-- | Serial (ordered) pitch-class operations on 'Z12'. module Music.Theory.Z12.SRO where import Data.List {- base -} import qualified Music.Theory.List as T import qualified Music.Theory.Z.SRO as Z import Music.Theory.Z12 -- | Transpose /p/ by /n/. -- -- > sro_tn 4 [1,5,6] == [5,9,10] sro_tn :: Z12 -> [Z12] -> [Z12] sro_tn = Z.z_sro_tn id -- | Invert /p/ about /n/. -- -- > sro_invert 6 [4,5,6] == [8,7,6] -- > sro_invert 0 [0,1,3] == [0,11,9] sro_invert :: Z12 -> [Z12] -> [Z12] sro_invert = Z.z_sro_invert id -- | Composition of 'invert' about @0@ and 'tn'. -- -- > tni 4 [1,5,6] == [3,11,10] -- > (sro_invert 0 . sro_tn 4) [1,5,6] == [7,3,2] sro_tni :: Z12 -> [Z12] -> [Z12] sro_tni = Z.z_sro_tni id -- | Modulo 12 multiplication -- -- > sro_mn 11 [0,1,4,9] == sro_tni 0 [0,1,4,9] sro_mn :: Z12 -> [Z12] -> [Z12] sro_mn = Z.z_sro_mn id -- | M5, ie. 'mn' @5@. -- -- > sro_m5 [0,1,3] == [0,5,3] sro_m5 :: [Z12] -> [Z12] sro_m5 = sro_mn 5 -- | T-related sequences of /p/. -- -- > length (sro_t_related [0,3,6,9]) == 12 sro_t_related :: [Z12] -> [[Z12]] sro_t_related = Z.z_sro_t_related id -- | T\/I-related sequences of /p/. -- -- > length (ti_related [0,1,3]) == 24 -- > length (ti_related [0,3,6,9]) == 24 -- > ti_related [0] == map return [0..11] sro_ti_related :: [Z12] -> [[Z12]] sro_ti_related = Z.z_sro_ti_related id -- | R\/T\/I-related sequences of /p/. -- -- > length (rti_related [0,1,3]) == 48 -- > length (rti_related [0,3,6,9]) == 24 sro_rti_related :: [Z12] -> [[Z12]] sro_rti_related = Z.z_sro_rti_related id -- | T\/M\/I-related sequences of /p/, duplicates removed. sro_tmi_related :: [Z12] -> [[Z12]] sro_tmi_related p = let q = sro_ti_related p in nub (q ++ map sro_m5 q) -- | R\/T\/M\/I-related sequences of /p/, duplicates removed. sro_rtmi_related :: [Z12] -> [[Z12]] sro_rtmi_related p = let q = sro_tmi_related p in nub (q ++ map reverse q) -- | r\/R\/T\/M\/I-related sequences of /p/, duplicates removed. sro_rrtmi_related :: [Z12] -> [[Z12]] sro_rrtmi_related p = nub (concatMap sro_rtmi_related (T.rotations p)) -- * Sequence operations -- | Variant of 'tn', transpose /p/ so first element is /n/. -- -- > sro_tn_to 5 [0,1,3] == [5,6,8] -- > map (sro_tn_to 0) [[0,1,3],[1,3,0],[3,0,1]] == [[0,1,3],[0,2,11],[0,9,10]] sro_tn_to :: Z12 -> [Z12] -> [Z12] sro_tn_to = Z.z_sro_tn_to id -- | Variant of 'invert', inverse about /n/th element. -- -- > map (sro_invert_ix 0) [[0,1,3],[3,4,6]] == [[0,11,9],[3,2,0]] -- > map (sro_invert_ix 1) [[0,1,3],[3,4,6]] == [[2,1,11],[5,4,2]] sro_invert_ix :: Int -> [Z12] -> [Z12] sro_invert_ix = Z.z_sro_invert_ix id -- | The standard t-matrix of /p/. -- -- > tmatrix [0,1,3] == [[0,1,3] -- > ,[11,0,2] -- > ,[9,10,0]] tmatrix :: [Z12] -> [[Z12]] tmatrix = Z.z_tmatrix id