Gann.hs

-- | Kyle Gann.
module Music.Theory.Tuning.Gann where

import Music.Theory.Tuning {- hmt -}

-- * Historical

-- | Cents for 'pietro_aaron_1523'.
--
-- > let c = [0,76,193,310,386,503,580,697,773,890,1007,1083]
-- > in map round pietro_aaron_1523_c == c
pietro_aaron_1523_c :: [Cents]
pietro_aaron_1523_c =
    [0,76.0
    ,193.2,310.3
    ,386.3
    ,503.4,579.5
    ,696.8,772.6
    ,889.7,1006.8
    ,1082.9]

-- | Pietro Aaron (1523) meantone temperament, see
-- <http://www.kylegann.com/histune.html>
--
-- > cents_i pietro_aaron_1523 == [0,76,193,310,386,503,580,697,773,890,1007,1083]
pietro_aaron_1523 :: Tuning
pietro_aaron_1523 = Tuning (Right pietro_aaron_1523_c) 2

-- | Andreas Werckmeister (1645-1706), <http://www.kylegann.com/histune.html>.
werckmeister_iii_c :: [Cents]
werckmeister_iii_c =
    [0,90.225
    ,192.18,294.135
    ,390.225
    ,498.045,588.27
    ,696.09,792.18
    ,888.27,996.09
    ,1092.18]

-- | Cents for 'thomas_young_1799'.
--
-- > let c = [0,94,196,298,392,500,592,698,796,894,1000,1092]
-- > in map round thomas_young_1799_c == c
thomas_young_1799_c :: [Cents]
thomas_young_1799_c =
    [0,93.9
    ,195.8,297.8
    ,391.7
    ,499.9,591.9
    ,697.9,795.8
    ,893.8,999.8
    ,1091.8]

-- | Thomas Young (1799), Well Temperament, <http://www.kylegann.com/histune.html>.
--
-- > cents_i thomas_young_1799 == [0,94,196,298,392,500,592,698,796,894,1000,1092]
thomas_young_1799 :: Tuning
thomas_young_1799 = Tuning (Right thomas_young_1799_c) 2

-- | Ratios for 'zarlino'.
zarlino_r :: [Rational]
zarlino_r = [1/1,25/24,10/9,9/8,32/27,6/5,5/4,4/3,25/18,45/32,3/2,25/16,5/3,16/9,9/5,15/8]

-- | Gioseffo Zarlino, 1588, see <http://www.kylegann.com/tuning.html>.
--
-- > divisions zarlino == 16
-- > cents_i zarlino == [0,71,182,204,294,316,386,498,569,590,702,773,884,996,1018,1088]
zarlino :: Tuning
zarlino = Tuning (Left zarlino_r) 2

-- * 20th Century

-- | Ratios for 'la_monte_young'.
--
-- > let c = [0,177,204,240,471,444,675,702,738,969,942,1173]
-- > in map (round . ratio_to_cents) la_monte_young_r == c
la_monte_young_r :: [Rational]
la_monte_young_r =
    [1,567/512
    ,9/8,147/128
    ,21/16
    ,1323/1024,189/128
    ,3/2,49/32
    ,7/4,441/256
    ,63/32]

-- | La Monte Young's \"The Well-Tuned Piano\", see
-- <http://www.kylegann.com/wtp.html>.
--
-- > cents_i la_monte_young == [0,177,204,240,471,444,675,702,738,969,942,1173]
la_monte_young :: Tuning
la_monte_young = Tuning (Left la_monte_young_r) 2

-- | Ratios for 'ben_johnston'.
--
-- > let c = [0,105,204,298,386,471,551,702,841,906,969,1088]
-- > in map (round . ratio_to_cents) ben_johnston_r == c
ben_johnston_r :: [Rational]
ben_johnston_r =
    [1,17/16
    ,9/8,19/16
    ,5/4
    ,21/16,11/8
    ,3/2,13/8
    ,27/16,7/4
    ,15/8]

-- | Ben Johnston's \"Suite for Microtonal Piano\" (1977), see
-- <http://www.kylegann.com/tuning.html>
--
-- > cents_i ben_johnston == [0,105,204,298,386,471,551,702,841,906,969,1088]
ben_johnston :: Tuning
ben_johnston = Tuning (Left ben_johnston_r) 2

-- * Gann

-- | Ratios for 'gann_arcana_xvi'.
gann_arcana_xvi_r :: [Rational]
gann_arcana_xvi_r =
    [1/1,21/20,16/15,9/8,7/6,6/5,11/9,5/4,21/16,4/3,27/20,7/5
    ,22/15,3/2,55/36,8/5,44/27,5/3,42/25,7/4,9/5,11/6,15/8,88/45]

-- | Kyle Gann, _Arcana XVI_, see <http://www.kylegann.com/Arcana.html>.
--
-- > let r = [0,84,112,204,267,316,347,386,471,498,520,583,663,702,734,814,845,884,898,969,1018,1049,1088,1161]
-- > in cents_i gann_arcana_xvi == r
gann_arcana_xvi :: Tuning
gann_arcana_xvi = Tuning (Left gann_arcana_xvi_r) 2

-- | Ratios for 'gann_superparticular'.
gann_superparticular_r :: [Rational]
gann_superparticular_r = [1/1,11/10,10/9,9/8,8/7,7/6,6/5,5/4,9/7,4/3,11/8,7/5,10/7,3/2,11/7,14/9,8/5,5/3,12/7,7/4,16/9,9/5]

-- | Kyle Gann, _Superparticular_, see <http://www.kylegann.com/Super.html>.
--
-- > divisions gann_superparticular == 22
--
-- > let r = [0,165,182,204,231,267,316,386,435,498,551,583,617,702,782,765,814,884,933,969,996,1018]
-- > in cents_i gann_superparticular == r
gann_superparticular :: Tuning
gann_superparticular = Tuning (Left gann_superparticular_r) 2