List of superparticular intervals

This is a list of superparticular intervals ordered by prime limit. It reaches to the 127-limit and is complete up to the 37-limit.

Størmer's theorem states that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. OEIS: A002071 gives the number of superparticular ratios in each prime limit, OEIS: A145604 shows the increment from limit to limit, and OEIS: A117581 gives the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit).

List of superparticular intervals

2-limit

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
2/1	1200.000	2/1	[1⟩	Octave, duple, 2nd harmonic, diapason

3-limit

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
3/2	701.955	3/2	[-1 1⟩	Perfect fifth, octave-reduced 3rd harmonic, diapente
4/3	498.045	22/3	[2 -1⟩	Perfect fourth, octave-reduced 3rd subharmonic, diatessaron	S2
9/8	203.910	32/23	[-3 2⟩	Pythagorean whole tone, Pythagorean major second, major whole tone, octave-reduced 9th harmonic, harmonic ninth	S3

5-limit

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
5/4	386.314	5/22	[-2 0 1⟩	Classic(al)/just major third, octave-reduced 5th harmonic
6/5	315.641	(2×3)/5	[1 1 -1⟩	Classic(al)/just minor third
10/9	182.404	(2×5)/32	[1 -2 1⟩	Classic(al) (whole) tone, classic major second, minor whole tone
16/15	111.731	24/(3×5)	[4 -1 -1⟩	Classic(al)/just diatonic semitone, 15th subharmonic	S4
25/24	70.672	52/(23×3)	[-3 -1 2⟩	Classic(al)/just chromatic semitone, chroma, Zarlinian semitone	S5
81/80	21.506	(3/2)4/5	[-4 4 -1⟩	Syntonic comma, Didymus comma	S9

7-limit

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
7/6	266.871	7/(2×3)	[-1 -1 0 1⟩	(Septimal) subminor third, septimal minor third
8/7	231.174	23/7	[3 0 0 -1⟩	(Septimal) supermajor second, septimal whole tone, octave-reduced 7th subharmonic
15/14	119.443	(3×5)/(2×7)	[-1 1 1 -1⟩	Septimal major semitone, septimal diatonic semitone
21/20	84.467	(3×7)/(22×5)	[-2 1 -1 1⟩	Septimal minor semitone, large septimal chroma
28/27	62.961	(22×7)/33	[2 -3 0 1⟩	Septimal 1/3-tone, small septimal chroma, (septimal) subminor second, septimal minor second, trienstonic comma
36/35	48.770	(2×3)2/(5×7)	[2 2 -1 -1⟩	Septimal 1/4-tone, mint comma	S6
49/48	35.697	72/(24×3)	[-4 -1 0 2⟩	Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma	S7
50/49	34.976	2×(5/7)2	[1 0 2 -2⟩	Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma
64/63	27.264	26/(32×7)	[6 -2 0 -1⟩	Septimal comma, Archytas' comma	S8
126/125	13.795	(2×32×7)/53	[1 2 -3 1⟩	Starling comma, septimal semicomma
225/224	7.7115	(3×5)2/(25×7)	[-5 2 2 -1⟩	Marvel comma, septimal kleisma	S15
2401/2400	0.72120	74/(25×3×52)	[-5 -1 -2 4⟩	Breedsma	S49
4375/4374	0.39576	(54×7)/(2×37)	[-1 -7 4 1⟩	Ragisma

11-limit

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
11/10	165.004	11/(2×5)	[-1 0 -1 0 1⟩	Large undecimal neutral second, undecimal submajor second, Ptolemy's second
12/11	150.637	(22×3)/11	[2 1 0 0 -1⟩	Small undecimal neutral second
22/21	80.537	(2×11)/(3×7)	[1 -1 0 -1 1⟩	Undecimal minor semitone
33/32	53.273	(3×11)/25	[-5 1 0 0 1⟩	Undecimal 1/4-tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
45/44	38.906	(3/2)2×(5/11)	[-2 2 1 0 -1⟩	Undecimal 1/5-tone, cake comma
55/54	31.767	(5×11)/(2×33)	[-1 -3 1 0 1⟩	Telepathma, eleventyfive comma, undecimal diasecundal comma
56/55	31.194	(23×7)/(5×11)	[3 0 -1 1 -1⟩	Undecimal tritonic comma, konbini comma
99/98	17.576	(3/7)2×(11/2)	[-1 2 0 -2 1⟩	Mothwellsma, small undecimal comma
100/99	17.399	((2×5)/3)2/11	[2 -2 2 0 -1⟩	Ptolemisma, Ptolemy's comma	S10
121/120	14.376	112/(23×3×5)	[-3 -1 -1 0 2⟩	Biyatisma, undecimal seconds comma	S11
176/175	9.8646	(24×11)/(52×7)	[4 0 -2 -1 1⟩	Valinorsma
243/242	7.1391	35/(2×112)	[-1 5 0 0 -2⟩	Rastma, neutral thirds comma
385/384	4.5026	(5×7×11)/(27×3)	[-7 -1 1 1 1⟩	Keenanisma
441/440	3.9302	(3×7)2/(23×5×11)	[-3 2 -1 2 -1⟩	Werckisma, Werckmeister's undecimal septenarian schisma	S21
540/539	3.2090	(2/7)2×((33×5)/11)	[2 3 1 -2 -1⟩	Swetisma, Swets' comma
3025/3024	0.57240	(5×11)2/(24×33×7)	[-4 -3 2 -1 2⟩	Lehmerisma	S55
9801/9800	0.17665	((32×11)/(5×7))2/23	[-3 4 -2 -2 2⟩	Kalisma, Gauss comma	S99

13-limit

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
13/12	138.573	13/(22×3)	[-2 -1 0 0 0 1⟩	Large tridecimal 2/3-tone, tridecimal neutral second
14/13	128.298	(2×7)/13	[1 0 0 1 0 -1⟩	Small tridecimal 2/3-tone, trienthird
26/25	67.900	(2×13)/52	[1 0 -2 0 0 1⟩	Large tridecimal 1/3-tone
27/26	65.337	33/(2×13)	[-1 3 0 0 0 -1⟩	Small tridecimal 1/3-tone
40/39	43.831	(23×5)/(3×13)	[3 -1 1 0 0 -1⟩	Tridecimal minor diesis
65/64	26.841	(5×13)/26	[-6 0 1 0 0 1⟩	Wilsorma, 13th-partial chroma
66/65	26.432	(2×3×11)/(5×13)	[1 1 -1 0 1 -1⟩	Winmeanma
78/77	22.339	(2×3×13)/(7×11)	[1 1 0 -1 -1 1⟩	Negustma
91/90	19.130	(7×13)/(2×32×5)	[-1 -2 -1 1 0 1⟩	Biome comma, superleap comma
105/104	16.567	(3×5×7)/(23×13)	[-3 1 1 1 0 -1⟩	Animist comma, small tridecimal comma
144/143	12.064	(22×3)2/(11×13)	[4 2 0 0 -1 -1⟩	Grossma	S12
169/168	10.274	132/(23×3×7)	[-3 -1 0 -1 0 2⟩	Buzurgisma, dhanvantarisma	S13
196/195	8.8554	(2×7)2/(3×5×13)	[2 -1 -1 2 0 -1⟩	Mynucuma	S14
325/324	5.3351	(5/(2×32))2×13	[-2 -4 2 0 0 1⟩	Marveltwin comma
351/350	4.9393	(33×13)/(2×52×7)	[-1 3 -2 -1 0 1⟩	Ratwolfsma
352/351	4.9253	(25×11)/(33×13)	[5 -3 0 0 1 -1⟩	Major minthma, major gentle comma
364/363	4.7627	(2/11)2×((7×13)/3)	[2 -1 0 1 -2 1⟩	Minor minthma, minor gentle comma
625/624	2.7722	(5/2)4/(3×13)	[-4 -1 4 0 0 -1⟩	Tunbarsma	S25
676/675	2.5629	((2×13)/5)2/33	[2 -3 -2 0 0 2⟩	Island comma	S26
729/728	2.3764	(32/2)3/(7×13)	[-3 6 0 -1 0 -1⟩	Squbema	S27
1001/1000	1.7304	(7×11×13)/(2×5)3	[-3 0 -3 1 1 1⟩	Sinbadma
1716/1715	1.0092	(22×3×11×13)/(5×73)	[2 1 -1 -3 1 1⟩	Lummic comma
2080/2079	0.83252	(25×5×13)/(33×7×11)	[5 -3 1 -1 -1 1⟩	Ibnsinma
4096/4095	0.42272	(26/3)2/(5×7×13)	[12 -2 -1 -1 0 -1⟩	Schismina, tridecimal schisma	S64
4225/4224	0.40981	(5×13)2/(27×3×11)	[-7 -1 2 0 -1 2⟩	Leprechaun comma	S65
6656/6655	0.26012	(23/11)3×(13/5)	[9 0 -1 0 -3 1⟩	Jacobin comma
10648/10647	0.16260	(2×11)3/((3×13)2×7)	[3 -2 0 -1 3 -2⟩	Harmonisma
123201/123200	0.014052	(3/2)6×(13/5)2/(7×11)	[-6 6 -2 -1 -1 2⟩	Chalmersia	S351

17-limit

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
17/16	104.955	17/24	[-4 0 0 0 0 0 1⟩	Large septendecimal semitone, octave-reduced 17th harmonic
18/17	98.955	(2×32)/17	[1 2 0 0 0 0 -1⟩	Small septendecimal semitone, Arabic lute index finger
34/33	51.682	(2×17)/(3×11)	[1 -1 0 0 -1 0 1⟩	Large septendecimal 1/4-tone
35/34	50.184	(5×7)/(2×17)	[-1 0 1 1 0 0 -1⟩	Small septendecimal 1/4-tone
51/50	34.283	(3×17)/(2×52)	[-1 1 -2 0 0 0 1⟩	Large septendecimal 1/6-tone
52/51	33.617	(22×13)/(3×17)	[2 -1 0 0 0 1 -1⟩	Small septendecimal 1/6-tone
85/84	20.488	(5×17)/(22×3×7)	[-2 -1 1 -1 0 0 1⟩	Monk comma
120/119	14.487	(23×3×5)/(7×17)	[3 1 1 -1 0 0 -1⟩	Lynchisma
136/135	12.777	(2/3)3×(17/5)	[3 -3 -1 0 0 0 1⟩	Diatisma, septendecimal major second comma
154/153	11.278	(2×7×11)/(32×17)	[1 -2 0 1 1 0 -1⟩	Augustma
170/169	10.214	(2×5×17)/132	[1 0 1 0 0 -2 1⟩	Major naiadma
221/220	7.8514	(13×17)/(22×5×11)	[-2 0 -1 0 -1 1 1⟩	Minor naiadma
256/255	6.7759	28/(3×5×17)	[8 -1 -1 0 0 0 -1⟩	Charisma, charic comma, septendecimal kleisma	S16
273/272	6.3532	(3×7×13)/(24×17)	[-4 1 0 1 0 1 -1⟩	Tannisma, prototannisma
289/288	6.0008	(17/3)2/25	[-5 -2 0 0 0 0 2⟩	Semitonisma	S17
375/374	4.6228	(3×53)/(2×11×17)	[-1 1 3 0 -1 0 -1⟩	Ursulisma
442/441	3.9213	(2×13×17)/(3×7)2	[1 -2 0 -2 0 1 1⟩	Seminaiadma
561/560	3.0887	(3×11×17)/(24×5×7)	[-4 1 -1 -1 1 0 1⟩	Monardisma, tsaharuk comma
595/594	2.9121	(5×7×17)/(2×33×11)	[-1 -3 1 1 -1 0 1⟩	Dakotisma
715/714	2.4230	(5×11×13)/(2×3×7×17)	[-1 -1 1 -1 1 1 -1⟩	September comma, septembrisma
833/832	2.0796	(72×17)/(26×13)	[-6 0 0 2 0 -1 1⟩	Horizma, horizon comma
936/935	1.8506	(23×32×13)/(5×11×17)	[3 2 -1 0 -1 1 -1⟩	Ainisma, ainic comma
1089/1088	1.5905	(3×11)2/(26×17)	[-6 2 0 0 2 0 -1⟩	Twosquare comma	S33
1156/1155	1.4983	(2×17)2/(3×5×7×11)	[2 -1 -1 -1 -1 0 2⟩	Quadrantonisma	S34
1225/1224	1.4138	(5×7)2/(23×32×17)	[-3 -2 2 2 0 0 -1⟩	Noellisma	S35
1275/1274	1.3584	(3×52×17)/(2×72×13)	[-1 1 2 -2 0 -1 1⟩	Cimbrisma
1701/1700	1.0181	(35×7)/((2×5)2×17)	[-2 5 -2 1 0 0 -1⟩	Palingenetic comma, palingenesis
2058/2057	0.84143	(2×3×73)/(112×17)	[1 1 0 3 -2 0 -1⟩	Xenisma
2431/2430	0.71230	(11×13×17)/(2×35×5)	[-1 -5 -1 0 1 1 1⟩	Heptacircle comma
2500/2499	0.69263	(2×52)2/(3×72×17)	[2 -1 4 -2 0 0 -1⟩	Sperasma	S50
2601/2600	0.66573	(3×17)2/(23×52×13)	[-3 2 -2 0 0 -1 2⟩	Sextantonisma	S51
4914/4913	0.35234	(2×33×7×13)/173	[1 3 0 1 0 1 -3⟩	Baladisma
5832/5831	0.29688	(2×32)3/(73×17)	[3 6 0 -3 0 0 -1⟩	Chlorisma
12376/12375	0.13989	(23×7×13×17)/(32×53×11)	[3 -2 -3 1 -1 1 1⟩	Flashma
14400/14399	0.12023	(23×3×5)2/(7×112×17)	[6 2 2 -1 -2 0 -1⟩	Sparkisma	S120
28561/28560	0.060616	(13/2)4/(3×5×7×17)	[-4 -1 -1 -1 0 4 -1⟩	Pisanoisma	S169
31213/31212	0.055466	(74×13)/(22×33×172)	[-2 -3 0 4 0 1 -2⟩	E-shaped comma
37180/37179	0.046564	(22×5×11×132)/(37×17)	[2 -7 1 0 1 2 -1⟩	Lateral comma
194481/194480	0.0089018	(3×7)4/(24×5×11×13×17)	[-4 4 -1 4 -1 -1 -1⟩	Scintillisma	S441
336141/336140	0.0051503	(32×133×17)/(22×5×75)	[-2 2 -1 -5 0 3 1⟩	Aksial comma

19-limit

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
19/18	93.603	19/(2×32)	[-1 -2 0 0 0 0 0 1⟩	Large undevicesimal semitone
20/19	88.801	(22×5)/19	[2 0 1 0 0 0 0 -1⟩	Small undevicesimal semitone
39/38	44.970	(3×13)/(2×19)	[-1 1 0 0 0 1 0 -1⟩	Undevicesimal diesis, undevicesimal 2/9-tone
57/56	30.642	(3×19)/(23×7)	[-3 1 0 -1 0 0 0 1⟩	Hendrix comma
76/75	22.931	(22×19)/(3×52)	[2 -1 -2 0 0 0 0 1⟩	Large undevicesimal 1/9-tone
77/76	22.631	(7×11)/(22×19)	[-2 0 0 1 1 0 0 -1⟩	Small undevicesimal 1/9-tone
96/95	18.128	(25×3)/(5×19)	[5 1 -1 0 0 0 0 -1⟩	19th-partial chroma
133/132	13.066	(7×19)/(22×3×11)	[-2 -1 0 1 -1 0 0 1⟩	Minithirdma
153/152	11.352	(32×17)/(23×19)	[-3 2 0 0 0 0 1 -1⟩	Ganassisma, Ganassi's comma
171/170	10.154	(32×19)/(2×5×17)	[-1 2 -1 0 0 0 -1 1⟩	Malcolmisma
190/189	9.1358	(2×5×19)/(33×7)	[1 -3 1 -1 0 0 0 1⟩	Cotylisma
209/208	8.3033	(11×19)/(24×13)	[-4 0 0 0 1 -1 0 1⟩	Yama comma
210/209	8.2637	(2×3×5×7)/(11×19)	[1 1 1 1 -1 0 0 -1⟩	Spleen comma
286/285	6.0639	(2×11×13)/(3×5×19)	[1 -1 -1 0 1 1 0 -1⟩	Chthonisma
324/323	5.3516	(2×32)2/(17×19)	[2 4 0 0 0 0 -1 -1⟩	Photisma	S18
343/342	5.0547	73/(2×32×19)	[-1 -2 0 3 0 0 0 -1⟩	Nutrisma
361/360	4.8023	192/(23×32×5)	[-3 -2 -1 0 0 0 0 2⟩	Go comma, Dudon comma	S19
400/399	4.3335	(22×5)2/(3×7×19)	[4 -1 2 -1 0 0 0 -1⟩	Devichroma	S20
456/455	3.8007	(23×3×19)/(5×7×13)	[3 1 -1 -1 0 -1 0 1⟩	Abnobisma
476/475	3.6409	(22×7×17)/(52×19)	[2 0 -2 1 0 0 1 -1⟩	Hedwigma
495/494	3.5010	(32×5×11)/(2×13×19)	[-1 2 1 0 1 -1 0 -1⟩	Eulalisma
513/512	3.3780	(33×19)/29	[-9 3 0 0 0 0 0 1⟩	Undevicesimal comma, undevicesimal schisma, Boethius' comma, 513th harmonic
969/968	1.7875	(3×17×19)/(23×112)	[-3 1 0 0 -2 0 1 1⟩	Kingfisher comma
1216/1215	1.4243	(26×19)/(35×5)	[6 -5 -1 0 0 0 0 1⟩	Password comma, Eratosthenes' comma
1331/1330	1.3012	113/(2×5×7×19)	[-1 0 -1 -1 3 0 0 -1⟩	Solvejgsma
1445/1444	1.1985	5×(17/(2×19))2	[-2 0 1 0 0 0 2 -2⟩	Aureusma
1521/1520	1.1386	(3×13)2/(24×5×19)	[-4 2 -1 0 0 2 0 -1⟩	Pinkanberry	S39
1540/1539	1.1245	(22×5×7×11)/(34×19)	[2 -4 1 1 1 0 0 -1⟩	Kevolisma
1729/1728	1.0016	(7×13×19)/(22×3)3	[-6 -3 0 1 0 1 0 1⟩	Ramanujanisma
2376/2375	0.72879	((2×3)/5)3×(11/19)	[3 3 -3 0 1 0 0 -1⟩	Trichthonisma
2432/2431	0.71200	(27×19)/(11×13×17)	[7 0 0 0 -1 -1 -1 1⟩	Blumeyer comma
2926/2925	0.59177	(2×7×11×19)/((3×5)2×13)	[1 -2 -2 1 1 -1 0 1⟩	Neovulture comma, neovulturisma
3136/3135	0.55214	(23×7)2/(3×5×11×19)	[6 -1 -1 2 -1 0 0 -1⟩	Neomirkwai comma, neomirkwaisma	S56
3250/3249	0.53277	(2×53×13)/(3×19)2	[1 -2 3 0 0 1 0 -2⟩	Martebisma
4200/4199	0.41225	(23×3×52×7)/(13×17×19)	[3 1 2 1 0 -1 -1 -1⟩	Neosatanisma
5776/5775	0.29975	(22×19)2/(3×52×7×11)	[4 -1 -2 -1 -1 0 0 2⟩	Neovish comma, neovishma	S76
5929/5928	0.29202	(7×11)2/(23×3×13×19)	[-3 -1 0 2 2 -1 0 -1⟩	Manzanisma	S77
5985/5984	0.28929	(32×5×7×19)/(25×11×17)	[-5 2 1 1 -1 0 -1 1⟩	Neogrendel comma, neogrendelisma
6175/6174	0.28038	(52×13×19)/(2×32×73)	[-1 -2 2 -3 0 1 0 1⟩	Neonewtisma
6860/6859	0.25238	(22×5×73)/193	[2 0 1 3 0 0 0 -3⟩	Devicubisma
10241/10240	0.16906	(72×11×19)/(211×5)	[-11 0 -1 2 1 0 0 1⟩
10830/10829	0.15986	(2×3×5×192)/(72×13×17)	[1 1 1 -2 0 -1 -1 2⟩
12636/12635	0.13701	(22×35×13)/(5×7×192)	[2 5 -1 -1 0 1 0 -2⟩	Padriellisma
13377/13376	0.12942	(3×73×13)/(26×11×19)	[-6 1 0 3 -1 1 0 -1⟩
14080/14079	0.12296	(28×5×11)/(3×13×192)	[8 -1 1 0 1 -1 0 -2⟩
14365/14364	0.12052	(5×132×17)/(22×33×7×19)	[-2 -3 1 -1 0 2 1 -1⟩
23409/23408	0.073957	((3/2)2×17)2/(7×11×19)	[-4 4 0 -1 -1 0 2 -1⟩		S153
27456/27455	0.063056	(26×3×11×13)/(5×172×19)	[6 1 -1 0 1 1 -2 -1⟩
28900/28899	0.059905	((2×5×17)/(3×13))2/19	[2 -2 2 0 0 -2 2 -1⟩		S170
43681/43680	0.039634	(11×19)2/(25×3×5×7×13)	[-5 -1 -1 -1 2 -1 0 2⟩		S209
89376/89375	0.019370	(25×3×72×19)/(54×11×13)	[5 1 -4 2 -1 -1 0 1⟩
104976/104975	0.016492	(2×32)4/(52×13×17×19)	[4 8 -2 0 0 -1 -1 -1⟩		S324
165376/165375	0.010469	(29×17×19)/((3×5)3×72)	[9 -3 -3 -2 0 0 1 1⟩	Decimillisma
228096/228095	0.0075900	((22×3)/7)4×(11/(5×19))	[8 4 -1 -4 1 0 0 -1⟩
601426/601425	0.0028786	(2×72×17×192)/(37×52×11)	[1 -7 -2 2 -1 0 1 2⟩
633556/633555	0.0027326	(22×7×113×17)/(33×5×13×192)	[2 -3 -1 1 3 -1 1 -2⟩	Devicisma
709632/709631	0.0024396	(210×32×7×11)/(133×17×19)	[10 2 0 1 1 -3 -1 -1⟩
5909761/5909760	0.00029294	(11×13×17)2/(28×35×5×19)	[-8 -5 -1 0 2 2 2 -1⟩		S2431
11859211/11859210	0.00014598	(19/(3×11))4×((7×13)/(2×5))	[-1 -4 -1 1 -4 1 0 4⟩

23-limit

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
23/22	76.956	23/(2×11)	[-1 0 0 0 -1 0 0 0 1⟩	Large vicesimotertial semitone
24/23	73.681	(23×3)/23	[3 1 0 0 0 0 0 0 -1⟩	Small vicesimotertial semitone
46/45	38.051	(2×23)/(32×5)	[1 -2 -1 0 0 0 0 0 1⟩	Vicesimotertial 1/5-tone
69/68	25.274	(3×23)/(22×17)	[-2 1 0 0 0 0 -1 0 1⟩	Large vicesimotertial 1/8-tone
70/69	24.910	(2×5×7)/(3×23)	[1 -1 1 1 0 0 0 0 -1⟩	Small vicesimotertial 1/8-tone
92/91	18.921	(22×23)/(7×13)	[2 0 0 -1 0 -1 0 0 1⟩	Undinisma
115/114	15.120	(5×23)/(2×3×19)	[-1 -1 1 0 0 0 0 -1 1⟩	Yarmanisma
161/160	10.787	(7×23)/(25×5)	[-5 0 -1 1 0 0 0 0 1⟩	Major kirnbergerisma
162/161	10.720	(2×34)/(7×23)	[1 4 0 -1 0 0 0 0 -1⟩	Minor kirnbergerisma
208/207	8.3433	(24×13)/(32×23)	[4 -2 0 0 0 1 0 0 -1⟩	Vicetone comma
231/230	7.5108	(3×7×11)/(2×5×23)	[-1 1 -1 1 1 0 0 0 -1⟩	Major neutravicema
253/252	6.8564	(11×23)/((2×3)2×7)	[-2 -2 0 -1 1 0 0 0 1⟩	Middle neutravicema
276/275	6.2840	(22×3×23)/(52×11)	[2 1 -2 0 -1 0 0 0 1⟩	Minor neutravicema
300/299	5.7804	((2×5)2×3)/(13×23)	[2 1 2 0 0 -1 0 0 -1⟩	Major naiadvicema
323/322	5.3682	(17×19)/(2×7×23)	[-1 0 0 -1 0 0 1 1 -1⟩	Major semivicema
391/390	4.4334	(17×23)/(2×3×5×13)	[-1 -1 -1 0 0 -1 1 0 1⟩	Minor naiadvicema
392/391	4.4221	(23×72)/(17×23)	[3 0 0 2 0 0 -1 0 -1⟩	Minor semivicema
460/459	3.7676	(22×5×23)/(33×17)	[2 -3 1 0 0 0 -1 0 1⟩	Scanisma, vicewolf comma
484/483	3.5806	(2×11)2/(3×7×23)	[2 -1 0 -1 2 0 0 0 -1⟩	Pittsburghisma	S22
507/506	3.4180	(3×132)/(2×11×23)	[-1 1 0 0 -1 2 0 0 -1⟩	Laodicisma
529/528	3.2758	232/(24×3×11)	[-4 -1 0 0 -1 0 0 0 2⟩	Preziosisma	S23
576/575	3.0082	((23×3)/5)2/23	[6 2 -2 0 0 0 0 0 -1⟩	Worcester comma	S24
736/735	2.3538	(25×23)/(3×5×72)	[5 -1 -1 -2 0 0 0 0 1⟩	Harvardisma
760/759	2.2794	(23×5×19)/(3×11×23)	[3 -1 1 0 -1 0 0 1 -1⟩	Squadronisma
875/874	1.9797	(53×7)/(2×19×23)	[-1 0 3 1 0 0 0 -1 -1⟩	Nymphisma
897/896	1.9311	(3×13×23)/(27×7)	[-7 1 0 -1 0 1 0 0 1⟩	Lysistratisma
1105/1104	1.5674	(5×13×17)/(24×3×23)	[-4 -1 1 0 0 1 1 0 -1⟩	Fragarisma
1197/1196	1.4469	(32×7×19)/(22×13×23)	[-2 2 0 1 0 -1 0 1 -1⟩	Rodessisma
1288/1287	1.3446	(23×7×23)/(32×11×13)	[3 -2 0 1 -1 -1 0 0 1⟩	Santisma, triaphonisma
1496/1495	1.1576	(23×11×17)/(5×13×23)	[3 0 -1 0 1 -1 1 0 -1⟩	Turkisma
1863/1862	0.92952	(34×23)/(2×72×19)	[-1 4 0 -2 0 0 0 -1 1⟩	Antinousisma
2024/2023	0.85556	(23×11×23)/(7×172)	[3 0 0 -1 1 0 -2 0 1⟩	Artifisma, insincere comma
2025/2024	0.85514	(32×5)2/(23×11×23)	[-3 4 2 0 -1 0 0 0 -1⟩	Cupcake comma, cupcakesma	S45
2185/2184	0.79251	(5×19×23)/(23×3×7×13)	[-3 -1 1 -1 0 -1 0 1 1⟩	Guangdongisma
2300/2299	0.75287	((2×5)/11)2×(23/19)	[2 0 2 0 -2 0 0 -1 1⟩	Travellisma
2646/2645	0.65441	(2×33×72)/(5×232)	[1 3 -1 2 0 0 0 0 -2⟩	Biyativice comma, biyativicema
2737/2736	0.63265	(7×17×23)/(24×32×19)	[-4 -2 0 1 0 0 1 -1 1⟩	Kotkisma
3060/3059	0.56586	((2×3)2×5×17)/(7×19×23)	[2 2 1 -1 0 0 1 -1 -1⟩	Vicious comma, viciousma
3381/3380	0.51212	(3×72×23)/(22×5×132)	[-2 1 -1 2 0 -2 0 0 1⟩	Mikkolisma
3520/3519	0.49190	(26×5×11)/(32×17×23)	[6 -2 1 0 1 0 -1 0 -1⟩	Vicedim comma, vicedimma
3888/3887	0.44533	(24×35)/(132×23)	[4 5 0 0 0 -2 0 0 -1⟩	Shoalma, vicetride comma
4693/4692	0.36893	(13×192)/(22×3×17×23)	[-2 -1 0 0 0 1 -1 2 -1⟩	Viceaug comma, viceaugma
4761/4760	0.36367	(3×23)2/(23×5×7×17)	[-3 2 -1 -1 0 0 -1 0 2⟩	Demiquartervice comma	S69
5083/5082	0.34063	(13×17×23)/(2×3×7×112)	[-1 -1 0 -1 -2 1 1 0 1⟩	Broadviewsma
7866/7865	0.22010	(2×32×19×23)/(5×112×13)	[1 2 -1 0 -2 -1 0 1 1⟩
8281/8280	0.20907	(7×13)2/(23×32×5×23)	[-3 -2 -1 2 0 2 0 0 -1⟩		S91
8625/8624	0.20073	(3×53×23)/(24×72×11)	[-4 1 3 -2 -1 0 0 0 1⟩	Beerglass comma
10626/10625	0.16293	(2×3×7×11×23)/(54×17)	[1 1 -4 1 1 0 -1 0 1⟩	Demiglace comma
11271/11270	0.15361	(3×13×172)/(2×5×72×23)	[-1 1 -1 -2 0 1 2 0 -1⟩
11662/11661	0.14846	(2×73×17)/(3×132×23)	[1 -1 0 3 0 -2 1 0 -1⟩
12168/12167	0.14228	(2/23)3×(3×13)2	[3 2 0 0 0 2 0 0 -3⟩	Vicetertisma
16929/16928	0.10227	(34×11×19)/(25×232)	[-5 4 0 0 1 0 0 1 -2⟩
19551/19550	0.088552	(3×73×19)/(2×52×17×23)	[-1 1 -2 3 0 0 -1 1 -1⟩
21505/21504	0.080506	(5×11×17×23)/(210×3×7)	[-10 -1 1 -1 1 0 1 0 1⟩
21736/21735	0.079650	(23×11×13×19)/(33×5×7×23)	[3 -3 -1 -1 1 1 0 1 -1⟩
23276/23275	0.074380	((2×23)/(5×7))2×(11/19)	[2 0 -2 -2 1 0 0 -1 2⟩
25025/25024	0.069182	(52×7×11×13)/(26×17×23)	[-6 0 2 1 1 1 -1 0 -1⟩	Joshuavoisma
25921/25920	0.066790	(7×23)2/(26×34×5)	[-6 -4 -1 2 0 0 0 0 2⟩	Diarithmedia	S161
43264/43263	0.040016	(24×13)2/(32×11×19×23)	[8 -2 0 0 -1 2 0 -1 -1⟩		S208
52326/52325	0.033086	(2×34×17×19)/(52×7×13×23)	[1 4 -2 -1 0 -1 1 1 -1⟩
71875/71874	0.024087	(55×23)/(2×(3×11)3)	[-1 -3 5 0 -3 0 0 0 1⟩
75141/75140	0.023040	(33×112×23)/(22×5×13×172)	[-2 3 -1 0 2 -1 -2 0 1⟩
76545/76544	0.022617	(37×5×7)/(28×13×23)	[-8 7 1 1 0 -1 0 0 -1⟩
104329/104328	0.016594	(17×19)2/(23×34×7×23)	[-3 -4 0 -1 0 0 2 2 -1⟩		S323
122452/122451	0.014138	(22×113×23)/(3×74×17)	[2 -1 0 -4 3 0 -1 0 1⟩
126225/126224	0.013716	(33×52×11×17)/(24×73×23)	[-4 3 2 -3 1 0 1 0 -1⟩
152881/152880	0.011324	(17×23)2/(24×3×5×72×13)	[-4 -1 -1 -2 0 -1 2 0 2⟩		S391
202125/202124	0.0085652	(3×53×72×11)/(22×133×23)	[-2 1 3 2 1 -3 0 0 -1⟩
264385/264384	0.0065482	(5×112×19×23)/(26×35×17)	[-6 -5 1 0 2 0 -1 1 1⟩
282625/282624	0.0061256	(53×7×17×19)/(212×3×23)	[-12 -1 3 1 0 0 1 1 -1⟩
328510/328509	0.0052700	(2×5×7×13×192)/(3×23)3	[1 -3 1 1 0 1 0 2 -3⟩
2023425/2023424	0.00085560	((3×5×23)2×17)/(213×13×19)	[-13 2 2 0 0 -1 1 -1 2⟩
4096576/4096575	0.00042261	((23×11×23)/(32×5×17))2/7	[6 -4 -2 -1 2 0 -2 0 2⟩		S2024
5142501/5142500	0.00033665	33×((7×13)/(2×52×11))2×(23/17)	[-2 3 -4 2 -2 2 -1 0 1⟩

29-limit

Main article: List of superparticular intervals/29-limit

31-limit

Main article: List of superparticular intervals/31-limit

37-limit

Main article: List of superparticular intervals/37-limit

41-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
41/40	42.749	41/(23×5)	2.5.41 [-3 -1 1⟩	Large quadracesimoprimal 1/5-tone
42/41	41.719	(2×3×7)/41	2.3.7.41 [1 1 1 -1⟩	Small quadracesimoprimal 1/5-tone
82/81	21.242	(2×41)/34	2.3.41 [1 -4 1⟩	41st-partial chroma
124/123	14.018	(22×31)/(3×41)	2.3.31.41 [2 -1 1 -1⟩
165/164	10.524	(3×5×11)/(22×41)	2.3.5.11.41 [-2 1 1 1 -1⟩
205/204	8.4657	(5×41)/(22×3×17)	2.3.5.17.41 [-2 -1 1 -1 1⟩
246/245	7.0519	(2×3×41)/(5×72)	2.3.5.7.41 [1 1 -1 -2 1⟩
247/246	7.0233	(13×19)/(2×3×41)	2.3.13.19.41 [-1 -1 1 1 -1⟩
287/286	6.0427	(7×41)/(2×11×13)	2.7.11.13.41 [-1 1 -1 -1 1⟩
288/287	6.0217	(25×32)/(7×41)	2.3.7.41 [5 2 -1 -1⟩
369/368	4.6981	(32×41)/(24×23)	2.3.23.41 [-4 2 -1 1⟩
370/369	4.6853	(2×5×37)/(32×41)	2.3.5.37.41 [1 -2 1 1 -1⟩
451/450	3.8429	(11×41)/(2×(3×5)2)	2.3.5.11.41 [-1 -2 -2 1 1⟩
493/492	3.5152	(17×29)/(22×3×41)	2.3.17.29.41 [-2 -1 1 1 -1⟩
533/532	3.2511	(13×41)/(22×7×19)	2.7.13.19.41 [-2 -1 1 -1 1⟩
575/574	3.0135	(52×23)/(2×7×41)	2.5.7.23.41 [-1 2 -1 1 -1⟩	Renatisma
616/615	2.8127	(23×7×11)/(3×5×41)	2.3.5.7.11.41 [3 -1 -1 1 1 -1⟩	Ellisma
697/696	2.4856	(17×41)/(23×3×29)	2.3.17.29.41 [-3 -1 1 -1 1⟩
780/779	2.2210	(22×3×5×13)/(19×41)	2.3.5.13.19.41 [2 1 1 1 -1 -1⟩	Wiesentisma
820/819	2.1125	(22×5×41)/(32×7×13)	2.3.5.7.13.41 [2 -2 1 -1 -1 1⟩
1025/1024	1.6898	(52×41)/210	2.5.41 [-10 2 1⟩	Kilobytisma
1026/1025	1.6882	(2×33×19)/(52×41)	2.3.5.19.41 [1 3 -2 1 -1⟩	Ingridisma
1148/1147	1.5087	(22×7×41)/(31×37)	2.7.31.37.41 [2 1 -1 -1 1⟩
1189/1188	1.4567	(29×41)/(22×33×11)	2.3.11.29.41 [-2 -3 -1 1 1⟩
1190/1189	1.4554	(2×5×7×17)/(29×41)	2.5.7.17.29.41 [1 1 1 1 -1 -1⟩	Pelagisma
1312/1311	1.3200	(25×41)/(3×19×23)	2.3.19.23.41 [5 -1 -1 -1 1⟩
1353/1352	1.2800	(3×11×41)/(23×132)	2.3.11.13.41 [-3 1 1 -2 1⟩
1395/1394	1.2415	(32×5×31)/(2×17×41)	2.3.5.17.31.41 [-1 2 1 -1 1 -1⟩
1518/1517	1.1408	(2×3×11×23)/(37×41)	2.3.11.23.37.41 [1 1 1 1 -1 -1⟩	Rovaniemisma
1600/1599	1.0824	(23×5)2/(3×13×41)	2.3.5.13.41 [6 -1 2 -1 -1⟩		S40
1681/1680	1.0302	412/(24×3×5×7)	2.3.5.7.41 [-4 -1 -1 -1 2⟩		S41
1682/1681	1.0296	(2×292)/412	2.29.41 [1 2 -2⟩	Shaftesburisma
1805/1804	0.95940	(5×192)/(22×11×41)	2.5.11.19.41 [-2 1 -1 2 -1⟩
1886/1885	0.91818	(2×23×41)/(5×13×29)	2.5.13.23.29.41 [1 -1 -1 1 -1 1⟩
1887/1886	0.91770	(3×17×37)/(2×23×41)	2.3.17.23.37.41 [-1 1 1 -1 1 -1⟩
2091/2090	0.82814	(3×17×41)/(2×5×11×19)	2.3.5.11.17.19.41 [-1 1 -1 -1 1 -1 1⟩
2255/2254	0.76790	(5×11×41)/(2×72×23)	2.5.7.11.23.41 [-1 1 -2 1 -1 1⟩	Qinghaisma
2296/2295	0.75419	(23×7×41)/(33×5×17)	2.3.5.7.17.41 [3 -3 -1 1 -1 1⟩
2542/2541	0.68119	(2×31×41)/(3×7×112)	2.3.7.11.31.41 [1 -1 -1 -2 1 1⟩
2584/2583	0.67011	(23×17×19)/(32×7×41)	2.3.7.17.19.41 [3 -2 -1 1 1 -1⟩
2625/2624	0.65964	(3×53×7)/(26×41)	2.3.5.7.41 [-6 1 3 1 -1⟩
2665/2664	0.64974	(5×13×41)/(23×32×37)	2.3.5.13.37.41 [-3 -2 1 1 -1 1⟩
2871/2870	0.60311	(32×11×29)/(2×5×7×41)	2.3.5.7.11.29.41 [-1 2 -1 -1 1 1 -1⟩	Schoberisma
3690/3689	0.46923	(2×32×5×41)/(7×17×31)	2.3.5.7.17.31.41 [1 2 1 -1 -1 -1 1⟩
3773/3772	0.45891	(73×11)/(22×23×41)	2.7.11.23.41 [-2 3 1 -1 -1⟩	Smithsonianisma
4060/4059	0.42646	(22×5×7×29)/(32×11×41)	2.3.5.7.11.29.41 [2 -2 1 1 -1 1 -1⟩	Deipylosisma
4264/4263	0.40606	(23×13×41)/(3×72×29)	2.3.7.13.29.41 [3 -1 -2 1 -1 1⟩
4551/4550	0.38045	(3×37×41)/(2×52×7×13)	2.3.5.7.13.37.41 [-1 1 -2 -1 -1 1 1⟩
4675/4674	0.37036	(52×11×17)/(2×3×19×41)	2.3.5.11.17.19.41 [-1 -1 2 1 1 -1 -1⟩	Ohbokisma
4921/4920	0.35184	(7×19×37)/(23×3×5×41)	2.3.5.7.19.37.41 [-3 -1 -1 1 1 1 -1⟩	Volontisma
4961/4960	0.34900	(112×41)/(25×5×31)	2.5.11.31.41 [-5 -1 2 -1 1⟩
5084/5083	0.34056	(22×31×41)/(13×17×23)	2.13.17.23.31.41 [2 -1 -1 -1 1 1⟩
5577/5576	0.31045	(3×11×132)/(23×17×41)	2.3.11.13.17.41 [-3 1 1 2 -1 -1⟩	Priestlisma
6069/6068	0.28528	(3×7×172)/(22×37×41)	2.3.7.17.37.41 [-2 1 1 2 -1 -1⟩	Cevolanisma
6273/6272	0.27600	(32×17×41)/(27×72)	2.3.7.17.41 [-7 2 -2 1 1⟩
6561/6560	0.26389	38/(25×5×41)	2.3.5.41 [-5 8 -1 -1⟩		S81
6601/6600	0.26229	(7×23×41)/(23×3×52×11)	2.3.5.7.11.23.41 [-3 -1 -2 1 -1 1 1⟩
6930/6929	0.24984	(2×32×5×7×11)/(132×41)	2.3.5.7.11.13.41 [1 2 1 1 1 -2 -1⟩	Bedanisma
7176/7175	0.24127	(23×3×13×23)/(52×7×41)	2.3.5.7.13.23.41 [3 1 -2 -1 1 1 -1⟩	Kunijisma
7216/7215	0.23993	(24×11×41)/(3×5×13×37)	2.3.5.11.13.37.41 [4 -1 -1 1 -1 -1 1⟩
7750/7749	0.22340	(2×53×31)/(33×7×41)	2.3.5.7.31.41 [1 -3 3 -1 1 -1⟩
8569/8568	0.20205	(11×19×41)/(23×32×7×17)	2.3.7.11.17.19.41 [-3 -2 -1 1 -1 1 1⟩	Mamelisma
8856/8855	0.19550	((2×3)3×41)/(5×7×11×23)	2.3.5.7.11.23.41 [3 3 -1 -1 -1 -1 1⟩
9472/9471	0.18278	(28×37)/(3×7×11×41)	2.3.7.11.37.41 [8 -1 -1 -1 1 -1⟩	Brugesisma
10045/10044	0.17236	(5×72×41)/(22×34×31)	2.3.5.7.31.41 [-2 -4 1 2 -1 1⟩
10374/10373	0.16689	(2×3×7×13×19)/(11×23×41)	2.3.7.11.13.19.23.41 [1 1 1 -1 1 1 -1 -1⟩	Etampesisma
10660/10659	0.16241	(22×5×13×41)/(3×11×17×19)	2.3.5.11.13.17.19.41 [2 -1 1 -1 1 -1 -1 1⟩
11440/11439	0.15134	(24×5×11×13)/(32×31×41)	2.3.5.11.13.31.41 [4 -2 1 1 1 -1 -1⟩	Massironisma
13776/13775	0.12567	(24×3×7×41)/(52×19×29)	2.3.5.7.19.29.41 [4 1 -2 1 -1 -1 1⟩
14145/14144	0.12240	(3×5×23×41)/(26×13×17)	2.3.5.13.17.23.41 [-6 1 1 -1 -1 1 1⟩
14801/14800	0.11697	(192×41)/(24×52×37)	2.5.19.37.41 [-4 -2 2 -1 1⟩
15376/15375	0.11260	(22×31)2/(3×53×41)	2.3.5.31.41 [4 -1 -3 2 -1⟩	Martakisma	S124
15457/15456	0.11201	(13×29×41)/(25×3×7×23)	2.3.7.13.23.29.41 [-5 -1 -1 1 -1 1 1⟩
16400/16399	0.10557	(24×52×41)/(232×31)	2.5.23.31.41 [4 2 -2 -1 1⟩
16524/16523	0.10477	(22×35×17)/(13×31×41)	2.3.13.17.31.41 [2 5 -1 1 -1 -1⟩
16606/16605	0.10426	(2×192×23)/(34×5×41)	2.3.5.19.23.41 [1 -4 -1 2 1 -1⟩
17425/17424	0.099356	(52×17×41)/(22×3×11)2	2.3.5.11.17.41 [-4 -2 2 -2 1 1⟩
17836/17835	0.097067	(22×73×13)/(3×5×29×41)	2.3.5.7.13.29.41 [2 -1 -1 3 1 -1 -1⟩	Canupisma
17918/17917	0.096623	(2×172×31)/(19×23×41)	2.17.19.23.31.41 [1 2 -1 -1 1 -1⟩
19721/19720	0.087789	(13×37×41)/(23×5×17×29)	2.5.13.17.29.37.41 [-3 -1 1 -1 -1 1 1⟩
19845/19844	0.087240	(34×5×72)/((2×11)2×41)	2.3.5.7.11.41 [-2 4 1 2 -2 -1⟩
76384/76383	0.022665	(25×7×11×31)/(34×23×41)	2.3.7.11.23.31.41 [5 -4 1 1 -1 1 -1⟩	Vernonisma
1048576/1048575	0.0016510	220/(3×52×11×31×41)	2.3.5.11.31.41 [20 -1 -2 -1 -1 -1⟩	Mebisma	S1024

43-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
43/42	40.737	43/(2×3×7)	2.3.7.43 [-1 -1 -1 1⟩	Large quadracesimotertial 1/5-tone
44/43	39.800	(22×11)/43	2.11.43 [2 1 -1⟩	Small quadracesimotertial 1/5-tone
86/85	20.249	(2×43)/(5×17)	2.5.17.43 [1 -1 -1 1⟩	Large quadracesimotertial 1/10-tone
87/86	20.014	(3×29)/(2×43)	2.3.29.43 [-1 1 1 -1⟩	Small quadracesimotertial 1/10-tone
129/128	13.473	(3×43)/27	2.3.43 [-7 1 1⟩	43rd-partial chroma
130/129	13.369	(2×5×13)/(3×43)	2.3.5.13.43 [1 -1 1 1 -1⟩
172/171	10.095	(22×43)/(32×19)	2.3.19.43 [2 -2 -1 1⟩
216/215	8.0336	(2×3)3/(5×43)	2.3.5.43 [3 3 -1 -1⟩
259/258	6.6972	(7×37)/(2×3×43)	2.3.7.37.43 [-1 -1 1 1 -1⟩
301/300	5.7612	(7×43)/((2×5)2×3)	2.3.5.7.43 [-2 -1 -2 1 1⟩
344/343	5.0400	(23×43)/73	2.7.43 [3 -3 1⟩
345/344	5.0254	(3×5×23)/(23×43)	2.3.5.23.43 [-3 1 1 1 -1⟩
430/429	4.0308	(2×5×43)/(3×11×13)	2.3.5.11.13.43 [1 -1 1 -1 -1 1⟩
559/558	3.0998	(13×43)/(2×32×31)	2.3.13.31.43 [-1 -2 1 -1 1⟩
560/559	3.0943	(24×5×7)/(13×43)	2.5.7.13.43 [4 1 1 -1 -1⟩
645/644	2.6862	(3×5×43)/(22×7×23)	2.3.5.7.23.43 [-2 1 1 -1 -1 1⟩
646/645	2.6820	(2×17×19)/(3×5×43)	2.3.5.17.19.43 [1 -1 -1 1 1 -1⟩	Kastalisma
775/774	2.2353	(52×31)/(2×32×43)	2.3.5.31.43 [-1 -2 2 1 -1⟩
817/816	2.1203	(19×43)/(24×3×17)	2.3.17.19.43 [-4 -1 -1 1 1⟩
861/860	2.0119	(3×7×41)/(22×5×43)	2.3.5.7.41.43 [-2 1 -1 1 1 -1⟩
903/902	1.9183	(3×7×43)/(2×11×41)	2.3.7.11.41.43 [-1 1 1 -1 -1 1⟩
946/945	1.8310	(2×11×43)/(33×5×7)	2.3.5.7.11.43 [1 -3 -1 -1 1 1⟩
989/988	1.7514	(23×43)/(22×13×19)	2.13.19.23.43 [-2 -1 -1 1 1⟩
990/989	1.7496	(2×32×5×11)/(23×43)	2.3.5.11.23.43 [1 2 1 1 -1 -1⟩	Yerkesisma
1161/1160	1.4918	(33×43)/(23×5×29)	2.3.5.29.43 [-3 3 -1 -1 1⟩
1248/1247	1.3878	(25×3×13)/(29×43)	2.3.13.29.43 [5 1 1 -1 -1⟩
1333/1332	1.2992	(31×43)/((2×3)2×37)	2.3.31.37.43 [-2 -2 1 -1 1⟩	Cevenolisma
1334/1333	1.2983	(2×23×29)/(31×43)	2.23.29.31.43 [1 1 1 -1 -1⟩
1376/1375	1.2586	(25×43)/(53×11)	2.5.11.43 [5 -3 -1 1⟩
1377/1376	1.2577	(34×17)/(25×43)	2.3.17.43 [-5 4 1 -1⟩	Roberbauxisma
1463/1462	1.1838	(7×11×19)/(2×17×43)	2.7.11.17.19.43 [-1 1 1 -1 1 -1⟩	Nordenmarkisma
1548/1547	1.1187	(22×32×43)/(7×13×17)	2.3.7.13.17.43 [2 2 -1 -1 -1 1⟩
1764/1763	0.98170	(2×3×7)2/(41×43)	2.3.7.41.43 [2 2 2 -1 -1⟩		S42
1806/1805	0.95887	(2×3×7×43)/(5×192)	2.3.5.7.19.43 [1 1 -1 1 -2 1⟩
1849/1848	0.93656	432/(23×3×7×11)	2.3.7.11.43 [-3 -1 -1 -1 2⟩		S43
1850/1849	0.93606	(2×52×37)/432	2.5.37.43 [1 2 1 -2⟩
1936/1935	0.89446	(22×11)2/(32×5×43)	2.3.5.11.43 [4 -2 -1 2 -1⟩		S44
2925/2924	0.59198	(32×52×13)/(22×17×43)	2.3.5.13.17.43 [-2 2 2 1 -1 -1⟩	Beattisma
3312/3311	0.52279	(24×32×23)/(7×11×43)	2.3.7.11.23.43 [4 2 -1 -1 1 -1⟩	Pedersenisma
4000/3999	0.43286	(25×53)/(3×31×43)	2.3.5.31.43 [5 -1 3 -1 -1⟩	Hipparchusisma
4301/4300	0.40257	(11×17×23)/(22×52×43)	2.5.11.17.23.43 [-2 -2 1 1 1 -1⟩	Boydenisma
4774/4773	0.36268	(2×7×11×31)/(3×37×43)	2.3.7.11.31.37.43 [1 -1 1 1 1 -1 -1⟩	Hobetsisma
5720/5719	0.30269	(23×5×11×13)/(7×19×43)	2.5.7.11.13.19.43 [3 1 -1 1 1 -1 -1⟩	Halweaverisma
7225/7224	0.23963	(5×17)2/(23×3×7×43)	2.3.5.7.17.43 [-3 -1 2 -1 2 -1⟩	Huntressisma	S85
7956/7955	0.21761	(22×32×13×17)/(5×37×43)	2.3.5.13.17.37.43 [2 2 -1 1 1 -1 -1⟩	Yajinisma
9504/9503	0.18217	(25×33×11)/(13×17×43)	2.3.11.13.17.43 [5 3 1 -1 -1 -1⟩	Lionelisma
9633/9632	0.17973	(3×132×19)/(25×7×43)	2.3.7.13.19.43 [-5 1 -1 2 1 -1⟩	Coturisma
10450/10449	0.16568	(2×52×11×19)/(35×43)	2.3.5.11.19.43 [1 -5 2 1 1 -1⟩	Girardisma
10880/10879	0.15912	(27×5×17)/(11×23×43)	2.5.11.17.23.43 [7 1 -1 1 -1 -1⟩	Kaguyisma
17545/17544	0.098677	(5×112×29)/(23×3×17×43)	2.3.5.11.17.29.43 [-3 -1 1 2 -1 1 -1⟩	Manheimisma
27048/27047	0.064007	(23×3×72×23)/(17×37×43)	2.3.7.17.23.37.43 [3 1 2 -1 1 -1 -1⟩	Jangongisma
29241/29240	0.059207	(32×19)2/(23×5×17×43)	2.3.5.17.19.43 [-3 4 -1 -1 2 -1⟩	Locquirecisma	S171
512001/512000	0.0033813	(35×72×43)/(212×53)	2.3.5.7.43 [-12 5 -3 2 1⟩		S126/S128

47-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
47/46	37.232	47/(2×23)	2.23.47 [-1 -1 1⟩
48/47	36.448	(24×3)/47	2.3.47 [4 1 -1⟩	47th-partial chroma
94/93	18.516	(2×47)/(3×31)	2.3.31.47 [1 -1 -1 1⟩
95/94	18.320	(5×19)/(2×47)	2.5.19.47 [-1 1 1 -1⟩
141/140	12.322	(3×47)/(22×5×7)	2.3.5.7.47 [-2 1 -1 -1 1⟩
188/187	9.2333	(22×47)/(11×17)	2.11.37.47 [2 -1 -1 1⟩
189/188	9.1843	(33×7)/(22×47)	2.3.7.47 [-2 3 1 -1⟩
235/234	7.3827	(5×47)/(2×32×13)	2.3.5.13.47 [-1 -2 1 -1 1⟩
329/328	5.2701	(7×47)/(23×41)	2.7.41.47 [-3 1 -1 1⟩
330/329	5.2541	(2×3×5×11)/(7×47)	2.3.5.7.11.47 [1 1 1 -1 1 -1⟩
376/375	4.6105	(23×47)/(3×53)	2.3.5.47 [3 -1 -3 1⟩
377/376	4.5982	(13×29)/(23×47)	2.13.29.47 [-3 1 1 -1⟩
1176/1175	1.4728	(23×3×72)/(52×47)	2.3.5.7.47 [3 1 -2 2 -1⟩	Lucidorisma
2116/2115	0.81836	(2×23)2/(32×5×47)	2.3.5.23.47 [2 -2 -1 2 -1⟩		S46
2209/2208	0.78390	472/(25×3×5)	2.3.23.47 [-5 -1 -1 2⟩		S47
2304/2303	0.75157	(24×3)2/(72×47)	2.3.7.47 [8 2 -2 -1⟩		S48

53-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
53/52	32.977	53/(22×13)	2.13.53 [-2 -1 1⟩
54/53	32.360	(2×33)/53	2.3.53 [1 3 -1⟩
106/105	16.410	(2×53)/(3×5×7)	2.3.5.7.53 [1 -1 -1 -1 1⟩
160/159	10.854	(25×5)/(3×53)	2.3.5.53 [5 -1 1 -1⟩
265/264	6.5453	(5×53)/(23×3×11)	2.3.5.11.53 [-3 -1 1 -1 1⟩
266/265	6.5207	(2×7×19)/(5×53)	2.5.7.19.53 [1 -1 1 1 -1⟩
319/318	5.4356	(11×29)/(2×3×53)	2.3.11.29.53 [-1 -1 1 1 -1⟩
371/370	4.6727	(7×53)/(2×5×37)	2.5.7.37.53 [-1 -1 1 -1 1⟩
372/371	4.6601	(22×3×31)/(7×53)	2.3.7.31.53 [2 1 -1 1 -1⟩
424/423	4.0879	(23×53)/(32×47)	2.3.47.53 [3 -2 -1 1⟩
425/424	4.0783	(52×17)/(23×53)	2.5.17.53 [-3 2 1 -1⟩
477/476	3.6332	(32×53)/(22×7×17)	2.3.7.17.53 [-2 2 -1 -1 1⟩
2809/2808	0.61643	532/(23×33×13)	2.3.13.53 [-3 -3 -1 2⟩		S53
4081/4080	0.42427	(7×11×53)/(24×3×5×17)	2.3.5.7.11.17.53 [-4 -1 -1 1 1 -1 1⟩

59-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
59/58	29.594	59/(2×29)	2.29.59 [-1 -1 1⟩
60/59	29.097	(22×3×5)/59	2.3.5.59 [2 1 1 -1⟩
118/117	14.734	(2×59)/(32×13)	2.3.13.59 [1 -2 -1 1⟩
119/118	14.610	(7×17)/(2×59)	2.7.17.59 [-1 1 1 -1⟩
177/176	9.8087	(3×59)/(24×11)	2.3.11.59 [-4 1 -1 1⟩
236/235	7.3513	(22×59)/(5×47)	2.5.47.59 [2 -1 -1 1⟩
295/294	5.8786	(5×59)/(2×3×72)	2.3.5.7.59 [-1 -1 1 -2 1⟩
296/295	5.8587	(23×37)/(5×59)	2.5.37.59 [3 -1 1 -1⟩
414/413	4.1868	(2×32×23)/(7×59)	2.3.7.23.59 [1 2 -1 1 -1⟩
473/472	3.6640	(11×43)/(23×59)	2.11.43.59 [-3 1 1 -1⟩
1121/1120	1.5451	(19×59)/(25×5×7)	2.5.7.19.59 [-5 -1 -1 1 1⟩
1122/1121	1.5437	(2×3×11×17)/(19×59)	2.3.11.17.19.59 [1 1 1 1 -1 -1⟩
3481/3480	0.49741	592/(23×3×5×29)	2.3.5.29.59 [-3 -1 -1 -1 2⟩		S59

61-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
61/60	28.616	61/(22×3×5)	2.3.5.61 [-2 -1 -1 1⟩
62/61	28.151	(2×31)/61	2.31.61 [1 1 -1⟩
122/121	14.249	(2×61)/(112)	2.11.61 [1 -2 1⟩
123/122	14.133	(3×41)/(2×61)	2.3.41.61 [-1 1 1 -1⟩
183/182	9.4862	(3×61)/(2×7×13)	2.3.7.13.61 [-1 1 -1 -1 1⟩
184/183	9.4345	(23×23)/(3×61)	2.3.23.61 [3 -1 1 -1⟩
244/243	7.1098	(22×61)/35	2.3.61 [2 -5 1⟩
245/244	7.0807	(5×72)/(22×61)	2.5.7.61 [-2 1 2 -1⟩
305/304	5.6855	(5×61)/(24×19)	2.5.19.61 [-4 1 -1 1⟩
306/305	5.6669	(2×32×17)/(5×61)	2.3.5.17.61 [1 2 -1 1 -1⟩
672/671	2.5782	(25×3×7)/(11×61)	2.3.7.11.61 [5 1 1 -1 -1⟩
1404/1403	1.2335	(22×33×13)/(23×61)	2.3.13.23.61 [2 3 1 -1 -1⟩
3721/3720	0.46532	612/(23×3×5×31)	2.3.5.31.61 [-3 -1 -1 -1 2⟩		S61

67-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
67/66	26.034	67/(2×3×11)	2.3.11.67 [-1 -1 -1 1⟩
68/67	25.648	(22×17)/67	2.17.67 [2 1 -1⟩
134/133	12.968	(2×67)/(7×19)	2.7.19.67 [1 -1 -1 1⟩
135/134	12.872	(33×5)/(2×67)	2.3.5.67 [-1 3 1 -1⟩
201/200	8.6346	(3×67)/(23×52)	2.3.5.67 [-3 1 -2 1⟩
336/335	5.1602	(24×3×7)/(5×67)	2.3.5.7.67 [4 1 -1 1 -1⟩
671/670	2.5820	(11×61)/(2×5×67)	2.5.11.61.67 [-1 -1 1 1 -1⟩
4489/4488	0.38570	672/(23×3×11×17)	2.3.11.17.67 [-3 -1 -1 -1 2⟩		S67

71-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
71/70	24.557	71/(2×5×7)	2.5.7.71 [-1 -1 -1 1⟩
72/71	24.213	(23×32)/71	2.3.71 [3 2 -1⟩
5041/5040	0.34346	712/(24×32×5×7)	2.3.5.7.71 [-4 -2 -1 -1 2⟩	Third brown pair comma	S71
160561400000 / 160561399999	1.0783×10-8	(26×55×19×29×31×47) / (7×112×13×593×71)	2.5.7.11.13.19.29.31.47.59.71 [6 5 -1 -2 -1 1 1 1 1 -3 -1⟩	Borcherdsma

73-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
73/72	23.879	73/(23×32)	2.3.73 [-3 -2 1⟩
74/73	23.555	(2×37)/73	2.37.73 [1 1 -1⟩
366/365	4.737	(2×3×61)/(5×73)	2.3.5.61.73 [1 1 -1 1 -1⟩	Sidereal comma

79-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
79/78	22.054	79/(2×3×13)	2.3.13.79 [-1 -1 -1 1⟩
80/79	21.777	(24×5)/79	2.5.79 [4 1 -1⟩

83-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
83/82	20.985	83/(2×41)	2.41.83 [-1 -1 1⟩
84/83	20.734	(22×3×7)/83	2.3.7.83 [2 1 1 -1⟩

89-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
89/88	19.562	89/(23×11)	2.11.89 [-3 -1 1⟩	Tailwind comma[idiosyncratic term]
90/89	19.344	(2×32×5)/89	2.3.5.89 [1 2 1 -1⟩

97-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
97/96	17.940	97/(25×3)	2.3.97 [-5 -1 1⟩
98/97	17.756	(2×72)/97	2.7.97 [1 2 -1⟩

101-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
101/100	17.226	101/(2×5)2	2.5.101 [-2 -2 1⟩
102/101	17.057	(2×3×17)/101	2.3.17.101 [1 1 1 -1⟩
7777/7776	0.223	7×11×101/(2×3)5	2.3.7.11.101 [-5 -5 1 1 1⟩	Pulsar comma

103-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
103/102	16.890	103/(2×3×17)	2.3.17.103 [-1 -1 -1 1⟩
104/103	16.727	(23×13)/103	2.13.103 [3 1 -1⟩

107-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
107/106	16.256	107/(2×53)	2.53.107 [-1 -1 1⟩
108/107	16.105	(22×33)/107	2.3.107 [2 3 -1⟩
750/749	2.3099	(2×3×53)/(7×107)	2.3.5.7.107 [1 1 3 -1 -1⟩	Ancient Chinese tempering comma

109-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
109/108	15.956	109/(22×33)	2.3.109 [-2 -3 1⟩
110/109	15.810	(2×5×11)/109	2.5.11.109 [1 1 1 -1⟩

113-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
113/112	15.389	113/(24×7)	2.7.113 [-4 -1 1⟩
114/113	15.253	(2×3×19)/113	2.3.19.113 [1 1 1 -1⟩
226/225	7.6773	(2×113)/(3×5)2	2.3.5.113 [1 -2 -2 1⟩	Reversed marvel comma

127-limit (incomplete)

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
127/126	13.686	127/(2×32×7)	2.3.7.127 [-1 -2 -1 1⟩
128/127	13.578	27/127	2.127 [7 -1⟩
381/380	4.5499	(3×127)/(22×5×19)	2.3.5.19.127 [-2 1 -1 -1 1⟩	Five feet comma
500000/499999	0.0034625	(25×56)/(31×1272)	2.5.31.127 [5 6 -1 -2⟩

See also

• Gallery of just intervals

External links

• List of intervals on the Huygens-Fokker Foundation website