Gallery of just intervals: Difference between revisions

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{| class="wikitable sortable"

|-

| | [[1/1|1/1]]

| | 0

| | unity, perfect prime, Tonic

|-

| | [[32805/32768|32805/32768]]

| | 1.953721

| |<nowiki> schisma, |-15, 8, 1</nowiki>&gt;

|-

| | [[225/224|225/224]]

| | 7.711523

| |<nowiki> septimal subcomma, |-5, 2, 2, -1</nowiki>&gt;

|-

| | [[100/99|100/99]]

| | 17.399484

| | Ptolemy's comma

|-

| | [[99/98|99/98]]

| | 17.576131

| | Mothwellsma

|-

| | 2048/2025

| | 19.552569

| |<nowiki> |11, -4, -2</nowiki>&gt;

|-

| | [[81/80|81/80]]

| | 21.506286

| | Syntonic comma, Didymus comma

|-

| | [[531441/524288|531441/524288]]

| | 23.460010

| |<nowiki> Pythagorean comma, Ditonic comma, |-19, 12</nowiki>&gt;

|-

| | [[66/65|66/65]]

| | 26.431568

| | Winmeanma

|-

| | [[65/64|65/64]]

| | 26.841376

| | Wilsorma, 13th-partial chroma

|-

| | [[64/63|64/63]]

| | 27.264092

| | Septimal comma, Archytas' comma

|-

| | [[3125/3072|3125/3072]]

| | 29.613568

| |<nowiki> Magic comma, small diesis, |-10, -1, 5</nowiki>&gt;

|-

| | [[50/49|50/49]]

| | 34.975615

| | septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis

|-

| | [[49/48|49/48]]

| | 35.696812

| | large septimal diesis, slendro diesis

|-

| | [[45/44|45/44]]

| | 38.905773

| | undecimal 1/5th tone

|-

| | [[128/125|128/125]]

| | 41.058858

| |<nowiki> Diesis, minor diesis, augmented comma, enharmonic comma, |7, 0, -3</nowiki>&gt;

|-

| | [[525/512|525/512]]

| | 43.408335

| |<nowiki> Avicenna's enharmonic diesis, |-9, 1, 2, 1</nowiki>&gt;

|-

| | [[36/35|36/35]]

| | 48.770381

| | double comma, septimal quarter tone

|-

| | [[250/243|250/243]]

| | 49.166137

| |<nowiki> Porcupine comma, |1, -5, 3</nowiki>&gt;

|-

| | [[59049/57344|59049/57344]]

| | 50.724102

| |<nowiki> Harrison's comma, |-13, 10, 0, -1</nowiki>&gt;

|-

| | [[100/97|100/97]]

| | 52.732017

| | shrutar quarter tone

|-

| | [[33/32|33/32]]

| | 53.272943

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

|-

| | [[648/625|648/625]]

| | 62.565148

| |<nowiki> diminished comma, major diesis, |8, 4, -4</nowiki>&gt;

|-

| | [[28/27|28/27]]

| | 62.960904

| | septimal chroma, small septimal chromatic semitone, septimal subminor second

|-

| | [[25/24|25/24]]

| | 70.672427

| | chroma, chromatic semitone, Zarlinian semitone

|-

| | [[68/65|68/65]]

| | 78.114034

| | valentine semitone

|-

| | [[22/21|22/21]]

| | 80.537035

| | undecimal minor semitone

|-

| | [[64/61|64/61]]

| | 83.115195

| | harry minor semitone

|-

| | [[21/20|21/20]]

| | 84.467193

| | minor semitone, large septimal chromatic semitone

|-

| | [[256/243|256/243]]

| | 90.224996

| |<nowiki> Pythagorean limma, Pythagorean minor second, |8, -5</nowiki>&gt;

|-

| | [[135/128|135/128]]

| | 92.178716

| |<nowiki> ma1oor limma, |-7, 3, 1</nowiki>&gt;

|-

| | [[18/17|18/17]]

| | 98.954592

| | small septendecimal semitone, Arabic lute index finger

|-

| | [[17/16|17/16]]

| | 104.955410

| | large septendecimal semitone, octave-reduced 17th harmonic

|-

| | [[16/15|16/15]]

| | 111.731285

| | diatonic semitone, classic minor second, octave-reduced 15th subharmonic

|-

| | [[2187/2048|2187/2048]]

| | 113.685006

| |<nowiki> apotome, |-11, 7</nowiki>&gt;

|-

| | [[77/72|77/72]]

| | 116.233847

| | undecimal secor

|-

| | [[15/14|15/14]]

| | 119.442808

| | septimal diatonic semitone

|-

| | [[14/13|14/13]]

| | 128.298245

| | 2/3-tone, trienthird, tridecimal supraminor second

|-

| | [[27/25|27/25]]

| | 133.237575

| | large limma

|-

| | [[13/12|13/12]]

| | 138.572661

| | tridecimal subtone, tridecimal 2/3-tone

|-

| | [[243/224|243/224]]

| | 140.949098

| |<nowiki> septimal subtone, |-5, 5, 0, -1</nowiki>&gt;

|-

| | [[88/81|88/81]]

| | 143.497939

| | undecimal subtone

|-

| | [[49/45|49/45]]

| | 147.428097

| | swetismic neutral second

|-

| | [[12/11|12/11]]

| | 150.637059

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

|-

| | [[35/32|35/32]]

| | 155.139620

| | septimal neutral second

|-

| | [[11/10|11/10]]

| | 165.004228

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

|-

| | [[54/49|54/49]]

| | 168.213190

| | Zalzal's mujannab

|-

| | [[10/9|10/9]]

| | 182.403712

| | minor whole tone

|-

| | [[49/44|49/44]]

| | 186.333871

| | werckismic minor second

|-

| | [[19/17|19/17]]

| | 192.557607

| | quasi-meantone

|-

| | [[28/25|28/25]]

| | 196.198479

| | middle major second

|-

| | [[55/49|55/49]]

| | 199.979843

| | werckismic tone

|-

| | [[9/8|9/8]]

| | 203.910002

| | major whole tone, Pythagorean tone, octave-reduced 9th harmonic

|-

| | [[17/15|17/15]]

| | 216.686695

| | septendecimal whole tone, septendecimal eventone

|-

| | [[8/7|8/7]]

| | 231.174094

| | supermajor second, septimal whole tone, diminished third, octave-reduced 7th subharmonic

|-

| | [[63/55|63/55]]

| | 235.104252

| | werckismic supermajor second

|-

| | [[55/48|55/48]]

| | 235.676655

| | keenanismic supermajor second

|-

| | [[15/13|15/13]]

| | 247.741053

| | semifourth, tridecimal ultramajor second, tridecimal inframinor third

|-

| | [[22/19|22/19]]

| | 253.804926

| | minimal minor third, godzilla third

|-

| | [[64/55|64/55]]

| | 262.368344

| | keenanismic subminor third, octave-reduced 55th subharmonic

|-

| | [[7/6|7/6]]

| | 266.870906

| | subminor third, septimal minor third, augmented second

|-

| | [[90/77|90/77]]

| | 270.079867

| | swetismic subminor third

|-

| | [[62/53|62/53]]

| | 271.531027

| | orwell subminor third

|-

| | [[75/64|75/64]]

| | 274.582429

| | classic augmented second

|-

| | [[20/17|20/17]]

| | 281.358304

| | septendecimal augmented second, septendecimal minor third

|-

| | [[13/11|13/11]]

| | 289.209179

| | tridecimal minor third

|-

| | [[32/27|32/27]]

| | 294.134997

| | Pythagorean minor third, octave-reduced 27th subharmonic

|-

| | [[19/16|19/16]]

| | 297.513016

| | otonal minor third, octave-reduced 19th harmonic

|-

| | [[25/21|25/21]]

| | 301.846520

| | quasi-tempered minor third

|-

| | [[61/51|61/51]]

| | 309.974395

| | myna third

|-

| | [[6/5|6/5]]

| | 315.641287

| | minor third, pental minor third

|-

| | [[77/64|77/64]]

| | 320.143849

| | keenanismic minor third, octave-reduced 77th harmonic

|-

| | 135/112

| | 323.352810

| |<nowiki> large septimal minor third, marvelous minor third, |-4, 3, 1, -1</nowiki>&gt;

|-

| | [[35/29|35/29]]

| | 325.562426

| | doublewide minor third

|-

| | [[17/14|17/14]]

| | 336.129503

| | septendecimal supraminor third

|-

| | [[73/60|73/60]]

| | 339.520756

| | amity supraminor third

|-

| | 625/512

| | 345.254855

| |<nowiki> 5-limit neutral third, |-9, 0, 4</nowiki>&gt;

|-

| | [[11/9|11/9]]

| | 347.407941

| | undecimal neutral third

|-

| | [[60/49|60/49]]

| | 350.616902

|-

| | [[49/40|49/40]]

| | 351.338099

|-

| | [[27/22|27/22]]

| | 354.547060

| | rastmic neutral third

|-

| | [[16/13|16/13]]

| | 359.472338

| | tridecimal neutral third

|-

| | [[21/17|21/17]]

| | 365.825498

| | septendecimal submajor third

|-

| | [[56/45|56/45]]

| | 378.602191

| | narrow perde segah, marvelous major third

|-

| | 51/41

| | 377.848005

| | maja third

|-

| | [[71/57|71/57]]

| | 380.228526

| | witchcraft major third

|-

| | [[76/61|76/61]]

| | 380.628211

| | magic major third

|-

| | [[96/77|96/77]]

| | 381.811152

| | undecimal perde segah, keenanismic major third

|-

| | [[5/4|5/4]]

| | 386.313714

| | major third, octave-reduced 5th harmonic, pental major third

|-

| | [[81/64|81/64]]

| | 407.820003

| | Pythagorean major third, octave-reduced 81st harmonic

|-

| | [[80/63|80/63]]

| | 413.577806

| | werckismic sharp major third

|-

| | [[14/11|14/11]]

| | 417.507964

| | undecimal major third, undecimal diminished fourth

|-

| | [[32/25|32/25]]

| | 427.372572

| | classic diminished fourth

|-

| | [[77/60|77/60]]

| | 431.875134

| | swetismic supermajor third

|-

| | [[9/7|9/7]]

| | 435.084095

| | supermajor third, septimal major third, septimal diminished fourth

|-

| | [[31/24|31/24]]

| | 443.080572

| | sensi supermajor third

|-

| | [[22/17|22/17]]

| | 446.362533

| | septendecimal supermajor third

|-

| | [[35/27|35/27]]

| | 449.274618

| | semi-diminished fourth

|-

| | [[13/10|13/10]]

| | 454.213948

| | Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramaor third

|-

| | [[64/49|64/49]]

| | 462.348187

| | septatonic major third

|-

| | [[17/13|17/13]]

| | 464.427748

| | septendecimal sub-fourth

|-

| | [[21/16|21/16]]

| | 470.780907

| | sub-fourth, narrow fourth, augmented third, 8ve-reduced 21st harmonic

|-

| | [[33/25|33/25]]

| | 480.645516

| | "5-EDO"-esque fourth

|-

| | 117/88

| | 493.119721

| |<nowiki> tridecimal gentle fourth, |-3, 2, 0, 0, -1, 1</nowiki>&gt;

|-

| | [[4/3|4/3]]

| | 498.044999

| | just perfect fourth, octave-reduced 3rd subharmonic, diatessaron

|-

| | [[75/56|75/56]]

| | 505.756522

| | marvelous fourth

|-

| | [[27/20|27/20]]

| | 519.551289

| | acute fourth

|-

| | [[19/14|19/14]]

| | 528.687110

| | 19-limit wide fourth

|-

| | [[49/36|49/36]]

| | 533.741811

| | Arabic lute acute fourth

|-

| | [[15/11|15/11]]

| | 536.950772

| | undecimal augmented fourth, subaugmented fourth

|-

| | [[48/35|48/35]]

| | 546.815381

| | septimal super-fourth

|-

| | [[11/8|11/8]]

| | 551.317942

| | super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa

|-

| | [[18/13|18/13]]

| | 563.382340

| | tridecimal augmented fourth

|-

| | [[25/18|25/18]]

| | 568.717426

| | classic augmented fourth, pental augmented fourth

|-

| | [[88/63|88/63]]

| | 578.582034

| | werckismic augmented fourth

|-

| | [[7/5|7/5]]

| | 582.512193

| | augmented fourth, septimal tritone, Huygen's tritone

|-

| | [[45/32|45/32]]

| | 590.223716

| |  

|-

| | [[108/77|108/77]]

| | 585.721154

| |<nowiki> swetismic augmented fourth, |2, 3, 0, -1, -1</nowiki>&gt;

|-

| | [[24/17|24/17]]

| | 596.999591

| | smaller septendecimal tritone

|-

| | [[17/12|17/12]]

| | 603.000409

| | larger septendecimal tritone

|-

| | [[64/45|64/45]]

| | 609.776284

| |  

|-

| | [[10/7|10/7]]

| | 617.487807

| | diminished fifth, Euler's tritone, superaugmented fourth

|-

| | [[23/16|23/16]]

| | 628.274347

| | 23-limit superaugmented fourth, octave-reduced 23rd harmonic

|-

| | [[36/25|36/25]]

| | 631.282574

| | pental diminished fifth, classic diminshed fifth

|-

| | [[13/9|13/9]]

| | 636.617660

| | tridecimal diminished fifth

|-

| | [[16/11|16/11]]

| | 648.682058

| | sub-fifth, octave-reduced 11th subharmonic

|-

| | [[35/24|35/24]]

| | 653.184619

| | septimal sub-fifth

|-

| | [[22/15|22/15]]

| | 663.049228

| | undecimal diminished fifth, semidiminished fifth

|-

| | [[72/49|72/49]]

| | 666.258889

| | septimal catafifth

|-

| | [[81/55|81/55]]

| | 670.188347

| | undecimal catafifth

|-

| | [[28/19|28/19]]

| | 671.312890

| | 19-limit narrow fifth

|-

| | [[40/27|40/27]]

| | 680.448711

| | grave fifth

|-

| | [[112/75|112/75]]

| | 694.243478

| | marvelous fifth

|-

| | [[just_perfect_fifth|3/2]]

| | 701.955001

| | [[perfect_fifth|just perfect fifth]], octave-reduced 3rd harmonic, diapente

|-

| | [[182/121|182/121]]

| | 706.717684

| |<nowiki> tridecimal gentle fifth, |1, 0, 0, 1, -2, 1 </nowiki>&gt;

|-

| | 176/117

| | 706.880279

| |<nowiki> tridecimal gentle fifth, |4, -2, 0, 0, 1, -1</nowiki>&gt;

|-

| | [[50/33|50/33]]

| | 719.354484

| | "[[5edo|5-EDO]]"-esque fifth

|-

| | [[32/21|32/21]]

| | 729.219093

| | super-fifth, wide fifth, diminished sixth, octave-reduced 21st subharmonic

|-

| | [[26/17|26/17]]

| | 735.572252

| | septendecimal super-fifth

|-

| | [[49/32|49/32]]

| | 737.651813

| | superduper fifth, octave-reduced 49th harmonic

|-

| | [[20/13|20/13]]

| | 745.786052

| | Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth

|-

| | [[17/11|17/11]]

| | 753.637467

| | septendecimal subminor sixth

|-

| | [[14/9|14/9]]

| | 764.915905

| | subminor sixth, septimal minor sixth, augmented fifth

|-

| | [[25/16|25/16]]

| | 772.627428

| | pental augmented fifth, classic augmented fifth, otonal minor sixth, octave-reduced 25th harmonic

|-

| | [[11/7|11/7]]

| | 782.492036

| | undecimal subminor sixth, undecimal augmented fifth

|-

| | 63/40

| | 786.422194

| |  

|-

| | [[128/81|128/81]]

| | 792.179997

| |  

|-

| | [[8/5|8/5]]

| | 813.686286

| | minor sixth, octave-reduced 5th subharmonic

|-

| | 413/256

| | 827.997565

| | octave-reduced 413th harmonic, homestuck sixth (2<span style="vertical-align: super;">-8</span> * 7 * 59)

|-

| | [[13/8|13/8]]

| | 840.527662

| | tridecimal neutral sixth, octave-reduced 13th harmonic

|-

| | [[80/49|80/49]]

| | 848.661901

| | (purple 6th)

|-

| | [[49/30|49/30]]

| | 849.383198

| | (purple 6th)

|-

| | [[18/11|18/11]]

| | 852.592059

| | undecimal neutral sixth

|-

| | [[28/17|28/17]]

| | 863.870497

| | septendecimal submajor sixth

|-

| | [[5/3|5/3]]

| | 884.358713

| | major sixth

|-

| | [[42/25|42/25]]

| | 898.153480

| |  

|-

| | [[27/16|27/16]]

| | 905.865003

| | Pythagorean major sixth, octave-reduced 27th harmonic

|-

| | [[22/13|22/13]]

| | 910.790821

| | tridecimal major sixth

|-

| | [[17/10|17/10]]

| | 918.641696

| | septendecimal diminished seventh, septendecimal major sixth

|-

| | [[12/7|12/7]]

| | 933.129094

| | supermajor sixth, septimal major sixth, diminished seventh

|-

| | [[26/15|26/15]]

| | 952.258947

| | semitwelfth, tridecimal inframinor seventh, tridecimal ultramajor sixth

|-

| | [[7/4|7/4]]

| | 968.825906

| | subminor seventh, harmonic seventh, augmented sixth, octave-reduced 7th harmonic

|-

| | [[225/128|225/128]]

| | 976.537429

| |<nowiki> marvel five-limit harmonic seventh, octave-reduced 225th harmonic, |-7, 2, 2</nowiki>&gt;

|-

| | [[30/17|30/17]]

| | 983.313305

| | septendecimal minor seventh

|-

| | [[16/9|16/9]]

| | 996.089998

| | Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic

|-

| | [[25/14|25/14]]

| | 1003.801521

| | Middle minor seventh

|-

| | [[34/19|34/19]]

| | 1007.442393

| | Quasi-meantone minor seventh

|-

| | [[9/5|9/5]]

| | 1017.596288

| | minor seventh, large minor seventh

|-

| | [[29/16|29/16]]

| | 1029.577194

| | 29-limit large minor seventh, octave-reduced 29th harmonic

|-

| | [[20/11|20/11]]

| | 1034.995772

| | undecimal minor seventh, small undecimal neutral seventh

|-

| | [[64/35|64/35]]

| | 1044.860380

| |  

|-

| | [[11/6|11/6]]

| | 1049.362941

| | undecimal neutral seventh, 21/4-tone

|-

| | [[24/13|24/13]]

| | 1061.427339

| | tridecimal neutral seventh

|-

| | [[13/7|13/7]]

| | 1071.701755

| | 16/3-tone, tridecimal submajor seventh

|-

| | [[28/15|28/15]]

| | 1080.557192

| | grave major seventh, octave minus a ruyo aug unison

|-

| | [[15/8|15/8]]

| | 1088.268715

| | major seventh, just major seventh, octave-reduced 15th harmonic

|-

| | [[32/17|32/17]]

| | 1095.044590

| | small septendecimal major seventh, 8ve-reduced 17th subharmonic

|-

| | [[17/9|17/9]]

| | 1101.045408

| | large septendecimal major seventh

|-

| | [[243/128|243/128]]

| | 1109.775004

| | Pythagorean major seventh, octave-reduced 243rd harmonic

|-

| | [[40/21|40/21]]

| | 1115.532907

| | acute major seventh

|-

| | [[61/32|61/32]]

| | 1116.884905

| | octave-reduced 61st harmonic

|-

| | [[48/25|48/25]]

| | 1129.327573

| | octave minus a yoyo augmented unison

|-

| | [[27/14|27/14]]

| | 1137.039096

| |  

|-

| | [[31/16|31/16]]

| | 1145.035572

| | 31-limit ultramajor seventh, octave-reduced 31st harmonic

|-

| | [[64/33|64/33]]

| | 1146.727057

| | octave-reduced 33rd subharmonic

|-

| | [[35/18|35/18]]

| | 1151.239619

| | octave minus a rugu comma

|-

| | [[96/49|96/49]]

| | 1164.303188

| |  

|-

| | [[49/25|49/25]]

| | 1165.024385

| |  

|-

| | [[160/81|160/81]]

| | 1178.493814

| | octave minus syntonic comma

|-

| | [[Octave|2/1]]

| | 1200

| | [[Octave|octave]], [http://en.wikipedia.org/wiki/Diapason diapason]

|}