Thread: Dodecaphonics
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Old 2006-11-03, 04:10
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Originally Posted by Unanything
The composer, when he begins, takes all twelve chromatic notes and arranges them into an order that pleases him. There are around 479 000 000 possibilities (I found the exact figure in an encyclopedia, John Mansley, you could probably calculate it, it something do to with factorials probably)

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.

[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.]
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