Xenharmonic Wiki

Gallery of just intervals

Revision as of 07:11, 21 September 2018 by Keenan Pepper (talk | contribs) (→Introduction: rm obsolete remarks)

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)

frequency ratio cents value

(six decimal places)

color notation some common names
1/1 0 w1 = white unison unity, perfect prime, Tonic
32805/32768 1.953721 Ly-2 = yellow subcomma schisma, |-15, 8, 1>
225/224 7.711523 ryy-2 = reddish-yellow subcomma septimal subcomma, |-5, 2, 2, -1>
100/99 17.399484 ayy1 = amber deep yellow comma Ptolemy's comma
99/98 17.576131 jrr-2 = jade deep red comma Mothwellsma
2048/2025 19.552569 sgg2 = small deep green comma |11, -4, -2>
81/80 21.506286 g1 = green comma Syntonic comma, Didymus comma
531441/524288 23.460010 LLw-2 = white comma Pythagorean comma, Ditonic comma, |-19, 12>
66/65 26.431568 ojg1 = oche-jadish comma Winmeanma
65/64 26.841376 ey1 = emerald-yellow comma Wilsorma, 13th-partial chroma
64/63 27.264092 r1 = red comma Septimal comma, Archytas' comma
3125/3072 29.613568 Ly5-2 = quintuple yellow comma Magic comma, small diesis, |-10, -1, 5>
50/49 34.975615 rryy-2 = deep reddish comma septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis
49/48 35.696812 bb2 = deep blue comma large septimal diesis, slendro diesis
45/44 38.905773 ay1 = amber-yellow comma undecimal 1/5th tone
128/125 41.058858 g32 = triple green comma Diesis, minor diesis, augmented comma, enharmonic comma, |7, 0, -3>
525/512 43.408335 Lyyb1 = large yellowish-yellow comma Avicenna's enharmonic diesis, |-9, 1, 2, 1>
36/35 48.770381 gr1 = greenish comma double comma, septimal quarter tone
250/243 49.166137 y31 = triple yellow comma Porcupine comma, |1, -5, 3>
59049/57344 50.724102 Lr-2 = large red comma Harrison's comma, |-13, 10, 0, -1>
100/97 52.732017 97qyy1 = 97esque deep yellow quarter-tone shrutar quarter tone
33/32 53.272943 j1 = jade quarter-tone undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
648/625 62.565148 g42 = quadruple green 2nd diminished comma, major diesis, |8, 4, -4>
28/27 62.960904 b2 = blue 2nd septimal chroma, small septimal chromatic semitone, septimal subminor second
25/24 70.672427 yy1 = deep yellow semitone chroma, chromatic semitone, Zarlinian semitone
68/65 78.114034 17iog2 = 17ish ochre green 2nd valentine semitone
22/21 80.537035 jr1 = jade-red semitone undecimal minor semitone
64/61 83.115195 61q2 = 61esque 2nd harry minor semitone
21/20 84.467193 bg2 = bluish 2nd minor semitone, large septimal chromatic semitone
256/243 90.224996 sw2 = small white 2nd Pythagorean limma, Pythagorean minor second, |8, -5>
135/128 92.178716 Ly1 = large yellow semitone major limma, |-7, 3, 1>
18/17 98.954592 17q1 = 17esque semitone small septendecimal semitone, Arabic lute index finger
17/16 104.955410 17i2 = 17ish 2nd large septendecimal semitone, octave-reduced 17th harmonic
16/15 111.731285 g2 = green 2nd diatonic semitone, classic minor second, octave-reduced 15th subharmonic
2187/2048 113.685006 Lw1 = large white semitone apotome, |-11, 7>
77/72 116.233847 jb2 = jade-blue 2nd undecimal secor
15/14 119.442808 ry1 = reddish semitone septimal diatonic semitone
14/13 128.298245 ob2 = ochre-blue 2nd 2/3-tone, trienthird, tridecimal supraminor second
27/25 133.237575 gg2 = deep green 2nd large limma
13/12 138.572661 e2 = emerald 2nd tridecimal subtone, tridecimal 2/3-tone
243/224 140.949098 Lr1 = large red semitone septimal subtone, |-5, 5, 0, -1>
88/81 143.497939 j2 = jade 2nd undecimal subtone
49/45 147.428097 bbg3 = bluish-blue 3rd swetismic neutral second
12/11 150.637059 a2 = amber 2nd small undecimal neutral second, 3/4-tone
35/32 155.139620 yb2 = yellowish 2nd septimal neutral second
78/71 162.786119 71qe2= 71esque emerald 2nd porcupine neutral second
11/10 165.004228 jg2 = jadish 2nd large undecimal neutral second, 4/5-tone, Ptolemy's second
54/49 168.213190 rr1 = deep red augmented unison Zalzal's mujannab
10/9 182.403712 y2 = yellow 2nd minor whole tone
49/44 186.333871 abb3 = amber deep blue 3rd werckismic minor second
19/17 192.557607 19i17q2 =19ish 17esque 2nd quasi-meantone
28/25 196.198479 bgg3 = bluish-green 3rd middle major second
55/49 199.979843 jrry1 = jade-red reddish unison werckismic tone
9/8 203.910002 w2 = white 2nd major whole tone, Pythagorean tone, octave-reduced 9th harmonic
17/15 216.686695 17ig3 = 17ish green 3rd septendecimal whole tone, septendecimal eventone
8/7 231.174094 r2 = red 2nd supermajor second, septimal whole tone, diminished third, octave-reduced 7th subharmonic
63/55 235.104252 abg3 = amber bluish 3rd werckismic supermajor second
55/48 235.676655 jy2 = jade-yellow 2nd keenanismic supermajor second
15/13 247.741053 oy2 = ochre-yellow 2nd semifourth, tridecimal ultramajor second, tridecimal inframinor third
22/19 253.804926 19qj2 = 19esque jade 2nd minimal minor third, godzilla third
64/55 262.368344 ag3 = amber-green 3rd keenanismic subminor third, octave-reduced 55th subharmonic
7/6 266.870906 b3 = blue 3rd subminor third, septimal minor third, augmented second
90/77 270.079867 ary2 = amber reddish 2nd swetismic subminor third
62/53 271.531027 53q31i2 = 53esque 31ish 2nd orwell subminor third
75/64 274.582429 yy2 = deep yellow 2nd classic augmented second
20/17 281.358304 17qy2 = 17esque yellow 2nd septendecimal augmented second, septendecimal minor third
13/11 289.209179 ea3 = emerald amber 3rd tridecimal minor third
32/27 294.134997 w3 = white 3rd Pythagorean minor third, octave-reduced 27th subharmonic
19/16 297.513016 19i3 = 19ish 3rd otonal minor third, octave-reduced 19th harmonic
25/21 301.846520 ryy2 = reddish-yellow 2nd quasi-tempered minor third
61/51 309.974395 61i17q2 = 61ish 17esque 2nd myna third
6/5 315.641287 g3 = green 3rd minor third, pental minor third
77/64 320.143849 jb3 = jade blue 3rd keenanismic minor third, octave-reduced 77th harmonic
135/112 323.352810 ry2 = reddish aug 2nd large septimal minor third, marvelous minor third, |-4, 3, 1, -1>
35/29 325.562426 29qyb3 = 29esque yellowish 3rd doublewide minor third
17/14 336.129503 17ir3 = 17ish red 3rd septendecimal supraminor third
73/60 339.520756 73ig3 = 73ish green 3rd amity supraminor third
625/512 345.254855 Ly42 = large quadruple yellow 2nd 5-limit neutral third, |-9, 0, 4>
11/9 347.407941 j3 = jade 3rd undecimal neutral third
60/49 350.616902 rry2 = reddish-red 2nd

(aka p3 = purple 3rd)

smaller septimal neutral third
49/40 351.338099 bbg4 = bluish blue 4th

(aka p3 = purple 3rd)

larger septimal neutral third
27/22 354.547060 a3 = amber 3rd rastmic neutral third
16/13 359.472338 o3 = ochre 3rd tridecimal neutral third
21/17 365.825498 17qb3 = 17esque blue 3rd septendecimal submajor third
56/45 378.602191 bg4 = bluish 4th narrow perde segah, marvelous major third
51/41 377.848005 41q17i4 = 41esque 17ish 4th maja third
71/57 380.228526 71i19q3 = 71ish 19esque 3rd witchcraft major third
76/61 380.628211 61q19i4 = 61esque 19ish 4th magic major third
96/77 381.811152 ar3 = amber-red 3rd undecimal perde segah, keenanismic major third
5/4 386.313714 y3 = yellow 3rd major third, octave-reduced 5th harmonic, pental major third
81/64 407.820003 Lw3 = large white 3rd Pythagorean major third, octave-reduced 81st harmonic
80/63 413.577806 ry3 = reddish 3rd werckismic sharp major third
14/11 417.507964 ab4 = amber-blue 4th undecimal major third, undecimal diminished fourth
32/25 427.372572 gg4 = deep green 4th classic diminished fourth
77/60 431.875134 jbg4 = jade-bluish 4th swetismic supermajor third
9/7 435.084095 r3 = red 3rd supermajor third, septimal major third, septimal diminished fourth
31/24 443.080572 31i3 = 31ish 3rd sensi supermajor third
22/17 446.362533 17qj3 = 17esque jade 3rd septendecimal supermajor third
35/27 449.274618 yb4 = yellowish 4th semi-diminished fourth
13/10 454.213948 eg4 = emerald-green 4th Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third
64/49 462.348187 rr3 = deep red 3rd septatonic major third
17/13 464.427748 17io4 = 17ish ochre 4th septendecimal sub-fourth
21/16 470.780907 b4 = blue 4th sub-fourth, narrow fourth, augmented third, 8ve-reduced 21st harmonic
33/25 480.645516 jgg4 = jadish green 4th "5-EDO"-esque fourth
117/88 493.119721 ea4 = emerald amber 4th tridecimal gentle fourth, |-3, 2, 0, 0, -1, 1>
4/3 498.044999 w4 = white 4th just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
75/56 505.756522 ryy3 = reddish-yellow 3rd marvelous fourth
27/20 519.551289 g4 = green 4th acute fourth
19/14 528.687110 19ir4 = 19ish red 4th 19-limit wide fourth
49/36 533.741811 bb5 = deep blue 5th Arabic lute acute fourth
15/11 536.950772 ay4 = amberish 4th undecimal augmented fourth, subaugmented fourth
48/35 546.815381 gr4 = greenish 4th septimal super-fourth
11/8 551.317942 j4 = jade 4th super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa
18/13 563.382340 o4 = ochre 4th tridecimal augmented fourth
25/18 568.717426 yy4 = deep yellow 4th classic augmented fourth, pental augmented fourth
88/63 578.582034 jr4 = jade-red 4th werckismic augmented fourth
7/5 582.512193 bg5 = bluish 5th augmented fourth, septimal tritone, Huygen's tritone
45/32 590.223716 y4 = yellow 4th
108/77 585.721154 ar4 = amber-red 4th swetismic augmented fourth, |2, 3, 0, -1, -1>
24/17 596.999591 17q4 = 17esque 4th smaller septendecimal tritone
17/12 603.000409 17i5 = 17ish 5th larger septendecimal tritone
64/45 609.776284 g5 = green 5th
10/7 617.487807 ry4 = reddish 4th diminished fifth, Euler's tritone, superaugmented fourth
23/16 628.274347 23i5 = 23ish 5th 23-limit superaugmented fourth, octave-reduced 23rd harmonic
36/25 631.282574 gg5 = deep green 5th pental diminished fifth, classic diminshed fifth
13/9 636.617660 e5 = emerald 5th tridecimal diminished fifth
16/11 648.682058 a5 = amber 5th sub-fifth, octave-reduced 11th subharmonic
35/24 653.184619 yb5 = yellowish 5th septimal sub-fifth
22/15 663.049228 jg5 = jadish 5th undecimal diminished fifth, semidiminished fifth
72/49 666.258889 rr4 = deep red 4th septimal catafifth
81/55 670.188347 ag5 = amber green 5th undecimal catafifth
28/19 671.312890 19qb5 = 19esque blue 5th 19-limit narrow fifth
40/27 680.448711 y5 = yellow 5th grave fifth
112/75 694.243478 bgg6 = bluish-green 6th marvelous fifth
3/2 701.955001 w5 = white 5th just perfect fifth, octave-reduced 3rd harmonic, diapente
182/121 706.717684 eaab6 = emerald blue deep amber 6th tridecimal gentle fifth, |1, 0, 0, 1, -2, 1 >
176/117 706.880279 oj5 = ochre-jade 5th tridecimal gentle fifth, |4, -2, 0, 0, 1, -1>
50/33 719.354484 ayy5 = amber deep yellow 5th "5-EDO"-esque fifth
32/21 729.219093 r5 = red 5th super-fifth, wide fifth, diminished sixth, octave-reduced 21st subharmonic
26/17 735.572252 17qe5 = 17esque emerald 5th septendecimal super-fifth
49/32 737.651813 bb6 = deep blue 6th superduper fifth, octave-reduced 49th harmonic
20/13 745.786052 oy5 = ochreish 5th Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth
17/11 753.637467 17ia6 = 17ish amber 6th septendecimal subminor sixth
14/9 764.915905 b6 = blue 6th subminor sixth, septimal minor sixth, augmented fifth
25/16 772.627428 yy5 = deep yellow 5th pental augmented fifth, classic augmented fifth, otonal minor sixth, octave-reduced 25th harmonic
11/7 782.492036 jr5 = jade-red 5th undecimal subminor sixth, undecimal augmented fifth
63/40 786.422194 bg6 = bluish 6th
128/81 792.179997 sw6 = small white 6th
8/5 813.686286 g6 = green 6th minor sixth, octave-reduced 5th subharmonic
413/256 827.997565 59ib6 = 59ish blue 6th octave-reduced 413th harmonic, homestuck sixth (2-8 * 7 * 59)
13/8 840.527662 e6 = emerald 6th tridecimal neutral sixth, octave-reduced 13th harmonic
80/49 848.661901 rryA5 = reddish-red 5th

(aka p6 = purple 6th)

49/30 849.383198 bbg7 = bluish-blue 7th

(aka p6 = purple 6th)

18/11 852.592059 a6 = amber 6th undecimal neutral sixth
28/17 863.870497 17qb6 = 17esque blue 6th septendecimal submajor sixth
5/3 884.358713 y6 = yellow 6th major sixth
42/25 898.153480 bgg7 = bluish-green 7th
27/16 905.865003 w6 = white 6th Pythagorean major sixth, octave-reduced 27th harmonic
22/13 910.790821 oj6 = ochre-jade 6th tridecimal major sixth
17/10 918.641696 17ig7 = 17ish green 7th septendecimal diminished seventh, septendecimal major sixth
12/7 933.129094 r6 = red 6th supermajor sixth, septimal major sixth, diminished seventh
26/15 952.258947 eg7 = emeraldish 7th semitwelfth, tridecimal inframinor seventh, tridecimal ultramajor sixth
7/4 968.825906 b7 = blue 7th subminor seventh, harmonic seventh, augmented sixth, octave-reduced 7th harmonic
225/128 976.537429 Lyy6 = large deep yellow 6th marvel five-limit harmonic seventh, octave-reduced 225th harmonic, |-7, 2, 2>
30/17 983.313305 17iy6 = 17ish yellow 6th septendecimal minor seventh
16/9 996.089998 w7 = white 7th Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic
25/14 1003.801521 ryy6 = reddish-yellow 6th Middle minor seventh
34/19 1007.442393 19q17i7 = 19esque 17ish 7th Quasi-meantone minor seventh
9/5 1017.596288 g5 = green 7th minor seventh, large minor seventh
29/16 1029.577194 29i7 = 29ish 7th 29-limit large minor seventh, octave-reduced 29th harmonic
20/11 1034.995772 ay7 = amberish 7th undecimal minor seventh, small undecimal neutral seventh
64/35 1044.860380 gr7 = greenish 7th
11/6 1049.362941 j7 = jade 7th undecimal neutral seventh, 21/4-tone
24/13 1061.427339 o7 = ochre 7th tridecimal neutral seventh
13/7 1071.701755 er7 = emerald-red 7th 16/3-tone, tridecimal submajor seventh
28/15 1080.557192 bg8 = bluish octave grave major seventh, octave minus a reddish aug unison
15/8 1088.268715 y7 = yellow 7th major seventh, just major seventh, octave-reduced 15th harmonic
32/17 1095.044590 17q7 = 17esque 7th small septendecimal major seventh, 8ve-reduced 17th subharmonic
17/9 1101.045408 17i8 = 17ish octave large septendecimal major seventh
243/128 1109.775004 Lw7 = large white 7th Pythagorean major seventh, octave-reduced 243rd harmonic
40/21 1115.532907 ry7 = reddish 7th acute major seventh
61/32 1116.884905 61i7 = 61ish 7th octave-reduced 61st harmonic
48/25 1129.327573 gg8 = deep green octave octave minus a deep yellow augmented unison
27/14 1137.039096 r7 = red 7th
31/16 1145.035572 31i7 = 31ish 7th 31-limit ultramajor seventh, octave-reduced 31st harmonic
64/33 1146.727057 a8 = amber octave octave-reduced 33rd subharmonic
35/18 1151.239619 yb8 = yellowish octave octave minus a greenish comma
96/49 1164.303188 rr7 = deep red 7th
49/25 1165.024385 bbgg9 = deep bluish 9th
160/81 1178.493814 y8 = yellow octave octave minus syntonic comma
2/1 1200 w8 = white octave octave, diapason

Intervals larger than 2/1

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
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

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