Consider the third of Bartók's Romanian Folk Dances, a little set of six he pieces he wrote for piano.
Against a simple left hand drone, the right hand plays an exotic little melody which you can hear here (played by Bartók!) at the 1:23 mark:
However, the radio performance I heard left me kind of cold because the version I really know and love is the violin/piano arrangement made by Zoltan Szekely - I've accompanied this version many times, including with my favorite home-grown violinist. Szekely has the violinist use artificial harmonics, presumably to imitate the glassy, pure sound of the piccolo or flute or pipe or whatever - but, of course, it doesn't really sound convincingly like any of those. What it sounds like (at 1:45) is eerie and haunting and odd and frail....and beautiful:
So, this pale imitation of a flute is by far my favorite way to hear this dance, even though the arrangement is just an imitation of the composer's orchestration. Imitation yields something new. Of course, personal bias plays a role, given that I've heard it most often this way, but I still think there's an argument that this is the most compelling version, and that's significantly because of its failings. It's a violin trying to sound like an orchestral flutist who presumably is trying to sound like a Romanian shepherd, and so it's a violin doing things the violin wasn't really even designed to do, using the artificial harmonics to take much of the body out of the sound and leave behind that ghostly trail.
Actually, I could easily imagine myself having made an argument on behalf of the piano version if that had been the one I'd known best, and though it's not my favorite here (the piano strikes me as too neutral), the truth is that, like most pianists, I have a very deep affection for all the ways in which the sound of a piano is weak and unevenly balanced and compromisingly tuned and poorly sustained. For all the great innovations that made the modern piano sound what it is, it is still a sonority sustained by smoke and mirrors, and we love it for its frailness, its vulnerability, its Walter Mitty-like attempts to imitate flutes and violins, horns and voices. We strive to make it sing with beautiful legato, but we don't really want it to do that perfectly. In fact, the bell-like tones of a Rhodes-style electric piano are the last thing most pianists want to hear when striking the keys to sing a Chopin nocturne. Modern synthesizer technology can fix a lot of the problems I've outlined, and many musical styles have taken advantage of that - but a "piano" can't be imitated; only the real thing fails in such a perfect way.
A favorite example is the piano opening of Strauss's incomparably perfect Morgen:
For some misguided reason (probably a singer who couldn't stand having to follow that perfect piano intro), Strauss decided to orchestrate this and give the halting, suspended piano melody to a sugary sweet violin and....well, here you go:
Sure, it's pretty, and if I didn't know the piano version, I might even love it, but...no. Pretty much every tune Chopin wrote falls into this category - tunes inspired by bel canto opera, but which sound most inspired when hammered on string.
There are many other ways to explore this question of imitation as improvement. I haven't yet played organ long enough to fall in love with all the bizarre organ stops that are supposedly trying to sound like flutes, and reeds, and trumpets, and violas, but apparently one can develop an actual affection for all of those imitations. I also was recently engaged in a Facebook discussion about computers composing music (inspired by this article), and when one commenter suggested that imitation can never replace inspiration, I openly wondered if inspiration might not sometimes result from mere imitation. Bach certainly got a lot of mileage out of copying Vivaldi. Or, to go in a different direction, one might note that, when going to see Shakespeare, we much prefer to see an imitation of someone being stabbed than the real thing.
But I'll leave those paths untaken and close with another bit of violin rep that's been on my mind. Daughter of MMmusing is now learning Ravel's great Tzigane, and we read it together for the first time last night. Here we have perhaps the most polished musical craftsman of all time creating a sort of imitation of a gypsy jam session (with the original piano part written for a piano that had an attachment designed to imitate the cimbalon!) - except, it's got some pretty meticulous stuff in there, and it's not really an invitation for the performers to unleash themselves with total abandon, at least not unless total abandon includes playing the tricky notes Ravel took the trouble to write down. Oh sure, there's still plenty of room for interpretive abandon, but as I've said about The Rite of Spring so many times, it's an imitation of the exotic/primitive that requires a very disciplined, high-culture brand of performance. That tension is at the heart of why music (and art) can be so compelling.
This isn't the place to argue whether such exotica is always better than the thing it's imitating (I heard one of the Liszt orchestral Hungarian Rhapsodies the other day and it kind of made me cringe), but I do think there's something extraordinarily satisfying about Ravel's fun-house imitation of the gypsy fiddler, even if it sounds no more like an authentic gypsy than Bartók/Szekely's violin sounds like a flute. The point is that the failure to imitate accurately may be the inspiration for something incomparably great.
UPDATE FROM YEARS LATER (11/12/14): I should have mentioned here that Jeremy Denk once complained that Tzigane is, in fact, too "clean":
Just the other day I was playing through Tzigane with Josh, in a rehearsal, and it was all a great deal of fun, and Josh sounded fabulous of course, and I was annoyed that I didn’t sound so fabulous in that annoying passage with the repeated notes … but I was thinking “it’s good, but it’s no Charles Ives.” Even the “dirty” gypsy notes in that piece sound clean, organized, shiny; everything is polished, glittering, sparkling, lush, perfectly voiced: sanitized? It smelt of PineSol, if PineSol were French. But not with Ives; he captures the Down & Dirty better than almost anyone. If he errs, he errs on the Dirty side; but his dirt is not vulgar, it is transcendental fertile earth with lots of terrific spiritual manure. Perhaps the hyper-cleanliness of Ravel is somewhat vulgar, in comparison with the honest, sprawling dirtiness of Ives? … at least that’s the way I feel. Bring on the hate mail!