Aberrismic theory: Difference between revisions

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stepsOfEdoInCents :: Int -> Int -> Double

stepsOfEdoInCents k edo = 1200*fromIntegral k/fromIntegral edo

-- Generate all possible combinations of sizes of L, M, and s.

generateCombinations :: Int -> [(Int, Int, Int)]

generateCombinations edoBound = [(l, m, s) | l <- [3..edoBound], m <- [2..l-1], s <- [1..m-1]]

-- Filter the combinations based on the step signature and the aberrismic range.

filterCombinations :: Double -> Double -> Int -> Int -> Int -> [(Int, Int, Int)] -> [(Int, (Int, Int, Int))]

filterCombinations aberLower aberUpper countL countM countS combos =

[(edo, (l, m, s)) | (l, m, s) <- combos,

let edo = countL*l + countM*m + countS*s,

let aberSize = stepsOfEdoInCents s edo,

aberLower <= aberSize && aberSize <= aberUpper]

{- Return a list of (edo, step ratio) tuples for the `(countL)L(countM)M(countS)s` aberrismic scale where `edo <= edoBound`,

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Non-coprime step ratios are reduced. -}

boundedEdosWithTernaryAberrismicScale :: Int -> Double -> Double -> Int -> Int -> Int -> [(Int, (Int, Int, Int))]

boundedEdosWithTernaryAberrismicScale edoBound aberLower aberUpper countL countM countS =

~~let~~

sortBy (\x y -> compare (fst x) (fst y)) -- sort by the edo

~~sizesOfS = [1..edoBound] -- smallest s possible in n-edo is 1\n~~

$ filter (\x -> fst x <= edoBound) -- filter edos exceeding edoBound

~~sizesOfM = [2..edoBound] -- smallest m possible in n-edo is 2\n~~

$ filterCombinations aberLower aberUpper countL countM countS

~~sizesOfL = [3..edoBound] -- smallest L possible in n-edo is 3\n~~

$ generateCombinations edoBound

in sortBy (\x y -> compare (fst x) (fst y)) -- sort ~~the list, which is finite,~~ by the edo

$ filter (\x -> (fst x) <= edoBound) -- filter edos ~~that exceed `~~edoBound`

~~[ (edo, (x, y, z)) -- divide step sizes by gcd~~

~~| x <- sizesOfL, y <- sizesOfM, z <- sizesOfS,~~

~~let edo =~~ countL*x + countM*y + countS*z,

~~let aberSize = stepsOfEdoInCents z edo, -- compute aberrisma size in given tuning~~

~~x > y && y > z && aberLower <= aberSize && aberSize <= aberUpper ]~~

{-

`boundedEdosWithTernaryAberrismicScale 53 20.0 60.0 5 2 3` returns:

`[(22,(3,2,1)),(27,(4,2,1)),(29,(4,3,1)),(32,(5,2,1)),(34,(5,3,1)),(36,(5,4,1)),(37,(6,2,1)),(39,(6,3,1)),(41,(6,4,1)),(42,(6,3,2)),(42,(7,2,1)),(43,(6,5,1)),(44,(6,4,2)),(44,(7,3,1)),(46,(6,5,2)),(46,(7,4,1)),(47,(7,3,2)),(47,(8,2,1)),(48,(7,5,1)),(49,(7,4,2)),(49,(8,3,1)),(50,(7,6,1)),(51,(7,5,2)),(51,(8,4,1)),(52,(8,3,2)),(52,(9,2,1)),(53,(7,6,2)),(53,(8,5,1))]`

-}

</syntaxhighlight>

[[Category:Terms]]

[[Category:Aberrismic theory|*]]

@@ Line 83: / Line 83: @@
 stepsOfEdoInCents :: Int -> Int -> Double
 stepsOfEdoInCents k edo = 1200*fromIntegral k/fromIntegral edo
+-- Generate all possible combinations of sizes of L, M, and s.
+generateCombinations :: Int -> [(Int, Int, Int)]
+generateCombinations edoBound = [(l, m, s) | l <- [3..edoBound], m <- [2..l-1], s <- [1..m-1]]
+-- Filter the combinations based on the step signature and the aberrismic range.
+filterCombinations :: Double -> Double -> Int -> Int -> Int -> [(Int, Int, Int)] -> [(Int, (Int, Int, Int))]
+filterCombinations aberLower aberUpper countL countM countS combos =
+    [(edo, (l, m, s)) | (l, m, s) <- combos,
+                        let edo = countL*l + countM*m + countS*s,
+                        let aberSize = stepsOfEdoInCents s edo,
+                        aberLower <= aberSize && aberSize <= aberUpper]
 {- Return a list of (edo, step ratio) tuples for the `(countL)L(countM)M(countS)s` aberrismic scale where `edo <= edoBound`,
@@ Line 88: / Line 100: @@
     Non-coprime step ratios are reduced. -}
 boundedEdosWithTernaryAberrismicScale :: Int -> Double -> Double -> Int -> Int -> Int -> [(Int, (Int, Int, Int))]
 boundedEdosWithTernaryAberrismicScale edoBound aberLower aberUpper countL countM countS =
-  let
+     sortBy (\x y -> compare (fst x) (fst y)) -- sort by the edo
-    sizesOfS = [1..edoBound] -- smallest s possible in n-edo is 1\n
+    $ filter (\x -> fst x <= edoBound) -- filter edos exceeding edoBound
-    sizesOfM = [2..edoBound] -- smallest m possible in n-edo is 2\n
+    $ filterCombinations aberLower aberUpper countL countM countS
-     sizesOfL = [3..edoBound] -- smallest L possible in n-edo is 3\n
+    $ generateCombinations edoBound
-  in sortBy (\x y -> compare (fst x) (fst y)) -- sort the list, which is finite, by the edo
-      $ filter (\x -> (fst x) <= edoBound) -- filter edos that exceed `edoBound`
-      [ (edo, (x, y, z)) -- divide step sizes by gcd
-      | x <- sizesOfL, y <- sizesOfM, z <- sizesOfS,
-        let edo = countL*x + countM*y + countS*z,
-        let aberSize = stepsOfEdoInCents z edo, -- compute aberrisma size in given tuning
-        x > y && y > z && aberLower <= aberSize && aberSize <= aberUpper ]
 {-
 `boundedEdosWithTernaryAberrismicScale 53 20.0 60.0 5 2 3` returns:
 `[(22,(3,2,1)),(27,(4,2,1)),(29,(4,3,1)),(32,(5,2,1)),(34,(5,3,1)),(36,(5,4,1)),(37,(6,2,1)),(39,(6,3,1)),(41,(6,4,1)),(42,(6,3,2)),(42,(7,2,1)),(43,(6,5,1)),(44,(6,4,2)),(44,(7,3,1)),(46,(6,5,2)),(46,(7,4,1)),(47,(7,3,2)),(47,(8,2,1)),(48,(7,5,1)),(49,(7,4,2)),(49,(8,3,1)),(50,(7,6,1)),(51,(7,5,2)),(51,(8,4,1)),(52,(8,3,2)),(52,(9,2,1)),(53,(7,6,2)),(53,(8,5,1))]`
 -}
 </syntaxhighlight>
 [[Category:Terms]]
 [[Category:Aberrismic theory|*]]<!--Main article-->