For keyboards which start with C, the first 12 notes are C, C sharp (or D flat), D, D sharp (or E flat), E, F, F sharp or (or G flat), G, G sharp (or A flat)  A, A sharp (or B flat) and B.
I have RSI problems and have tried 30 different computer keyboards which all caused me pain.
This question exists because it has historical significance, but it is not considered a good, on-topic question for this site, so please do not use it as evidence that you can ask similar questions here. Questions on Stack Overflow are expected to relate to programming within the scope defined by the community. I haven't done any MIDI programming in years, but your fundamental idea is very sound (no pun).
MIDI is a stream of "events" (or "messages"), two of the most fundamental being "note on" and "note off" which carry with them the note number (0 = C five octaves below middle C, through 127 = G five octaves above the G above middle C, in semi-tones).
Between velocity, chording, and the pedals, I'd think you could come up with quite a good "typing" interface for the piano keyboard.
To be most broadly-compatible with software, you'd have to write this as a keyboard device driver. However, since you're just generating keystrokes (not trying to intercept them, which I was trying to do years ago), you may be able to use whatever features the operating system has for sending artificial keystrokes.
In machine stenography, the stenographer writes by pressing multiple keys on the stenotype machine at the same time, then releasing them all. Note that A starts multiple entries, and also note that how you translate a C stroke depends on whether you've previously seen an A, a B, or you're starting fresh.
Also note that (although not shown in the very small sample above), there may be multiple ways to "play" the same word or phrase, rather than just one. When translating steno into standard text, again we use a "longest-prefix match" search: The translation algorithm starts with the first stroke ever written, and looks for entries starting with that stroke. Note that you could jam all the chords in a linear array and do traversal every time you receive a midi event, and still not experience any noticable slowdown. It sounds to me like you're looking less for advice on how to build this yourself and more asking what resources are already out there to accomplish what you want. On piano and when you're a good player, you can have 10 fingers on the keyboard and if the matrix is usable you can be much more quickly that any computer keyboard user I think. I studied piano performance in college and then got into interaction design, programming, and using Vim, so I have actually spent a lot of time prototyping things like this.
You can get this working pretty quick in Linux by using the graphical programming language for multimedia artists, "Pure Data," along with the x11key external by Alex Andre. When I got it working, I never stuck with it, because I couldn't stop tooling with the layout.
AutoHotKey is a free open source utility for Windows that allows you to remap keys and buttons on your devices to macros.
However, I was able to find an implementation supporting the specific mapping you are looking for.

Basically, it looks like AutoHotKey, along with this user's custom patch, will provide exactly what you need to create a mapping from a MIDI keyboard to a QWERTY keyboard's input signal.
Some of the other answers have given you much more extensive information on MIDI and MIDI programming, in general, but as your post states that doesn't seem to be quite what you are looking for. All you do is keep on repeating this group of 12 notes until there are no more keys to label. The blacks keys in order are C sharp (or D flat) E flat (or D sharp) F sharp (or G flat), A flat (or G sharp) and B flat (or A sharp. The order of notes for a keyboard diagram starting with F is F, F sharp (or G flat), G, G sharp (or A flat), A, A sharp (or B flat), B, C, C sharp (or D flat), D, D sharp (or E flat) and E. The 5 black keys from lowest to highest are C sharp (or D flat), E flat (or D sharp), F sharp (or G flat), A flat (or G sharp) and B flat (or A sharp). These events carry a "velocity" number on keyboards that are velocity sensitive ("touch sensitive"), with a force of (you guessed it) between 0 and 127. This is a plug-in to the operating system that serves as a source for keyboard events, talking to the underlying hardware (in your case, the piano keyboard). Windows has an interface for doing that (probably several, the one I'm thinking of is SendInput but I know there's some "journal" interface that does something similar), and I'm sure other operating systems do as well. Stenographers do that to make it easier to flow from a preceding word to the next depending on hand position. If there is only one entry, and it's one stroke long, then we can reliably say "that's the entry to use", output the corresponding text, and then start fresh with the next stroke. There was nothing remotely premature about using an optimizing strategy, we were dealing with 12 MHz 386s. Also I am able to support mobile devices and Webservice for community work or work wireless on devices.
MIDI technology is fairly straight-forward once you grasp it, but it can be confusing at the outset. The author was looking for a program that could detect MIDI IN input and translate that to keypresses.
I would like to help you more if possible, but it would be easier if you could be more specific about the type of information you are looking for.
What you need to do is to recognize that there are two black keys then a gap with no black key, then 3 black keys, a gap with no black key, then 2 black  keys, and the pattern keeps repeating over and over. The black key to the immediate left of a white key is flat (?) while the one to the right is sharp ( ?).
As with machine stenography, you'd need a "dictionary" of the meanings of chords and sequences of chords.
Edit: Apparently, the Java Sound API supports MIDI, including receiving events from MIDI controllers. There's an obvious analogy to music there, and you could use that to make your typing flow more akin to playing music, in order to both prevent this from negatively affecting your piano playing and to maximize the likelihood of this actually helping with the RSI.

You probably want to disallow them in your project, and in fact when steno used to be translated manually by the stenographer, conflicts were fine because they'd know just by where in the sentence they were what the right choice was, but with the rise of machine translation, conflict-free theories of steno arose specifically to avoid having to go through the resulting translated text and "fix" conflicts.
In I___'s case, if he goes with the Arduino idea (which is a really cool idea), he too will be dealing with fairly underpowered hardware for the modern era, though of course stuff ridiculously faster than what we had. It looks like the largest pre-designed boards have 256k of Flash (of which 8k is used by the bootloader).
It initially appears to be more geared towards AutoHotkey-type usage, but on further looking I think it could do what you want nicely. Not exactly a "ready out of the box" solution, but if you are comfortable with basic device configuration, it shouldn't be too bad. Please see my public profile for contact and write with high priority in case of spam emails.
One of the resources that has been tremendously helpful for me in understanding the foundations for MIDI (which are certainly necessary if you want to program MIDI interactions), is a book called MIDI for the Technophobe. For instance the black key to the left of D is D flat, while that same key, since it’s to the right of C can be called C sharp as well. I would like to know if there is a way to capture MIDI from a MIDI keyboard and output keyboard strokes. Like syllables, sometimes one stroke (chord) has meaning all on its own, other times it only has meaning combined with following strokes.
So we look at the next stroke and see if there are entries that start with those two strokes in order; and so on until we get a match. I believe Patrice Colet made a windows external for Pure Data that worked as well, but I can't seem to locate it anymore. The black key to the left of B is B flat, while that same black key, since it’s to the right of A, is A sharp as well. I know nothing at all about MIDI but I would like some guidance on how to convert this signal into a keystroke. When you go higher, the tone becomes sharp, while when you go lower, the tone becomes flat. Although they'll be heavily influenced by the school at which they studied, each stenographer will have their own "dictionary" of what strokes they use to mean what, a dictionary they will continuously hone over the course of their working lives. The dictionary will have entries where the stenographic part ("steno", for short) is one stroke long, or multiple strokes long.
Frequently, there will be several entries with the same starting stroke which are differentiated by their length and by the subsequent strokes.

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