Gallery of just intervals

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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.

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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 = 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	tridecimal gentle fourth, |-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	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	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

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

• Regions of the Interval Spectrum by Margo Schulter Permalink
• Manuel Op de Coul interval list*
• Anantomy of an Octave by Kyle Gann
• Alternative Tunings: Theory, Notation and Practice by Kite Giedraitis
• Stichting Huygens-Fokker: List of intervals