Music.Theory.Tuning.Gann

Kyle Gann.

Historical

pietro_aaron_1523_c :: [Cents]

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 :: Tuning

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]

werckmeister_iii_c :: [Cents]

Andreas Werckmeister (1645-1706), http://www.kylegann.com/histune.html.

thomas_young_1799_c :: [Cents]

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 :: Tuning

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]

zarlino_r :: [Rational]

Ratios for zarlino.

zarlino :: Tuning

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]

20th Century

la_monte_young_r :: [Rational]

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 :: Tuning

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]

ben_johnston_r :: [Rational]

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 :: Tuning

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]

Gann

gann_arcana_xvi_r :: [Rational]

Ratios for gann_arcana_xvi.

gann_arcana_xvi :: Tuning

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_superparticular_r :: [Rational]

Ratios for gann_superparticular.

gann_superparticular :: Tuning

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