Gallery of just intervals

Revision as of 21:57, 14 June 2020 by Xenwolf (talk | contribs) (Gallery of Just Intervals: names for 23/19 and 38/23 found, todo: color names)

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.

Explanation of the color names is here.


Gallery of Just Intervals

See also list of superparticular intervals and List of intervals (Huygens-Fokker foundation)

Many of the FJS names are still missing, please add them.

frequency ratio cents value
(six decimal places)
color notation 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-25 schisma, [-15, 8, 1
225/224 7.711523 ryy-2, ruyoyo comma d-2257 septimal subcomma, marvel comma, [-5, 2, 2, -1
126/125 13.794767 zg32, zotrigu comma d27125 septimal semicomma, starling comma, [1, 2, -3, 1
100/99 17.399484 1uyy1, luyoyo comma A12511 Ptolemy's comma
99/98 17.576131 1orr-2, loruru comma m-21149 Mothwellsma
2048/2025 19.552569 sgg2, sagugu comma d225 Diaschisma, [11, -4, -2
81/80 21.506286 g1, gu comma P15 Meantone comma, Syntonic comma, Didymus comma
531441/524288 23.460010 LLw-2, wa comma d-2 Pythagorean comma, Ditonic comma, [-19, 12
66/65 26.431568 3u1og1, thulogu comma P11165 Winmeanma
65/64 26.841376 3oy1, thoyo comma P165 Wilsorma, 13th-partial chroma
64/63 27.264092 r1, ru comma P17 Septimal comma, Archytas' comma
3125/3072 29.613568 Ly5-2, laquinyo comma dd-23125 Magic comma, small diesis, [-10, -1, 5
50/49 34.975615 rryy-2, biruyo comma d-22549 septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis
49/48 35.696812 zz2, zozo comma m249 large septimal diesis, slendro diesis
45/44 38.905773 1uy1, luyo comma A1511 undecimal 1/5th tone
128/125 41.058858 g32, trigu comma d2125 Diesis, minor diesis, augmented comma, enharmonic comma, [7, 0, -3
525/512 43.408335 Lzyy1, lazoyoyo comma A1525 Avicenna's enharmonic diesis, [-9, 1, 2, 1
36/35 48.770381 rg1, rugu comma P135 double comma, septimal quarter tone
250/243 49.166137 y31, triyo comma A1125 Porcupine comma, [1, -5, 3
59049/57344 50.724102 Lr-2, laru comma d-27 Harrison's comma, [-13, 10, 0, -1
100/97 52.732017 97uyy1, ninety-suyoyo unison A12597 shrutar quarter tone
33/32 53.272943 1o1, ilo unison P111 undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
648/625 62.565148 g42, quadgu 2nd d2625 diminished comma, major diesis, [8, 4, -4
28/27 62.960904 z2, zo 2nd m27 septimal chroma, small septimal chromatic semitone, subminor second, septimal minor second
27/26 65.337341 3u1, thu unison A113 small tridecimal third tone
26/25 67.900234 3ogg2, thogugu 2nd d21325 large tridecimal third tone
25/24 70.672427 yy1, yoyo unison A125 chroma, chromatic semitone, Zarlinian semitone
68/65 78.114034 17o3ug2, sothugu 2nd m21765 valentine semitone
22/21 80.537035 1or1, loru unison P1117 undecimal minor semitone
64/61 83.115195 61u2, sixty-wu 2nd m261 harry minor semitone
21/20 84.467193 zg2, zogu 2nd m275 minor semitone, large septimal chromatic semitone
20/19 88.800698 19uy1, nuyo unison A1519 small undevicesimal limma, small undevicesimal semitone
256/243 90.224996 sw2, small wa 2nd m2 Pythagorean limma, Pythagorean minor second, [8, -5
135/128 92.178716 Ly1, layo unison A15 major limma, [-7, 3, 1
19/18 93.603014 19o2, ino 2nd m219 large undevicesimal limma, large undevicesimal semitone
18/17 98.954592 17u1, su unison A117 small septendecimal semitone, Arabic lute index finger
17/16 104.955410 17o2, iso 2nd m217 large septendecimal semitone, octave-reduced 17th harmonic
16/15 111.731285 g2, gu 2nd m25 diatonic semitone, classic minor second, octave-reduced 15th subharmonic
2187/2048 113.685006 Lw1, large wa unison A1 apotome, [-11, 7
77/72 116.233847 1oz2, lozo 2nd undecimal secor
15/14 119.442808 ry1, ruyo unison A157 septimal diatonic semitone
14/13 128.298245 3uz2, thuzo 2nd tridecimal 2/3-tone, trienthird, tridecimal supraminor second
27/25 133.237575 gg2, gugu 2nd m225 large limma
13/12 138.572661 3o2, tho 2nd tridecimal subtone, tridecimal 2/3-tone
243/224 140.949098 Lr1, large ru unison A17 septimal subtone, [-5, 5, 0, -1
88/81 143.497939 1o2, ilo 2nd undecimal subtone
49/45 147.428097 zzg3, zozogu 3rd swetismic neutral second
12/11 150.637059 1u2, lu 2nd M211 small undecimal neutral second, 3/4-tone
35/32 155.139620 zy2, zoyo 2nd M235 septimal neutral second
78/71 162.786119 71u3o2, seventy-wutho 2nd porcupine neutral second
11/10 165.004228 1og2, logu 2nd m2115 large undecimal neutral second, 4/5-tone, Ptolemy's second
54/49 168.213190 rr1, ruru unison Zalzal's mujannab
10/9 182.403712 y2, yo 2nd M25 minor whole tone
49/44 186.333871 1uzz3, luzozo 3rd werckismic minor second
6272/5625 188.486956 szzg44, small bizogugu 4th ddd449625 marvelous second, marvelous (whole) tone
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
64/57 200.531983 19u2, inu 2nd quasi-tempered whole tone, octave-reduced 57th subharmonic
9/8 203.910002 w2, wa 2nd M2 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 M27 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 A2513 semifourth, tridecimal ultramajor second, tridecimal inframinor third
97/84 249.114503 97or2, ninety-soru 2nd M2977 homothetic semifourth
22/19 253.804926 19u1o2, nulo 2nd M21119 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 m37 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 A225 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 m3 Pythagorean minor third, octave-reduced 27th subharmonic
19/16 297.513016 19o3, ino 3rd m319 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 m35 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 2nd large septimal minor third, marvelous minor third, [-4, 3, 1, -1
35/29 325.562426 29uzy3, twenty-nuzoyo 3rd doublewide minor third
23/19 330.761331 vicesimotertial supraminor 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 quadyo 2nd AA2625 5-limit neutral third, [-9, 0, 4
11/9 347.407941 1o3, ilo 3rd m311 undecimal neutral third
60/49 350.616902 rry2, ruruyo 2nd smaller septimal neutral third, (purple 3rd)
49/40 351.338099 zzg4, zozogu 4th larger septimal neutral third, (purple 3rd)
27/22 354.547060 1u3, lu 3rd rastmic neutral third
16/13 359.472338 3u3, thu 3rd M313 tridecimal neutral third
21/17 365.825498 17uz3, suzo 3rd septendecimal submajor third
51/41 377.848005 41u17o4, forty-wuso 4th maja third
56/45 378.602191 zg4, zogu 4th narrow perde segah, marvelous major 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 M35 major third, octave-reduced 5th harmonic, pental major third
161/128 397.100254 23oz4 M37,23 just/Pythagorean major third meantone, octave-reduced 161th harmonic
63/50 400.108480 zgg4, zogugu 4th quasi-tempered major third
81/64 407.820003 Lw3, large wa 3rd M3 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 P4711 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 M37 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 d4135 Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramaor third
64/49 462.348187 rr3, ruru 3rd M349 septatonic major third
17/13 464.427748 17o3u4, sothu 4th septendecimal sub-fourth
21/16 470.780907 z4, zo 4th P47 sub-fourth, narrow fourth, augmented third, 8ve-reduced 21st harmonic
33/25 480.645516 1ogg4, logugu 4th d41125 "5-EDO"-esque fourth
117/88 493.119721 3o1u4, tholu 4th tridecimal gentle fourth, [-3, 2, 0, 0, -1, 1
4/3 498.044999 w4, wa 4th P4 just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
75/56 505.756522 ryy3, ruyoyo 3rd marvelous fourth
27/20 519.551289 g4, gu 4th P45 acute fourth
19/14 528.687110 19or4, noru 4th undevicesimal wide fourth
49/36 533.741811 zz5, zozo 5th d549 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, ilo 4th P411 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 A425 classic augmented fourth, pental augmented fourth, [-1 -2 2
88/63 578.582034 1or4, loru 4th werckismic augmented fourth
7/5 582.512193 zg5, zogu 5th d575 augmented fourth, septimal tritone, Huygen's tritone
45/32 590.223716 y4, yo 4th A45 smaller pental tritone, diatonic tritone, [-5 2 1
108/77 585.721154 1ur4, luru 4th swetismic augmented fourth, [2, 3, 0, -1, -1
24/17 596.999591 17u4, su 4th A417 smaller septendecimal tritone
99/70 600.088324 1org4, lorugu 4th P41135 homothetic quasi-tempered tritone
17/12 603.000409 17o5, iso 5th d517 larger septendecimal tritone
64/45 609.776284 g5, gu 5th d55 larger pental tritone, diatonic tritone, [6 -2 -1
10/7 617.487807 ry4, ruyo 4th A457 diminished fifth, Euler's tritone, superaugmented fourth
23/16 628.274347 23o5, twenty-tho 5th A423 23-limit superaugmented fourth, octave-reduced 23rd harmonic
36/25 631.282574 gg5, gugu 5th d525 pental diminished fifth, classic diminshed fifth, [2 2 -2
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 undevicesimal narrow fifth
40/27 680.448711 y5, yo 5th P55 grave fifth
112/75 694.243478 zgg6, zogugu 6th marvelous fifth
16384/10935 700.001280 sg6, sagu 6th d65 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 tridecimal gentle fifth, [1, 0, 0, 1, -2, 1
176/117 706.880279 3u1o5, thulo 5th tridecimal gentle fifth, [4, -2, 0, 0, 1, -1
50/33 719.354484 1uyy5, luyoyo 5th "5-EDO"-esque fifth
32/21 729.219093 r5, ru 5th P57 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 m649 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 m67 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 m675
128/81 792.179997 sw6, small wa 6th m6
8/5 813.686286 g6, gu 6th m65 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 m613 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
38/23 869.238669 vicesimotertial submajor sixth
5/3 884.358713 y6, yo 6th M65 major sixth
42/25 898.153480 zgg7, zogugu 7th
32/19 902.486984 utonal major sixth?
27/16 905.865003 w6, wa 6th M6 Pythagorean major sixth, octave-reduced 27th harmonic
22/13 910.790821 3u1o6, thulo 6th tridecimal major sixth
17/10 918.641696 17og7, sogu 7th d7175 septendecimal diminished seventh, septendecimal major sixth
12/7 933.129094 r6, ru 6th M67 supermajor sixth, septimal major sixth, diminished seventh
19/11 946.195074 19o1u7, nolu 7th m71911 maximal major sixth, undevicesimal major sixth
97/56 951.069504 97or6, ninety-soru 6th M6977 homothetic semitwelve
26/15 952.258947 3og7, thogu 7th d7135 semitwelfth, tridecimal inframinor seventh, tridecimal ultramajor sixth
7/4 968.825906 z7, zo 7th m77 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
127/72 982.511622 127o7 m7127 harmonic/Pythagorean minor seventh meantone
30/17 983.313305 17uy6, suyo 6th septendecimal minor seventh
71/40 993.382830 71oy7 m7715 harmonic/just minor seventh meantone
959/540 994.285690 137ozy8 dd87,1375 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 Middle minor seventh
34/19 1007.442393 19u17o7, nuso 7th Quasi-meantone minor seventh
9/5 1017.596288 g5, gu 7th m75 classic 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 M7511 undecimal minor seventh, small undecimal neutral seventh
64/35 1044.860380 rg7, rugu 7th
11/6 1049.362941 1o7, ilo 7th m711 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 M75 major seventh, just major seventh, octave-reduced 15th harmonic
32/17 1095.044590 17u7, su 7th M717 small septendecimal major seventh, octave-reduced 17th subharmonic
17/9 1101.045408 17o8, iso octave d817 large septendecimal major seventh
36/19 1106.396986 19u7, nu 7th M719 small undevicesimal major seventh
243/128 1109.775004 Lw7, large wa 7th M7 Pythagorean major seventh, octave-reduced 243rd harmonic
19/10 1111.199302 19og8, nogu 8ve d8195 large undevicesimal major seventh
40/21 1115.532907 ry7, ruyo 7th M757 acute major seventh
61/32 1116.884905 61o7, sixty-wo 7th M761 octave-reduced 61st harmonic
48/25 1129.327573 gg8, gugu octave d825 octave minus a yoyo augmented unison
27/14 1137.039096 r7, ru 7th M77 supermajor seventh, septimal major seventh
31/16 1145.035572 31o7, thirty-wo 7th M731 31-limit ultramajor seventh, octave-reduced 31st harmonic
64/33 1146.727057 1u8, lu octave P811 octave-reduced 33rd subharmonic
35/18 1151.239619 zy8, zoyo octave P835 octave minus a rugu comma
96/49 1164.303188 rr7, ruru 7th M749
49/25 1165.024385 zzgg9, bizogu 9th d94925
160/81 1178.493814 y8, yo octave P85 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
13/6 1338.573 3o9 tho 9th m913
11/5 1365.004 1o9 ilo 9th m9115
16/7 1431.174 r9 ru 9th m97
7/3 1466.871 z10 zo 10th m107 septimal minor tenth
5/2 1586.314 y10 yo 10th M105 just major tenth
8/3 1698.045 w11, cw4 wa 11th, co wa 4th P11
11/4 1751.318 1o11, c1o4 ilo 11th, co lo 4th P1111
3/1 1901.955 w12, cw5 wa 12th, co wa 5th P12 tritave
16/5 2013.686 g13, cg6 gu 13th, co gu 6th m135
13/4 2040.528 3o13, c3o6 tho 13th, co tho 6th
10/3 2084.359 y13, cy6 yo 13th, co yo 6th
7/2 2168.826 cz7 co zo 7th
11/3 2249.363 c1o7 co ilo 7th
15/4 2288.269 cy7 co yo 7th
4/1 2400.000 cw8 wa double 8ve P15 4th harmonic, two octaves
13/3 2538.573 c3o9, cc3o2 co tho 9th, coco tho 2nd
9/2 2603.910 cw9, ccw2 co wa 9th, coco yo 2nd
14/3 2666.871 cz10, ccz3 co zo 10th, coco zo 3rd
5/1 2786.314 cy10, ccy3 co yo 10th, coco yo 3rd M175 5th harmonic
16/3 2898.045 ccw4 coco wa 4th
11/2 2951.318 cc1o4 coco ilo 4th
6/1 3101.955 ccw5 coco wa 5th
13/2 3240.528 cc3o6 coco tho 6th
7/1 3368.826 ccz7 coco zo 7th
15/2 3488.269 ccy7 coco yo 7th
8/1 3600.000 c3w1 wa triple 8ve
9/1 3803.910 c3w2 trico wa 2nd
10/1 3986.314 c3y3 trico yo 3rd
11/1 4151.318 c31o4 trico ilo 4th
12/1 4301.955 c3w5 trico wa 5th
13/1 4440.528 c33o6 trico tho 6th
14/1 4568.826 c3z7 trico zo 7th
15/1 4688.269 c3y7 trico yo 7th
16/1 4800.000 c4w1 wa quadruple 8ve

See also

Links