Piano midi files are MECHANICAL!
 
"Humanize" doesn't address the real problem: notes being played/sounded EXACTLY at the same time.... no pianist plays that way!
 
How about a CAL script that breaks up every occurrence of a "chord", that is, prevents notes from sounding simultaneously: pushes all events away from each other by a few ticks, perhaps with the treble being pushed a few ticks to the right (delayed), in general, relative to the bass???
 
Is there a CAL script that does this?  Randtime.cal?   Any way to make randtime move the HIGHEST notes the farthest right?
 
IF not, what's the reigning CAL editor?
 
JG

I'm not sure I understand your complaint. MIDI can record exactly what a keyboard player plays down to very tiny nuances including after-touch. 
 
If your complaining about some file you downloaded and it is badly played, then guess what, it was badly played, Turd polish won't fix a bad performance. 
Often those download files are not even played by real musicians, They were drawn manually or worse yet, created with Band in a Box. 
It's amazing how badly done the majority of midi floating around the internet is. 
 
The good stuff is out there but with a price. 
 
If your complaining about your own piano parts then don't quantize them. Just edit out the real clunkers. 

Thanks, Johnny. I have composed several answers to this, but they didn't come across quite right, so I didn't post them. You said it nicely.

Ha Ha Bob thanks for the encouragement.. , I had to edit mine a few times  as one has to be careful how we put certain things to avoid saying things that might be taken the wrong way. 
 
I download a lot of files myself as a bit of a hobby. Being someone who used to spend a whole day or two just to create my own MIDI backing tracks I now will look first before I embark on my own creations.  I am amazed by the plethora of material now within a few clicks. But only 1 in 20 are even close to what would call a usable track. Mostly I'm looking for a good drum track, The rest is rarely used by me, I play real bass and sure as heck don't want those sad attempts at guitar parts in my band. 

I'll just add that I think the importance of note start timing to the realism/naturalness of a piano performance is over-rated. In my experience as a piano/keyboard player, note duration, velocity, and sustain/sostenuto usage are far more important to the sound and feel of a MIDI track than whether chords are rolled or triplets have the perfect amount of swing. I think start timing gets an inordinate amount of attention because its the easiest thing to see and edit, but the payoff is minimal. Conversely, editing in a natural articulation of duration and velocity might be more rewarding, but is much more difficult, if not impossible, to do.
 
As with acoustic instruments (and non-MIDI electric ones), when it comes to MIDI, there's no substitute for capturing the live performance of a human playing a keyboard or other MIDI controller in real time and responding to the dynamic and timbral characteristics of the particular patch being played at the moment.

What MIDI files are you talking about? Something that came with your particular keyboard?
Not being 100% sure of where the snake sleeps, I just mention Snap To Grid. Have you got it on, or maybe  Input Quantize as well? They are the tools to make your recordings mechanical.
 
There are no humanize functions (IMO) that really understand the content of the music. That's why they practically never produce convincing results.

Sorry: I overstated my issue: of course most midi files are crap (meaning quantized, or step-inputted etc., etc.).
 
What I was curious about is whether any advances had been made over the years in modeling human touch, beyond "HUMANIZE," et. al., which are crude and pretty much useless.
 
"There are no humanize functions (IMO) that really understand the content of the music."   If this is true, it answers my question in a general way.
 
But the "randtime.cal", in theory at least, is an exception.   A literally "solid" or "unbroken" chord at the piano is never heard in performance, and probably never intended.  In fact, midi files of live performances show that the leading note, usually at the top of the chord,  is ususally sounded AFTER the other notes of the chord.   In Chopin the phenomenon is almost a necessity.   Ergo: how about a CAL script that takes RANDTIME and adds a provision that allows the user to specify which note will sound LAST or FIRST in the random sequence?   
 

But your still taking about having a computer make up for a poorly played part. That's is what I think we are all saying. How on earth can a machine worth $500-$1,000 have creative AI. 
I don't think NASA has come close yet. 
 
A quick Google search of the topic AI : 
 
Computers can already solve problems in limited realms. The basic idea of AI problem-solving is very simple, though its execution is complicated. First, the AI robot or computer gathers facts about a situation through sensors or human input. The computer compares this information to stored data and decides what the information signifies. The computer runs through various possible actions and predicts which action will be most successful based on the collected information. Of course, the computer can only solve problems it's programmed to solve -- it doesn't have any generalized analytical ability. Chess computers are one example of this sort of machine, computers are not creative. 

I imagine a fairly convincing humanizing algorithm could be written for specific genres by a genius programmer with lots of input from musicians and analysis of live MIDI recordings from them... but it's easier to learn to play the piano half-way competently and edit out your mistakes. 
 
As I implied before, just having a CAL script roll the chords for you is not going to significantly improve things by itself.

Agreed 1) a computer can't "create," via programming alone, what most folks would judge, or perceive as, a "musical" result; 2)  a cal script for chords isn't going to turn a mechanical (as in "quantified") midi file into something musically better. 
 
I have a very different situation on my hands, and this wasn't (in fact) the purpose/intent of my question.
 
There are some limiting cases, though, where fairly crude midi files (meaning simple transcriptions from the original notation, with relatively few changes to vel and tempo) will "fool" the uninitiated listener: some baroque organ music and harpsichord music rendered on sampled organs and harpsichords and smaller claviers.   That's because those instruments have (depending on the particular instrument being sampled) quite limited tonal and velocity variables.   You can strike an organ key as hard as you want, but you'll only get the sound that the stop makes.  Timing is everything, though.
 
JG