Music.Theory.Tuning.Microtonal_Synthesis

http://www.microtonal-synthesis.com/scales.html

Documentation

pythagorean_r :: [Rational]

Ratios for pythagorean.

let c = [0,90,204,294,408,498,612,702,792,906,996,1110]
in map (round . ratio_to_cents) pythagorean_r == c

pythagorean :: Tuning

Pythagorean tuning, http://www.microtonal-synthesis.com/scale_pythagorean.html.

divisions pythagorean == 12
cents_i pythagorean == [0,90,204,294,408,498,612,702,792,906,996,1110]

five_limit_tuning_r :: [Rational]

Ratios for five_limit_tuning.

let c = [0,112,204,316,386,498,590,702,814,884,996,1088]
in map (round . ratio_to_cents) five_limit_tuning_r == c

five_limit_tuning :: Tuning

Five-limit tuning (five limit just intonation).

cents_i five_limit_tuning == [0,112,204,316,386,498,590,702,814,884,996,1088]

septimal_tritone_just_intonation_r :: [Rational]

Ratios for septimal_tritone_just_intonation.

let c = [0,112,204,316,386,498,583,702,814,884,1018,1088]
in map (round . ratio_to_cents) septimal_tritone_just_intonation == c

septimal_tritone_just_intonation :: Tuning

Septimal tritone Just Intonation, see http://www.microtonal-synthesis.com/scale_just_intonation.html

cents_i septimal_tritone_just_intonation == [0,112,204,316,386,498,583,702,814,884,1018,1088]

seven_limit_just_intonation_r :: [Rational]

Ratios for seven_limit_just_intonation.

let c = [0,112,204,316,386,498,583,702,814,884,969,1088]
in map (round . ratio_to_cents) seven_limit_just_intonation == c

seven_limit_just_intonation :: Tuning

Seven limit Just Intonation.

cents_i seven_limit_just_intonation == [0,112,204,316,386,498,583,702,814,884,969,1088]

kirnberger_iii_ar :: [Approximate_Ratio]

Approximate ratios for kirnberger_iii.

let c = [0,90,193,294,386,498,590,697,792,890,996,1088]
in map (round.to_cents) kirnberger_iii_ar == c

kirnberger_iii :: Tuning

http://www.microtonal-synthesis.com/scale_kirnberger.html.

cents_i kirnberger_iii == [0,90,193,294,386,498,590,697,792,890,996,1088]

vallotti_c :: [Cents]

vallotti :: Tuning

Vallotti & Young scale (Vallotti version), see http://www.microtonal-synthesis.com/scale_vallotti_young.html.

cents_i vallotti == [0,94,196,298,392,502,592,698,796,894,1000,1090]

mayumi_reinhard_r :: [Rational]

mayumi_reinhard :: Tuning

Mayumi Reinhard 13-limit Just Intonation scale, http://www.microtonal-synthesis.com/scale_reinhard.html.

cents_i mayumi_reinhard == [0,128,139,359,454,563,637,746,841,911,1072,1183]

lou_harrison_16_r :: [Rational]

Ratios for lou_harrison_16.

length lou_harrison_16_r == 16

let c = [0,112,182,231,267,316,386,498,603,702,814,884,933,969,1018,1088]
in map (round . ratio_to_cents) lou_harrison_16_r == c

lou_harrison_16 :: Tuning

Lou Harrison 16 tone Just Intonation scale, see http://www.microtonal-synthesis.com/scale_harrison_16.html

let r = [0,112,182,231,267,316,386,498,603,702,814,884,933,969,1018,1088]
in cents_i lou_harrison_16 == r

partch_43_r :: [Rational]

Ratios for partch_43.

partch_43 :: Tuning

Harry Partch 43 tone scale, see http://www.microtonal-synthesis.com/scale_partch.html

cents_i partch_43 == [0,22,53,84,112,151,165
                     ,182,204,231,267,294,316
                     ,347,386,418,435
                     ,471,498,520,551,583,617,649
                     ,680,702,729,765,782,814,853,884,906,933
                     ,969,996,1018,1035,1049,1088,1116,1147,1178]

ben_johnston_25_r :: [Rational]

Ratios for ben_johnston_25.

ben_johnston_25 :: Tuning

Ben Johnston 25 note just enharmonic scale, see http://www.microtonal-synthesis.com/scale_johnston_25.html