Douglas Hofstadter, author of Gödel, Escher, Bach: An Eternal Golden Braid, in an article titled "Sounds Like Bach" on computer programed classical music:
In my lectures, I usually have a second musical interlude, this time involving mazurkas -- one by Chopin and one by EMI [Experiments in Musical Intelligence]. One time, when I gave this lecture at the world-famous Eastman School of Music in Rochester, New York, nearly all the composition and music-theory faculty was fooled by the EMI mazurka, taking it for genuine Chopin (and the genuine Chopin piece, by contrast, for a computer-manufactured ditty). An Eastman music student, Kala Pierson, wrote me an email about this event in which she said, 'I voted real-Chopin for the second piece, as did most of my friends. When you announced that the first was Chopin and the second was EMI, there was a collective gasp and an aftermath of what I can only describe as delighted horror. I've never seen so many theorists and their composers shocked out of their smug complacency in one fell swoop (myself included)! It was truly a thing of beauty.'
Much, much more here
Marvin Minsky, called the "father of AI", takes up the same topic but a little earlier than Hofstadter. His argument is more theoretical so he's making a slightly different point from Hofstadter: basically, that the formalistic models of classical music are incomplete but that does not mean we have to give up on the project:
Minsky: In a computation-based treatment of musical expression youwould expect to see attempts to describe and explain such sorts ofstructure. Yet the most "respectable" present-day analyses -- e.g., thewell-known Lerdahl & Jackendoff work on generative grammars fortonal music -- seem to me insufficiently concerned with suchrelationships. The so-called "generative" approach purports to describeall choices open to a speaker or composer -- but it also tries to abstractaway the actual procedure, the temporal evolution of the compositionalprocess. Consequently, it cannot even begin to describe the choicescomposers must actually face -- and we can understand that only bymaking models of the cognitive constraints that motivate an author orcomposer. I suspect that when we learn how to do that, manyregularities that today are regarded as grammatical will be seen asresults of how the composer's motivations interact with theknowledge-representation mechanisms shared by the composer and thelistener. In any case it seems to me that, both in music and language,one must understand the semantics of tension-producing elements -- atleast in the forms that resemble narrative. Each initial discord, be itmelodic, rhythmic, harmonic, or whatever, can be seen as a problem tobe later resolved. A lot of what a composer does is setting upexpectations, and then figuring out how to frustrate them. That givesthe composer some problems to solve. The problems and theirsolutions are then like elements of a plot, and composition becomes akind of story telling.Otto Laske: To look at composing as a variety of story-telling, and at music asa pseudo-story, wouldn't that help us to arrive at a theory of musicaldiscourse?
Just a few paragraphs down we come to what I find to be the most interesting aspect, the (partial) answer to the above:
OL: So, then, for you to apply AI to music, if one can say apply...MM: ... would be making composers, or at least listeners...OL: By "making," do you mean to produce a robot-like creature thatdoes certain things like, observably composing?MM: Yes, indeed. And in the case of listening it would have to knowwhen to say "oh, this is exciting," or "how very tender," and the like. Ihaven't seen much of that.OL: In Japan, one has built a robot that is capable of reading music,and play it on the piano.MM: Yes, that fellow at Mazda.OL: Is that something you have in mind here?MM: Not at all. Because I'm more concerned about what happens atlarger scales of phrase and plot. Our listening machine would have tounderstand the music well enough to recognize from each moment tothe next which problems have been solved, and which remain open.OL: How would that understanding have to become manifest?MM: Well, for example, an understanding listener can hear a pianoconcerto and appropriately say things like "that was a good idea here inthe cadenza, but he didn't carry it through." I'd want the robot to makesimilar analyses.OL: To do that, the robot must be able to recognize solutions, good orbad. But then how would it communicate this to others?MM: One way might be to have it write the sorts of sentences thatcritics write. Or to have work more in the musical realm by performingas a teacher does, explaining differences by demonstration -- "Look howmuch better it would be to delay a little these notes here, and makethose near the end more staccato, like this, and this." And of course ifour machine turned out to able to produce interesting enoughinterpretations, then we might be satisfied by that alone -- if manylisteners were to agree that "really, that performer has a lot of good ideasabout this music, and brings out stuff that I didn't realize was there."
Here is the lengthy conversation. All emphases my own. See about halfway down for the quoted passages. To defend him, he does consider the possibility of alternative logics (even mentioning Hegel), but "the idea is not carried through." :)
See this comment thread which took place on Joe Rebello's blog back in August where we have a spirited discussion of formalism(s) in economics which directly relates to Minsky's discussion of alternative formalisms in the article.