Gallery of just intervals
The following is a gallery of many of just intervals that contributors to this wiki have found notable. It is of course not meant to be comprehensive, and is not the result of a systematic search.
Introduction
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.
Gallery of Just Intervals
See also list of superparticular intervals and List of intervals (Huygens-Fokker foundation)
If any FJS names are missing, please add them.
Frequency Ratio | Cents Value (six decimal places) |
Color Name | FJS Name | Some common names |
---|---|---|---|---|
1/1 | 0 | w1, wa unison | P1 | unity, perfect prime, Tonic |
32805/32768 | 1.953721 | Ly-2, Layo comma | d-2^{5} | schisma ([-15, 8, 1⟩) |
225/224 | 7.711523 | ryy-2, Ruyoyo comma | d-2^{25}_{7} | septimal kleisma, marvel comma ([-5, 2, 2, -1⟩) |
126/125 | 13.794767 | zg^{3}2, Zotrigu comma | d2^{7}_{125} | septimal semicomma, starling comma ([1, 2, -3, 1⟩) |
100/99 | 17.399484 | 1uyy1, Luyoyo comma | A1^{25}_{11} | Ptolemy's comma, ptolemisma |
99/98 | 17.576131 | 1orr-2, Loruru comma | m-2^{11}_{49} | mothwellsma |
2048/2025 | 19.552569 | sgg2, Sagugu comma | d2_{25} | diaschisma ([11, -4, -2⟩) |
81/80 | 21.506286 | g1, Gu comma | P1_{5} | meantone comma, syntonic comma, Didymus comma |
531441/524288 | 23.460010 | LLw-2, Lalawa comma | d-2 | Pythagorean comma, ditonic comma ([-19, 12⟩) |
66/65 | 26.431568 | 3u1og1, Thulogu comma | P1^{11}_{65} | winmeanma |
65/64 | 26.841376 | 3oy1, Thoyo comma | P1^{65} | wilsorma, 13th-partial chroma |
64/63 | 27.264092 | r1, Ru comma | P1_{7} | septimal comma, Archytas' comma |
3125/3072 | 29.613568 | Ly5-2, Laquinyo comma | dd-2^{3125} | magic comma, small diesis ([-10, -1, 5⟩) |
50/49 | 34.975615 | rryy-2, Biruyo comma | d-2^{25}_{49} | septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis |
49/48 | 35.696812 | zz2, Zozo comma | m2^{49} | large septimal diesis, slendro diesis |
45/44 | 38.905773 | 1uy1, Luyo comma | A1^{5}_{11} | undecimal 1/5th tone |
128/125 | 41.058858 | g32, Trigu comma | d2_{125} | diesis, minor diesis, augmented comma, enharmonic comma ([7, 0, -3⟩) |
525/512 | 43.408335 | Lzyy1, Lazoyoyo comma | A1^{175} | Avicenna's enharmonic diesis, avicennma ([-9, 1, 2, 1⟩) |
1053/1024 | 48.347665 | L3o1, Latho comma | P1^{13} | tridecimal quartertone, tridecimal comma |
36/35 | 48.770381 | rg1, Rugu comma | P1_{35} | septimal quarter tone, double comma |
250/243 | 49.166137 | y31, Triyo comma | A1^{125} | porcupine comma ([1, -5, 3⟩) |
59049/57344 | 50.724102 | Lr-2, Laru comma | d-2_{7} | Harrison's comma ([-13, 10, 0, -1⟩) |
100/97 | 52.732017 | 97uyy1, ninety-suyoyo unison | A1^{25}_{97} | shrutar quarter tone |
33/32 | 53.272943 | 1o1, ilo unison | P1^{11} | undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic |
648/625 | 62.565148 | g42, quadgu 2nd | d2_{625} | diminished comma, major diesis ([8, 4, -4⟩) |
28/27 | 62.960904 | z2, zo 2nd | m2^{7} | small septimal chroma, septimal third-tone, subminor second, septimal minor second |
27/26 | 65.337341 | 3u1, thu unison | A1_{13} | small tridecimal third tone |
26/25 | 67.900234 | 3ogg2, thogugu 2nd | d2^{13}_{25} | large tridecimal third tone |
25/24 | 70.672427 | yy1, yoyo unison | A1^{25} | chroma, classic chromatic semitone, Zarlinian semitone |
24/23 | 73.680654 | 23u1, twethu unison | m2_{23} | lesser vicesimotertial semitone |
23/22 | 76.956405 | 23o1u2, twetholu 2nd | A1^{23}_{11} | greater vicesimotertial semitone |
68/65 | 78.114034 | 17o3ug2, sothugu 2nd | m2^{17}_{65} | valentine semitone |
22/21 | 80.537035 | 1or1, loru unison | P1^{11}_{7} | undecimal minor semitone |
64/61 | 83.115195 | 61u2, siwu 2nd | m2_{61} | harry minor semitone |
21/20 | 84.467193 | zg2, zogu 2nd | m2^{7}_{5} | minor semitone, large septimal chroma |
20/19 | 88.800698 | 19uy1, nuyo unison | A1^{5}_{19} | small undevicesimal semitone, undevicesimal chroma, Eratosthenes' semitone |
256/243 | 90.224996 | sw2, sawa 2nd | m2 | Pythagorean limma, Pythagorean diatonic semitone, Pythagorean minor second ([8, -5⟩) |
135/128 | 92.178716 | Ly1, layo unison | A1^{5} | major limma ([-7, 3, 1⟩) |
19/18 | 93.603014 | 19o2, ino 2nd | m2^{19} | large undevicesimal semitone, undevicesimal limma, Boethius' semitone |
18/17 | 98.954592 | 17u1, su unison | A1_{17} | small septendecimal semitone, Arabic lute index finger |
17/16 | 104.955410 | 17o2, iso 2nd | m2^{17} | large septendecimal semitone, octave-reduced 17th harmonic |
16/15 | 111.731285 | g2, gu 2nd | m2_{5} | classic diatonic semitone, classic minor second, octave-reduced 15th subharmonic |
2187/2048 | 113.685006 | Lw1, lawa unison | A1 | apotome, Pythagorean chromatic semitone, Pythagorean augmented unison ([-11, 7⟩) |
77/72 | 116.233847 | 1oz2, lozo 2nd | m2^{77} | undecimal secor |
15/14 | 119.442808 | ry1, ruyo unison | A1^{5}_{7} | septimal diatonic semitone |
14/13 | 128.298245 | 3uz2, thuzo 2nd | M2^{7}_{13} | tridecimal 2/3-tone, trienthird, tridecimal supraminor second |
27/25 | 133.237575 | gg2, gugu 2nd | m2_{25} | large limma |
13/12 | 138.572661 | 3o2, tho 2nd | m2^{13} | tridecimal neutral second, tridecimal 2/3-tone |
243/224 | 140.949098 | Lr1, laru unison | A1_{7} | septimal subtone ([-5, 5, 0, -1⟩) |
88/81 | 143.497939 | 1o2, ilo 2nd | m2^{11} | undecimal subtone |
25/23 | 144.353081 | 23uyy1, twethuyoyo unison | M2^{5,5}_{23} | small vicesimotertial neutral second |
49/45 | 147.428097 | zzg3, zozogu 3rd | d3^{49}_{5} | swetismic neutral second |
12/11 | 150.637059 | 1u2, lu 2nd | M2_{11} | small undecimal neutral second, 3/4-tone |
35/32 | 155.139620 | zy2, zoyo 2nd | M2^{35} | septimal neutral second |
23/21 | 157.493440 | 23or2, twethoru 2nd | A1^{23}_{7} | large vicesimotertial neutral second |
78/71 | 162.786119 | 71u3o2, seventy-wutho 2nd | m2^{13}_{71} | porcupine neutral second |
11/10 | 165.004228 | 1og2, logu 2nd | m2^{11}_{5} | undecimal submajor second, large undecimal neutral second, 4/5-tone, Ptolemy's second |
54/49 | 168.213190 | rr1, ruru unison | A1_{49} | Zalzal's mujannab |
21/19 | 173.267891 | 19uz2, nuzo 2nd | M2^{7}_{19} | large neutral undevicesimal second |
10/9 | 182.403712 | y2, yo 2nd | M2^{5} | classic (whole) tone, minor (whole) tone |
49/44 | 186.333871 | 1uzz3, luzozo 3rd | m3^{49}_{11} | mothwellsmic major second |
39/35 | 187.343042 | 3org2, thorugu 2nd | m2^{13}_{35} | animist major second |
6272/5625 | 188.486956 | szzg^{4}4, sabizogugu 4th | ddd4^{49}_{625} | double marvelous second, double marvelous (whole) tone |
19/17 | 192.557607 | 19o17u2, nosu 2nd | M2^{19}_{17} | quasi-meantone |
28/25 | 196.198479 | zgg3, zogugu 3rd | d3^{7}_{25} | middle major second |
55/49 | 199.979843 | 1orry1, loruruyo unison | A1^{55}_{49} | werckismic tone |
64/57 | 200.531983 | 19u2, inu 2nd | M2_{19} | quasi-tempered whole tone, octave-reduced 57th subharmonic |
9/8 | 203.910002 | w2, wa 2nd | M2 | Pythagorean (whole) tone, major (whole) tone, octave-reduced 9th harmonic |
26/23 | 212.253315 | 23u3o2, twethutho 2nd | d3^{13}_{23} | vicesimotertial whole tone |
17/15 | 216.686695 | 17og3, sogu 3rd | d3^{17}_{5} | septendecimal whole tone, septendecimal eventone |
25/22 | 221.309485 | 1uyy2, luyoyo 2nd | A2^{25}_{11} | ptolemismic whole tone, undecimal acute whole tone |
57/50 | 226.840589 | 19ogg3, nogugu 3rd | d3^{19}_{25} | devichromic supermajor second |
8/7 | 231.174094 | r2, ru 2nd | M2_{7} | supermajor second, septimal whole tone, octave-reduced 7th subharmonic |
63/55 | 235.104252 | 1uzg3, luzogu 3rd | m3^{7}_{55} | werckismic supermajor second |
55/48 | 235.676655 | 1oy2, loyo 2nd | M2^{55} | keenanismic supermajor second |
224/195 | 240.029530 | 3uzg3, thuzogu 3rd | m3^{7}_{65} | quasi-tempered 1/5-octave, "5EDO"-esque tone |
23/20 | 241.960633 | 23og3, twethogu 3rd | M2^{23}_{5} | vicesimotertial inframinor third, vicesimotertial ultramajor second, vicesimotertial semifourth |
15/13 | 247.741053 | 3uy2, thuyo 2nd | A2^{5}_{13} | tridecimal semifourth, tridecimal ultramajor second, tridecimal inframinor third |
97/84 | 249.114503 | 97or2, ninety-soru 2nd | M2^{97}_{7} | homothetic semifourth |
81/70 | 252.268038 | rg2, rugu 2nd | M2_{35} | septimal semi-augmented second, septimal ultramajor second |
22/19 | 253.804926 | 19u1o2, nulo 2nd | M2^{11}_{19} | undevicesimal semifourth, minimal minor third, godzilla semifourth |
64/55 | 262.368344 | 1ug3, lugu 3rd | m3_{55} | keenanismic subminor third, octave-reduced 55th subharmonic |
7/6 | 266.870906 | z3, zo 3rd | m3^{7} | subminor third, septimal minor third |
90/77 | 270.079867 | 1ury2, luruyo 2nd | A2^{5}_{77} | swetismic subminor third |
62/53 | 271.531027 | 53u31o2, fithu-thiwo 2nd | M2^{31}_{53} | orwell subminor third |
75/64 | 274.582429 | yy2, yoyo 2nd | A2^{25} | classic augmented second |
27/23 | 277.590655 | twethu 2nd, 23u2 | m3_{23} | vicesimotertial augmented second |
20/17 | 281.358304 | 17uy2, suyo 2nd | A2^{5}_{17} | septendecimal augmented second, septendecimal minor third |
13/11 | 289.209719 | 3o1u3, tholu 3rd | m3^{13}_{11} | tridecimal minor third |
32/27 | 294.134997 | w3, wa 3rd | m3 | Pythagorean minor third, octave-reduced 27th subharmonic |
19/16 | 297.513016 | 19o3, ino 3rd | m3^{19} | otonal minor third, octave-reduced 19th harmonic |
25/21 | 301.846520 | ryy2, ruyoyo 2nd | A2^{25}_{7} | quasi-tempered minor third |
61/51 | 309.974395 | 61o17u2, siwosu 2nd | A2^{61}_{17} | myna third |
6/5 | 315.641287 | g3, gu 3rd | m3_{5} | classic minor third, just minor third |
77/64 | 320.143849 | 1oz3, lozo 3rd | m3^{77} | keenanismic minor third, octave-reduced 77th harmonic |
135/112 | 323.352810 | ry2, ruyo 2nd | A2^{5}_{7} | large septimal minor third, marvelous minor third ([-4, 3, 1, -1⟩) |
35/29 | 325.562426 | 29uzy3, twenuzoyo 3rd | M3^{35}_{29} | doublewide minor third |
23/19 | 330.761331 | 23o19u3, twethonu 3rd | A2^{23}_{19} | vicesimotertial supraminor third |
17/14 | 336.129503 | 17or3, soru 3rd | m3^{17}_{5} | septendecimal supraminor third |
73/60 | 339.520756 | 73og3, seventy-thogu 3rd | m3^{73}_{5} | amity supraminor third |
28/23 | 340.551559 | 23uz3, twethuzo 3rd | d4^{7}_{23} | vicesimotertial neutral third |
39/32 | 342.482663 | 3o3, tho 3rd | m3^{13} | lesser tridecimal neutral third, octave-reduced 39th harmonic |
128/105 | 342.905379 | rg3, rugu 3rd | m3_{35} | quasi-tempered 2/7-octave, 105th subharmonic |
625/512 | 345.254855 | Ly^{4}2, laquadyo 2nd | AA2^{625} | 5-limit neutral third ([-9, 0, 4⟩) |
11/9 | 347.407941 | 1o3, ilo 3rd | m3^{11} | undecimal neutral third |
60/49 | 350.616902 | rry2, ruruyo 2nd | A2^{5}_{49} | smaller septimal neutral third, (purple 3rd) |
49/40 | 351.338099 | zzg4, zozogu 4th | d4^{49}_{5} | larger septimal neutral third, (purple 3rd) |
27/22 | 354.547060 | 1u3, lu 3rd | M3_{11} | rastmic neutral third |
16/13 | 359.472338 | 3u3, thu 3rd | M3_{13} | greater tridecimal neutral third, octave reduced 13subharmonic |
21/17 | 365.825498 | 17uz3, suzo 3rd | M3^{7}_{17} | septendecimal submajor third |
26/21 | 369.746754 | thoru 3rd, 3or3 | m3^{13}_{7} | tridecimal submajor third |
51/41 | 377.848005 | 41u17o4, fowuso 4th | d4^{17}_{41} | maja third |
56/45 | 378.602191 | zg4, zogu 4th | d4^{7}_{5} | narrow perde segah, marvelous major third |
71/57 | 380.228526 | 71o19u3, seventy-wonu 3rd | M3^{71}_{19} | witchcraft major third |
76/61 | 380.628211 | 61u19o4, siwuno 4th | d4^{19}_{61} | magic major third |
96/77 | 381.811152 | 1ur3, luru 3rd | M3_{77} | undecimal perde segah, keenanismic major third |
5/4 | 386.313714 | y3, yo 3rd | M3^{5} | classic major third, just major third, octave-reduced 5th harmonic |
161/128 | 397.100254 | 23oz4, twethozo 4th | M3^{161} | just/Pythagorean major third meantone, octave-reduced 161th harmonic |
34/27 | 399.090407 | 17o4, iso 4th | d4^{17} | septendecimal quasi-tempered major third |
63/50 | 400.108480 | zgg4, zogugu 4th | d4^{7}_{25} | quasi-tempered major third |
24/19 | 404.441985 | 19u3, inu 3rd | M3_{19} | Boethius' major third |
81/64 | 407.820003 | Lw3, lawa 3rd | M3 | Pythagorean major third, octave-reduced 81st harmonic |
19/15 | 409.244301 | 19og4, nogu 4th | d4^{19}_{5} | Eratosthenes' major third |
33/26 | 412.745281 | 3u1o3, thulo 3rd | M3^{11}_{13} | tridecimal major third |
80/63 | 413.577806 | ry3, ruyo 3rd | M3^{5}_{7} | 5/7-kleismic major third |
14/11 | 417.507964 | 1uz4, luzo 4th | P4^{7}_{11} | undecimal major third, undecimal diminished fourth |
23/18 | 424.364346 | 23o4, twetho 4th | M3^{23} | vicesimotertial diminished fourth |
32/25 | 427.372572 | gg4, gugu 4th | d4_{25} | classic diminished fourth |
77/60 | 431.875134 | 1ozg4, lozogu 4th | d4^{77}_{5} | swetismic supermajor third |
9/7 | 435.084095 | r3, ru 3rd | M3_{7} | supermajor third, septimal major third |
31/24 | 443.080572 | 31o3, thiwo 3rd | M3^{31} | sensi supermajor third |
22/17 | 446.362533 | 17u1o3, sulo 3rd | M3^{11}_{17} | septendecimal supermajor third |
35/27 | 449.274618 | zy4, zoyo 4th | P4^{35} | septimal semidiminished fourth |
83/64 | 450.047318 | 83o4 | P4^{83} | octave-reduced 83rd harmonic, octacesimotertial harmonic semisixth |
13/10 | 454.213948 | 3og4, thogu 4th | d4^{13}_{5} | tridecimal semisixth, Barbados third, tridecimal 9/4 tone |
30/23 | 459.994368 | 23uy3, twethuyo 3rd | P4^{5}_{23} | vicesimotertial ultramajor third |
64/49 | 462.348187 | rr3, ruru 3rd | M3_{49} | septatonic major third |
17/13 | 464.427748 | 17o3u4, sothu 4th | P4^{17}_{13} | septendecimal sub-fourth |
21/16 | 470.780907 | z4, zo 4th | P4^{7} | sub-fourth, narrow fourth, 8ve-reduced 21st harmonic |
25/19 | 475.114412 | 19uyy3, nuyoyo 3rd | A3^{5,5}_{19} | undevicesimal augmented third, undevicesimal grave fourth |
128/97 | 480.104589 | 97u4 | P4_{97} | nonacesimoseptimal subharmonic fourth |
33/25 | 480.645516 | 1ogg4, logugu 4th | d4^{11}_{25} | ptolemismic fourth, "5EDO"-esque fourth |
160/121 | 483.677829 | 1uuy4, luluyo 4th | A4^{5}_{11,11} | narrow biyatismic fourth |
117/88 | 493.119721 | 3o1u4, tholu 4th | P4^{13}_{11} | minthmic fourth ([-3, 2, 0, 0, -1, 1⟩) |
4/3 | 498.044999 | w4, wa 4th | P4 | just perfect fourth, octave-reduced 3rd subharmonic, diatessaron |
171/128 | 501.42302 | P4^{19} | octave-reduced 171st harmonic | |
75/56 | 505.756522 | ryy3, ruyoyo 3rd | A3^{25}_{7} | marvelous fourth |
216/161 | 508.764749 | 23ur3, twethuru 3th | P4_{7,23} | wide minor-kirnbergerismic fourth |
161/120 | 508.831539 | 23ozg5, twethozogu 5th | P4^{7,23}_{5} | wide major-kirnbergerismic fourth |
980/729 | 512.235522 | zzy5, zozoyo 5th | d5^{5,7,7} | sensamagic fourth, septimal sesquidiminished grave fifth |
121/90 | 512.412169 | 1oog4, lologu 4th | d4^{11,11}_{5} | wide biyatismic fourth |
35/26 | 514.611959 | 3uzy4, thuzoyo 4th | A4^{5,7}_{13} | animist fourth |
27/20 | 519.551289 | g4, gu 4th | P4_{5} | acute fourth, wolf fourth |
23/17 | 523.318938 | 23o17u4, twethosu 4th | A3^{23}_{17} | vicesimotertial acute fourth |
19/14 | 528.687110 | 19or4, noru 4th | P4^{19}_{7} | hendrix fourth |
34/25 | 532.327982 | 17ogg5, sogugu 5th | dd5^{17}_{5,5} | vengeance superfourth |
49/36 | 533.741811 | zz5, zozo 5th | d5^{49} | Arabic lute acute fourth |
15/11 | 536.950772 | 1uy4, luyo 4th | A4^{5}_{11} | undecimal augmented fourth, subaugmented fourth |
26/19 | 543.014646 | 19u3o4, nutho 4th | P4^{13}_{19} | undevicesimal superfourth |
48/35 | 546.815381 | rg4, rugu 4th | P4_{35} | septimal super-fourth |
11/8 | 551.317942 | 1o4, ilo 4th | P4^{11} | super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa |
18/13 | 563.382340 | 3u4, thu 4th | A4_{13} | tridecimal augmented fourth |
25/18 | 568.717426 | yy4, yoyo 4th | A4^{25} | classic augmented fourth, pental augmented fourth ([-1 -2 2⟩) |
32/23 | 571.725653 | 23u4, twethu 4th | d5_{23} | vicesimotertial narrow tritone, octave-reduced 23rd subharmonic |
88/63 | 578.582034 | 1or4, loru 4th | P4^{11}_{7} | pentacircle diminished fifth |
7/5 | 582.512193 | zg5, zogu 5th | d5^{7}_{5} | augmented fourth, septimal tritone, Huygen's tritone |
108/77 | 585.721154 | 1ur4, luru 4th | A4_{77} | swetismic augmented fourth ([2, 3, 0, -1, -1⟩) |
45/32 | 590.223716 | y4, yo 4th | A4^{5} | smaller pental tritone, diatonic tritone ([-5 2 1⟩) |
128/91 | 590.646432 | 3ur4, thuru 4th | A4_{91} | smaller huntmic tritone, 91st subharmonic |
38/27 | 591.648014 | ino 5th, 19o5 | d5^{19} | smaller undevicesimal tritone |
55/39 | 595.148994 | 3u1oy4, thuloyo 4th | A4^{55}_{13} | smaller gassormic tritone |
24/17 | 596.999591 | 17u4, su 4th | A4_{17} | smaller septendecimal tritone |
99/70 | 600.088324 | 1org4, lorugu 4th | P4^{11}_{35} | homothetic quasi-tempered tritone |
17/12 | 603.000409 | 17o5, iso 5th | d5^{17} | larger septendecimal tritone |
78/55 | 604.851006 | 3o1ug5, tholugu 5th | d5^{13}_{55} | larger gassormic tritone |
27/19 | 608.351987 | inu 4th, 19u4 | A4_{19} | larger undevicesimal tritone |
91/64 | 609.353568 | 3oz5, thozo 5th | d5^{91} | larger huntmic tritone, octave-reduced 91st harmonic |
64/45 | 609.776284 | g5, gu 5th | d5_{5} | larger pental tritone, diatonic tritone ([6 -2 -1⟩) |
10/7 | 617.487807 | ry4, ruyo 4th | A4^{5}_{7} | diminished fifth, Euler's tritone, superaugmented fourth |
23/16 | 628.274347 | 23o5, twetho 5th | A4^{23} | vicesimotertial superaugmented fourth, octave-reduced 23rd harmonic |
36/25 | 631.282574 | gg5, gugu 5th | d5_{25} | pental diminished fifth, classic diminshed fifth ([2 2 -2⟩) |
13/9 | 636.617660 | 3o5, tho 5th | d5^{13} | tridecimal diminished fifth |
16/11 | 648.682058 | 1u5, lu 5th | P5_{11} | sub-fifth, octave-reduced 11th subharmonic |
35/24 | 653.184619 | zy5, zoyo 5th | P5^{35} | septimal sub-fifth |
19/13 | 656.985354 | 19o3u5, nothu 5th | P5^{19}_{13} | undevicesimal subfifth |
22/15 | 663.049228 | 1og5, logu 5th | d5^{11}_{5} | undecimal diminished fifth, semidiminished fifth |
72/49 | 666.258889 | rr4, ruru 4th | A4_{49} | septimal catafifth |
25/17 | 667.672018 | 17uyy4, suyoyo 4th | AA4^{5,5}_{17} | vengeance subfifth |
81/55 | 670.188347 | 1ug5, lugu 5th | P5_{55} | undecimal catafifth |
28/19 | 671.312890 | 19uz5, nuzo 5th | P5^{7}_{19} | hendrix fifth |
34/23 | 676.681062 | 23u17o5, twethuso 5th | d6^{17}_{23} | vicesimotertial grave fifth |
262144/177147 | 678.494990 | sasawa 6th, ssw6 | d6 | Pythagorean wolf fifth |
40/27 | 680.448711 | y5, yo 5th | P5^{5} | grave fifth |
52/35 | 685.388041 | 3org5, thorugu 5th | d5^{13}_{35} | animist fifth |
180/121 | 687.587831 | 1uuy5, luluyo 5th | A5^{5}_{11,11} | narrow biyatismic fifth |
729/490 | 687.764478 | rrg5, rurugu 4th | A4_{5,7,7} | sensamagic fifth, septimal sesquiaugmented acute fourth |
240/161 | 691.168461 | 23ury4, twethuruyo 4th | P5^{5}_{7,23} | narrow major-kirnbergerismic fifth |
161/108 | 691.235251 | 23oz6, twethozo 6th | P5^{7,23} | narrow minor-kirnbergerismic fifth |
112/75 | 694.243478 | zgg6, zogugu 6th | d6^{7}_{25} | marvelous fifth |
121/81 | 694.815881 | 1oo5, lolo 5th | d5^{11,11} | rastmic fifth, Alpharabian narrow fifth |
323/216 | 696.603423 | 19o17o6, noso 6th | d6^{17,19} | undevicesimal meantone fifth |
175/117 | 697.015671 | 3uzy5, thuzoyoyo 5th | A5^{5,5,7}_{13} | ratwolfsmic fifth |
16384/10935 | 700.001280 | sg6, sagu 6th | d6_{5} | Kirnberger's fifth ("12-EDO"-esque fifth) |
3/2 | 701.955001 | w5, wa 5th | P5 | just perfect fifth, octave-reduced 3rd harmonic, diapente |
182/121 | 706.717684 | 3o1uuz6, tholuluzo 6th | m6^{7,13}_{11,11} | tridecimal gentle fifth ([1, 0, 0, 1, -2, 1⟩) |
176/117 | 706.880279 | 3u1o5, thulo 5th | P5^{11}_{13} | minthmic fifth ([4, -2, 0, 0, 1, -1⟩) |
243/161 | 712.674751 | 23ur4, twethuru 4th | P5_{7,23} | wide minor-kirnbergerismic fifth |
121/80 | 716.322171 | 1oog5, lologu 5th | d5^{121}_{5} | wide biyatismic fifth |
50/33 | 719.354484 | 1uyy5, luyoyo 5th | A5^{25}_{11} | ptolemismic fifth, "5EDO"-esque fifth |
97/64 | 719.895411 | 97o5 | P5^{97} | nonacesimoseptimal harmonic fifth |
38/25 | 724.885588 | 19ogg6, nogugu 6th | d6^{19}_{5,5} | undevicesimal diminished sixth, undevicesimal acute fifth |
32/21 | 729.219093 | r5, ru 5th | P5_{7} | super-fifth, wide fifth, octave-reduced 21st subharmonic |
26/17 | 735.572252 | 17u3o5, sutho 5th | P5^{13}_{17} | septendecimal super-fifth |
49/32 | 737.651813 | zz6, zozo 6th | m6^{49} | superduper fifth, octave-reduced 49th harmonic |
23/15 | 740.005633 | 23og6, twethogu 6th | P5^{23}_{5} | vicesimotertial ultraminor sixth |
20/13 | 745.786052 | 3uy5, thuyo 5th | A5^{5}_{13} | tridecimal semitenth, Barbados sixth, ratwolf wolf fifth |
128/83 | 749.952682 | 83u5 | P5_{83} | 83rd subharmonic, octacesimotertial subharmonic semitenth |
17/11 | 753.637467 | 17o1u6, solu 6th | m6^{17}_{11} | septendecimal subminor sixth |
14/9 | 764.915905 | z6, zo 6th | m6^{7} | subminor sixth, septimal minor sixth |
25/16 | 772.627428 | yy5, yoyo 5th | A5^{25} | pental augmented fifth, classic augmented fifth, otonal minor sixth, octave-reduced 25th harmonic |
36/23 | 775.635654 | 23u5, twethu 5th | m6_{23} | vicesimotertial augmented fifth |
11/7 | 782.492036 | 1or5, loru 5th | P5^{11}_{7} | undecimal subminor sixth, undecimal augmented fifth |
63/40 | 786.422194 | zg6, zogu 6th | m6^{7}_{5} | narrow minor sixth |
52/33 | 787.254719 | 3o1u6, tholu 6th | m6^{13}_{11} | tridecimal minor sixth |
30/19 | 790.755699 | 19uy5, nuyo 5th | A5^{5}_{19} | small undevicesimal minor sixth, Eratosthenes' minor sixth |
128/81 | 792.179997 | sw6, sawa 6th | m6 | Pythagorean minor sixth, octave-reduced 81st subharmonic |
19/12 | 795.558015 | 19o6, ino 6th | m6^{19} | large undevicesimal minor sixth, Boethius' minor sixth |
27/17 | 800.909593 | 17u5, su 5th | A5_{17} | septendecimal quasi-tempered minor sixth |
8/5 | 813.686286 | g6, gu 6th | m6_{5} | classic minor sixth, just minor sixth, octave-reduced 5th subharmonic |
21/13 | 830.253246 | 3uz6, thuzo 6th | M6^{7}_{13} | tridecimal supraminor sixth |
34/21 | 834.174502 | 17or6, soru 6th | m6^{17}_{7} | septendecimal supraminor sixth |
13/8 | 840.527662 | 3o6, tho 6th | m6^{13} | lesser tridecimal neutral sixth, octave-reduced 13th harmonic |
80/49 | 848.661901 | rry5, ruruyo aug 5th | A5^{5}_{49} | (purple 6th) |
49/30 | 849.383198 | zzg7, zozogu 7th | d7^{49}_{5} | (purple 6th) |
18/11 | 852.592059 | 1u6, lu 6th | M6_{11} | undecimal neutral sixth |
105/64 | 857.094621 | zy6, zoyo 6th | M6^{35} | quasi-tempered 5/7-octave, octave-reduced 105th harmonic |
23/14 | 859.448441 | 23or6, twethoru 6th | A5^{23}_{7} | vicesimotertial neutral sixth |
28/17 | 863.870497 | 17uz6, suzo 6th | M6^{7}_{17} | septendecimal submajor sixth |
38/23 | 869.238669 | 23u19o6, twethuno 6th | d7^{19}_{23} | vicesimotertial submajor sixth |
5/3 | 884.358713 | y6, yo 6th | M6^{5} | classic major sixth, just major sixth |
42/25 | 898.153480 | zgg7, zogugu 7th | d7^{7}_{25} | quasi-tempered major sixth |
32/19 | 902.486984 | 19u6, inu 6th | M6_{19} | utonal major sixth, octave-reduced 19th subharmonic |
27/16 | 905.865003 | w6, wa 6th | M6 | Pythagorean major sixth, octave-reduced 27th harmonic |
22/13 | 910.790821 | 3u1o6, thulo 6th | M6^{11}_{13} | tridecimal major sixth |
17/10 | 918.641696 | 17og7, sogu 7th | d7^{17}_{5} | septendecimal diminished seventh, septendecimal major sixth |
46/27 | 922.409345 | twetho 7th, 23o7 | M6^{23} | vicesimotertial diminished seventh, vicesiomtertial supermajor sixth |
12/7 | 933.129094 | r6, ru 6th | M6_{7} | supermajor sixth, septimal major sixth |
55/32 | 937.631656 | 1oy6, loyo 6th | M6^{55} | keenanismic supermajor sixth, octave-reduced 55th harmonic |
19/11 | 946.195074 | 19o1u7, nolu 7th | m7^{19}_{11} | undevicesimal semitwelfth, maximal major sixth |
140/81 | 947.319617 | zy7, zoyo 7th | m7^{35} | septimal semidiminished seventh, septimal inframinor seventh |
97/56 | 951.069504 | 97or6, ninety-soru 6th | M6^{97}_{7} | homothetic semitwelth |
26/15 | 952.258947 | 3og7, thogu 7th | d7^{13}_{5} | tridecimal semitwelfth |
40/23 | 958.039367 | 23uy6, twethuyo 6th | m7^{5}_{23} | vicesimotertial ultramajor sixth, vicesimotertial inframinor seventh, vicesimotertial semitwelfth |
7/4 | 968.825906 | z7, zo 7th | m7^{7} | subminor seventh, septimal minor seventh, harmonic seventh, natural seventh, octave-reduced 7th harmonic |
225/128 | 976.537429 | Lyy6, layoyo 6th | A6^{25} | marvel five-limit harmonic seventh, octave-reduced 225th harmonic ([-7, 2, 2⟩) |
44/25 | 978.690515 | 1ogg7, logugu 7th | d7^{11}_{5,5} | ptolemismic minor seventh, undecimal grave minor seventh |
127/72 | 982.511622 | 127o7 | m7^{127} | harmonic/Pythagorean minor seventh meantone |
30/17 | 983.313305 | 17uy6, suyo 6th | A6^{5}_{17} | septendecimal minor seventh |
23/13 | 987.746686 | 23o3u7, twethothu 7th | A6^{23}_{13} | vicesimotertial minor seventh |
71/40 | 993.382830 | 71oy7 | m7^{71}_{5} | harmonic/just minor seventh meantone |
959/540 | 994.285690 | 137ozy8 | dd8^{959}_{5} | harmonic/Pythagorean/just minor seventh meantone |
16/9 | 996.089998 | w7, wa 7th | m7 | Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic |
25/14 | 1003.801521 | ryy6, ruyoyo 6th | A6^{25}_{7} | middle minor seventh |
34/19 | 1007.442393 | 19u17o7, nuso 7th | m7^{17}_{19} | quasi-meantone minor seventh |
9/5 | 1017.596288 | g5, gu 7th | m7_{5} | classic minor seventh, large minor seventh |
38/21 | 1026.732109 | 19or7, noru 7th | m7^{19}_{7} | minor neutral undevicesimal seventh |
29/16 | 1029.577194 | 29o7, tweno 7th | m7^{29} | vicesimononal supraminor seventh, octave-reduced 29th harmonic |
20/11 | 1034.995772 | 1uy7, luyo 7th | M7^{5}_{11} | undecimal supraminor seventh, small undecimal neutral seventh |
42/23 | 1042.506560 | 23uz7, twethuzo 7th | d8^{7}_{23} | small vicesimotertial neutral seventh |
64/35 | 1044.860380 | rg7, rugu 7th | m7_{35} | septimal neutral seventh |
11/6 | 1049.362941 | 1o7, ilo 7th | m7^{11} | undecimal neutral seventh, 21/4-tone |
46/25 | 1055.646920 | twethogugu octave, 23ogg8 | m7^{23}_{5,5} | large vicesimotertial neutral seventh |
24/13 | 1061.427339 | 3u7, thu 7th | M7_{13} | tridecimal neutral seventh |
50/27 | 1066.762425 | yoyo 7th, yy7 | M7^{5,5} | grave major seventh |
13/7 | 1071.701755 | 3or7, thoru 7th | m7^{13}_{7} | tridecimal submajor seventh, 16/3-tone |
28/15 | 1080.557192 | zg8, zogu octave | d8^{7}_{5} | grave major seventh, octave minus a ruyo aug unison |
15/8 | 1088.268715 | y7, yo 7th | M7^{5} | classic major seventh, just major seventh, octave-reduced 15th harmonic |
32/17 | 1095.044590 | 17u7, su 7th | M7_{17} | septendecimal major seventh (FJS), septendecimal diminished octave (HEJI), octave-reduced 17th subharmonic |
17/9 | 1101.045408 | 17o8, iso octave | d8^{17} | septendecimal major seventh (HEJI), septendecimal diminished octave (FJS) |
36/19 | 1106.396986 | 19u7, inu 7th | M7_{19} | undevicesimal major seventh, Boethius' major seventh |
243/128 | 1109.775004 | Lw7, lawa 7th | M7 | Pythagorean major seventh, octave-reduced 243rd harmonic |
19/10 | 1111.199302 | 19og8, nogu 8ve | d8^{19}_{5} | undevicesimal diminished octave, Eratosthenes' major seventh |
40/21 | 1115.532907 | ry7, ruyo 7th | M7^{5}_{7} | septimal acute major seventh |
61/32 | 1116.884905 | 61o7, siwo 7th | M7^{61} | octave-reduced 61st harmonic |
21/11 | 1119.462965 | 1uz8, luzo 8ve | P8^{7}_{11} | large undecimal diminished octave, undecimal major seventh |
44/23 | 1123.043595 | 23u1o7, twethulo 7th | d8^{11}_{23} | vicesimotertial major seventh |
23/12 | 1126.319346 | 23o8, twetho 8ve | M7^{23} | vicesimotertial major seventh |
48/25 | 1129.327573 | gg8, gugu octave | d8_{25} | classic diminished octave |
25/13 | 1132.099766 | 3uyy7, thuyoyo 7th | A7^{5,5}_{13} | lesser tridecimal diminished octave |
27/14 | 1137.039096 | r7, ru 7th | M7_{7} | supermajor seventh, septimal major seventh |
31/16 | 1145.035572 | 31o7, thiwo 7th | M7^{31} | tricesimoprimal ultramajor seventh (FJS), tricesimoprimal semidiminished octave (HEJI), octave-reduced 31st harmonic |
64/33 | 1146.727057 | 1u8, lu octave | P8_{11} | undecimal semidiminished octave, octave-reduced 33rd subharmonic |
35/18 | 1151.239619 | zy8, zoyo octave | P8^{35} | septimal semidiminished octave |
96/49 | 1164.303188 | rr7, ruru 7th | M7_{49} | septimal ultramajor seventh |
49/25 | 1165.024385 | zzgg9, bizogu 9th | d9^{49}_{25} | BP eighth |
160/81 | 1178.493814 | y8, yo octave | P8^{5} | octave minus syntonic comma |
2/1 | 1200 | w8, wa octave | P8 | octave, diapason |
Intervals larger than an octave
In the color names, "co" or "c" stands for compound, a conventional music term.
Frequency Ratio | Cents Value (three decimal places) |
Color Name | FJS Name | Some common names | |
---|---|---|---|---|---|
15/7 | 1319.443 | ry8 | ruyo 8ve | A8^{5}_{7} | septimal minor ninth |
13/6 | 1338.573 | 3o9 | tho 9th | m9^{13} | tridecimal minor ninth |
11/5 | 1365.004 | 1o9 | ilo 9th | m9^{11}_{5} | neutral ninth |
9/4 | 1403.910 | w9 | wa 9th | M9 | major ninth |
16/7 | 1431.174 | r9 | ru 9th | M9_{7} | septimal major ninth |
7/3 | 1466.871 | z10 | zo 10th | m10^{7} | septimal minor tenth |
12/5 | 1515.641 | g10 | gu 10th | m10_{5} | classic minor tenth |
5/2 | 1586.314 | y10 | yo 10th | M10^{5} | classic major tenth |
13/5 | 1654.214 | 3og11 | thogu 11th | d11^{13}_{5} | tridecimal eleventh |
8/3 | 1698.045 | w11, cw4 | wa 11th, cowa 4th | P11 | perfect eleventh |
11/4 | 1751.318 | 1o11, c1o4 | ilo 11th, colo 4th | P11^{11} | undecimal semi-augmented eleventh |
14/5 | 1782.512 | zg12, czg5 | zogu 12th, cozogu 5th | d12^{7}_{5} | short hexatone |
3/1 | 1901.955 | w12, cw5 | wa 12th, cowa 5th | P12 | 3rd harmonic, perfect twelfth, tritave |
16/5 | 2013.686 | g13, cg6 | gu 13th, cogu 6th | m13_{5} | just minor thirteenth |
13/4 | 2040.528 | 3o13, c3o6 | tho 13th, cotho 6th | m13^{13} | tridecimal neutral thirteenth |
10/3 | 2084.359 | y13, cy6 | yo 13th, coyo 6th | M13^{5} | just/classic(al)/ptolemaic major thirteenth |
7/2 | 2168.826 | cz7 | cozo 7th | m14^{7} | harmonic fourteenth |
11/3 | 2249.363 | c1o7 | colo 7th | m14^{11} | undecimal neutral fifteenth |
15/4 | 2288.269 | cy7 | coyo 7th | M14^{5} | just/classic(al)/ptolemaic major fifteenth |
4/1 | 2400.000 | cw8, ccw1 | wa double 8ve | P15 | 4th harmonic, two octaves |
13/3 | 2538.573 | c3o9, cc3o2 | cotho 9th, cocotho 2nd | m16^{13} | tridecimal minor sixteenth |
9/2 | 2603.910 | cw9, ccw2 | cowa 9th, cocoyo 2nd | M16 | major sixteenth |
14/3 | 2666.871 | cz10, ccz3 | cozo 10th, cocozo 3rd | m17^{7} | two octaves and a subminor third |
5/1 | 2786.314 | cy10, ccy3 | coyo 10th, cocoyo 3rd | M17^{5} | 5th harmonic, pentave |
16/3 | 2898.045 | ccw4 | cocowa 4th | P18 | two octaves and a perfect fourth |
11/2 | 2951.318 | cc1o4 | cocolo 4th | P18^{11} | two octaves and an undecimal semi-augmented fourth |
6/1 | 3101.955 | ccw5 | cocowa 5th | P19 | 6th harmonic |
13/2 | 3240.528 | cc3o6 | cocotho 6th | m20^{13} | two octaves and a tridecimal neutral sixth |
7/1 | 3368.826 | ccz7 | cocozo 7th | m21^{7} | 7th harmonic |
15/2 | 3488.269 | ccy7 | cocoyo 7th | M21^{5} | two octaves and a just/classic(al)/ptolemaic major seventh |
8/1 | 3600.000 | c^{3}w1 | wa triple 8ve | P22 | 8th harmonic, three octaves |
9/1 | 3803.910 | c^{3}w2 | tricowa 2nd | M23 | 9th harmonic |
10/1 | 3986.314 | c^{3}y3 | tricoyo 3rd | M24^{5} | 10th harmonic, decade |
11/1 | 4151.318 | c^{3}1o4 | tricolo 4th | P25^{11} | 11th harmonic |
12/1 | 4301.955 | c^{3}w5 | tricowa 5th | P26 | 12th harmonic |
13/1 | 4440.528 | c^{3}3o6 | tricotho 6th | m27^{13} | 13th harmonic |
14/1 | 4568.826 | c^{3}z7 | tricozo 7th | m28^{7} | 14th harmonic |
15/1 | 4688.269 | c^{3}y7 | tricoyo 7th | M28^{5} | 15th harmonic |
16/1 | 4800.000 | c^{4}w1 | wa quadruple 8ve | P29 | 16th harmonic, four octaves |
17/1 | 4904.955 | m30^{17} | 17th harmonic | ||
18/1 | 5004.910 | M30 | 18th harmonic | ||
19/1 | 5097.513 | m31^{19} | 19th harmonic | ||
20/1 | 5186.314 | M31^{5} | 20th harmonic | ||
21/1 | 5270.781 | P32^{7} | 21st harmonic | ||
22/1 | 5351.318 | P32^{11} | 22nd harmonic | ||
23/1 | 5428.274 | A32^{23} | 23rd harmonic | ||
24/1 | 5501.955 | P33 | 24th harmonic | ||
49/1 | 6737.652 | 49th harmonic |