What are the best loudspeakers under $4000 to re-create lifelike piano

Aside from system requirements, I find that a lot of recordings of piano to be unconvincing. Two "tells" for me- (the loss of) the harmonic overtones and their decay, and the gravitas of the deeper bass registers. There is also the issue of perspective in size and placement relative to other instruments, particularly if a large orchestra is involved. (Jazz combo recordings are easier because there are fewer instruments and they are less "dense"). Sometimes, the piano is mic’d so that it is disproportionate in scale and placement relative to other instruments. One record that I find pretty convincing (though it may not be your cup of... musically) is: https://www.discogs.com/Amina-Claudine-Myers-Salutes-Bessie-Smith/release/7460514 (The original on Leo, not the audiophile reissue).
This record sounds close to a real piano in my room, using Avantgarde Duos supplemented by a pair of 15" subwoofers.
I have had concert sized pianos in my homes over the years and know the sound of a "real" piano, both from the driver’s seat and from an audience perspective. The difficulty is generally ascribed to the range of the instrument, but I think it’s more than that- timing, harmonics, power to deliver bass energy and, in my estimation, difficulty in finding convincing sounding recordings.

@bdp24 - I’d settle for being 1/2 right 1/2 the time, but thank you.
There was a pretty serious piano restoration house near me when I lived in Westchester, NY- they had a warehouse full of big old grand pianos, some virtually shells, others complete but in need of work. Two otherwise "identical" pianos from the same manufacturer that were set up in the same room could sound vastly different from one another, depending on how the piano was voiced, the materials used for the hammers, action, etc. I’m hardly a guru on that stuff, but I know when I was struggling to maintain an ancient Bosendorfer, the piano swami would spend hours tweaking it- it was like a voice from heaven for a week, maybe two, and then began to slide into disc(h)ord.
I kind of miss having a big piano here. Gotta find a solution to that, though I don’t play very much any more. (Have a Nord, which is a decent electronic keyboard but it ain’t even close- even the Rhodes sound isn’t really very convincing (though I suppose there are downloads or tweaks one can do, I dunno).
I used to steal away when I was a youngster to play the grand piano in the large school auditorium when it wasn’t in use-- it was fabulous to play in a big empty hall as a kid, and I never had to worry about the audience. :)

@martykl - not sure if you were referring to my earlier post about the Nord not sounding like a real piano (or a Rhodes for that matter). Just to be clear if you were referring to my post, I wasn't talking about the recording process, digital v analog, but the instrument itself. Yet, at least live, I've heard some electronic keyboards that do a pretty impressive job of emulating an acoustic piano. 
On the history of pianos, those old "reproducing pianos" (which were more sophisticated than a plain 'ole player piano) could let you hear Gershwin playing his compositions. Crazy. Apparently, some (or all?) have been ported over to the Disclavier. 

@shadorne - thanks for all of that. My Nord is older- probably 8 or 9 years? I had a Motion Sound? amp- not sure it is still in production. Now that I'm in Austin, it's on my list to have the amp repaired or replaced and update the Nord. I actually did like the B-3 emulator, which is mainly why I bought it at the time, but I don't play professionally, so my dabbling in electronic keyboards isn't that deep. I did play some Yamaha electric pianos at one point that had good feel and sounded pretty good. 

@snapsc- I would venture that if a system produces piano convincingly it ought to do most everything else well, given not only the range of the instrument, but the other demands placed on its reproduction-- dynamics, power, timing, harmonics, etc. 
When I listen for evaluation purposes (as opposed to enjoyment), I try to use a range of different material, almost none of which is "audiophile"-- I don't mean that in a pejorative way, just that I don't want records that are known sonic spectaculars to find the weak points- i want to hear what a system can do "on average" since much of what I listen to was never released in audiophile quality issues though some recordings are still pretty killer. (and some aren't).