Kent,
With all due respect, Radiohead is not 12 tone music. That is, if you are referring to the 12 tone(note) system used by Schoenberg (I think he originated this way of looking at "atonal" music), Berg, and related composers. Neither is every atonal or dissonant music twelve-tone. So yes, Radiohead do play some dissonant things, but I don't think of their music as "atonal" in the usual sense.
If you do find the atonal "sound" interesting, I would highly recommend Das Klavierwerk by Schoenberg (the only complete piano works he ever composed). And for the freely improvised piano Cecil Taylor's "Air Above Mountains" (absolute masterpiece), although his work is more a jazz improvisation using extended dissonances, and there are definite Schoenbergian elements in his music. It is very cool to first listen to the Schoenberg, and then to Cecil. See what you think.
To be truly atonal, though, the instrument itself must have the octave divided up differently. You might find the instruments designed by Harry Partch very interesting, and there are a couple of web sites about him..just dial up on your search engine.
Gene
