I don’t have any practical reason for asking this mainly just curious. If every key on my keyboard had a specific musical note attached to it would my brain eventually be able to read the notes as letters with my ears instead of my eyes. Suppose someone else was typing. Would I eventually know exactly what they were typing just by listening??
If you were intent enough on listening closely, the answer is yes. Each time is like a different letter, except in a piano keyboard there are 88 of them, and they are harder to distinguish at the extreme bass and treble ends.
I wonder how one would strategically go about assigning notes to letters?
Seeing the thread title and hovering to get the first sentence +, I was going 
I was of course assuming you meant this kind of thing when you said “keyboard”.
And thinking “if?!? Whaddaya ya mean ‘if’? You saying yours doesn’t?”
Can you tell which key on a piano is being pressed just by listening to it? I certainly can’t but my musical skills are abysmal. Would you need to have perfect pitch to do this, or can most musically-educated people do it?
When I’m in the same room as a family member, calling a familiar number, I can often recognize the number being called (at least, if it’s a phone that still makes the familiar touch-tone sounds when you dial). That’s only 10 keys, not however many are on a computer keyboard, but it’s a similar problem.
To answer question #1: yes. Perfect pitch is not needed; good, educated, well-developed relative pitch is.
In ear training class in music school, we would practice this when the professor would play various notes on a piano and we had to tell him which pitches were played. I presume most music schools include this kind of training for a music degree.
I used to make my living in Hollywood by doing “takedowns,” where the exact notes and durations were transferred from a sound recording to paper notation. At the time, there were no computer programs adequate for the task.
The quality of the sound recording is very important. If you can’t hear the sound, you can’t transcribe it.
Solfège is a system whereby every note of a scale is given its own unique syllable. Basic solfège has seven “letters”/notes - Do Re Mi Fa Sol La Ti Do - although there are other forms of solfège that add more notes with different syllables.
Similar systems are used in other musics of the world, such as sargam in Indian music, which names the seven notes: Sa Re Ga Ma Pa Dha Ni Sa. Afghan sargam is expanded to twelve syllables, for the twelve notes of the chromatic scale - Sa Ra Re Ga Ge Ma Me Pe Da De Na Ni Sa.
The twelve notes of the chromatic scale are easy enough for the trained ear to recognise and identify. So it would be possible to assign 26 letters to 26 notes and musically communicate them by using the twelve chromatic notes of the middle register, plus the seven adjoining notes in each of the lower and upper registers.
One could do it a different way by using a heptatonic (seven note) scale and using all the relevant notes in the lower, middle and upper registers, plus five more notes from a register above or below.
The space bar could be the tonic/fundamental/root note. The regular spaces in written texts would therefore act as a reminder of the tonic note. One would need to play the space key at the start of a piece of text to establish the tonic note.
While the 26 notes of the alphabet would be possible, I think it would be much harder to do it for all 104 keys on a standard computer keyboard, for two reasons. Firstly, I think it’s harder to distinguish notes outside of the chromatic scale. Having said that, a quarter tone scale is used in Arabic music, which divides the octave into twenty-four equal parts, rather than the twelve of the chromatic scale that we are used to. So maybe it would be possible. The second problem could be that the number of octaves needed - more than 8 1/2 if using a 12-tone chromatic scale - might go beyond our hearing range, as well as it being harder to differentiate the octaves/registers from each other.
Here are three browser-based virtual pianos to instantly turn your computer keyboard into a musical keyboard:
Virtual Piano Keyboard | Online Piano at Apronus.com (can play chords with one keystroke)
There are whistled languages, but the different whistles may emulate speech (tone, articulation, etc.) rather than correspond directly to letters. These are languages people actually use, so they presumably have some successful features.
That is what got me thinking about this. I noticed that I recognized certain numbers by the sound
I would go middle-C on the H key and ascend/descend from there; it only gives you a couple octaves but that would cover a lot of tunes. Number keys could be chords and the other keys different organ-like settings.
Now going away from having a musical quality to it – same basic start but include the numbers and ; ’ , . as different notes. And make the shift key a volume control so anytime you hit a D or & it registers as louder.
But that is just two fast approaches off the top of my head. Like before QWERTY almost anything could work.
You could find someone with synesthesia. I can assign notes, as well as colors, to well over half the keys, but not all. But another synesthete would find it all wrong.
I would have thought that to identify a single note played with no other context you must have perfect pitch. Otherwise, what are you judging it “relative” to?
As for the OP, words would become short musical phrases. I think you’d be able to learn the phrases better than you could learn to distinguish a single letter out of context. I’d be curious to know how many words would have the same “tune” as another word but in a different key.
It is probable that associating tones with (latin) letters to spell (English) words would not be an efficient way of communicating.
On the other hand, if you knew Cherokee and the Cherokke Syllabary, then converting that to tone changes (rather than tones) would probably be doable.
I’m not aware of any efficient method of coding English at all. If I had to try, I think I’d start with shorthand.
OP asks:
According to an anecdote I read, in the days of communication by telegraph, the operators learned to read Morse Code by ear in real time as they heard incoming messages.
An average professional typist goes about 70 words a minute, which is (about) 350 characters a minute.
Here is a metronome going at 350 BPM. So every one of those ticks would be a distinct note and a distinct letter.
Seems, to put it mildly, very difficult.
But think about what it takes to read. Think about recognizing the shape of each individual letter, then the next, then the next, a lot faster than 350 characters a minute. Is the pitch of a sound more complex than the shape of a character? I don’t think so. Besides, we don’t actually read one character at a time; we read words and phrases. Why should “sound-reading” be any different? We’d learn to recognize words and phrases, just like with reading, and just like our understanding of human speech.
Relative to your memory of another note, sometimes heard minutes or even days before. At least, that usually works for me. Dunno if that is universal.
Isn’t that what perfect pitch is? What do you consider the difference between this skill and perfect pitch?