Quote:
Originally Posted by USS
This is only for instruments with a fretboard or a keyboard.
A C with twelve sharps does still not sound like a C. Phisically, this is quite logic. The proportion between a tone and the chromatic second above is 15/16. When we cound twelve sharps at a note, its proportion is 15 to the twelfth power divided by 16 to the twelfth power, which is 129,746,337,890,625 divided by 281,474,976,710,656 and that is less than 0.5, which means that C############ is higher than a C. Therefore, your maximum is not correct.
There are infinite possibilities for dodecaphonics.

You're speaking about pure intonation, not equal temperament. (I think maybe you didn't make this clear enough.)
As I understand it, dodecaphonics, or 12tone music, presupposes equal temperament, in which each note relates to the next by the 12th root of 2, not 15/16. That way, C sharped 12 times is exactly C an octave higher.
If it was not based on equal temperament, then  seems to me  one note of the 12 would dominate, inasmuch as others were measured from it in a series of simple ratios. Therefore we would not have a truly atonal music (which I think is how 12tone music is regarded).
Of course, many other scale and intonation systems are possible. Who says the octave has to have only 12 divisions?.....
http://en.wikipedia.org/wiki/Microtonal_music
http://en.wikipedia.org/wiki/19_tone_equal_temperament
http://en.wikipedia.org/wiki/22_tone_equal_temperament
http://en.wikipedia.org/wiki/31_equal_temperament
...and there's more where they came from...