We do strange things to ourselves in the process of acquiring culture with a capital K. We get ourselves to believe that there are twelve tones in the octave and are so surprised that composers come up with twenty-three (see Allan Kozzin's article in yesterday's New York Times). There are actually millions of tones out of which different cultures choose a manageable number to which they pitch their songs and their instruments. When western composers write well for the traditional orchestra they are releasing many more tones than those in the notated score: all them overtones!
And the piano? It was always a microtonal instrument and it still is. Only our insistence on those twelve keys keeps us from hearing that.
I had a great row with a quite prominent musician/teacher/authority on the subject. He was aghast at the notion. Then why, I ask, did Brahms routinely account for 21 tones in the octave, and Schubert 24 in his posthumous B-flat Sonata?
The keys are not the sound.