me that di Lassus's Bicinia was used as a pedagogical tool for his voice students.

The last one was just this past spring, and the trombone entrance was so bad my eyes were burning from trying to hold back laughter.

It takes a trombone player to appreciate how hard that solo is to play. After a gazillion measures rest you have to come in on a high Bb in one of the most exposed passages in all the literature. It takes a very accomplished trombonist to be able to pull that off consistently (although I suppose having to sit through the first three movements of Beethoven's Fifth and then come in on a high C would be worse, but that entrance is not nearly as exposed and Beethoven had an alto trombone in mind when he wrote it). There's a reason it (Bolero solo) is often included in audition repertoire. Any ensemble with a less than professional caliber trombonist programs that piece at their peril!

I find performances of that solo more satisfying (if Bolero can ever be satisfying) when the trombone soloist leaves out the glissandi and just plays legato. It seems as if French composers of that period had to prove they knew what a trombone was by writing in glissandi where they made no musical sense, just to prove they knew which glissandi were possible and which were not. (I have heard that Ravel wrote this as an orchestration exercise, so from that point of view, it might make sense to write the glissandi in, but I would prefer they be left out in performance.)

As an aside, related to Liam's comment about Tuckwell, I wonder if the abilities of (especially young) musicians, and even audience members, to deal with errors appropriately in live performance have diminished in the age of recordings?

@Torculus and Liam: The trombonists in that particular orchestra are of the kind who show up loaded to rehearsals (if they show up at all), and the bassoonist is in his 80s now. Fun.Times. :-D

...hand copying...

I have done this a few times. It is an incredibly time consuming, but a wondrously intense and astonishingly fruitful way of learning a piece, be it an organ, choral, piano, or any kind of work. There is no practice method or study regimen by which the mind absorbs the content and method of a composition as organically as it does with such copying.. I have even had students hand copy passages that gave them particular trouble, and was gifted with praiseworthy results. When doing this one actually becomes a vicarious composer of the very music that he is copying.

This is what 'they' did before they had affordable printing sources, copiers, and fingertip computers - all of which have resulted in relatively lazy minds which learn relatively less of substance.

Salieri, my experience hears that the newer generations of brass players have raised the bar. Experience also shows that there are still the same number of musicians at the highest level. The next tier down musician group is just larger.