Music.Theory.Z.Boros_1990

James Boros. "Some Properties of the All-Trichord Hexachord". _In Theory Only_, 11(6):19--41, 1990.

Util

singular :: String -> [t] -> t

set_eq :: Ord t => [t] -> [t] -> Bool

elem_by :: (t -> t -> Bool) -> t -> [t] -> Bool

Tto

tto_tni_univ :: Integral i => [Tto i]

all_tn :: Integral i => [i] -> [[i]]

all_tni :: Integral i => [i] -> [[i]]

uniq_tni :: Integral i => [i] -> [[i]]

type Pc = Int

type Pcset = [Pc]

type Sc = Pcset

pcset_trs :: Int -> Pcset -> Pcset

trichords :: [Pcset]

Forte prime forms of the twelve trichordal set classes.

length trichords == 12

self_inv :: Pcset -> Bool

Is a pcset self-inversional, ie. is the inversion of p a transposition of p.

map (\p -> (p,self_inv p)) trichords

pcset_pp :: Pcset -> String

Pretty printer, comma separated.

pcset_pp [0,3,7,10] == "0,3,7,10"

pcset_pp_hex :: Pcset -> String

Pretty printer, hexadecimal, no separator.

pcset_pp_hex [0,3,7,10] == "037A"

Ath

ath :: Pcset

Forte prime form of the all-trichord hexachord.

T.sc_name ath == "6-Z17"
T.sc "6-Z17" == ath

is_ath :: Pcset -> Bool

Is p an instance of ath.

ath_univ :: [Pcset]

Table 1, p.20

length ath_univ == 24

ath_tni :: Pcset -> Tto Pc

Calculate Tto of pcset, which must be an instance of ath.

ath_tni [1,2,3,7,8,11] == T.Tto 3 1 True

ath_pp :: Pcset -> String

Give label for instance of ath, prime forms are written H and inversions h.

ath_pp [1,2,3,7,8,11] == "h3"

ath_trichords :: [Pcset]

The twenty three-element subsets of ath.

length ath_trichords == 20

ath_complement :: Pcset -> Pcset

\\ of ath and p, ie. the pitch classes that are in ath and not in p.

ath_complement [0,1,2] == [4,7,8]

ath_completions :: Pcset -> Sc -> [Pcset]

p is a pcset, q a sc, calculate pcsets in q that with p form ath.

ath_completions [0,1,2] (T.sc "3-3") == [[6,7,10],[4,7,8]]
ath_completions [6,7,10] (T.sc "3-5") == [[1,2,8]]

realise_ath_seq :: [Pcset] -> [[Pcset]]

ath_gr_extend :: [Edge Pcset] -> Pcset -> [Edge Pcset]

gr_trs :: Int -> [Edge Pcset] -> [Edge Pcset]

Tables

table_3 :: [((Pcset, Sc, SC_Name), (Pcset, Sc, SC_Name))]

pp_tbl :: Text_Table -> [String]

table_3_md :: [String]

table_4 :: [((Pcset, Pcset, SC_Name), (Pcset, Pcset, SC_Name))]

table_4_md :: [String]

table_5 :: [(Pcset, Int)]

table_5_md :: [String]

table_6 :: [(Pcset, Int, Int)]

table_6_md :: [String]

Figures

fig_1 :: [Edge Pcset]

fig_1_gr :: Gr Pcset ()

fig_2 :: [[Pcset]]

fig_3 :: [[Edge Pcset]]

fig_3_gr :: [Gr Pcset ()]

fig_4 :: [[Edge Pcset]]

fig_5 :: [[Edge Pcset]]

Drawing

uedge_set :: Ord v => [Edge v] -> [Edge v]

set_shape :: Pcset -> Dot_Attr

Self-inversional pcsets are drawn in a double circle, other pcsets in a circle.

type Gr = Gr Pcset ()

gr_pp' :: (Pcset -> String) -> Graph_Pp Pcset ()

gr_pp :: Graph_Pp Pcset ()

d_fig_1 :: [String]

d_fig_3_g :: Gr

d_fig_3 :: [String]

d_fig_3' :: [[String]]

d_fig_4_g :: Gr

d_fig_4 :: [String]

d_fig_5_g :: Gr

d_fig_5 :: [String]

d_fig_5_e :: [Edge_Lbl Pcset Pcset]

d_fig_5_g' :: Gr Pcset Pcset

d_fig_5' :: [String]