Stephen Tetley wrote:
Hello Mike
A pitch class set represents Z12 numbers so I'd define a Z12 number type then store it in a list (if you have need a multiset - duplicates) or Data.Set (if you need uniqueness).
If you want an efficient implementation for *sets* of Z12 numbers I'd recommend using bit arithmetic. Pick some Word type with at least 12 bits and use bit0 to represent including 0 in the set, bit1 to represent including 1, bit2 for 2, etc. This can be generalized for any Zn provided n is a suitably small number. Z16 may be a good place to start if you want wider applicability, though you'd want to wrap that with error checking code in order to exclude 12..15. import Data.Word import Data.Bits newtype Z16 = Z16 Word16 z16_0 = 1 `shiftL` 0 z16_1 = 1 `shiftL` 1 z16_2 = 1 `shiftL` 2 ... union = (.|.) intersection = (.&.) ... But I don't know whether you need to deal more with sets or with the elements therein, so that might reduce the efficiency of this approach. -- Live well, ~wren