Music.Theory.Z.Tto

Generalised twelve-tone operations on un-ordered pitch-class sets with arbitrary Z.

Tto

data Tto t

Twelve-tone operator, of the form TMI.

Constructors

Tto

Fields

• tto_T :: t
• tto_M :: t
• tto_I :: Bool

Instances

Show t => Show (Tto t)

Defined in Music.Theory.Z.Tto

Methods

showsPrec :: Int -> Tto t -> ShowS

show :: Tto t -> String

showList :: [Tto t] -> ShowS

Eq t => Eq (Tto t)

Defined in Music.Theory.Z.Tto

Methods

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

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

tto_identity :: Num t => Tto t

T0

tto_pp :: (Show t, Num t, Eq t) => Tto t -> String

Pretty printer. It is an error here is M is not 1 or 5.

p_tto :: Integral t => t -> P (Tto t)

Parser for Tto, requires value for M (ordinarily 5 for 12-tone Tto).

tto_parse :: Integral i => i -> String -> Tto i

Parser, transposition must be decimal.

map (tto_pp . tto_parse 5) (words "T5 T3I T11M T9MI") == ["T5","T3I","T11M","T9MI"]

tto_M_set :: Integral t => t -> Tto t -> Tto t

Set M at Tto.

Z

z_tto_univ :: Integral t => t -> Z t -> [Tto t]

The set of all Tto, given Z.

length (z_tto_univ 5 z12) == 48
map tto_pp (z_tto_univ 5 z12)

z_tto_f :: Integral t => Z t -> Tto t -> t -> t

Apply Tto to pitch-class.

map (z_tto_f z12 (tto_parse 5 "T1M")) [0,1,2,3] == [1,6,11,4]

z_tto_apply :: Integral t => Z t -> Tto t -> [t] -> [t]

nub of sort of z_tto_f. (nub because M may be 0).

z_tto_apply z12 (tto_parse 5 "T1M") [0,1,2,3] == [1,4,6,11]

z_tto_rel :: (Ord t, Integral t) => t -> Z t -> [t] -> [t] -> [Tto t]

Find Ttos that map pc-set x to pc-set y given m and z.

map tto_pp (z_tto_rel 5 z12 [0,1,2,3] [1,4,6,11]) == ["T1M","T4MI"]

Plain

z_pcset :: (Integral t, Ord t) => Z t -> [t] -> [t]

nub of sort of z_mod of z.

z_pcset z12 [1,13] == [1]
map (z_pcset z12) [[0,6],[6,12],[12,18]] == replicate 3 [0,6]

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

Transpose by n.

z_tto_tn z12 4 [1,5,6] == [5,9,10]
z_tto_tn z12 4 [0,4,8] == [0,4,8]

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

Invert about n.

z_tto_invert z12 6 [4,5,6] == [6,7,8]
z_tto_invert z12 0 [0,1,3] == [0,9,11]

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

Composition of z_tto_invert about 0 and z_tto_tn.

z_tto_tni z12 4 [1,5,6] == [3,10,11]
(z_tto_invert z12 0 . z_tto_tn z12 4) [1,5,6] == [2,3,7]

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

Modulo-z multiplication

z_tto_mn z12 11 [0,1,4,9] == z_tto_invert z12 0 [0,1,4,9]

z_tto_m5 :: Integral i => Z i -> [i] -> [i]

M5, ie. mn 5.

z_tto_m5 z12 [0,1,3] == [0,3,5]

Sequence

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

T-related sets of p.

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

Unique elements of z_tto_t_related_seq.

length (z_tto_t_related z12 [0,1,3]) == 12
z_tto_t_related z12 [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]

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

T/I-related set of p.

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

Unique elements of z_tto_ti_related_seq.

length (z_tto_ti_related z12 [0,1,3]) == 24
z_tto_ti_related z12 [0,3,6,9] == [[0,3,6,9],[1,4,7,10],[2,5,8,11]]