Documentation

Ratios for pythagorean.

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

cents_i pythagorean_12 == [0,114,204,294,408,498,612,702,816,906,996,1110]

scl <- scl_load "pyth_12"
cents_i (scale_tuning 0.1 scl) == cents_i pythagorean_12

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 (five limit just intonation), Alexander Malcolm's Monochord (1721).

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

scl <- scl_load "malcolm"
cents_i (scale_tuning 0.1 scl) == cents_i five_limit_tuning

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, see http://www.microtonal-synthesis.com/scale_just_intonation.html

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

scl <- scl_load "ji_12"
cents_i (scale_tuning 0.1 scl) == cents_i septimal_tritone_just_intonation

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.

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

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

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

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

scl <- scl_load "kirnberger"
cents_i (scale_tuning 0.1 scl) == cents_i kirnberger_iii

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]

scl <- scl_load "vallotti"
cents_i (scale_tuning 0.1 scl) == cents_i vallotti

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

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

scl <- scl_load "tsuda13"
cents_i (scale_tuning 0.1 scl) == cents_i mayumi_tsuda

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 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

import Music.Theory.Tuning.Scala
scl <- scl_load "harrison_16"
cents_i (scale_tuning 0.1 scl) == cents_i lou_harrison_16

Ratios for partch_43.

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]

scl <- scl_load "partch_43"
cents_i (scale_tuning 0.1 scl) == cents_i partch_43

Ratios for ben_johnston_25.

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

scl <- scl_load "johnston_25"
cents_i (scale_tuning 0.1 scl) == cents_i ben_johnston_25