Gallery of Just Intervals

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Introduction[edit]

In Just Intonation, a musical interval is specified as a ratio of two frequencies.. When two (or more) pitches are sounded that are in simple proportions to one another, there is a "fusing" quality to the sound which is often described as pleasing; hence the interest in tuning the pitches of musical systems according to such proportions. There is much debate as to what "consonance" means in a musical system, but in Just Intonation, it is generally assumed that lower numbers in frequency ratios lead to greater consonance. In the actual performance of a piece of music, the number of factors involved are enormous, and it is not often helpful to reduce a musical experience to a one-dimensional description of "consonance versus dissonance." Hence the need for this gallery, to give life to conversation about what an interval means beyond the numerical description: "5/3" or "21/16" or what have you.

What follows is a Gallery of Just Intervals in ascending order from 1/1 to 2/1 and beyond. No such list could possibly be complete (as there are infinite possible ratios), so please add intervals of interest as you see fit. Any rational interval is welcome, as long as the wiki author has some interest in it. Contributions to an interval's lore could include: descriptions of common usage, technical notes, poetry, links, reservations, complaints, chords or compositions that feature it, edos that approximate it, intervals that are functionally (or emotionally) related to it, nicknames, love letters, fan art, etc. If your contribution is unconventional, feel free to sign your name to it.

This page lists links to dedicated pages for each interval.

Explanation of the color names is here.

Gallery of Just Intervals[edit]

See also List of Superparticular Intervals and List of intervals (Huygens-Fokker foundation)

frequency ratio cents value

(six decimal places)

color notation some common names
1/1 0 w1, wa unison unity, perfect prime, Tonic
32805/32768 1.953721 Ly-2, yo minicomma schisma, |-15, 8, 1>
225/224 7.711523 ryy-2, ruyoyo minicomma septimal subcomma, |-5, 2, 2, -1>
100/99 17.399484 1uyy1, luyoyo comma Ptolemy's comma
99/98 17.576131 1orr-2, loruru comma Mothwellsma
2048/2025 19.552569 sgg2, small gugu comma |11, -4, -2>
81/80 21.506286 g1, gu comma Syntonic comma, Didymus comma
531441/524288 23.460010 LLw-2, wa comma Pythagorean comma, Ditonic comma, |-19, 12>
66/65 26.431568 3u1og1, thulogu comma Winmeanma
65/64 26.841376 3oy1, thoyo comma Wilsorma, 13th-partial chroma
64/63 27.264092 r1, ru comma Septimal comma, Archytas' comma
3125/3072 29.613568 Ly⁵-2, quintuple yo comma Magic comma, small diesis, |-10, -1, 5>
50/49 34.975615 rryy-2, double ruyo comma septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis
49/48 35.696812 zz2, zozo comma large septimal diesis, slendro diesis
45/44 38.905773 1uy1, luyo comma undecimal 1/5th tone
128/125 41.058858 g³2, triple gu comma Diesis, minor diesis, augmented comma, enharmonic comma, |7, 0, -3>
525/512 43.408335 Lzyy1, large zoyoyo comma Avicenna's enharmonic diesis, |-9, 1, 2, 1>
36/35 48.770381 rg1, rugu comma double comma, septimal quarter tone
250/243 49.166137 y³1, triple yo comma Porcupine comma, |1, -5, 3>
59049/57344 50.724102 Lr-2, large ru comma Harrison's comma, |-13, 10, 0, -1>
100/97 52.732017 97uyy1, ninety-suyoyo quarter-tone shrutar quarter tone
33/32 53.272943 1o1, lo quarter-tone undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
648/625 62.565148 g⁴2, quadruple gu 2nd diminished comma, major diesis, |8, 4, -4>
28/27 62.960904 z2, zo 2nd septimal chroma, small septimal chromatic semitone, septimal subminor second
25/24 70.672427 yy1, yoyo semitone chroma, chromatic semitone, Zarlinian semitone
68/65 78.114034 17o3ug2, sothugu 2nd valentine semitone
22/21 80.537035 1or1, loru semitone undecimal minor semitone
64/61 83.115195 61u2, sixty-wu 2nd harry minor semitone
21/20 84.467193 zg2, zogu 2nd minor semitone, large septimal chromatic semitone
256/243 90.224996 sw2, small wa 2nd Pythagorean limma, Pythagorean minor second, |8, -5>
135/128 92.178716 Ly1, large yo semitone ma1oor limma, |-7, 3, 1>
18/17 98.954592 17u1, su semitone small septendecimal semitone, Arabic lute index finger
17/16 104.955410 17o2, sova 2nd large septendecimal semitone, octave-reduced 17th harmonic
16/15 111.731285 g2, gu 2nd diatonic semitone, classic minor second, octave-reduced 15th subharmonic
2187/2048 113.685006 Lw1, large wa semitone apotome, |-11, 7>
77/72 116.233847 1oz2, lozo 2nd undecimal secor
15/14 119.442808 ry1, ruyo semitone septimal diatonic semitone
14/13 128.298245 3uz2, thuzo 2nd 2/3-tone, trienthird, tridecimal supraminor second
27/25 133.237575 gg2, gugu 2nd large limma
13/12 138.572661 3o2, tho 2nd tridecimal subtone, tridecimal 2/3-tone
243/224 140.949098 Lr1, large ru semitone septimal subtone, |-5, 5, 0, -1>
88/81 143.497939 1o2, lova 2nd undecimal subtone
49/45 147.428097 zzg3, zozogu 3rd swetismic neutral second
12/11 150.637059 1u2, lu 2nd small undecimal neutral second, 3/4-tone
35/32 155.139620 zy2, zoyo 2nd septimal neutral second
78/71 162.786119 71u3o2= seventy-wutho 2nd porcupine neutral second
11/10 165.004228 1og2, logu 2nd large undecimal neutral second, 4/5-tone, Ptolemy's second
54/49 168.213190 rr1, ruru augmented unison Zalzal's mujannab
10/9 182.403712 y2, yo 2nd minor whole tone
49/44 186.333871 1uzz3, luzozo 3rd werckismic minor second
19/17 192.557607 19o17u2, nosu 2nd quasi-meantone
28/25 196.198479 zgg3, zogugu 3rd middle major second
55/49 199.979843 1orry1, loruruyo unison werckismic tone
9/8 203.910002 w2, wa 2nd major whole tone, Pythagorean tone, octave-reduced 9th harmonic
17/15 216.686695 17og3, sogu 3rd septendecimal whole tone, septendecimal eventone
8/7 231.174094 r2, ru 2nd supermajor second, septimal whole tone, diminished third, octave-reduced 7th subharmonic
63/55 235.104252 1uzg3, luzogu 3rd werckismic supermajor second
55/48 235.676655 1oy2, loyo 2nd keenanismic supermajor second
15/13 247.741053 3uy2, thuyo 2nd semifourth, tridecimal ultramajor second, tridecimal inframinor third
22/19 253.804926 19u1o2, nulo 2nd minimal minor third, godzilla third
64/55 262.368344 1ug3, lugu 3rd keenanismic subminor third, octave-reduced 55th subharmonic
7/6 266.870906 z3, zo 3rd subminor third, septimal minor third, augmented second
90/77 270.079867 1ury2, luruyo 2nd swetismic subminor third
62/53 271.531027 53u31o2, fifty-thu-thirty-wo 2nd orwell subminor third
75/64 274.582429 yy2, yoyo 2nd classic augmented second
20/17 281.358304 17uy2, suyo 2nd septendecimal augmented second, septendecimal minor third
13/11 289.209179 3o1u3, tholu 3rd tridecimal minor third
32/27 294.134997 w3, wa 3rd Pythagorean minor third, octave-reduced 27th subharmonic
19/16 297.513016 19o3, nova 3rd otonal minor third, octave-reduced 19th harmonic
25/21 301.846520 ryy2, ruyoyo 2nd quasi-tempered minor third
61/51 309.974395 61o17u2, sixty-wosu 2nd myna third
6/5 315.641287 g3, gu 3rd minor third, pental minor third
77/64 320.143849 1oz3, lozo 3rd keenanismic minor third, octave-reduced 77th harmonic
135/112 323.352810 ry2, ruyo aug 2nd large septimal minor third, marvelous minor third, |-4, 3, 1, -1>
35/29 325.562426 29uzy3, twenty-nuzoyo 3rd doublewide minor third
17/14 336.129503 17or3, soru 3rd septendecimal supraminor third
73/60 339.520756 73og3, seventy-thogu 3rd amity supraminor third
625/512 345.254855 Ly⁴2, large quadruple yo 2nd 5-limit neutral third, |-9, 0, 4>
11/9 347.407941 1o3, lova 3rd undecimal neutral third
60/49 350.616902 rry2, ruruyo 2nd smaller septimal neutral third, (p3, purple 3rd)
49/40 351.338099 zzg4, zozogu 4th larger septimal neutral third, (p3, purple 3rd)
27/22 354.547060 1u3, lu 3rd rastmic neutral third
16/13 359.472338 3u3, thu 3rd tridecimal neutral third
21/17 365.825498 17uz3, suzo 3rd septendecimal submajor third
56/45 378.602191 zg4, zogu 4th narrow perde segah, marvelous major third
51/41 377.848005 41u17o4, forty-wuso 4th maja third
71/57 380.228526 71o19u3, seventy-wonu 3rd witchcraft major third
76/61 380.628211 61u19o4, sixty-wuno 4th magic major third
96/77 381.811152 1ur3, luru 3rd undecimal perde segah, keenanismic major third
5/4 386.313714 y3, yo 3rd major third, octave-reduced 5th harmonic, pental major third
81/64 407.820003 Lw3, large wa 3rd Pythagorean major third, octave-reduced 81st harmonic
80/63 413.577806 ry3, ruyo 3rd werckismic sharp major third
14/11 417.507964 1uz4, luzo 4th undecimal major third, undecimal diminished fourth
32/25 427.372572 gg4, gugu 4th classic diminished fourth
77/60 431.875134 1ozg4, lozogu 4th swetismic supermajor third
9/7 435.084095 r3, ru 3rd supermajor third, septimal major third, septimal diminished fourth
31/24 443.080572 31o3, thirty-wo 3rd sensi supermajor third
22/17 446.362533 17u1o3, sulo 3rd septendecimal supermajor third
35/27 449.274618 zy4, zoyo 4th semi-diminished fourth
13/10 454.213948 3og4, thogu 4th Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramaor third
64/49 462.348187 rr3, ruru 3rd septatonic major third
17/13 464.427748 17o3u4, sothu 4th septendecimal sub-fourth
21/16 470.780907 z4, zo 4th sub-fourth, narrow fourth, augmented third, 8ve-reduced 21st harmonic
33/25 480.645516 1ogg4, logugu 4th "5-EDO"-esque fourth
117/88 493.119721 3o1u4, tholu 4th |-3, 2, 0, 0, -1, 1>
4/3 498.044999 w4, wa 4th just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
75/56 505.756522 ryy3, ruyoyo 3rd marvelous fourth
27/20 519.551289 g4, gu 4th acute fourth
19/14 528.687110 19or4, noru 4th 19-limit wide fourth
49/36 533.741811 zz5, zozo 5th Arabic lute acute fourth
15/11 536.950772 1uy4, luyo 4th undecimal augmented fourth, subaugmented fourth
48/35 546.815381 rg4, rugu 4th septimal super-fourth
11/8 551.317942 1o4, lova 4th super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa
18/13 563.382340 3u4, thu 4th tridecimal augmented fourth
25/18 568.717426 yy4, yoyo 4th classic augmented fourth, pental augmented fourth
88/63 578.582034 1or4, loru 4th werckismic augmented fourth
7/5 582.512193 zg5, zogu 5th augmented fourth, septimal tritone, Huygen's tritone
45/32 590.223716 y4, yo 4th
108/77 585.721154 1ur4, luru 4th swetismic augmented fourth, |2, 3, 0, -1, -1>
24/17 596.999591 17u4, su 4th smaller septendecimal tritone
17/12 603.000409 17o5, sova 5th larger septendecimal tritone
64/45 609.776284 g5, gu 5th
10/7 617.487807 ry4, ruyo 4th diminished fifth, Euler's tritone, superaugmented fourth
23/16 628.274347 23o5, twenty-tho 5th 23-limit superaugmented fourth, octave-reduced 23rd harmonic
36/25 631.282574 gg5, gugu 5th pental diminished fifth, classic diminshed fifth
13/9 636.617660 3o5, tho 5th tridecimal diminished fifth
16/11 648.682058 1u5, lu 5th sub-fifth, octave-reduced 11th subharmonic
35/24 653.184619 zy5, zoyo 5th septimal sub-fifth
22/15 663.049228 1og5, logu 5th undecimal diminished fifth, semidiminished fifth
72/49 666.258889 rr4, ruru 4th septimal catafifth
81/55 670.188347 1ug5, lugu 5th undecimal catafifth
28/19 671.312890 19uz5, nuzo 5th 19-limit narrow fifth
40/27 680.448711 y5, yo 5th grave fifth
112/75 694.243478 zgg6, zogugu 6th marvelous fifth
3/2 701.955001 w5, wa 5th just perfect fifth, octave-reduced 3rd harmonic, diapente
182/121 706.717684 3o1uuz6, tholuluzo 6th |1, 0, 0, 1, -2, 1 >
176/117 706.880279 3u1o5, thulo 5th |4, -2, 0, 0, 1, -1>
50/33 719.354484 1uyy5, luyoyo 5th "5-EDO"-esque fifth
32/21 729.219093 r5, ru 5th super-fifth, wide fifth, diminished sixth, octave-reduced 21st subharmonic
26/17 735.572252 17u3o5, sutho 5th septendecimal super-fifth
49/32 737.651813 zz6, zozo 6th superduper fifth, octave-reduced 49th harmonic
20/13 745.786052 3uy5, thuyo 5th Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth
17/11 753.637467 17o1u6, solu 6th septendecimal subminor sixth
14/9 764.915905 z6, zo 6th subminor sixth, septimal minor sixth, augmented fifth
25/16 772.627428 yy5, yoyo 5th pental augmented fifth, classic augmented fifth, otonal minor sixth, octave-reduced 25th harmonic
11/7 782.492036 1or5, loru 5th undecimal subminor sixth, undecimal augmented fifth
63/40 786.422194 zg6, zogu 6th
128/81 792.179997 sw6, small wa 6th
8/5 813.686286 g6, gu 6th minor sixth, octave-reduced 5th subharmonic
413/256 827.997565 59oz6, fifty-nozo 6th octave-reduced 413th harmonic, homestuck sixth (2⁻⁸ * 7 * 59)
13/8 840.527662 3o6, tho 6th tridecimal neutral sixth, octave-reduced 13th harmonic
80/49 848.661901 rry5, ruruyo aug 5th (purple 6th)
49/30 849.383198 zzg7, zozogu 7th (purple 6th)
18/11 852.592059 1u6, lu 6th undecimal neutral sixth
28/17 863.870497 17uz6, suzo 6th septendecimal submajor sixth
5/3 884.358713 y6, yo 6th major sixth
42/25 898.153480 zgg7, zogugu 7th
27/16 905.865003 w6, wa 6th Pythagorean major sixth, octave-reduced 27th harmonic
22/13 910.790821 3u1o6, thulo 6th tridecimal major sixth
17/10 918.641696 17og7, sogu 7th septendecimal diminished seventh, septendecimal major sixth
12/7 933.129094 r6, ru 6th supermajor sixth, septimal major sixth, diminished seventh
26/15 952.258947 3og7, thogu 7th semitwelfth, tridecimal inframinor seventh, tridecimal ultramajor sixth
7/4 968.825906 z7, zo 7th subminor seventh, harmonic seventh, augmented sixth, octave-reduced 7th harmonic
225/128 976.537429 Lyy6, large yoyo 6th marvel five-limit harmonic seventh, octave-reduced 225th harmonic, |-7, 2, 2>
30/17 983.313305 17uy6, suyo 6th septendecimal minor seventh
16/9 996.089998 w7, wa 7th Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic
25/14 1003.801521 ryy6, ruyoyo 6th Middle minor seventh
34/19 1007.442393 19u17o7, nuso 7th Quasi-meantone minor seventh
9/5 1017.596288 g5, gu 7th minor seventh, large minor seventh
29/16 1029.577194 29o7, twenty-no 7th 29-limit large minor seventh, octave-reduced 29th harmonic
20/11 1034.995772 1uy7, luyo 7th undecimal minor seventh, small undecimal neutral seventh
64/35 1044.860380 rg7, rugu 7th
11/6 1049.362941 1o7, lova 7th undecimal neutral seventh, 21/4-tone
24/13 1061.427339 3u7, thu 7th tridecimal neutral seventh
13/7 1071.701755 3or7, thoru 7th 16/3-tone, tridecimal submajor seventh
28/15 1080.557192 zg8, zogu octave grave major seventh, octave minus a ruyo aug unison
15/8 1088.268715 y7, yo 7th major seventh, just major seventh, octave-reduced 15th harmonic
32/17 1095.044590 17u7, su 7th small septendecimal major seventh, 8ve-reduced 17th subharmonic
17/9 1101.045408 17o8, sova octave large septendecimal major seventh
243/128 1109.775004 Lw7, large wa 7th Pythagorean major seventh, octave-reduced 243rd harmonic
40/21 1115.532907 ry7, ruyo 7th acute major seventh
61/32 1116.884905 61o7, sixty-wo 7th octave-reduced 61st harmonic
48/25 1129.327573 gg8, gugu octave octave minus a yoyo augmented unison
27/14 1137.039096 r7, ru 7th
31/16 1145.035572 31o7, thirty-wo 7th 31-limit ultramajor seventh, octave-reduced 31st harmonic
64/33 1146.727057 1u8, lu octave octave-reduced 33rd subharmonic
35/18 1151.239619 zy8, zoyo octave octave minus a rugu comma
96/49 1164.303188 rr7, ruru 7th
49/25 1165.024385 zzgg9, double zogu 9th
160/81 1178.493814 y8, yo octave octave minus syntonic comma
2/1 1200 w8, wa octave octave, diapason

Intervals larger than 2/1[edit]

frequency ratio cents value

(three decimal places)

13/6 1338.573
11/5 1365.004
16/7 1431.174
5/2 1586.314
8/3 1698.045
11/4 1751.318
3/1 1901.955
16/5 2013.686
13/4 2040.528
10/3 2084.359
7/2 2168.826
11/3 2249.363
15/4 2288.269
4/1 2400.000
13/3 2538.573
9/2 2603.910
14/3 2666.871
5/1 2786.314
16/3 2898.045
11/2 2951.318
6/1 3101.955
13/2 3240.528
7/1 3368.826
15/2 3488.269
8/1 3600.000
9/1 3803.910
10/1 3986.314
11/1 4151.318
12/1 4301.955
13/1 4440.528
14/1 4568.826
15/1 4688.269
16/1 4800.000

Links[edit]

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