Quote:
Originally Posted by johnmansley
Yes it is, that number is just 12! (said "twelve factorial") rounded to three significant figures. The actual number of possibilities is 479,001,600.

This is only for instruments with a fretboard or a keyboard.
Quote:
Originally Posted by johnmansley
[Aside: This figure doesn't allow for repetition of notes, the total number of arrangements  including twelve of the same note  is 12 to the twelfth power, which is 8,916,100,448,256. The total number of arrangements of twelve notes without any note being the same as the previous note is 12 multiplied by 11 to the eleventh power, which is 3,423,740,047,332.]

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.
