use std::{borrow::Cow, collections::HashMap};
use crate::{math, pitch::Ratio};
pub fn huygens_fokker_intervals() -> Vec<Comma> {
let commas: &[(&str, &[i8])] = &[
("unison, perfect prime", &[]),
("octave", &[1]),
("perfect fifth", &[-1, 1]),
("perfect fourth", &[2, -1]),
("major sixth, BP sixth", &[0, -1, 1]),
("major third", &[-2, 0, 1]),
("minor third", &[1, 1, -1]),
("minimal tenth, BP tenth", &[0, -1, 0, 1]),
("harmonic seventh", &[-2, 0, 0, 1]),
("septimal or Huygens' tritone, BP fourth", &[0, 0, -1, 1]),
("septimal minor third", &[-1, -1, 0, 1]),
("minor sixth", &[3, 0, -1]),
("septimal whole tone", &[3, 0, 0, -1]),
("major ninth", &[-2, 2]),
("just minor seventh, BP seventh", &[0, 2, -1]),
("septimal major third, BP third", &[0, 2, 0, -1]),
("major whole tone", &[-3, 2]),
("Euler's tritone", &[1, 0, 1, -1]),
("minor whole tone", &[1, -2, 1]),
("neutral ninth", &[0, 0, -1, 0, 1]),
("21/4-tone, undecimal neutral seventh", &[-1, -1, 0, 0, 1]),
("undecimal augmented fifth", &[0, 0, 0, -1, 1]),
("undecimal semi-augmented fourth", &[-3, 0, 0, 0, 1]),
("undecimal neutral third", &[0, -2, 0, 0, 1]),
("4/5-tone, Ptolemy's second", &[-1, 0, -1, 0, 1]),
("septimal major sixth", &[2, 1, 0, -1]),
("3/4-tone, undecimal neutral second", &[2, 1, 0, 0, -1]),
("16/3-tone", &[0, 0, 0, -1, 0, 1]),
("tridecimal neutral sixth", &[-3, 0, 0, 0, 0, 1]),
("tridecimal diminished fifth", &[0, -2, 0, 0, 0, 1]),
("tridecimal semi-diminished fourth", &[-1, 0, -1, 0, 0, 1]),
("tridecimal minor third", &[0, 0, 0, 0, -1, 1]),
("tridecimal 2/3-tone", &[-2, -1, 0, 0, 0, 1]),
("septimal minor sixth", &[1, -2, 0, 1]),
(
"undecimal diminished fourth or major third",
&[1, 0, 0, 1, -1],
),
("2/3-tone", &[1, 0, 0, 1, 0, -1]),
("septimal minor ninth, BP ninth", &[0, 1, 1, -1]),
("classic major seventh", &[-3, 1, 1]),
("undecimal augmented fourth", &[0, 1, 1, 0, -1]),
("tridecimal 5/4-tone", &[0, 1, 1, 0, 0, -1]),
("major diatonic semitone", &[-1, 1, 1, -1]),
("septimal major ninth", &[4, 0, 0, -1]),
("Pythagorean minor seventh", &[4, -2]),
("undecimal semi-diminished fifth", &[4, 0, 0, 0, -1]),
("tridecimal neutral third", &[4, 0, 0, 0, 0, -1]),
("minor diatonic semitone", &[4, -1, -1]),
("septendecimal minor ninth", &[-3, 0, 0, 0, 0, 0, 1]),
("septendecimal major seventh", &[0, -2, 0, 0, 0, 0, 1]),
("septendecimal diminished seventh", &[-1, 0, -1, 0, 0, 0, 1]),
("2nd septendecimal tritone", &[-2, -1, 0, 0, 0, 0, 1]),
("supraminor third", &[-1, 0, 0, -1, 0, 0, 1]),
("septendecimal whole tone", &[0, -1, -1, 0, 0, 0, 1]),
("17th harmonic", &[-4, 0, 0, 0, 0, 0, 1]),
("undecimal neutral sixth", &[1, 2, 0, 0, -1]),
("tridecimal augmented fourth", &[1, 2, 0, 0, 0, -1]),
("Arabic lute index finger", &[1, 2, 0, 0, 0, 0, -1]),
("undevicesimal major seventh", &[-1, 0, -1, 0, 0, 0, 0, 1]),
("undevicesimal minor sixth", &[-2, -1, 0, 0, 0, 0, 0, 1]),
("undevicesimal ditone", &[0, -1, -1, 0, 0, 0, 0, 1]),
("19th harmonic", &[-4, 0, 0, 0, 0, 0, 0, 1]),
("quasi-meantone", &[0, 0, 0, 0, 0, 0, -1, 1]),
("undevicesimal semitone", &[-1, -2, 0, 0, 0, 0, 0, 1]),
("small ninth", &[2, -2, 1]),
("large minor seventh", &[2, 0, 1, 0, -1]),
("tridecimal semi-augmented fifth", &[2, 0, 1, 0, 0, -1]),
("septendecimal augmented second", &[2, 0, 1, 0, 0, 0, -1]),
("small undevicesimal semitone", &[2, 0, 1, 0, 0, 0, 0, -1]),
("undecimal major seventh", &[0, 1, 0, 1, -1]),
("narrow fourth", &[-4, 1, 0, 1]),
("submajor third", &[0, 1, 0, 1, 0, 0, -1]),
("minor semitone", &[-2, 1, -1, 1]),
("tridecimal major sixth", &[1, 0, 0, 0, 1, -1]),
("undecimal diminished fifth", &[1, -1, -1, 0, 1]),
("undecimal minor semitone", &[1, -1, 0, -1, 1]),
(
"vicesimotertial major seventh",
&[-2, -1, 0, 0, 0, 0, 0, 0, 1],
),
("23rd harmonic", &[-4, 0, 0, 0, 0, 0, 0, 0, 1]),
(
"vicesimotertial major third",
&[-1, -2, 0, 0, 0, 0, 0, 0, 1],
),
("tridecimal neutral seventh", &[3, 1, 0, 0, 0, -1]),
("1st septendecimal tritone", &[3, 1, 0, 0, 0, 0, -1]),
(
"smaller undevicesimal major third",
&[3, 1, 0, 0, 0, 0, 0, -1],
),
(
"vicesimotertial minor semitone",
&[3, 1, 0, 0, 0, 0, 0, 0, -1],
),
("classic augmented eleventh, BP twelfth", &[0, -2, 2]),
("classic augmented octave", &[-2, -1, 2]),
("middle minor seventh", &[-1, 0, 2, -1]),
("classic augmented fifth", &[-4, 0, 2]),
("classic augmented fourth", &[-1, -2, 2]),
("BP second, quasi-equal minor third", &[0, -1, 2, -1]),
("undecimal acute whole tone", &[-1, 0, 2, 0, -1]),
("classic chromatic semitone, minor chroma", &[-3, -1, 2]),
("tridecimal semi-augmented sixth", &[1, -1, -1, 0, 0, 1]),
("tridecimal 1/3-tone", &[1, 0, -2, 0, 0, 1]),
("septimal major seventh", &[-1, 3, 0, -1]),
("Pythagorean major sixth", &[-4, 3]),
("septendecimal minor sixth", &[0, 3, 0, 0, 0, 0, -1]),
("acute fourth", &[-2, 3, -1]),
(
"neutral third, Zalzal wosta of al-Farabi",
&[-1, 3, 0, 0, -1],
),
("vicesimotertial minor third", &[0, 3, 0, 0, 0, 0, 0, 0, -1]),
(
"large limma, BP small semitone, Zarlino semitone",
&[0, 3, -2],
),
("tridecimal comma", &[-1, 3, 0, 0, 0, -1]),
("grave major seventh", &[2, -1, -1, 1]),
("submajor sixth", &[2, 0, 0, 1, 0, 0, -1]),
("middle second", &[2, 0, -2, 1]),
("Archytas' 1/3-tone", &[2, -3, 0, 1]),
("29th harmonic", &[-4, 0, 0, 0, 0, 0, 0, 0, 0, 1]),
("septendecimal minor seventh", &[1, 1, 1, 0, 0, 0, -1]),
(
"smaller undevicesimal minor sixth",
&[1, 1, 1, 0, 0, 0, 0, -1],
),
("31st harmonic", &[-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),
("31st-partial chroma", &[-1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1]),
("minor ninth", &[5, -1, -1]),
("17th subharmonic", &[5, 0, 0, 0, 0, 0, -1]),
("19th subharmonic", &[5, 0, 0, 0, 0, 0, 0, -1]),
("wide fifth", &[5, -1, 0, -1]),
("23rd subharmonic", &[5, 0, 0, 0, 0, 0, 0, 0, -1]),
("classic diminished fourth", &[5, 0, -2]),
("Pythagorean minor third", &[5, -3]),
("29th subharmonic", &[5, 0, 0, 0, 0, 0, 0, 0, 0, -1]),
(
"Greek enharmonic 1/4-tone",
&[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1],
),
("2 pentatones", &[0, 1, -2, 0, 1]),
("tridecimal major third", &[-1, 1, 0, 0, 1, -1]),
("undecimal minor third", &[-2, 1, 0, -1, 1]),
("undecimal comma, al-Farabi's 1/4-tone", &[-5, 1, 0, 0, 1]),
("quasi-mean seventh", &[1, 0, 0, 0, 0, 0, 1, -1]),
("supraminor sixth", &[1, -1, 0, -1, 0, 0, 1]),
("septendecimal major third", &[1, -3, 0, 0, 0, 0, 1]),
("septimal semi-diminished octave", &[-1, -2, 1, 1]),
("septimal semi-diminished fifth", &[-3, -1, 1, 1]),
("9/4-tone, septimal semi-diminished fourth", &[0, -3, 1, 1]),
("septimal neutral second", &[-5, 0, 1, 1]),
("septendecimal 1/4-tone", &[-1, 0, 1, 1, 0, 0, -1]),
(
"smaller undevicesimal major seventh",
&[2, 2, 0, 0, 0, 0, 0, -1],
),
("classic diminished fifth", &[2, 2, -2]),
("septimal diesis, 1/4-tone", &[2, 2, -1, -1]),
("37th harmonic", &[-5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),
(
"39th harmonic, Zalzal wosta of Ibn Sina",
&[-5, 1, 0, 0, 0, 1],
),
("acute major seventh", &[3, -1, 1, -1]),
("grave fifth", &[3, -3, 1]),
("tridecimal minor diesis", &[3, -1, 1, 0, 0, -1]),
("quasi-equal major sixth", &[1, 1, -2, 1]),
("undecimal grave minor seventh", &[2, 0, -2, 0, 1]),
("neutral sixth", &[2, -3, 0, 0, 1]),
("septimale wide minor sixth", &[-2, 2, 1, -1]),
("diatonic tritone", &[-5, 2, 1]),
("1/5-tone", &[-2, 2, 1, 0, -1]),
("23rd-partial chroma", &[1, -2, -1, 0, 0, 0, 0, 0, 1]),
("classic diminished octave", &[4, 1, -2]),
("septimal semi-augmented fourth", &[4, 1, -1, -1]),
("BP eighth", &[0, 0, -2, 2]),
("larger approximation to neutral sixth", &[-1, -1, -1, 2]),
("Arabic lute acute fourth", &[-2, -2, 0, 2]),
("larger approximation to neutral third", &[-3, 0, -1, 2]),
("BP minor semitone", &[0, -2, -1, 2]),
("undecimal minor whole tone", &[-2, 0, 0, 2, -1]),
("slendro diesis, septimal 1/6-tone", &[-4, -1, 0, 2]),
("grave major seventh", &[1, -3, 2]),
("3 pentatones", &[1, -1, 2, 0, -1]),
("Erlich's decatonic comma, tritonic diesis", &[1, 0, 2, -2]),
("septendecimal diminished fourth", &[-3, 1, -1, 0, 0, 0, 1]),
("17th-partial chroma", &[-1, 1, -2, 0, 0, 0, 1]),
("tridecimal minor sixth", &[2, -1, 0, 0, -1, 1]),
("septimal semi-augmented fifth", &[1, 3, -1, -1]),
("Zalzal's mujannab", &[1, 3, 0, -2]),
("undecimal semi-augmented fifth", &[-2, -2, 1, 0, 1]),
("undecimal semi-augmented whole tone", &[-4, -1, 1, 0, 1]),
("quasi-equal major second", &[0, 0, 1, -2, 1]),
("telepathma", &[-1, -3, 1, 0, 1]),
("septimal narrow major third", &[3, -2, -1, 1]),
("undecimal diesis, konbini comma", &[3, 0, -1, 1, -1]),
("undevicesimal minor seventh", &[-5, 1, 0, 0, 0, 0, 0, 1]),
("Hendrix comma", &[-3, 1, 0, -1, 0, 0, 0, 1]),
("smaller approximation to neutral third", &[2, 1, 1, -2]),
("quasi-equal major tenth, BP eleventh", &[0, 2, -2, 1]),
("octave - septimal comma", &[-5, 2, 0, 1]),
("submajor seventh", &[-1, 2, 0, 1, 0, 0, -1]),
("narrow minor sixth", &[-3, 2, -1, 1]),
("quasi-equal major third", &[-1, 2, -2, 1]),
("33rd subharmonic", &[6, -1, 0, 0, -1]),
("septimal neutral seventh", &[6, 0, -1, -1]),
("37th subharmonic", &[6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]),
("39th subharmonic", &[6, -1, 0, 0, 0, -1]),
("2nd tritone", &[6, -2, -1]),
("2 septatones or septatonic major third", &[6, 0, 0, -2]),
("septimal comma, Archytas' comma", &[6, -2, 0, -1]),
("13th-partial chroma", &[-6, 0, 1, 0, 0, 1]),
("Winmeanma", &[1, 1, -1, 0, 1, -1]),
("23/4-tone", &[2, 0, -1, -1, 0, 0, 1]),
("supraminor second", &[2, -2, 0, -1, 0, 0, 1]),
("Valentine semitone", &[2, 0, -1, 0, 0, -1, 1]),
("Arabic lute grave fifth", &[3, 2, 0, -2]),
("undecimal semi-diminished fourth", &[3, 2, -1, 0, -1]),
(
"Ibn Sina's neutral third",
&[3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1],
),
(
"approximation to Pythagorean comma",
&[
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1,
],
),
("BP fifth", &[0, 1, 2, -2]),
("marvelous fourth", &[-3, 1, 2, -1]),
("classic augmented second", &[-6, 1, 2]),
("Keemun minor third", &[-6, 0, 0, 1, 1]),
("undecimal secor", &[-3, -2, 0, 1, 1]),
(
"approximation to 53-tone comma",
&[-2, 0, 0, 1, 1, 0, 0, -1],
),
(
"porcupine neutral second",
&[1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1],
),
("tridecimal minor third comma", &[1, 1, 0, -1, -1, 1]),
("smaller approximation to neutral sixth", &[4, 0, 1, -2]),
("wide major third", &[4, -2, 1, -1]),
("2nd undecimal neutral seventh", &[-2, 4, 0, 0, -1]),
("acute minor sixth", &[-1, 4, -2]),
("Pythagorean major third", &[-6, 4]),
("Persian wosta", &[-2, 4, 0, 0, 0, 0, -1]),
("Al-Hwarizmi's lute middle finger ", &[-1, 4, -1, -1]),
("syntonic comma, Didymus comma", &[-4, 4, -1]),
("septendecimal minor third", &[-3, -2, 1, 0, 0, 0, 1]),
("undecimal minor seventh", &[3, 0, 0, -2, 1]),
("2nd undecimal neutral second", &[3, -4, 0, 0, 1]),
(
"quasi-equal semitone",
&[
-2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
],
),
(
"15/4-tone",
&[0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1],
),
("medium tridecimal comma, superleap", &[-1, -2, -1, 1, 0, 1]),
("19th-partial chroma", &[5, 1, -1, 0, 0, 0, 0, -1]),
("quasi-equal minor seventh", &[1, 0, -1, 2, -1]),
("2nd quasi-equal tritone", &[-1, 2, -1, -1, 1]),
("small undecimal comma", &[-1, 2, 0, -2, 1]),
("quasi-equal minor sixth", &[2, -2, 2, -1]),
("grave major third", &[2, -4, 2]),
("Ptolemy's comma", &[2, -2, 2, 0, -1]),
("septimal neutral sixth", &[-6, 1, 1, 1]),
("small tridecimal comma", &[-3, 1, 1, 1, 0, -1]),
("marvelous fifth", &[4, -1, -2, 1]),
("tridecimal gentle fourth", &[-3, 2, 0, 0, -1, 1]),
("undecimal seconds comma, biyatisma", &[-3, -1, -1, 0, 2]),
(
"classic augmented seventh, octave - minor diesis",
&[-6, 0, 3],
),
("classic augmented sixth", &[-3, -2, 3]),
("classic augmented third", &[-5, -1, 3]),
("semi-augmented whole tone", &[-2, -3, 3]),
("classic augmented semitone", &[-4, 0, 3, -1]),
("septimal semicomma, Starling comma", &[1, 2, -3, 1]),
("diminished seventh", &[7, -1, -2]),
("Pythagorean minor sixth", &[7, -4]),
("septimal neutral third", &[7, -1, -1, -1]),
("undecimal semitone", &[7, 0, 0, 0, -2]),
("minor diesis, diesis", &[7, 0, -3]),
("septimal wide minor third", &[-4, 3, 1, -1]),
("major chroma, major limma", &[-7, 3, 1]),
("quasi-equal tritone", &[2, -2, 1, 1, -1]),
("classic diminished third", &[4, 2, -3]),
("Grossma", &[4, 2, 0, 0, -1, -1]),
("29th-partial chroma", &[-4, -2, 1, 0, 0, 0, 0, 0, 0, 1]),
("7/4-tone", &[0, 2, -3, 0, 0, 0, 1]),
("Ganassi's comma", &[-3, 2, 0, 0, 0, 0, 1, -1]),
("octave - syntonic comma", &[5, -4, 1]),
("19/4-tone", &[0, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1]),
(
"Persian neutral second",
&[
1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, -1,
],
),
(
"quasi-equal major seventh",
&[
3, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1,
],
),
("Schulter's comma", &[-3, -1, 0, -1, 0, 2]),
("valinorsma", &[4, 0, -2, -1, 1]),
("classic diminished sixth", &[6, 1, -3]),
("septimal 4/5-tone", &[6, 1, -2, -1]),
("mynucuma", &[2, -1, -1, 2, 0, -1]),
("spleen comma", &[1, 1, 1, 1, -1, 0, 0, -1]),
("semi-augmented sixth", &[3, 3, -3]),
("narrow septimal major sixth", &[5, -3, -1, 1]),
("augmented sixth", &[-7, 2, 2]),
("septimal kleisma", &[-5, 2, 2, -1]),
("5/4-tone", &[-3, 1, -2, 1, 1]),
(
"Meshaqah's 3/4-tone",
&[
0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
],
),
("octave - maximal diesis", &[0, 5, -3]),
("Pythagorean major seventh", &[-7, 5]),
("acute fifth", &[-5, 5, -1]),
("acute minor third", &[-3, 5, -2]),
("Archytas' 2/3-tone", &[-5, 5, 0, -1]),
("neutral third comma, rastma", &[-1, 5, 0, 0, -2]),
("Nautilus comma", &[-1, 0, 1, 2, -2]),
("minor BP diesis, Sensamagic comma", &[0, -5, 1, 2]),
(
"Meshaqah's 1/4-tone",
&[
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1,
],
),
("tricesoprimal comma", &[3, -5, 0, 0, 0, 0, 0, 0, 0, 0, 1]),
("17/4-tone", &[1, -2, 3, 0, 0, 0, -1]),
("maximal diesis, Porcupine comma", &[1, -5, 3]),
("octave - major chroma", &[8, -3, -1]),
("diminished third", &[8, -2, -2]),
("limma, Pythagorean minor second", &[8, -5]),
("septimal minor semitone", &[8, 0, -1, -2]),
("septendecimal kleisma", &[8, -1, -1, 0, 0, 0, -1]),
("vicesimononal comma", &[-8, 2, 0, 0, 0, 0, 0, 0, 0, 1]),
("Kirnberger's sixth", &[1, 3, 1, -1, 0, 0, 0, 0, -1]),
("Persian whole tone", &[4, -5, 0, 0, 0, 0, 1]),
("Ibn Sina's minor second", &[-8, 1, 0, 1, 0, 1]),
("Tannisma", &[-4, 1, 0, 1, 0, 1, -1]),
("Garibert comma", &[0, -1, 2, -1, 1, -1]),
("septendecimal minor second comma", &[-5, -2, 0, 0, 0, 0, 2]),
("grave fourth", &[6, -5, 1]),
("marveltwin", &[-2, -4, 2, 0, 0, 1]),
("ratwolf comma", &[-1, 3, -2, -1, 0, 1]),
("supracomma", &[5, 0, 0, -3, 1]),
("minthma", &[5, -3, 0, 0, 1, -1]),
("Dudon comma", &[-3, -2, -1, 0, 0, 0, 0, 2]),
("gentle comma", &[2, -1, 0, 1, -2, 1]),
("double augmented fourth", &[-8, 1, 3]),
("BP major semitone, minor BP chroma", &[0, 1, 3, -3]),
("undecimal kleisma, Keemun comma", &[-7, -1, 1, 1, 1]),
("grave major sixth", &[4, -5, 2]),
("wide augmented fifth", &[-8, 4, 1]),
("greenwoodma", &[-3, 4, 1, -2]),
(
"Werckmeister's undecimal septenarian schisma",
&[-3, 2, -1, 2, -1],
),
("3 septatones or septatonic fifth", &[9, 0, 0, -3]),
("double diminished fifth", &[9, -1, -3]),
("narrow diminished fourth", &[9, -4, -1]),
("tridecimal neutral third comma", &[9, -1, 0, 0, 0, -2]),
(
"undevicesimal comma, Boethius' comma",
&[-9, 3, 0, 0, 0, 0, 0, 1],
),
("Avicenna enharmonic diesis", &[-9, 1, 2, 1]),
("Swets' comma", &[2, 3, 1, -2, -1]),
("octave - major diesis", &[-2, -4, 4]),
("classic neutral third", &[-9, 0, 4]),
("BP great semitone, major BP chroma", &[0, -4, 4, -1]),
("huntma", &[7, 0, 1, -2, 0, -1]),
("major diesis", &[3, 4, -4]),
("wide augmented third", &[-9, 3, 2]),
("island comma", &[2, -3, -2, 0, 0, 2]),
("senga", &[1, -3, -2, 3]),
(
"11/4-tone",
&[
-2, 1, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
],
),
("septendecimal bridge comma", &[-1, -1, 1, -1, 1, 1, -1]),
("acute minor seventh", &[-4, 6, -2]),
("Pythagorean tritone", &[-9, 6]),
("acute major second", &[-7, 6, -1]),
("undecimal major diesis", &[-6, 6, 0, 0, -1]),
("squbema", &[-3, 6, 0, -1, 0, -1]),
("vicesimotertial comma", &[5, -6, 0, 0, 0, 0, 0, 0, 1]),
(
"ancient Chinese quasi-equal fifth",
&[
-2, 0, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1,
],
),
(
"ancient Chinese tempering",
&[
1, 1, 3, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-1,
],
),
("grave whole tone", &[5, -6, 2]),
("Cuthbert comma", &[0, 0, -1, 1, 2, -2]),
("keema", &[-5, -3, 3, 1]),
("undecimal semicomma, pentacircle", &[7, -4, 0, 1, -1]),
("fairytale comma", &[-3, 0, -3, 1, 1, 1]),
("narrow diminished sixth", &[10, -3, -2]),
("Pythagorean diminished fifth", &[10, -6]),
("keega", &[-3, 1, -3, 3]),
("gamelan residue", &[-10, 1, 0, 3]),
("tridecimal major diesis", &[-10, 4, 0, 0, 0, 1]),
("double augmented prime", &[-10, 2, 3]),
("kestrel comma", &[2, 3, 0, -1, 1, -2]),
("wide augmented second", &[-10, 5, 1]),
("Eratosthenes' comma", &[6, -5, -1, 0, 0, 0, 0, 1]),
("sensmus", &[4, -5, -1, 1, 1]),
("grave minor seventh", &[8, -6, 1]),
("triaphonisma", &[3, -2, 0, 1, -1, -1, 0, 0, 1]),
("aphrowe", &[0, -3, 0, -2, 3]),
("hemimin", &[6, 1, 0, 1, -3]),
("moctdel", &[-2, 0, 3, -3, 1]),
("Nicola", &[0, 2, 2, 1, -2, -1]),
("lummic comma", &[2, 1, -1, -3, 1, 1]),
("Orwell comma", &[6, 3, -1, -3]),
("double augmented sixth", &[-10, 1, 4]),
("2 tritones", &[-10, 4, 2]),
("double diminished octave", &[11, -2, -3]),
("narrow diminished seventh", &[11, -5, -1]),
("double diminished third", &[11, -1, -4]),
("diaschisma", &[11, -4, -2]),
("Blume comma", &[-11, 0, 0, 0, 2, 0, 1]),
("xenisma", &[1, 1, 0, 3, -2, 0, -1]),
("ibnsinma", &[5, -3, 1, -1, -1, 1]),
("acute major sixth", &[-8, 7, -1]),
("Gorgo limma", &[-4, 7, -3]),
("apotome", &[-11, 7]),
("septendecimal comma", &[-7, 7, 0, 0, 0, 0, -1]),
("Parizek comma, petrma", &[3, 0, 2, 0, 1, -3]),
("Breedsma", &[-5, -1, -2, 4]),
("nuwell comma", &[1, 5, 1, -4]),
("grave minor third", &[9, -7, 1]),
("Lehmerisma", &[-4, -3, 2, -1, 2]),
("small diesis, magic comma", &[-10, -1, 5]),
("major BP diesis", &[0, -2, 5, -3]),
("middle second comma", &[6, 0, -5, 2]),
("double augmented fifth", &[-11, 3, 3]),
("myhemiwell", &[2, -3, -3, 1, 2]),
("wide augmented sixth", &[-11, 6, 1]),
("small septimal comma", &[5, -4, 3, -2]),
("undecimal schisma", &[5, -1, 3, 0, -3]),
("Pythagorean diminished octave", &[12, -7]),
("4 septatones or septatonic major sixth", &[12, 0, 0, -4]),
("double diminished fourth", &[12, -3, -3]),
("narrow diminished third", &[12, -6, -1]),
(
"tridecimal schisma, Sagittal schismina",
&[12, -2, -1, -1, 0, -1],
),
("Hunt flat 2 comma", &[-12, 5, 0, 0, 0, 0, 1]),
("leprechaun comma", &[-7, -1, 2, 0, -1, 2]),
("ragisma", &[-1, -7, 4, 1]),
("Arabic neutral second", &[9, 2, -1, -1, -2]),
("Beta 5, Garibaldi comma", &[10, -6, 1, -1]),
("double augmented third", &[-12, 2, 4]),
("octave - small diesis", &[11, 1, -5]),
("porwell comma", &[11, 1, -3, -2]),
("Pythagorean augmented fifth", &[-12, 8]),
("acute major third", &[-10, 8, -1]),
("BP major link", &[0, 8, -3, -2]),
("ripple", &[-1, 8, -5]),
("Mathieu superdiesis", &[-8, 8, -2]),
("Triple BP comma", &[0, -8, 1, 0, 3]),
("jacobin comma", &[9, 0, -1, 0, -3, 1]),
("double diminished sixth", &[13, -2, -4]),
("Pythagorean diminished fourth", &[13, -8]),
("undecimal minor diesis", &[13, -6, 0, 0, -1]),
("kalisma, Gauss' comma", &[-3, 4, -2, -2, 2]),
("double augmented second", &[-13, 4, 3]),
("grave minor sixth", &[11, -8, 1]),
("harmonisma", &[3, -2, 0, -1, 3, -2]),
(
"fourth + schisma, 5-limit approximation to ET fourth",
&[-13, 7, 1],
),
("hemimage", &[5, -7, -1, 3]),
("cantonisma", &[-5, 0, 1, -3, 0, 3]),
("great BP diesis", &[0, -7, 6, -1]),
("kleisma, semicomma majeur", &[-6, -5, 6]),
("double diminished seventh", &[14, -4, -3]),
(
"fifth - schisma, 5-limit approximation to ET fifth",
&[14, -7, -1],
),
("cloudy", &[-14, 0, 0, 5]),
("double augmentation diesis, Negri comma", &[-14, 3, 4]),
("small BP diesis, mirkwai comma", &[0, 3, 4, -5]),
("septimal major diesis", &[3, 7, 0, -5]),
("minimal BP chroma", &[0, 6, 2, -5]),
("octave - minimal diesis", &[-4, 9, -4]),
("acute major seventh", &[-11, 9, -1]),
("Pythagorean augmented second", &[-14, 9]),
("cataharry comma", &[-4, 9, -2, -2]),
("minimal diesis", &[5, -9, 4]),
("grave minor second", &[12, -9, 1]),
("maximal BP chroma", &[0, -9, 5, 1]),
("mechanism comma", &[-2, -8, 0, 4, 1]),
("Secorian", &[12, -7, 0, 1, 0, -1]),
("octave - double augmentation diesis", &[15, -3, -4]),
("Pythagorean diminished seventh", &[15, -9]),
(
"5 septatones or septatonic diminished octave",
&[15, 0, 0, -5],
),
("schisma", &[-15, 8, 1]),
("mirwomo comma", &[-15, 3, 2, 2]),
("hemigail", &[-7, 1, 0, -3, 4]),
("trimyna", &[-4, 1, -5, 5]),
("Pythagorean augmented sixth", &[-15, 10]),
("Harrison's comma", &[-13, 10, 0, -1]),
("Squalentine", &[-9, 3, -3, 4]),
("octave - schisma", &[16, -8, -1]),
("Pythagorean diminished third", &[16, -10]),
("orgonisma", &[16, 0, 0, -2, -3]),
("horwell comma", &[-16, 1, 5, 1]),
("Woolhouse semitone", &[-13, -2, 7]),
("medium semicomma, Sensi comma", &[2, 9, -7]),
("BP minor link", &[0, 5, -7, 3]),
("stearnsma", &[1, 10, 0, -6]),
("chalmersia", &[-6, 6, -2, -1, -1, 2]),
("Hunt 19-cycle comma", &[17, 0, 0, 0, 0, 0, 0, -4]),
("Woolhouse major seventh", &[14, 2, -7]),
("odiheim", &[-1, 2, -4, 5, -2]),
("Pythagorean augmented third", &[-17, 11]),
("tolerma", &[10, -11, 2, 1]),
("supraminor scintillisma", &[-4, 4, -1, 4, -1, -1, -1]),
("sesdecal", &[-4, 1, 7, 0, -4]),
("Landscape comma", &[-4, 6, -6, 3]),
("Pythagorean diminished sixth", &[18, -11]),
("Passion comma", &[18, -4, -5]),
("varunisma", &[-9, 8, -4, 2]),
("octave - Würschmidt's comma", &[-16, -1, 8]),
("doublewide", &[-9, -6, 8]),
("dimcomp comma", &[-1, -4, 8, -4]),
("Würschmidt's comma", &[17, 1, -8]),
("BP small link", &[0, 10, -8, 1]),
("wizma", &[-6, -8, 2, 5]),
("Pythagorean augmented seventh", &[-18, 12]),
("Pythagorean comma, ditonic comma", &[-19, 12]),
("quince", &[-15, 0, -2, 7]),
("complementary BP diesis", &[0, -8, -3, 7]),
("Pythagorean diminished ninth", &[20, -12]),
("Pythagorean double augmented fourth", &[-20, 13]),
("Unicorn comma", &[-2, 13, -8]),
("Amity comma, kleisma - schisma", &[9, -13, 5]),
("Immunity comma", &[16, -13, 2]),
("Shibboleth comma", &[-5, -10, 9]),
("Pythagorean double diminished fifth", &[21, -13]),
("semicomma, Fokker's comma", &[-21, 3, 7]),
("Pythagorean double augmented prime", &[-22, 14]),
("sevond", &[6, -14, 7]),
("Pythagorean double diminished octave", &[23, -14]),
("Fifives comma", &[-1, -14, 10]),
("mynic", &[9, 9, -10]),
("Pythagorean double augmented fifth", &[-23, 15]),
("Pythagorean double diminished fourth", &[24, -15]),
("Freivald comma", &[22, -1, -10, 1]),
("Beta 2, septimal schisma", &[25, -14, 0, -1]),
("Ampersand's comma", &[-25, 7, 6]),
("Pythagorean double augmented second", &[-25, 16]),
("Sycamore comma", &[-16, -6, 11]),
("nusecond", &[5, 13, -11]),
("Pythagorean double diminished seventh", &[26, -16]),
("Misty comma, diaschisma - schisma", &[26, -12, -3]),
("Pythagorean double augmented sixth", &[-26, 17]),
("gravity comma", &[-13, 17, -6]),
("roda", &[20, -17, 3]),
(
"whole tone - 2 schismas, 5-limit approximation to ET whole tone",
&[27, -14, -2],
),
("Pythagorean double diminished third", &[27, -17]),
("wadisma", &[-26, -1, 1, 9]),
("Pythagorean double augmented third", &[-28, 18]),
("Pythagorean double diminished sixth", &[29, -18]),
("Blackjack comma", &[-10, 7, 8, -7]),
("Pythagorean double augmented seventh", &[-29, 19]),
("Pythagorean-19 comma", &[-30, 19]),
("Trithagorean comma", &[0, -19, 13]),
("ditonma", &[-27, -2, 13]),
("parakleisma", &[8, 14, -13]),
("Vishnu comma", &[23, 6, -14]),
("semithirds comma", &[38, -2, -15]),
("ennealimmal comma", &[1, -27, 18]),
("'19-tone' comma", &[-14, -19, 19]),
("monzisma", &[54, -37, 2]),
("'41-tone' comma", &[65, -41]),
("Mercator's comma", &[-84, 53]),
];
commas
.iter()
.map(|&(description, prime_factors)| Comma::new(description, prime_factors))
.collect()
}
#[derive(Clone, Debug)]
pub struct Comma {
description: Cow<'static, str>,
prime_factors: Cow<'static, [i8]>,
}
impl Comma {
pub fn new(
description: impl Into<Cow<'static, str>>,
prime_factors: impl Into<Cow<'static, [i8]>>,
) -> Self {
Self {
description: description.into(),
prime_factors: prime_factors.into(),
}
}
pub fn description(&self) -> &str {
&self.description
}
pub fn prime_factors(&self) -> &[i8] {
&self.prime_factors
}
pub fn prime_limit(&self) -> u8 {
if self.prime_factors.is_empty() {
1
} else {
math::U8_PRIMES[self.prime_factors.len() - 1]
}
}
pub fn as_ratio(&self) -> Ratio {
Ratio::from_float(
self.prime_factors
.iter()
.zip(math::U8_PRIMES)
.map(|(&power, &prime)| f64::from(prime).powi(i32::from(power)))
.product(),
)
}
pub fn as_fraction(&self) -> Option<(u128, u128)> {
let mut numer: u128 = 1;
let mut denom: u128 = 1;
for (&power, &prime) in self.prime_factors.iter().zip(math::U8_PRIMES) {
if power >= 0 {
numer = numer
.checked_mul(u128::from(prime).checked_pow(u32::try_from(power).unwrap())?)?;
} else {
denom = denom
.checked_mul(u128::from(prime).checked_pow(u32::try_from(-power).unwrap())?)?;
}
}
Some((numer, denom))
}
}
#[derive(Clone, Debug)]
pub struct CommaCatalog {
commas_by_limit: HashMap<u8, Vec<Comma>>,
comma_ref_by_name: HashMap<String, (u8, usize)>,
}
impl CommaCatalog {
pub fn new(commas: Vec<Comma>) -> Self {
let mut commas_by_limit = HashMap::new();
let mut comma_ref_by_name = HashMap::new();
for comma in commas {
let prime_limit = comma.prime_limit();
let commas_for_limit = commas_by_limit.entry(prime_limit).or_insert_with(Vec::new);
for name in comma.description().split(',') {
comma_ref_by_name.insert(normalize(name), (prime_limit, commas_for_limit.len()));
}
commas_for_limit.push(comma);
}
Self {
commas_by_limit,
comma_ref_by_name,
}
}
}
impl CommaCatalog {
pub fn commas_for_limit(&self, prime_limit: u8) -> &[Comma] {
self.commas_by_limit
.get(&prime_limit)
.map(Vec::as_slice)
.unwrap_or(&[])
}
pub fn comma_for_name(&self, name: &str) -> Option<&Comma> {
let &(prime_limit, index) = self.comma_ref_by_name.get(&normalize(name))?;
self.commas_by_limit.get(&prime_limit)?.get(index)
}
}
fn normalize(name: &str) -> String {
name.trim().to_lowercase()
}