hmt-0.20: Haskell Music Theory
Safe HaskellSafe-Inferred
LanguageHaskell2010

Music.Theory.Tuning.Wilson

Description

Erv Wilson, archives http://anaphoria.com/wilson.html

Synopsis

Geom (see Data.CG.Minus.Plain)

type V2 n = (n, n) Source #

v2_map :: (t -> u) -> V2 t -> V2 u Source #

v2_zip :: (a -> b -> c) -> V2 a -> V2 b -> V2 c Source #

v2_add :: Num n => V2 n -> V2 n -> V2 n Source #

v2_sum :: Num n => [V2 n] -> V2 n Source #

v2_scale :: Num n => n -> V2 n -> V2 n Source #

Pt Set

pt_set_normalise_sym :: (Fractional n, Ord n) => [V2 n] -> [V2 n] Source #

Normalise set of points to lie in (-1,-1) - (1,1), scaling symetrically about (0,0)

pt_set_normalise_sym [(40,0),(0,40),(13,11),(-8,4)] == [(1,0),(0,1),(0.325,0.275),(-0.2,0.1)]
pt_set_normalise_sym [(-10,0),(1,10)] == [(-1,0),(0.1,1)]

Lattice Design

type Lattice_Design n = (Int, [V2 n]) Source #

k-unit co-ordinates for k-lattice.

ew_lc_std :: Num n => Lattice_Design n Source #

Erv Wilson standard lattice, unit co-ordinates for 5-dimensions, ie. [3,5,7,11,13]

http://anaphoria.com/wilsontreasure.html

kg_lc_std :: Num n => Lattice_Design n Source #

Kraig Grady standard lattice, unit co-ordinates for 5-dimensions, ie. [3,5,7,11,13]

http://anaphoria.com/wilsontreasure.html

ew_lc_tetradic :: Num n => Lattice_Design n Source #

Erv Wilson tetradic lattice (3-lattice), used especially when working with hexanies or 7 limit tunings

http://anaphoria.com/wilsontreasure.html

Lattice_Factors

type Lattice_Factors i = (Int, [i]) Source #

A discrete k-lattice is described by a sequence of k-factors. Values are ordinarily though not necessarily primes beginning at three.

type Lattice_Position = (Int, [Int]) Source #

Positions in a k-lattice are given as a k-list of steps.

lc_pos_del :: Int -> Lattice_Position -> Lattice_Position Source #

Delete entry at index.

lc_pos_to_pt :: (Fractional n, Ord n) => Lattice_Design n -> Lattice_Position -> V2 n Source #

Resolve Lattice_Position against Lattice_Design to V2

pos_pp_ws :: Lattice_Position -> String Source #

White-space pretty printer for Lattice_Position.

pos_pp_ws (3,[0,-2,1]) == "  0 -2  1"

lat_res :: Integral i => Lattice_Factors i -> Lattice_Position -> Ratio i Source #

Given Lattice_Factors [X,Y,Z..] and Lattice_Position [x,y,z..], calculate the indicated ratio.

lat_res (2,[3,5]) (2,[-5,2]) == (5 * 5) / (3 * 3 * 3 * 3 * 3)

Rat (n,d)

type Rat = (Integer, Integer) Source #

Ratio given as (n,d)

rat_rem_oct :: Rat -> Rat Source #

Remove all octaves from n and d.

rat_lift_1 :: (Rat -> Rat) -> Rational -> Rational Source #

Lift Rat function to Rational.

rat_to_ratio :: Rat -> Rational Source #

Convert Rat to Rational

rat_mediant :: Rat -> Rat -> Rat Source #

Mediant, ie. n1+n2/d1+d2

rat_mediant (0,1) (1,2) == (1,3)

rat_pp :: Rat -> String Source #

Rat written as n/d

Rational

r_rem_oct :: Rational -> Rational Source #

Lifted rat_rem_oct.

map ew_r_rem_oct [256/243,7/5,1/7] == [1/243,7/5,1/7]

r_verify_oct :: Rational -> Rational Source #

Assert that n is in [1,2).

r_seq_limit :: [Rational] -> Integer Source #

Find limit of set of ratios, ie. largest factor in either numerator or denominator.

r_seq_limit [1] == 1

r_seq_factors :: [Rational] -> [Integer] Source #

Find factors of set of ratios, ie. the union of all factor in both numerator & denominator.

r_seq_factors [1/3,5/7,9/8,13,27,31] == [2,3,5,7,13,31]

Table

rat_fact_lm :: Integer -> Rational -> Lattice_Position Source #

Vector of prime-factors up to limit.

map (rat_fact_lm 11) [3,5,7,2/11] == [(5,[0,1,0,0,0]),(5,[0,0,1,0,0]),(5,[0,0,0,1,0]),(5,[1,0,0,0,-1])]

tbl_txt :: Bool -> Integer -> [Rational] -> [[String]] Source #

tbl_wr :: Bool -> [Rational] -> IO () Source #

Graph

type Ew_Gr_Opt = (Maybe (Lattice_Design Rational, Maybe [Integer]), [Dot_Meta_Attr], Rational -> String) Source #

(maybe (maybe lattice-design, maybe primes),gr-attr,vertex-pp)

ew_gr_opt_pos :: Ew_Gr_Opt -> Bool Source #

ew_gr_r_pos :: Lattice_Design Rational -> Maybe [Integer] -> Rational -> Dot_Attr Source #

ew_gr_udot :: Ew_Gr_Opt -> Lbl Rational () -> [String] Source #

lbl_to_udot add position attribute if a Lattice_Design is given.

ew_gr_udot_wr :: Ew_Gr_Opt -> FilePath -> Lbl Rational () -> IO () Source #

writeFile of ew_gr_udot

ew_gr_udot_wr_svg :: Ew_Gr_Opt -> FilePath -> Lbl Rational () -> IO () Source #

Zig-Zag

zz_seq_1 :: (Eq n, Num n) => Int -> (n, n) -> (n, n) -> [(n, n)] Source #

zz_next :: (Eq n, Num n) => Int -> [(n, n)] -> [(n, n)] Source #

zz_recur :: (Eq n, Num n) => [Int] -> [(n, n)] -> [[(n, n)]] Source #

zz_seq :: (Eq n, Num n) => [Int] -> [[(n, n)]] Source #

Mos

gen_coprime :: Integral a => a -> [a] Source #

mos_2 :: Num n => n -> n -> (n, n) Source #

mos_step :: (Ord a, Num a) => (a, a) -> (a, a) Source #

Divide MOS, keeps retained value on same side

mos_step (5,7) == (5,2)
mos_step (5,2) == (3,2)
mos_step (3,2) == (1,2)

mos_unfold :: (Ord b, Num b) => (b, b) -> [(b, b)] Source #

mos_verify :: Integral a => a -> a -> Bool Source #

mos :: (Ord b, Integral b) => b -> b -> [(b, b)] Source #

mos_seq :: (Ord b, Integral b) => b -> b -> [[b]] Source #

mos_cell_pp :: (Integral i, Show i) => i -> String Source #

mos_row_pp :: (Integral i, Show i) => [i] -> String Source #

mos_tbl_pp :: (Integral i, Show i) => [[i]] -> [String] Source #

mos_tbl_wr :: (Integral i, Show i) => [[i]] -> IO () Source #

Mos/Log

mos_recip_seq :: Double -> [(Int, Double)] Source #

mos_log :: Double -> [(Int, Double)] Source #

mos_log_kseq :: Double -> [Int] Source #

Stern-Brocot Tree

data SBT_DIV Source #

Constructors

NIL 
LHS 
RHS 

Instances

Instances details
Show SBT_DIV Source # 
Instance details

Defined in Music.Theory.Tuning.Wilson

Methods

showsPrec :: Int -> SBT_DIV -> ShowS #

show :: SBT_DIV -> String #

showList :: [SBT_DIV] -> ShowS #

type Sbt_Node = (SBT_DIV, Rat, Rat, Rat) Source #

sbt_step :: Sbt_Node -> [Sbt_Node] Source #

sbt_root :: Sbt_Node Source #

sbt_half :: Sbt_Node Source #

sbt_from :: Sbt_Node -> [[Sbt_Node]] Source #

sbt_k_from :: Int -> Sbt_Node -> [[Sbt_Node]] Source #

sbt_node_to_edge :: Sbt_Node -> String Source #

sbt_node_elem :: Sbt_Node -> [Rat] Source #

sbt_dot :: [Sbt_Node] -> [String] Source #

M-Gen

(^.) :: Rational -> Int -> Rational Source #

r_normalise :: [Rational] -> [Rational] Source #

type M_Gen = (Rational, Rational, Int) Source #

(ratio,multiplier,steps)

m_gen_unfold :: M_Gen -> [Rational] Source #

m_gen_to_r :: [M_Gen] -> [Rational] Source #

M3-Gen

type M3_Gen = (Rational, Int) Source #

(ratio,M3-steps)

m3_to_m :: M3_Gen -> M_Gen Source #

m3_gen_unfold :: M3_Gen -> [Rational] Source #

m3_gen_to_r :: [M3_Gen] -> [Rational] Source #

Scala

r_to_scale :: String -> String -> [Rational] -> Scale Source #

ew_scl_find_r :: [Rational] -> [Scale] -> [String] Source #

http://anaphoria.com/1-3-5-7-9Genus.pdf

ew_1357_3_gen :: [M3_Gen] Source #

ew_1357_3_r :: [Rational] Source #

P.3 7-limit {Scala=nil}

db <- Scala.scl_load_db
ew_scl_find_r (1 : ew_1357_3_r) db

ew_1357_3_scl :: Scale Source #

http://anaphoria.com/earlylattices12.pdf

ew_el12_7_r :: [Rational] Source #

P.7 11-limit {Scala=nil}

ew_scl_find_r ew_el12_7_r db

ew_el12_7_scl :: Scale Source #

ew_el12_9_r :: [Rational] Source #

P.9 7-limit {Scala=wilson_class}

ew_scl_find_r ew_el12_9_r db

ew_el12_12_r :: [Rational] Source #

P.12 11-limit {Scala=nil}

ew_scl_find_r ew_el12_12_r db

ew_el12_12_scl :: Scale Source #

http://anaphoria.com/earlylattices22.pdf

ew_el22_2_r :: [Rational] Source #

P.2 11-limit {Scala=wilson_l4}

ew_scl_find_r ew_el22_2_r db

ew_el22_3_r :: [Rational] Source #

P.3 11-limit {Scala=wilson_l5}

ew_scl_find_r ew_el22_3_r db

ew_el22_4_r :: [Rational] Source #

P.4 11-limit {Scala=wilson_l3}

ew_scl_find_r ew_el22_4_r db

ew_el22_5_r :: [Rational] Source #

P.5 11-limit {Scala=wilson_l1}

ew_scl_find_r ew_el22_5_r db

ew_el22_6_r :: [Rational] Source #

P.6 11-limit {Scala=wilson_l2}

ew_scl_find_r ew_el22_6_r db

http://anaphoria.com/diamond.pdf

ew_diamond_mk :: [Integer] -> [Rational] Source #

ew_diamond_12_gen :: [M3_Gen] Source #

ew_diamond_12_r :: [Rational] Source #

P.7 & P.12 11-limit {Scala=partch_29}

1,3,5,7,9,11 diamond

ew_scl_find_r ew_diamond_12_r db -- partch_29

ew_diamond_13_r :: [Rational] Source #

P.10 & P.13 13-limit {Scala=novaro15}

1,3,5,7,9,11,13,15 diamond

ew_scl_find_r ew_diamond_13_r db -- novaro15

http://anaphoria.com/hel.pdf

hel_r_asc :: (Integer, Integer) -> [Rational] Source #

type HEL = ([Rational], [Rational]) Source #

hel_1_i :: HEL Source #

P.6

hel_2_i :: HEL Source #

P.6

hel_3_i :: HEL Source #

P.10

hel_r :: HEL -> [[Rational]] Source #

ew_hel_12_r :: [Rational] Source #

P.12 {Scala=nil}

22-tone 23-limit Evangalina tuning (2001)

ew_scl_find_r ew_hel_12_r db

ew_hel_12_scl :: Scale Source #

http://anaphoria.com/HexanyStellatesExpansions.pdf

she_div :: Eq a => [a] -> [[[a]]] Source #

she_div_r :: [Rational] -> [Rational] Source #

she_mul_r :: [Rational] -> [Rational] Source #

she :: [Rational] -> [Rational] Source #

she = Stellate Hexany Expansions, P.10 {Scala=stelhex1,stelhex2,stelhex5,stelhex6}

she [1,3,5,7] == [1,21/20,15/14,35/32,9/8,5/4,21/16,35/24,3/2,49/32,25/16,105/64,7/4,15/8]
mapM (flip ew_scl_find_r db . she) [[1,3,5,7],[1,3,5,9],[1,3,7,9],[1,3,5,11]]
ew_scl_find_r (she [1,(5*7)/(3*3),1/(3 * 5),1/3]) db -- NIL

http://anaphoria.com/meru.pdf

every_nth :: [t] -> Int -> [t] Source #

meru :: Num n => [[n]] Source #

meru_k :: Num n => Int -> [[n]] Source #

meru_1 :: Num n => Int -> [n] Source #

meru_1_direct :: Num n => [n] Source #

meru_2 :: Num n => Int -> [n] Source #

Meru 2 = META-PELOG

map (sum . meru_2) [1 .. 14] == [1,1,1,2,3,4,6,9,13,19,28,41,60,88]

meru_2_direct :: Num n => [n] Source #

meru_3 :: Num n => Int -> [[n]] Source #

meru_3 = META-SLENDRO

meru_3_seq :: Num n => Int -> [[n]] Source #

meru_3_direct :: Num n => [n] Source #

meru_4 :: Num n => Int -> [n] Source #

meru_4_direct :: Num n => [n] Source #

meru_5 :: Num n => Int -> [[n]] Source #

meru_5_seq :: Num n => Int -> [[n]] Source #

meru_5_direct :: Num n => [n] Source #

meru_6 :: Num n => Int -> [n] Source #

meru_6_direct :: Num n => [n] Source #

meru_7_direct :: Num n => [n] Source #

http://anaphoria.com/mos.pdf

ew_mos_13_tanabe_r :: [Rational] Source #

P.13, tanabe {Scala=chin_7}

ew_scl_find_r ew_mos_13_tanabe_r db

http://anaphoria.com/novavotreediamond.pdf (Novaro)

ew_novarotreediamond_1 :: ([[Rational]], [[Rational]]) Source #

ew_novarotreediamond_1_r :: [Rational] Source #

P.1 {Scala=nil}

23-tone 7-limit (2004)

ew_scl_find_r ew_novarotreediamond_1_r db

ew_novarotreediamond_1_scl :: Scale Source #

http://anaphoria.com/Pelogflute.pdf

ew_Pelogflute_2_r :: Fractional n => [n] Source #

P.2 {Scala=nil}

9-tone Pelog cycle (1988)

ew_scl_find_r ew_Pelogflute_2_r db

ew_Pelogflute_2_scl :: Scale Source #

http://anaphoria.com/xen1.pdf

xen1_fig3 :: (Sbt_Node, Int) Source #

P.9, Fig. 3

xen1_fig4 :: (Sbt_Node, Int) Source #

P.9, Fig. 4

http://anaphoria.com/xen3b.pdf

ew_xen3b_3_gen :: [(Rational, Int)] Source #

P.3 Turkisk Baglama Scale {11-limit, Scala=nil}

ew_xen3b_3_r :: [Rational] Source #

ew_xen3b_3_scl :: Scale Source #

xen3b_9_i :: [[Rational]] Source #

xen3b_9_r :: [[Rational]] Source #

P.9 {SCALA 5=nil 7=ptolemy_idiat 12=nil 19=wilson2 31=wilson_31}

mapM ew_scl_find_r xen3b_9_r db

xen3b_13_i :: [[Rational]] Source #

xen3b_13_r :: [[Rational]] Source #

P.13 {SCALA 5=slendro5_2 7=ptolemy_diat2 12=nil 17=nil 22=wilson7_4}

http://anaphoria.com/xen3bappendix.pdf

ew_xen3b_apx_gen :: [(Int, [M3_Gen])] Source #

PP.1-2 {SCALA: 22=wilson7_4}

17,31,41 lattices from XEN3B (1975)

ew_xen3b_apx_r :: [(Int, [Rational])] Source #

http://anaphoria.com/xen456.pdf

ew_xen456_7_gen :: [M3_Gen] Source #

ew_xen456_7_r :: [Rational] Source #

ew_xen456_9_gen :: [M3_Gen] Source #

ew_xen456_9_r :: [Rational] Source #

P.9 {Scala=nil ; Scala:Rot=wilson11}

19-tone scale for the Clavichord-19 (1976)

ew_scl_find_r ew_xen456_9_r db
import qualified Music.Theory.List as List 
Scala.scl_find_ji List.is_subset ew_xen456_9_r db -- NIL

ew_xen456_9_scl :: Scale Source #

Gems

ew_poole_r :: [Rational] Source #

http://wilsonarchives.blogspot.com/2010/10/scale-for-rod-poole.html

13-limit 22-tone scale {Scala=nil}

ew_scl_find_r ew_poole_r db

ew_poole_scl :: Scale Source #

ew_centaur17_r :: [Rational] Source #

http://wilsonarchives.blogspot.com/2014/05/an-11-limit-centaur-implied-in-wilson.html

11-limit 17-tone scale {Scala=wilcent17}

ew_scl_find_r ew_centaur17_r db

ew_two_22_7_r :: [Rational] Source #

http://wilsonarchives.blogspot.com/2018/03/an-unusual-22-tone-7-limit-tuning.html

7-limit 22-tone scale {Scala=nil}

ew_scl_find_r ew_two_22_7_r db

ew_two_22_7_scl :: Scale Source #

Db

ew_scl_db :: [Scale] Source #

Scales not present in the standard scala file set.

mapM_ (Scala.scale_wr_dir "/home/rohan/sw/hmt/data/scl/") ew_scl_db
map Scala.scale_name ew_scl_db