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 T.mod12 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 False 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 :: GRAPH PCSET -> PCSET -> [EDGE PCSET]

gr_trs :: Int -> GRAPH PCSET -> GRAPH PCSET

TABLES

table_3 :: [((PCSET, SC, SC_Name), (PCSET, SC, SC_Name))]

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 :: GRAPH PCSET

fig_1_gr :: Gr PCSET ()

fig_2 :: [[PCSET]]

fig_3 :: [GRAPH PCSET]

fig_3_gr :: [Gr PCSET ()]

fig_4 :: [GRAPH PCSET]

fig_5 :: [GRAPH PCSET]

Drawing

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

set_shape :: PCSET -> String

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

type GR = Gr PCSET ()

gr_pp' :: (PCSET -> String) -> GR_PP PCSET ()

gr_pp :: GR_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_L PCSET PCSET]

d_fig_5_g' :: Gr PCSET PCSET

d_fig_5' :: [String]