Music.Theory.Tuning.Db.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]
map round pietro_aaron_1523_c == c

map ((+ 60) . (/ 100)) pietro_aaron_1523_c

pietro_aaron_1523 :: Tuning

Pietro Aaron (1523) meantone temperament, see http://www.kylegann.com/histune.html

tn_cents_i pietro_aaron_1523 == [0,76,193,310,386,503,580,697,773,890,1007,1083]

import Music.Theory.Tuning.Scala
scl <- scl_load "meanquar"
tn_cents_i (scale_to_tuning 0.01 scl) == [0,76,193,310,386,503,579,697,773,890,1007,1083]

thomas_young_1799_c :: [Cents]

Cents for thomas_young_1799.

let c = [0,94,196,298,392,500,592,698,796,894,1000,1092]
map round thomas_young_1799_c == c

thomas_young_1799 :: Tuning

Thomas Young (1799), Well Temperament, http://www.kylegann.com/histune.html.

tn_cents_i thomas_young_1799 == [0,94,196,298,392,500,592,698,796,894,1000,1092]

scl <- scl_load "young2"
tn_cents_i (scale_to_tuning 0.01 scl) == tn_cents_i thomas_young_1799

zarlino_1588_r :: [Rational]

Ratios for zarlino.

length zarlino_1588_r == 16

zarlino_1588 :: Tuning

Gioseffo Zarlino, 1588, see http://www.kylegann.com/tuning.html.

tn_divisions zarlino_1588 == 16
tn_cents_i zarlino_1588 == [0,71,182,204,294,316,386,498,569,590,702,773,884,996,1018,1088]

scl <- scl_load "zarlino2"
tn_cents_i (scale_to_tuning 0.01 scl) == tn_cents_i zarlino_1588

20th Century

ben_johnston_mtp_1977_r :: [Rational]

Ratios for ben_johnston_mtp_1977.

let c = [0,105,204,298,386,471,551,702,841,906,969,1088]
map (round . ratio_to_cents) ben_johnston_mtp_1977_r == c

ben_johnston_mtp_1977 :: Tuning

Ben Johnston's "Suite for Microtonal Piano" (1977), see http://www.kylegann.com/tuning.html

tn_cents_i ben_johnston_mtp_1977 == [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]
tn_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.

tn_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]
tn_cents_i gann_superparticular == r

scl <- scl_load "gann_super"
tn_cents_i (scale_to_tuning 0.01 scl) == tn_cents_i gann_superparticular