hmt-0.15: Haskell Music Theory

Safe Haskell | Safe
Language | Haskell98

Music.Theory.Tuning.Microtonal_Synthesis

Description

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

Synopsis

- pythagorean_r :: [Rational]
- pythagorean :: Tuning
- five_limit_tuning_r :: [Rational]
- five_limit_tuning :: Tuning
- septimal_tritone_just_intonation_r :: [Rational]
- septimal_tritone_just_intonation :: Tuning
- seven_limit_just_intonation_r :: [Rational]
- seven_limit_just_intonation :: Tuning
- kirnberger_iii_ar :: [Approximate_Ratio]
- kirnberger_iii :: Tuning
- vallotti_c :: [Cents]
- vallotti :: Tuning
- mayumi_reinhard_r :: [Rational]
- mayumi_reinhard :: Tuning
- lou_harrison_16_r :: [Rational]
- lou_harrison_16 :: Tuning
- partch_43_r :: [Rational]
- partch_43 :: Tuning
- ben_johnston_25_r :: [Rational]
- ben_johnston_25 :: Tuning

# Documentation

pythagorean_r :: [Rational] Source #

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 Source #

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] Source #

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 Source #

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] Source #

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 Source #

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] Source #

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 Source #

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] Source #

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 Source #

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] Source #

vallotti :: Tuning Source #

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] Source #

mayumi_reinhard :: Tuning Source #

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] Source #

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 Source #

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] Source #

Ratios for `partch_43`.

partch_43 :: Tuning Source #

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] Source #

Ratios for `ben_johnston_25`.

ben_johnston_25 :: Tuning Source #

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