Answer: Currently the rest of the Roman alphabet is left underutilized - the first seven letters are as far as we go. Even the German use of 'h' for B natural derives not from extending the alphabet, but from a sort of misreading of the old symbol for "hard B," or "B Durum," a B raised above its normal flatted position in the system of pitches known before the keyboard was fully equipped with black keys. Early writers wrote that "b" with hard square corners, making it look a little like an "h."

The answer to question 104 has an impressive explanation of our limitation to the letters A-G. But you might be glad to hear that some old authorities took in more of the alphabet. There are treatises dating before the first millenium in which the letters get as far as P, which is done by not paying any attention to the octaves. For example,

C D E F G A B C1 D1 E1 F1 G1 A1

becomes

A B C D E F G H I K L M N O P

They had to skip J, because Latin doesn't have a J.

So: if you want to spell words using musical pitches you could try the above, sometimes called "Boethian notation." But since it stops at P it wouldn't be good for a winning hand in scrabble.