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-25	schisma ([-15, 8, 1⟩)
225/224	7.711523	ryy-2, Ruyoyo comma	d-2257	septimal kleisma, 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, ptolemisma
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, Lalawa 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	A1175	Avicenna's enharmonic diesis, avicennma ([-9, 1, 2, 1⟩)
1053/1024	48.347665	L3o1, Latho comma	P113	tridecimal quartertone, tridecimal flattone comma
36/35	48.770381	rg1, Rugu comma	P135	septimal quarter tone, double comma
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	small septimal chroma, septimal third-tone, 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, classic chromatic semitone, Zarlinian semitone
24/23	73.680654	23u1, twethu unison	m223	lesser vicesimotertial semitone
23/22	76.956405	23o1u2, twetholu 2nd	A12311	greater vicesimotertial 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, siwu 2nd	m261	harry minor semitone
21/20	84.467193	zg2, zogu 2nd	m275	minor semitone, large septimal chroma
20/19	88.800698	19uy1, nuyo unison	A1519	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	A15	major limma ([-7, 3, 1⟩)
19/18	93.603014	19o2, ino 2nd	m219	large undevicesimal semitone, undevicesimal limma, Boethius' 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	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	m277	undecimal secor
15/14	119.442808	ry1, ruyo unison	A157	septimal diatonic semitone
14/13	128.298245	3uz2, thuzo 2nd	M2713	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	m213	tridecimal neutral second, tridecimal 2/3-tone
243/224	140.949098	Lr1, laru unison	A17	septimal subtone ([-5, 5, 0, -1⟩)
88/81	143.497939	1o2, ilo 2nd	m211	undecimal subtone
25/23	144.353081	23uyy1, twethuyoyo unison	M25,523	small vicesimotertial neutral second
49/45	147.428097	zzg3, zozogu 3rd	d3495	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
23/21	157.493440	23or2, twethoru 2nd	A1237	large vicesimotertial neutral second
78/71	162.786119	71u3o2, seventy-wutho 2nd	m21371	porcupine neutral second
11/10	165.004228	1og2, logu 2nd	m2115	undecimal submajor second, large undecimal neutral second, 4/5-tone, Ptolemy's second
54/49	168.213190	rr1, ruru unison	A149	Zalzal's mujannab
21/19	173.267891	19uz2, nuzo 2nd	M2719	large neutral undevicesimal second
10/9	182.403712	y2, yo 2nd	M25	classic (whole) tone, minor (whole) tone
49/44	186.333871	1uzz3, luzozo 3rd	m34911	mothwellsmic major second
39/35	187.343042	3org2, thorugu 2nd	m21335	animist major second
6272/5625	188.486956	szzg44, sabizogugu 4th	ddd449625	double marvelous second, double marvelous (whole) tone
19/17	192.557607	19o17u2, nosu 2nd	M21917	quasi-meantone
28/25	196.198479	zgg3, zogugu 3rd	d3725	middle major second
55/49	199.979843	1orry1, loruruyo unison	A15549	werckismic tone
64/57	200.531983	19u2, inu 2nd	M219	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	d31323	vicesimotertial whole tone
17/15	216.686695	17og3, sogu 3rd	d3175	septendecimal whole tone, septendecimal eventone
25/22	221.309485	1uyy2, luyoyo 2nd	A22511	ptolemismic whole tone, undecimal acute whole tone
57/50	226.840589	19ogg3, nogugu 3rd	d31925	devichromic supermajor second
8/7	231.174094	r2, ru 2nd	M27	supermajor second, septimal whole tone, octave-reduced 7th subharmonic
63/55	235.104252	1uzg3, luzogu 3rd	m3755	werckismic supermajor second
55/48	235.676655	1oy2, loyo 2nd	M255	keenanismic supermajor second
224/195	240.029530	3uzg3, thuzogu 3rd	m3765	quasi-tempered 1/5-octave, "5EDO"-esque tone
23/20	241.960633	23og3, twethogu 3rd	M2235	vicesimotertial inframinor third, vicesimotertial ultramajor second, vicesimotertial semifourth
15/13	247.741053	3uy2, thuyo 2nd	A2513	tridecimal semifourth, tridecimal ultramajor second, tridecimal inframinor third
97/84	249.114503	97or2, ninety-soru 2nd	M2977	homothetic semifourth
81/70	252.268038	rg2, rugu 2nd	M235	septimal semi-augmented second, septimal ultramajor second
22/19	253.804926	19u1o2, nulo 2nd	M21119	undevicesimal semifourth, minimal minor third, godzilla semifourth
64/55	262.368344	1ug3, lugu 3rd	m355	keenanismic subminor third, octave-reduced 55th subharmonic
7/6	266.870906	z3, zo 3rd	m37	subminor third, septimal minor third
90/77	270.079867	1ury2, luruyo 2nd	A2577	swetismic subminor third
62/53	271.531027	53u31o2, fithu-thiwo 2nd	M23153	orwell subminor third
75/64	274.582429	yy2, yoyo 2nd	A225	classic augmented second
27/23	277.590655	twethu 2nd, 23u2	m323	vicesimotertial augmented second
20/17	281.358304	17uy2, suyo 2nd	A2517	septendecimal augmented second, septendecimal minor third
13/11	289.209719	3o1u3, tholu 3rd	m31311	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	A2257	quasi-tempered minor third
61/51	309.974395	61o17u2, siwosu 2nd	A26117	myna third
6/5	315.641287	g3, gu 3rd	m35	classic minor third, just minor third
77/64	320.143849	1oz3, lozo 3rd	m377	keenanismic minor third, octave-reduced 77th harmonic
135/112	323.352810	ry2, ruyo 2nd	A257	large septimal minor third, marvelous minor third ([-4, 3, 1, -1⟩)
35/29	325.562426	29uzy3, twenuzoyo 3rd	M33529	doublewide minor third
23/19	330.761331	23o19u3, twethonu 3rd	A22319	vicesimotertial supraminor third
17/14	336.129503	17or3, soru 3rd	m3175	septendecimal supraminor third
73/60	339.520756	73og3, seventy-thogu 3rd	m3735	amity supraminor third
28/23	340.551559	23uz3, twethuzo 3rd	d4723	vicesimotertial neutral third
39/32	342.482663	3o3, tho 3rd	m313	lesser tridecimal neutral third, octave-reduced 39th harmonic
128/105	342.905379	rg3, rugu 3rd	m335	quasi-tempered 2/7-octave, 105th subharmonic
625/512	345.254855	Ly42, laquadyo 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	A2549	smaller septimal neutral third, (purple 3rd)
49/40	351.338099	zzg4, zozogu 4th	d4495	larger septimal neutral third, (purple 3rd)
27/22	354.547060	1u3, lu 3rd	M311	rastmic neutral third
16/13	359.472338	3u3, thu 3rd	M313	greater tridecimal neutral third, octave reduced 13subharmonic
21/17	365.825498	17uz3, suzo 3rd	M3717	septendecimal submajor third
26/21	369.746754	thoru 3rd, 3or3	m3137	tridecimal submajor third
51/41	377.848005	41u17o4, fowuso 4th	d41741	maja third
56/45	378.602191	zg4, zogu 4th	d475	narrow perde segah, marvelous major third
71/57	380.228526	71o19u3, seventy-wonu 3rd	M37119	witchcraft major third
76/61	380.628211	61u19o4, siwuno 4th	d41961	magic major third
96/77	381.811152	1ur3, luru 3rd	M377	undecimal perde segah, keenanismic major third
5/4	386.313714	y3, yo 3rd	M35	classic major third, just major third, octave-reduced 5th harmonic
161/128	397.100254	23oz4, twethozo 4th	M3161	just/Pythagorean major third meantone, octave-reduced 161th harmonic
34/27	399.090407	17o4, iso 4th	d417	septendecimal quasi-tempered major third
63/50	400.108480	zgg4, zogugu 4th	d4725	quasi-tempered major third
24/19	404.441985	19u3, inu 3rd	M319	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	d4195	Eratosthenes' major third
33/26	412.745281	3u1o3, thulo 3rd	M31113	tridecimal major third
80/63	413.577806	ry3, ruyo 3rd	M357	5/7-kleismic major third
14/11	417.507964	1uz4, luzo 4th	P4711	undecimal major third, undecimal diminished fourth
23/18	424.364346	23o4, twetho 4th	M323	vicesimotertial diminished fourth
32/25	427.372572	gg4, gugu 4th	d425	classic diminished fourth
77/60	431.875134	1ozg4, lozogu 4th	d4775	swetismic supermajor third
9/7	435.084095	r3, ru 3rd	M37	supermajor third, septimal major third
31/24	443.080572	31o3, thiwo 3rd	M331	sensi supermajor third
22/17	446.362533	17u1o3, sulo 3rd	M31117	septendecimal supermajor third
35/27	449.274618	zy4, zoyo 4th	P435	septimal semidiminished fourth
83/64	450.047318	83o4	P483	octave-reduced 83rd harmonic, octacesimotertial harmonic semisixth
13/10	454.213948	3og4, thogu 4th	d4135	tridecimal semisixth, Barbados third, tridecimal 9/4 tone
30/23	459.994368	23uy3, twethuyo 3rd	P4523	vicesimotertial ultramajor third
64/49	462.348187	rr3, ruru 3rd	M349	septatonic major third
17/13	464.427748	17o3u4, sothu 4th	P41713	septendecimal sub-fourth
21/16	470.780907	z4, zo 4th	P47	sub-fourth, narrow fourth, 8ve-reduced 21st harmonic
25/19	475.114412	19uyy3, nuyoyo 3rd	A35,519	undevicesimal augmented third, undevicesimal grave fourth
128/97	480.104589	97u4	P497	nonacesimoseptimal subharmonic fourth
33/25	480.645516	1ogg4, logugu 4th	d41125	ptolemismic fourth, "5EDO"-esque fourth
160/121	483.677829	1uuy4, luluyo 4th	A4511,11	narrow biyatismic fourth
117/88	493.119721	3o1u4, tholu 4th	P41311	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		P419	octave-reduced 171st harmonic
75/56	505.756522	ryy3, ruyoyo 3rd	A3257	marvelous fourth
216/161	508.764749	23ur3, twethuru 3th	P47,23	wide minor-kirnbergerismic fourth
161/120	508.831539	23ozg5, twethozogu 5th	P47,235	wide major-kirnbergerismic fourth
980/729	512.235522	zzy5, zozoyo 5th	d55,7,7	sensamagic fourth, septimal sesquidiminished grave fifth
121/90	512.412169	1oog4, lologu 4th	d411,115	wide biyatismic fourth
35/26	514.611959	3uzy4, thuzoyo 4th	A45,713	animist fourth
27/20	519.551289	g4, gu 4th	P45	acute fourth, wolf fourth
23/17	523.318938	23o17u4, twethosu 4th	A32317	vicesimotertial acute fourth
19/14	528.687110	19or4, noru 4th	P4197	hendrix fourth
34/25	532.327982	17ogg5, sogugu 5th	dd5175,5	vengeance superfourth
49/36	533.741811	zz5, zozo 5th	d549	Arabic lute acute fourth
15/11	536.950772	1uy4, luyo 4th	A4511	undecimal augmented fourth, subaugmented fourth
26/19	543.014646	19u3o4, nutho 4th	P41319	undevicesimal superfourth
48/35	546.815381	rg4, rugu 4th	P435	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	A413	tridecimal augmented fourth
25/18	568.717426	yy4, yoyo 4th	A425	classic augmented fourth, pental augmented fourth ([-1 -2 2⟩)
32/23	571.725653	23u4, twethu 4th	d523	vicesimotertial narrow tritone, octave-reduced 23rd subharmonic
88/63	578.582034	1or4, loru 4th	P4117	pentacircle diminished fifth
7/5	582.512193	zg5, zogu 5th	d575	augmented fourth, septimal tritone, Huygen's tritone
108/77	585.721154	1ur4, luru 4th	A477	swetismic augmented fourth ([2, 3, 0, -1, -1⟩)
45/32	590.223716	y4, yo 4th	A45	smaller pental tritone, diatonic tritone ([-5 2 1⟩)
128/91	590.646432	3ur4, thuru 4th	A491	smaller huntmic tritone, 91st subharmonic
38/27	591.648014	ino 5th, 19o5	d519	smaller undevicesimal tritone
55/39	595.148994	3u1oy4, thuloyo 4th	A45513	smaller gassormic tritone
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
78/55	604.851006	3o1ug5, tholugu 5th	d51355	larger gassormic tritone
27/19	608.351987	inu 4th, 19u4	A419	larger undevicesimal tritone
91/64	609.353568	3oz5, thozo 5th	d591	larger huntmic tritone, octave-reduced 91st harmonic
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, twetho 5th	A423	vicesimotertial 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	d513	tridecimal diminished fifth
16/11	648.682058	1u5, lu 5th	P511	sub-fifth, octave-reduced 11th subharmonic
35/24	653.184619	zy5, zoyo 5th	P535	septimal sub-fifth
19/13	656.985354	19o3u5, nothu 5th	P51913	undevicesimal subfifth
22/15	663.049228	1og5, logu 5th	d5115	undecimal diminished fifth, semidiminished fifth
72/49	666.258889	rr4, ruru 4th	A449	septimal catafifth
25/17	667.672018	17uyy4, suyoyo 4th	AA45,517	vengeance subfifth
81/55	670.188347	1ug5, lugu 5th	P555	undecimal catafifth
28/19	671.312890	19uz5, nuzo 5th	P5719	hendrix fifth
34/23	676.681062	23u17o5, twethuso 5th	d61723	vicesimotertial grave fifth
262144/177147	678.494990	sasawa 6th, ssw6	d6	Pythagorean wolf fifth
40/27	680.448711	y5, yo 5th	P55	grave fifth
52/35	685.388041	3org5, thorugu 5th	d51335	animist fifth
180/121	687.587831	1uuy5, luluyo 5th	A5511,11	narrow biyatismic fifth
729/490	687.764478	rrg5, rurugu 4th	A45,7,7	sensamagic fifth, septimal sesquiaugmented acute fourth
240/161	691.168461	23ury4, twethuruyo 4th	P557,23	narrow major-kirnbergerismic fifth
161/108	691.235251	23oz6, twethozo 6th	P57,23	narrow minor-kirnbergerismic fifth
112/75	694.243478	zgg6, zogugu 6th	d6725	marvelous fifth
121/81	694.815881	1oo5, lolo 5th	d511,11	rastmic fifth, Alpharabian narrow fifth
323/216	696.603423	19o17o6, noso 6th	d617,19	undevicesimal meantone fifth
175/117	697.015671	3uzy5, thuzoyoyo 5th	A55,5,713	ratwolfsmic 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	m67,1311,11	tridecimal gentle fifth ([1, 0, 0, 1, -2, 1⟩)
176/117	706.880279	3u1o5, thulo 5th	P51113	minthmic fifth ([4, -2, 0, 0, 1, -1⟩)
243/161	712.674751	23ur4, twethuru 4th	P57,23	wide minor-kirnbergerismic fifth
121/80	716.322171	1oog5, lologu 5th	d51215	wide biyatismic fifth
50/33	719.354484	1uyy5, luyoyo 5th	A52511	ptolemismic fifth, "5EDO"-esque fifth
97/64	719.895411	97o5	P597	nonacesimoseptimal harmonic fifth
38/25	724.885588	19ogg6, nogugu 6th	d6195,5	undevicesimal diminished sixth, undevicesimal acute fifth
32/21	729.219093	r5, ru 5th	P57	super-fifth, wide fifth, octave-reduced 21st subharmonic
26/17	735.572252	17u3o5, sutho 5th	P51317	septendecimal super-fifth
49/32	737.651813	zz6, zozo 6th	m649	superduper fifth, octave-reduced 49th harmonic
23/15	740.005633	23og6, twethogu 6th	P5235	vicesimotertial ultraminor sixth
20/13	745.786052	3uy5, thuyo 5th	A5513	tridecimal semitenth, Barbados sixth, ratwolf wolf fifth
128/83	749.952682	83u5	P583	83rd subharmonic, octacesimotertial subharmonic semitenth
17/11	753.637467	17o1u6, solu 6th	m61711	septendecimal subminor sixth
14/9	764.915905	z6, zo 6th	m67	subminor sixth, septimal minor sixth
25/16	772.627428	yy5, yoyo 5th	A525	pental augmented fifth, classic augmented fifth, otonal minor sixth, octave-reduced 25th harmonic
36/23	775.635654	23u5, twethu 5th	m623	vicesimotertial augmented fifth
11/7	782.492036	1or5, loru 5th	P5117	undecimal subminor sixth, undecimal augmented fifth
63/40	786.422194	zg6, zogu 6th	m675	narrow minor sixth
52/33	787.254719	3o1u6, tholu 6th	m61311	tridecimal minor sixth
30/19	790.755699	19uy5, nuyo 5th	A5519	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	m619	large undevicesimal minor sixth, Boethius' minor sixth
27/17	800.909593	17u5, su 5th	A517	septendecimal quasi-tempered minor sixth
8/5	813.686286	g6, gu 6th	m65	classic minor sixth, just minor sixth, octave-reduced 5th subharmonic
21/13	830.253246	3uz6, thuzo 6th	M6713	tridecimal supraminor sixth
34/21	834.174502	17or6, soru 6th	m6177	septendecimal supraminor sixth
13/8	840.527662	3o6, tho 6th	m613	lesser tridecimal neutral sixth, octave-reduced 13th harmonic
80/49	848.661901	rry5, ruruyo aug 5th	A5549	(purple 6th)
49/30	849.383198	zzg7, zozogu 7th	d7495	(purple 6th)
18/11	852.592059	1u6, lu 6th	M611	undecimal neutral sixth
105/64	857.094621	zy6, zoyo 6th	M635	quasi-tempered 5/7-octave, octave-reduced 105th harmonic
23/14	859.448441	23or6, twethoru 6th	A5237	vicesimotertial neutral sixth
28/17	863.870497	17uz6, suzo 6th	M6717	septendecimal submajor sixth
38/23	869.238669	23u19o6, twethuno 6th	d71923	vicesimotertial submajor sixth
5/3	884.358713	y6, yo 6th	M65	classic major sixth, just major sixth
42/25	898.153480	zgg7, zogugu 7th	d7725	quasi-tempered major sixth
32/19	902.486984	19u6, inu 6th	M619	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	M61113	tridecimal major sixth
17/10	918.641696	17og7, sogu 7th	d7175	septendecimal diminished seventh, septendecimal major sixth
46/27	922.409345	twetho 7th, 23o7	M623	vicesimotertial diminished seventh, vicesiomtertial supermajor sixth
12/7	933.129094	r6, ru 6th	M67	supermajor sixth, septimal major sixth
55/32	937.631656	1oy6, loyo 6th	M655	keenanismic supermajor sixth, octave-reduced 55th harmonic
19/11	946.195074	19o1u7, nolu 7th	m71911	undevicesimal semitwelfth, maximal major sixth
140/81	947.319617	zy7, zoyo 7th	m735	septimal semidiminished seventh, septimal inframinor seventh
97/56	951.069504	97or6, ninety-soru 6th	M6977	homothetic semitwelth
26/15	952.258947	3og7, thogu 7th	d7135	tridecimal semitwelfth
40/23	958.039367	23uy6, twethuyo 6th	m7523	vicesimotertial ultramajor sixth, vicesimotertial inframinor seventh, vicesimotertial semitwelfth
7/4	968.825906	z7, zo 7th	m77	subminor seventh, septimal minor seventh, harmonic seventh, natural seventh, octave-reduced 7th harmonic
225/128	976.537429	Lyy6, layoyo 6th	A625	marvel five-limit harmonic seventh, octave-reduced 225th harmonic ([-7, 2, 2⟩)
44/25	978.690515	1ogg7, logugu 7th	d7115,5	ptolemismic minor seventh, undecimal grave minor seventh
127/72	982.511622	127o7	m7127	harmonic/Pythagorean minor seventh meantone
30/17	983.313305	17uy6, suyo 6th	A6517	septendecimal minor seventh
23/13	987.746686	23o3u7, twethothu 7th	A62313	vicesimotertial minor seventh
71/40	993.382830	71oy7	m7715	harmonic/just minor seventh meantone
959/540	994.285690	137ozy8	dd89595	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	A6257	middle minor seventh
34/19	1007.442393	19u17o7, nuso 7th	m71719	quasi-meantone minor seventh
9/5	1017.596288	g5, gu 7th	m75	classic minor seventh, large minor seventh
38/21	1026.732109	19or7, noru 7th	m7197	minor neutral undevicesimal seventh
29/16	1029.577194	29o7, tweno 7th	m729	vicesimononal supraminor seventh, octave-reduced 29th harmonic
20/11	1034.995772	1uy7, luyo 7th	M7511	undecimal supraminor seventh, small undecimal neutral seventh
42/23	1042.506560	23uz7, twethuzo 7th	d8723	small vicesimotertial neutral seventh
64/35	1044.860380	rg7, rugu 7th	m735	septimal neutral seventh
11/6	1049.362941	1o7, ilo 7th	m711	undecimal neutral seventh, 21/4-tone
46/25	1055.646920	twethogugu octave, 23ogg8	m7235,5	large vicesimotertial neutral seventh
24/13	1061.427339	3u7, thu 7th	M713	tridecimal neutral seventh
50/27	1066.762425	yoyo 7th, yy7	M75,5	grave major seventh
13/7	1071.701755	3or7, thoru 7th	m7137	tridecimal submajor seventh, 16/3-tone
28/15	1080.557192	zg8, zogu octave	d875	grave major seventh, octave minus a ruyo aug unison
15/8	1088.268715	y7, yo 7th	M75	classic major seventh, just major seventh, octave-reduced 15th harmonic
32/17	1095.044590	17u7, su 7th	M717	septendecimal major seventh (FJS), septendecimal diminished octave (HEJI), octave-reduced 17th subharmonic
17/9	1101.045408	17o8, iso octave	d817	septendecimal major seventh (HEJI), septendecimal diminished octave (FJS)
36/19	1106.396986	19u7, inu 7th	M719	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	d8195	undevicesimal diminished octave, Eratosthenes' major seventh
40/21	1115.532907	ry7, ruyo 7th	M757	septimal acute major seventh
61/32	1116.884905	61o7, siwo 7th	M761	octave-reduced 61st harmonic
21/11	1119.462965	1uz8, luzo 8ve	P8711	large undecimal diminished octave, undecimal major seventh
44/23	1123.043595	23u1o7, twethulo 7th	d81123	vicesimotertial major seventh
23/12	1126.319346	23o8, twetho 8ve	M723	vicesimotertial major seventh
48/25	1129.327573	gg8, gugu octave	d825	classic diminished octave
25/13	1132.099766	3uyy7, thuyoyo 7th	A75,513	lesser tridecimal diminished octave
27/14	1137.039096	r7, ru 7th	M77	supermajor seventh, septimal major seventh
31/16	1145.035572	31o7, thiwo 7th	M731	tricesimoprimal ultramajor seventh (FJS), tricesimoprimal semidiminished octave (HEJI), octave-reduced 31st harmonic
64/33	1146.727057	1u8, lu octave	P811	undecimal semidiminished octave, octave-reduced 33rd subharmonic
35/18	1151.239619	zy8, zoyo octave	P835	septimal semidiminished octave
96/49	1164.303188	rr7, ruru 7th	M749	septimal ultramajor seventh
49/25	1165.024385	zzgg9, bizogu 9th	d94925	BP eighth
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
23/11	1276.956				vicesimotertial minor ninth
15/7	1319.443	ry8	ruyo 8ve	A857	septimal minor ninth
13/6	1338.573	3o9	tho 9th	m913	tridecimal minor ninth
11/5	1365.004	1o9	ilo 9th	m9115	neutral ninth
9/4	1403.910	w9	wa 9th	M9	major ninth
16/7	1431.174	r9	ru 9th	M97	septimal major ninth
7/3	1466.871	z10	zo 10th	m107	septimal minor tenth
12/5	1515.641	g10	gu 10th	m105	classic minor tenth
5/2	1586.314	y10	yo 10th	M105	classic major tenth
13/5	1654.214	3og11	thogu 11th	d11135	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	P1111	undecimal semi-augmented eleventh
14/5	1782.512	zg12, czg5	zogu 12th, cozogu 5th	d1275	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	m135	just minor thirteenth
13/4	2040.528	3o13, c3o6	tho 13th, cotho 6th	m1313	tridecimal neutral thirteenth
10/3	2084.359	y13, cy6	yo 13th, coyo 6th	M135	just/classic(al)/ptolemaic major thirteenth
7/2	2168.826	cz7	cozo 7th	m147	harmonic fourteenth
11/3	2249.363	c1o7	colo 7th	m1411	undecimal neutral fifteenth
15/4	2288.269	cy7	coyo 7th	M145	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	m1613	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	m177	two octaves and a subminor third
5/1	2786.314	cy10, ccy3	coyo 10th, cocoyo 3rd	M175	5th harmonic, pentave
16/3	2898.045	ccw4	cocowa 4th	P18	two octaves and a perfect fourth
11/2	2951.318	cc1o4	cocolo 4th	P1811	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	m2013	two octaves and a tridecimal neutral sixth
7/1	3368.826	ccz7	cocozo 7th	m217	7th harmonic
15/2	3488.269	ccy7	cocoyo 7th	M215	two octaves and a just/classic(al)/ptolemaic major seventh
8/1	3600.000	c3w1	wa triple 8ve	P22	8th harmonic, three octaves
9/1	3803.910	c3w2	tricowa 2nd	M23	9th harmonic
10/1	3986.314	c3y3	tricoyo 3rd	M245	10th harmonic, decade
11/1	4151.318	c31o4	tricolo 4th	P2511	11th harmonic
12/1	4301.955	c3w5	tricowa 5th	P26	12th harmonic
13/1	4440.528	c33o6	tricotho 6th	m2713	13th harmonic
14/1	4568.826	c3z7	tricozo 7th	m287	14th harmonic
15/1	4688.269	c3y7	tricoyo 7th	M285	15th harmonic
16/1	4800.000	c4w1	wa quadruple 8ve	P29	16th harmonic, four octaves
17/1	4904.955			m3017	17th harmonic
18/1	5004.910			M30	18th harmonic
19/1	5097.513			m3119	19th harmonic
20/1	5186.314			M315	20th harmonic
21/1	5270.781			P327	21st harmonic
22/1	5351.318			P3211	22nd harmonic
23/1	5428.274			A3223	23rd harmonic
24/1	5501.955			P33	24th harmonic
49/1	6737.652				49th harmonic

See also

• List of superparticular intervals

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
• FJS interval calculators
• Stichting Huygens-Fokker: List of intervals