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Introduction | Gallery of Just Intervals | Intervals larger than 2/1 | Links

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. Wiki page names are formatted "n_d" (where n is the numerator and d is the denominator of the interval) because both colons and slashes cannot be part of page names on wikispaces, but the links as they appear on the page are in the form n/d.

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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