List of superparticular intervals: Difference between revisions

| 1200.000

| 2/1

| octave, duple; ''after [[octave reduction]]:'' (perfect) unison, unity, perfect prime, tonic

|-

| 701.955

| 3/2

| [[perfect fifth]], 3rd harmonic (octave reduced), diapente

|-

| 498.045

| 2²/3

| perfect fourth, 3rd subharmonic (octave reduced), diatessaron

|-

| 203.910

| 3²/2³

| (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)

|-

| 386.314

| 5/2²

| (classic) (5-limit) major third, 5th harmonic (octave reduced)

|-

| 315.641

| (2*3)/5

| (classic) (5-limit) minor third

|-

| 182.404

| (2*5)/3²

| classic (whole) tone, classic major second, minor whole tone

|-

| 111.731

| 2⁴/(3*5)

| minor diatonic semitone, 15th subharmonic

|-

| 70.672

| 5²/(2³*3)

| chroma, (classic) chromatic semitone, Zarlinian semitone

|-

| 21.506

| (3/2)⁴/5

| syntonic comma, Didymus comma

|-

| 266.871

| 7/(2*3)

| (septimal) subminor third, septimal minor third

|-

| 231.174

| 2³/7

| (septimal) supermajor second, septimal whole tone, 7th subharmonic

|-

| 119.443

| (3*5)/(2*7)

| septimal diatonic semitone

|-

| 84.467

| (3*7)/(2²*5)

| minor semitone, large septimal chroma

|-

| 62.961

| (2²*7)/3³

| septimal third-tone, small septimal chroma, (septimal) subminor second, septimal minor second, trienstonic comma

|-

| 48.770

| (2²*3³)/(5*7)

| septimal quarter tone, septimal diesis

|-

| 35.697

| 7²/(2⁴*3)

| large septimal diesis, slendro diesis, septimal 1/6-tone

|-

| 34.976

| 2*(5/7)²

| septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma

|-

| 27.264

| 2⁶/(3²*7)

| septimal comma, Archytas' comma

|-

| 13.795

| (2*3²*7)/5³

| starling comma, septimal semicomma

|-

| 7.7115

| (3*5)²/(2⁵*7)

| marvel comma, septimal kleisma

|-

| 0.72120

| 7⁴/(2⁵*3*5²)

| breedsma

|-

| 0.39576

| (5⁴*7)/(2*3⁷)

| ragisma

|-

| 165.004

| 11/(2*5)

| (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second

|-

| 150.637

| (2²*3)/11

| (small) (undecimal) neutral second, 3/4-tone

|-

| 80.537

| (2*11)/(3*7)

| undecimal minor semitone

|-

| 53.273

| (3*11)/2⁵

| undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)

|-

| 38.906

| (3/2)²*(5/11)

| undecimal 1/5-tone

|-

| 31.767

| (5*11)/(2*3³)

| undecimal diasecundal comma, eleventyfive comma

|-

| 31.194

| (2³*7)/(5*11)

| undecimal tritonic comma, konbini comma

|-

| 17.576

| (3/7)²*(11/2)

| small undecimal comma, mothwellsma

|-

| 17.399

| (2*5/3)²/11)

| Ptolemy's comma, ptolemisma

|-

| 14.376

| 11²/(2³*3*5)

| undecimal seconds comma, [[Biyatismic chords|biyatisma]]

|-

| 9.8646

| (2⁴*11)/(5²*7)

| valinorsma

|-

| 7.1391

| 3⁵/(2*11²)

| neutral third comma, rastma

|-

| 4.5026

| (5*7*11)/(2⁷*3)

| keenanisma

|-

| 3.9302

| (3*7)²/(2³*5*11)

| Werckmeister's undecimal septenarian schisma, werckisma

|-

| 3.2090

| (2/7)²*3³*5/11

| Swets' comma, swetisma

|-

| 0.57240

| (5*11)²/(2⁴*3²*7)

| Lehmerisma

|-

| 0.17665

| (11/(5*7))²*3⁴/2³

| Gauss comma, kalisma

|-

| 138.573

| 13/(2²*3)

| (large) tridecimal 2/3-tone, tridecimal neutral second

|-

| 128.298

| (2*7)/13

| (small) tridecimal 2/3-tone, trienthird

|-

| 67.900

| (2*13)/5²

| (large) tridecimal 1/3-tone

|-

| 65.337

| 3³/(2*13)

| (small) tridecimal 1/3-tone

|-

| 43.831

| (2³*5)/(3*13)

| tridecimal minor diesis

|-

| 26.841

| (5*13)/2⁶

| wilsorma, 13th-partial chroma

|-

| 26.432

| (2*3*11)/(5*13)

| winmeanma

|-

| 22.339

| (2*3*13)/(7*11)

| negustma

|-

| 19.130

| (7*13)/(2*3²*5)

| [[The_Biosphere|Biome]] comma, superleap comma

|-

| 16.567

| (3*5*7)/(2³*13)

| small tridecimal comma, animist comma

|-

| 12.064

| (2²*3)²/(11*13)

| grossma

|-

| 10.274

| 13²/(2³*3*7)

| buzurgisma, dhanvantarisma

|-

| 8.8554

| (2*7)²/(3*5*13)

| [[Mynucumic_chords|mynucuma]]

|-

| 5.3351

| (5²*13)/(2²*3⁴)

| [[Marveltwin|marveltwin comma]]

|-

| 4.9393

| (3/5)²*13/(2*7)

| ratwolfsma

|-

| 4.9253

| (2⁵*11)/(3²*13)

| minthma

|-

| 4.7627

| (2/11)²*7*13/3

| gentle comma

|-

| 2.7722

| (5/2)⁴/(3*13)

| tunbarsma

|-

| 2.5629

| (2*13/5)²/3³

| island comma

|-

| 2.3764

| (3²/2)³/(7*13)

| squbema

|-

| 1.7304

| 7*11*13/(2*5)³

| sinbadma

|-

| 1.0092

| 2²*3*11*13/(5*7³)

| lummic comma

|-

| 0.83252

| 2⁵*5*13/(3³*7*11)

| ibnsinma

|-

| 0.42272

| (2⁶/3)²/(5*7*13)

| tridecimal schisma, Sagittal schismina

|-

| 0.40981

| (5*13)²/(2⁷*3*11)

| leprechaun comma

|-

| 0.26012

| (2³/11)³*13/5

| jacobin comma

|-

| 0.16260

| (2*11)³/((3*13)²*7)

| harmonisma

|-

| 0.014052

| (3/2)⁶*(13/5)²/(7*11)

| chalmersia

|-

| 104.955

| 17/2⁴

| large septendecimal semitone, 17th harmonic (octave reduced)

|-

| 98.955

| (2*3²)/17

| small septendecimal semitone, Arabic lute index finger

|-

| 51.682

| (2*17)/(3*11)

| large septendecimal 1/4-tone

|-

| 50.184

| (5*7)/(2*17)

| small septendecimal 1/4-tone

|-

| 34.283

| (3*17)/(2*5²)

| large septendecimal 1/6-tone

|-

| 33.617

| (2²*13)/(3*17)

| small septendecimal 1/6-tone

|-

| 20.488

| (5*17)/(2²*3*7)

| septendecimal comma (?)

|-

| 14.487

| (2³*3*5)/(7*17)

|  

|-

| 12.777

| (2/3)³*17/5

| septendecimal major second comma

|-

| 11.278

| (2*7*11)/(3²*17)

|  

|-

| 10.214

| (2*5*17)/13²

|  

|-

| 7.8514

| (13*17)/(2²*5*11)

|  

|-

| 6.7759

| (2⁸)/(3*5*17)

| septendecimal kleisma, 255th subharmonic

|-

| 6.3532

| (3*7*13)/(2⁴*17)

| tannisma

|-

| 6.0008

| (17/3)²/2⁵

| septendecimal 6-cent comma

|-

| 4.6228

| (3*5³)/(2*11*17)

|  

|-

| 3.9213

| (2*13*17)/(3*7)²

|  

|-

| 3.0887

| (3*11*17)/(2⁴*5*7)

|  

|-

| 2.9121

| (5*7*17)/(2*3³*11)

|  

|-

| 2.4230

| (5*11*13)/(2*3*7*17)

|  

|-

| 2.0796

| (7²*17)/(2⁶*13)

|  

|-

| 1.8506

| (2³*3²*13)/(5*11*17)

| ainos comma, ainma

|-

| 1.5905

| (3²*11²)/(2⁶*17)

| twosquare comma

|-

| 1.4983

| (2²*17²)/(3*5*7*11)

|  

|-

| 1.4138

| (5²*7²)/(2³*3²*17)

|  

|-

| 1.3584

| (3*5²*17)/(2*7²*13)

|  

|-

| 1.0181

| (3⁵*7)/[(2*5)²*17]

|  

|-

| 0.84143

| (2*3*7³)/(11²*17)

| xenisma

|-

| 0.71230

| (11*13*17)/(2*3⁵*5)

|  

|-

| 0.69263

| (2²*5⁴)/(3*7²*17)

|  

|-

| 0.66573

| (3²*17²)/(2³*5²*13)

|  

|-

| 0.35234

| (2*3³*7*13)/(17³)

|  

|-

| 0.29688

| (2³*3⁶)/(7³*17)

|  

|-

| 0.13989

| (2³*7*13*17)/(3²*5³*11)

| flashma

|-

| 0.12023

| (2⁶*3²*5²)/(7*11²*17)

| sparkisma

|-

| 0.060616

| (13⁴)/(2⁴*3*5*7*17)

|  

|-

| 0.055466

| (7⁴*13)/(2²*3³*17²)

|  

|-

| 0.046564

| (2²*5*11*13²)/(3⁷*17)

|  

|-

| 0.008902

| (3⁴*7⁴)/(2⁴*5*11*13*17)

| scintillisma

|-

| 0.005150

| (3²*13³*17)/(2²*5*7⁵)

|  

|-

| 93.603

| 19/(2*3²)

| large undevicesimal semitone

|-

| 88.801

| (2²*5)/19

| small undevicesimal semitone

|-

| 44.970

| (3*13)/(2*19)

| undevicesimal 2/9-tone

|-

| 30.642

| (3*19)/(2³*7)

| hendrix comma

|-

| 22.931

| (2²*19)/(3*5²)

| undevicesimal 1/9-tone (greater)

|-

| 22.631

| (7*11)/(2²*19)

| undevicesimal 1/9-tone (lesser)

|-

| 18.128

| (2⁵*3)/(5*19)

|  

|-

| 13.066

| (19*7)/(2²*3*11)

|  

|-

| 11.352

| (3²*17)/(2³*19)

|  

|-

| 10.154

| (3²*19)/(2*5*17)

|  

|-

| 9.1358

| (2*5*19)/(3³*7)

|  

|-

| 8.3033

| (11*19)/(2⁴*13)

| yama comma

|-

| 8.2637

| (2*3*5*7)/(11*19)

| spleen comma

|-

| 6.0639

| (2*11*13)/(3*5*19)

|  

|-

| 5.3516

| (2²*3⁴)/(17*19)

|  

|-

| 5.0547

| 7⁴/(2*3³*19)

|  

|-

| 4.8023

| 19²/(2³*3²*5)

| go comma

|-

| 4.3335

| (2⁴*5²)/(3*7*19)

|  

|-

| 3.8007

| (2³*3*19)/(5*7*13)

|  

|-

| 3.6409

| (2²*7*17)/(5²*19)

|  

|-

| 3.5010

| (3²*5*11)/(2*13*19)

|  

|-

| 3.3780

| (3³*19)/2⁹

| undevicesimal comma, undevicesimal schisma, 513th harmonic

|-

| 1.7875

| (3*17*19)/(2³*11²)

|  

|-

| 1.4243

| (2⁶*19)/(3⁵*5)

| password comma, Eratosthenes' comma

|-

| 1.3012

| 11³/(2*5*7*19)

|  

|-

| 1.1985

| 5*(17/(2*19))²

|  

|-

| 1.1386

| (3*13)²/(2⁴*5*19)

|  

|-

| 1.1245

| (2²*5*7*11)/(3⁴*19)

|  

|-

| 1.0016

| (7*13*19)/(2⁶*3³)

|  

|-

| 0.7288

| (5³*19)/(2³*3³*11)

|  

|-

| 0.7120

| (11*13*17)/(2⁷*19)

| Blumeyer comma

|-

| 0.5918

| (2*7*11*19)/(3²*5²*13)

|  

|-

| 0.5521

| (2⁶*7²)/(3*5*11*19)

|  

|-

| 0.5328

| (2*5³*13)/(3²*19²)

|  

|-

| 0.4123

| (2³*3*5²*7)/(13*17*19)

|  

|-

| 0.2998

| (2⁴*19²)/(3*5²*7*11)

|  

|-

| 0.2920

| (7²*11²)/(2³*3*13*19)

|  

|-

| 0.2893

| (2⁵*11*17)/(3²*5*7*19)

|  

|-

| 0.2804

| (5²*13*19)/(2*3²*7³)

|  

|-

| 0.2524

| (2²*5*7³)/(19³)

|  

|-

| 0.1691

| (7²*11*19)/(2¹¹*5)

|  

|-

| 0.1599

| (2*3*5*19²)/(7²*13*17)

|  

|-

| 0.1370

| (2²*3⁵*13)/(5*7*19²)

|  

|-

| 0.1294

| (3*7³*13)/(2⁶*11*19)

|  

|-

| 0.1230

| (2⁸*5*11)/(3*13*19²)

|  

|-

| 0.1205

| (5*13²*17)/(2²*3³*7*19)

|  

|-

| 0.07396

| (3⁴*17²)/(2⁴*7*11*19)

|  

|-

| 0.06306

| (2⁶*3*11*17)/(5*17²*19)

|  

|-

| 0.05991

| (2²*5²*17²)/(3²*13²*19)

|  

|-

| 0.03963

| (11²*19²)/(2⁵*3*5*7*13)

|  

|-

| 0.01937

| (2⁵*3*7²*19)/(5⁴*11*13)

|  

|-

| 0.01649

| (2⁴*3⁸)/(5²*13*17*19)

|  

|-

| 0.01047

| (2⁹*17*19)/(3³*5³*7²)

|  

|-

| 0.007590

| (2⁸*3⁴*11)/(5*7⁴*19)

|  

|-

| 0.002879

| (2*7²*17*19²)/(3⁷*5²*11)

|  

|-

| 0.002733

| (2²*7*11³*17)/(3³*5*13*19²)

|  

|-

| 0.002440

| (2¹⁰*3²*7*11)/(13³*17*19)

|  

|-

| 0.0002929

| (11²*13²*17²)/(2⁸*3⁵*5*19)

|  

|-

| 0.0001460

| (7*13*19⁴)/(2*3⁴*5*11⁴)

|  

|-