2:1 is also known as an "octave", named after 8, because it is traditionally expressed as the product of a certain sequence of 7 ratios.
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in all seriousness you can easily check this with https://github.com/ejlilley/AbstractMusic … type in: _A1 ^* 12 and the output is: AAAAAAAAAAAA1
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as in order to get an octave (P8) you need (_A1 ^* 12) ^+^ (d2 ^* 7)
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The more I look at your code the angrier I get. What is the middle operator?
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these are all from https://hackage.haskell.org/package/vector-space … ^+^ is vector addition
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