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Math Help - How many scales are possible?

  1. #1
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    How many scales are possible?

    Western music is based on a twelve tone scale. Standard diatonic scales use 7 of those tones
    ie, do re mi fa sol la ti/si [do]
    That example uses 1 3 5 6 8 10 12 [13]

    I want to know how many scales can be made from 12 tones.
    that is to say...
    How many different combinations of these 12 tones can be made when you can only ascend (not decend or stay static), and can have an interval of anywhere from 1 to 11?
    ... or, actually, I would only be interested in scales of three or more notes... therefore, an interval of 1 to 10 would be the largest possible (then an interval of 1 to make three notes within the 12 note range)

    A straight answer to my question would be welcome. Descriptions of the mathematical methods that would be used to solve it are especially welcome.
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  2. #2
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    May 2009
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    I thought the answer would rely on factorials (and it does), but after a little searching, combination seems to be the function I'm looking for...
    C(1,12) + C(2,12) + C(3,12) + ... + C (12,12) = 4095
    Does this fit?

    That would include one- and two-tone combinations. How might I find the answer if only (three-and-greater)-tone scales are considered?

    Also, this may be a question for programmers, how could I get a list of all those scales?
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