Music.Theory.Z.SRO

Serial (ordered) pitch-class operations on Z.

Documentation

data SRO t

Serial operator,of the form rRTMI.

Constructors

SRO

Fields

• sro_r :: Int
• sro_R :: Bool
• sro_T :: t
• sro_M :: Bool
• sro_I :: Bool

Instances

Eq t => Eq (SRO t)

Methods

(==) :: SRO t -> SRO t -> Bool

(/=) :: SRO t -> SRO t -> Bool

Show t => Show (SRO t)

Methods

showsPrec :: Int -> SRO t -> ShowS

show :: SRO t -> String

showList :: [SRO t] -> ShowS

sro_pp :: Show t => SRO t -> String

Printer in rnRTnMI form.

p_sro :: Integral t => GenParser Char () (SRO t)

sro_parse :: Integral i => String -> SRO i

Parse a Morris format serial operator descriptor.

sro_parse "r2RT3MI" == SRO 2 True 3 True True

z_sro_univ :: Integral i => Int -> Z i -> [SRO i]

The total set of serial operations.

let u = z_sro_univ 3 mod12
zip (map sro_pp u) (map (\o -> z_sro_apply 5 mod12 o [0,1,3]) u)

z_sro_Tn :: Integral i => Z i -> [SRO i]

The set of transposition SROs.

z_sro_TnI :: Integral i => Z i -> [SRO i]

The set of transposition and inversion SROs.

z_sro_RTnI :: Integral i => Z i -> [SRO i]

The set of retrograde and transposition and inversion SROs.

z_sro_TnMI :: Integral i => Z i -> [SRO i]

The set of transposition, M5 and inversion SROs.

z_sro_RTnMI :: Integral i => Z i -> [SRO i]

The set of retrograde,transposition,M5 and inversion SROs.

Serial operations

z_sro_apply :: Integral i => i -> Z i -> SRO i -> [i] -> [i]

Apply SRO. M is ordinarily 5, but can be specified here.

z_sro_apply 5 mod12 (SRO 1 True 1 True False) [0,1,2,3] == [11,6,1,4]
z_sro_apply 5 mod12 (SRO 1 False 4 True True) [0,1,2,3] == [11,6,1,4]

z_sro_tn :: (Integral i, Functor f) => Z i -> i -> f i -> f i

Transpose p by n.

z_sro_tn mod5 4 [0,1,4] == [4,0,3]
z_sro_tn mod12 4 [1,5,6] == [5,9,10]

z_sro_invert :: (Integral i, Functor f) => Z i -> i -> f i -> f i

Invert p about n.

z_sro_invert mod5 0 [0,1,4] == [0,4,1]
z_sro_invert mod12 6 [4,5,6] == [8,7,6]
z_sro_invert mod12 0 [0,1,3] == [0,11,9]

import Data.Word {- base -}
z_sro_invert mod12 (0::Word8) [1,4,8]

z_sro_tni :: (Integral i, Functor f) => Z i -> i -> f i -> f i

Composition of invert about 0 and tn.

z_sro_tni mod5 1 [0,1,3] == [1,0,3]
z_sro_tni mod12 4 [1,5,6] == [3,11,10]
(z_sro_invert mod12 0 . z_sro_tn mod12 4) [1,5,6] == [7,3,2]

z_sro_mn :: (Integral i, Functor f) => Z i -> i -> f i -> f i

Modulo multiplication.

z_sro_mn mod12 11 [0,1,4,9] == z_tni mod12 0 [0,1,4,9]

z_sro_t_related :: (Integral i, Functor f) => Z i -> f i -> [f i]

T-related sequences of p.

length (z_sro_t_related mod12 [0,3,6,9]) == 12
z_sro_t_related mod5 [0,2] == [[0,2],[1,3],[2,4],[3,0],[4,1]]

z_sro_ti_related :: (Eq (f i), Integral i, Functor f) => Z i -> f i -> [f i]

T/I-related sequences of p.

length (z_sro_ti_related mod12 [0,1,3]) == 24
length (z_sro_ti_related mod12 [0,3,6,9]) == 24
z_sro_ti_related mod12 [0] == map return [0..11]

z_sro_rti_related :: Integral i => Z i -> [i] -> [[i]]

R/T/I-related sequences of p.

length (z_sro_rti_related mod12 [0,1,3]) == 48
length (z_sro_rti_related mod12 [0,3,6,9]) == 24

Sequence operations

z_sro_tn_to :: Integral i => Z i -> i -> [i] -> [i]

Variant of tn, transpose p so first element is n.

z_sro_tn_to mod12 5 [0,1,3] == [5,6,8]
map (z_sro_tn_to mod12 0) [[0,1,3],[1,3,0],[3,0,1]]

z_sro_invert_ix :: Integral i => Z i -> Int -> [i] -> [i]

Variant of invert, inverse about nth element.

map (z_sro_invert_ix mod12 0) [[0,1,3],[3,4,6]] == [[0,11,9],[3,2,0]]
map (z_sro_invert_ix mod12 1) [[0,1,3],[3,4,6]] == [[2,1,11],[5,4,2]]

z_tmatrix :: Integral i => Z i -> [i] -> [[i]]

The standard t-matrix of p.

z_tmatrix mod12 [0,1,3] == [[0,1,3],[11,0,2],[9,10,0]]