List of superparticular intervals

This list of superparticular intervals ordered by prime limit. It reaches to the 101-limit and is complete up to the 23-limit.

Superparticular numbers are ratios of the form (n + 1)/n, or 1 + 1/n, where n is a whole number other than 1. They appear frequently in just intonation and harmonic series music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio 21/20. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common commas are superparticular ratios.

The list below is ordered by harmonic limit, or the largest prime involved in the prime factorization. 36/35, for instance, is an interval of the 7-limit, as it factors to (2²×3²)/(5×7), while 37/36 would belong 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).

See also gallery of just intervals. Many of the names below come from the Scala website.

Ratio	Cents	Factorization	Monzo	Name(s)	Meta
2-limit (complete)
2/1	1200.000	2/1	[1⟩	octave, duple; after octave reduction: (perfect) unison, unity, perfect prime, tonic
3-limit (complete)
3/2	701.955	3/2	[-1 1⟩	perfect fifth, 3rd harmonic (octave reduced), diapente
4/3	498.045	22/3	[2 -1⟩	perfect fourth, 3rd subharmonic (octave reduced), diatessaron	3/2 to 2/1
9/8	203.910	32/23	[-3 2⟩	(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)	4/3 to 3/2
5-limit (complete)
5/4	386.314	5/22	[-2 0 1⟩	classic/just major third, 5th harmonic (octave reduced)
6/5	315.641	(2*3)/5	[1 1 -1⟩	classic/just minor third
10/9	182.404	(2*5)/32	[1 -2 1⟩	classic (whole) tone, classic major second, minor whole tone
16/15	111.731	24/(3*5)	[4 -1 -1⟩	classic/just diatonic semitone, 15th subharmonic	5/4 to 4/3
25/24	70.672	52/(23*3)	[-3 -1 2⟩	classic/just chromatic semitone, chroma, Zarlinian semitone	6/5 to 5/4
81/80	21.506	(3/2)4/5	[-4 4 -1⟩	syntonic comma, Didymus comma	10/9 to 9/8
7-limit (complete)
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, 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	(22*33)/(5*7)	[2 2 -1 -1⟩	septimal 1/4-tone, septimal diesis	7/6 to 6/5
49/48	35.697	72/(24*3)	[-4 -1 0 2⟩	slendro diesis, large septimal diesis, large septimal 1/6-tone	8/7 to 7/6
50/49	34.976	2*(5/7)2	[1 0 2 -2⟩	jubilisma, small septimal diesis, small septimal 1/6-tone, tritonic diesis, Erlich's decatonic comma
64/63	27.264	26/(32*7)	[6 -2 0 -1⟩	septimal comma, Archytas' comma	9/8 to 8/7
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	16/15 to 15/14
2401/2400	0.72120	74/(25*3*52)	[-5 -1 -2 4⟩	breedsma	50/49 to 49/48
4375/4374	0.39576	(54*7)/(2*37)	[-1 -7 4 1⟩	ragisma
11-limit (complete)
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, 33rd harmonic (octave reduced)
45/44	38.906	(3/2)2*(5/11)	[-2 2 1 0 -1⟩	undecimal 1/5-tone
55/54	31.767	(5*11)/(2*33)	[-1 -3 1 0 1⟩	undecimal diasecundal comma, eleventyfive 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	11/10 to 10/9
121/120	14.376	112/(23*3*5)	[-3 -1 -1 0 2⟩	biyatisma, undecimal seconds comma	12/11 to 11/10
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	22/21 to 21/20
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*32*7)	[-4 -3 2 -1 2⟩	lehmerisma	56/55 to 55/54
9801/9800	0.17665	(11/(5*7))2*34/23	[-3 4 -2 -2 2⟩	kalisma, Gauss comma	100/99 to 99/98
13-limit (complete)
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	13/12 to 12/11
169/168	10.274	132/(23*3*7)	[-3 -1 0 -1 0 2⟩	buzurgisma, dhanvantarisma	14/13 to 13/12
196/195	8.8554	(2*7)2/(3*5*13)	[2 -1 -1 2 0 -1⟩	mynucuma	15/14 to 14/13
325/324	5.3351	(52*13)/(22*34)	[-2 -4 2 0 0 1⟩	marveltwin comma
351/350	4.9393	(3/5)2*13/(2*7)	[-1 3 -2 -1 0 1⟩	ratwolfsma
352/351	4.9253	(25*11)/(32*13)	[5 -3 0 0 1 -1⟩	minthma
364/363	4.7627	(2/11)2*7*13/3	[2 -1 0 1 -2 1⟩	gentle comma
625/624	2.7722	(5/2)4/(3*13)	[-4 -1 4 0 0 -1⟩	tunbarsma	26/25 to 25/24
676/675	2.5629	(2*13/5)2/33	[2 -3 -2 0 0 2⟩	island comma	27/26 to 26/25
729/728	2.3764	(32/2)3/(7*13)	[-3 6 0 -1 0 -1⟩	squbema	28/27 to 27/26
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	65/64 to 64/63
4225/4224	0.40981	(5*13)2/(27*3*11)	[-7 -1 2 0 -1 2⟩	leprechaun comma	66/65 to 65/64
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	352/351 to 351/350
17-limit (complete)
17/16	104.955	17/24	[-4 0 0 0 0 0 1⟩	large septendecimal semitone, 17th harmonic (octave reduced)
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⟩	septendecimal 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⟩	septendecimal major second comma
154/153	11.278	(2*7*11)/(32*17)	[1 -2 0 1 1 0 -1⟩
170/169	10.214	(2*5*17)/132	[1 0 1 0 0 -2 1⟩
221/220	7.8514	(13*17)/(22*5*11)	[-2 0 -1 0 -1 1 1⟩
256/255	6.7759	(28)/(3*5*17)	[8 -1 -1 0 0 0 -1⟩	septendecimal kleisma, 255th subharmonic	17/16 to 16/15
273/272	6.3532	(3*7*13)/(24*17)	[-4 1 0 1 0 1 -1⟩	tannisma
289/288	6.0008	(17/3)2/25	[-5 -2 0 0 0 0 2⟩	septendecimal 6-cent comma	18/17 to 17/16
375/374	4.6228	(3*53)/(2*11*17)	[-1 1 3 0 -1 0 -1⟩
442/441	3.9213	(2*13*17)/(3*7)2	[1 -2 0 -2 0 1 1⟩
561/560	3.0887	(3*11*17)/(24*5*7)	[-4 1 -1 -1 1 0 1⟩
595/594	2.9121	(5*7*17)/(2*33*11)	[-1 -3 1 1 -1 0 1⟩
715/714	2.4230	(5*11*13)/(2*3*7*17)	[-1 -1 1 -1 1 1 -1⟩	September comma, septembrisma, septendecimal bridge comma
833/832	2.0796	(72*17)/(26*13)	[-6 0 0 2 0 -1 1⟩	horizon comma
936/935	1.8506	(23*32*13)/(5*11*17)	[3 2 -1 0 -1 1 -1⟩	ainos comma, ainma
1089/1088	1.5905	(32*112)/(26*17)	[-6 2 0 0 2 0 -1⟩	twosquare comma	34/33 to 33/32
1156/1155	1.4983	(22*172)/(3*5*7*11)	[2 -1 -1 -1 -1 0 2⟩	septendecimal 1/4-tones comma	35/34 to 34/33
1225/1224	1.4138	(52*72)/(23*32*17)	[-3 -2 2 2 0 0 -1⟩	noellisma	36/35 to 35/34
1275/1274	1.3584	(3*52*17)/(2*72*13)	[-1 1 2 -2 0 -1 1⟩
1701/1700	1.0181	(35*7)/[(2*5)2*17]	[-2 5 -2 1 0 0 -1⟩	palingenesis comma, palingenetic comma, palingenesma
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⟩
2500/2499	0.69263	(22*54)/(3*72*17)	[2 -1 4 -2 0 0 -1⟩		51/50 to 50/49
2601/2600	0.66573	(32*172)/(23*52*13)	[-3 2 -2 0 0 -1 2⟩	septendecimal 1/6-tones comma	52/51 to 51/50
4914/4913	0.35234	(2*33*7*13)/(173)	[1 3 0 1 0 1 -3⟩
5832/5831	0.29688	(23*36)/(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	(26*32*52)/(7*112*17)	[6 2 2 -1 -2 0 -1⟩	sparkisma	121/120 to 120/119
28561/28560	0.060616	(134)/(24*3*5*7*17)	[-4 -1 -1 -1 0 4 -1⟩		170/169 to 169/168
31213/31212	0.055466	(74*13)/(22*33*172)	[-2 -3 0 4 0 1 -2⟩
37180/37179	0.046564	(22*5*11*132)/(37*17)	[2 -7 1 0 1 2 -1⟩
194481/194480	0.008902	(34*74)/(24*5*11*13*17)	[-4 4 -1 4 -1 -1 -1⟩	scintillisma	442/441 to 441/440
336141/336140	0.005150	(32*133*17)/(22*5*75)	[-2 2 -1 -5 0 3 1⟩
19-limit (complete)
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 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	(19*7)/(22*3*11)	[-2 -1 0 1 -1 0 0 1⟩
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⟩
190/189	9.1358	(2*5*19)/(33*7)	[1 -3 1 -1 0 0 0 1⟩
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⟩
324/323	5.3516	(22*34)/(17*19)	[2 4 0 0 0 0 -1 -1⟩	nusu comma	19/18 to 18/17
343/342	5.0547	74/(2*33*19)	[-1 -2 0 3 0 0 0 -1⟩
361/360	4.8023	192/(23*32*5)	[-3 -2 -1 0 0 0 0 2⟩	go comma	20/19 to 19/18
400/399	4.3335	(24*52)/(3*7*19)	[4 -1 2 -1 0 0 0 -1⟩		21/20 to 20/19
456/455	3.8007	(23*3*19)/(5*7*13)	[3 1 -1 -1 0 -1 0 1⟩
476/475	3.6409	(22*7*17)/(52*19)	[2 0 -2 1 0 0 1 -1⟩
495/494	3.5010	(32*5*11)/(2*13*19)	[-1 2 1 0 1 -1 0 -1⟩
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⟩
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⟩
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	40/39 to 39/38
1540/1539	1.1245	(22*5*7*11)/(34*19)	[2 -4 1 1 1 0 0 -1⟩
1729/1728	1.0016	(7*13*19)/(26*33)	[-6 -3 0 1 0 1 0 1⟩
2376/2375	0.7288	(23*33*11)/(53*19)	[3 3 -3 0 1 0 0 -1⟩
2432/2431	0.7120	(11*13*17)/(27*19)	[-7 0 0 0 1 1 1 -1⟩	Blumeyer comma
2926/2925	0.5918	(2*7*11*19)/(32*52*13)	[1 -2 -2 1 1 -1 0 1⟩
3136/3135	0.5521	(26*72)/(3*5*11*19)	[6 -1 -1 2 -1 0 0 -1⟩		57/56 to 56/55
3250/3249	0.5328	(2*53*13)/(32*192)	[1 -2 3 0 0 1 0 -2⟩
4200/4199	0.4123	(23*3*52*7)/(13*17*19)	[3 1 2 1 0 -1 -1 -1⟩
5776/5775	0.2998	(24*192)/(3*52*7*11)	[4 -1 -2 -1 -1 0 0 2⟩		77/76 to 76/75
5929/5928	0.2920	(72*112)/(23*3*13*19)	[-3 -1 0 2 2 -1 0 -1⟩		78/77 to 77/76
5985/5984	0.2893	(32*5*7*19)/(25*11*17)	[-5 2 1 1 -1 0 -1 1⟩
6175/6174	0.2804	(52*13*19)/(2*32*73)	[-1 -2 2 -3 0 1 0 1⟩
6860/6859	0.2524	(22*5*73)/(193)	[2 0 1 3 0 0 0 -3⟩
10241/10240	0.1691	(72*11*19)/(211*5)	[-11 0 -1 2 1 0 0 1⟩
10830/10829	0.1599	(2*3*5*192)/(72*13*17)	[1 1 1 -2 0 -1 -1 2⟩
12636/12635	0.1370	(22*35*13)/(5*7*192)	[2 5 -1 -1 0 1 0 -2⟩
13377/13376	0.1294	(3*73*13)/(26*11*19)	[-6 1 0 3 -1 1 0 -1⟩
14080/14079	0.1230	(28*5*11)/(3*13*192)	[8 -1 1 0 1 -1 0 -2⟩
14365/14364	0.1205	(5*132*17)/(22*33*7*19)	[-2 -3 1 -1 0 1 1 -1⟩
23409/23408	0.07396	(34*172)/(24*7*11*19)	[-4 4 0 -1 -1 0 1 -1⟩		154/153 to 153/152
27456/27455	0.06306	(26*3*11*17)/(5*172*19)	[6 1 -1 0 1 0 -2 -1⟩
28900/28899	0.05991	(22*52*172)/(32*132*19)	[2 -2 2 0 0 -2 2 -1⟩		171/170 to 170/169
43681/43680	0.03963	(112*192)/(25*3*5*7*13)	[-5 -1 -1 -1 2 -1 0 2⟩		210/209 to 209/208
89376/89375	0.01937	(25*3*72*19)/(54*11*13)	[5 1 -4 2 -1 -1 0 1⟩
104976/104975	0.01649	(24*38)/(52*13*17*19)	[4 8 -2 0 0 0 -1 -1 -1⟩		325/324 to 324/323
165376/165375	0.01047	(29*17*19)/(33*53*72)	[9 -3 -3 -2 0 0 1 1⟩	decimillisma
228096/228095	0.007590	(28*34*11)/(5*74*19)	[8 4 -1 -4 1 0 0 -1⟩
601426/601425	0.002879	(2*72*17*192)/(37*52*11)	[2 -7 -2 2 -1 0 1 2⟩
633556/633555	0.002733	(22*7*113*17)/(33*5*13*192)	[2 -3 -1 1 3 -1 1 -2⟩
709632/709631	0.002440	(210*32*7*11)/(133*17*19)	[10 2 0 1 1 -3 -1 -1⟩
5909761/5909760	0.0002929	(112*132*172)/(28*35*5*19)	[-8 -5 -1 0 2 2 2 -1⟩		2432/2431 to 2431/2430
11859211/11859210	0.0001460	(7*13*194)/(2*34*5*114)	[-1 -4 -1 1 -4 1 0 4⟩
23-limit (complete)
23/22	76.956	23/(2*11)		greater vicesimotertial semitone
24/23	73.681	(23*3)/23		small vicesimotertial semitone
46/45	38.051	(2*23)/(32*5)		vicesimotertial 1/5-tone
69/68	25.274	(3*23)/(22*17)		large vicesimotertial 1/8-tone
70/69	24.910	(2*5*7)/(3*23)		small vicesimotertial 1/8-tone
92/91	18.921	(22*23)/(7*13)
115/114	15.120	(5*23)/(2*3*19)
161/160	10.787	(7*23)/(25*5)
162/161	10.720	(2*34)/(7*23)
208/207	8.3433	(24*13)/(32*23)
231/230	7.5108	(3*7*11)/(2*5*23)
253/252	6.8564	(11*23)/((2*3)2*7)
276/275	6.2840	(22*3*23)/(52*11)
300/299	5.7804	((2*5)2*3)/(13*23)
323/322	5.3682	(17*19)/(2*7*23)
391/390	4.4334	(17*23)/(2*3*5*13)
392/391	4.4221	(23*7*7)/(17*23)
460/459	3.7676	(22*5*23)/(33*17)
484/483	3.5806	(2*11)2/(3*7*23)			23/22 to 22/21
507/506	3.4180	(3*132)/(2*11*23)
529/528	3.2758	232/(24*3*11)			24/23 to 23/22
576/575	3.0082	(26*32)/(23*52)			25/24 to 24/23
736/735	2.3538	(25*23)/(3*5*72)
760/759	2.2794	(23*5*19)/(3*11*23)
875/874	1.9797	(53*7)/(2*19*23)
897/896	1.9311	(3*13*23)/(27*7)
1105/1104	1.5674	(5*13*17)/(24*3*23)
1197/1196	1.4469	(32*17*19)/(22*13*23)
1288/1287	1.3446	(23*7*23)/(32*11*13)
1496/1495	1.1576	(23*11*17)/(5*13*23)
1863/1862	0.92952	(34*23)/(2*72*19)
2024/2023	0.85556	(23*11*23)/(7*172)
2025/2024	0.85514	(34*52)/(23*11*23)			46/45 to 45/44
2185/2184	0.79251	(5*19*23)/(23*3*7*13)
2300/2299	0.75287	(22*52*23)/(112*19)
2646/2645	0.65441	(2*33*72)/(5*232)
2737/2736	0.63265	(7*17*23)/(24*32*19)
3060/3059	0.56586	(22*32*5*17)/(7*19*23)
3381/3380	0.51212	(3*72*23)/(22*5*132)
3520/3519	0.49190	(26*5*11)/(32*17*23)
3888/3887	0.44533	(24*35)/(132*23)
4693/4692	0.36893	(13*192)/(22*3*17*23)
4761/4760	0.36367	(32*232)/(23*5*7*17)			70/69 to 69/68
5083/5082	0.34063	(13*17*23)/(2*3*7*112)
7866/7865	0.22010	(2*32*19*23)/(5*112*13)
8281/8280	0.20907	(72*132)/(23*32*5*23)			92/91 to 91/90
8625/8624	0.20073	(3*53*23)/(24*72*11)
10626/10625	0.16293	(2*3*7*11*23)/(54*17)
11271/11270	0.15361	(3*13*172)/(2*5*72*23)
11662/11661	0.14846	(2*73*17)/(3*132*23)
12168/12167	0.14228	(23*32*132)/(233)
16929/16928	0.10227	(34*11*19)/(25*232)
19551/19550	0.088552	(3*73*19)/(2*52*17*23)
21505/21504	0.080506	(5*11*17*23)/(210*3*7)
21736/21735	0.079650	(23*11*13*19)/(33*5*7*23)
23276/23275	0.074380	(22*11*232)/(52*72*19)
25025/25024	0.069182	(52*7*11*13)/(26*17*23)
25921/25920	0.066790	(72*232)/(26*34*5)			162/161 to 161/160
43264/43263	0.040016	(28*132)/(32*11*19*23)			209/208 to 208/207
52326/52325	0.033086	(2*34*17*19)/(52*7*13*23)
71875/71874	0.024087	(55*23)/(2*33*113)
75141/75140	0.023040	(33*112*23)/(22*5*13*172)
76545/76544	0.022617	(37*5*7)/(28*13*23)
104329/104328	0.016594	(172*192)/(23*34*7*23)			324/323 to 323/322
122452/122451	0.014138	(22*113*23)/(3*74*17)
126225/126224	0.013716	(33*52*11*17)/(24*73*23)
152881/152880	0.011324	(172*232)/(24*3*5*72*13)			392/391 to 391/390
202125/202124	0.0085652	(3*53*72*11)/(22*133*23)
264385/264384	0.0065482	(5*112*19*23)/(26*35*17)
282625/282624	0.0061256	(53*7*17*19)/(212*3*23)
328510/328509	0.0052700	(2*5*7*13*192)/(33*233)
2023425/2023424	0.00085560	(32*52*17*232)/(213*13*19)
4096576/4096575	0.00042261	(26*112*232)/(34*52*7*172)			2025/2024 to 2024/2023
5142501/5142500	0.00033665	(33*72*132*23)/(22*54*112*17)
29-limit (incomplete)
29/28	60.751	29/(22*7)		Large vicesimononal 1/4 tone
30/29	58.692	(2*3*5)/29		Small vicesimononal 1/4 tone
58/57	30.109	(2*29)/(3*19)
88/87	19.786	(23*11)/(3*29)
116/115	14.989	(22*29)/(5*23)
117/116	14.860	(33*13)/(22*29)
145/144	11.981	(5*29)/(24*32)
175/174	9.9211	(52*7)/(2*3*29)
204/203	8.5073
232/231	7.4783
261/260	6.6458
290/289	5.9801
320/319	5.4186
378/377	4.5861
406/405	4.2694
494/493	3.5081
551/550	3.1448
552/551	3.1391
609/608	2.8451
638/637	2.7157
726/725	2.3863
31-limit (incomplete)
31/30	56.767	31/(2*3*5)		large tricesimoprimal 1/4-tone
32/31	54.964	25/31		small tricesimoprimal 1/4-tone, 31st subharmonic
63/62	27.700	(32*7)/(2*31)
93/92	18.716	(3*31)/(22*23)
125/124	13.906	(53)/(22*31)		twizzler
621/620	2.7901	(3³*23)/(2²*5*31)		owowhatsthisma
3969/3968	0.43624	(34*72)/(27*31)		yunzee comma	64/63 to 63/62
37-limit (incomplete)
37/36	47.434	37/(22*32)		Large 37-limit quarter tone, 37th-partial chroma
38/37	46.169	(2*19)/37		Small 37-limit quarter tone
75/74	23.238	(3*52)/(2*37)
41-limit (incomplete)
41/40	42.749	41/(23*5)		Large 41-limit fifth tone
42/41	41.719	(2*3*7)/41		Small 41-limit fifth tone
82/81	21.242	(2*41)/34		41st-partial chroma
43-limit (incomplete)
43/42	40.737	43/(2*3*7)		Large 43-limit fifth tone
44/43	39.800	(22*11)/43		Small 43-limit fifth tone
86/85	20.249	(2*43)/(5*17)
87/86	20.014	(3*29)/(2*43)
129/128	13.473	(3*43)/27		43rd-partial chroma
47-limit (incomplete)
47/46	37.232	47/(2*23)
48/47	36.448	(24*3)/47
94/93	18.516	(2*47)/(3*31)
95/94	18.320	(5*19)/(2*47)
53-limit (incomplete)
53/52	32.977	53/(22*13)
54/53	32.360	(2*33)/53
59-limit (incomplete)
59/58	29.594	59/(2*29)
60/59	29.097	(22*3*5)/59
61-limit (incomplete)
61/60	28.616	61/(22*3*5)
62/61	28.151	(2*31)/61
67-limit (incomplete)
67/66	26.034	67/(2*3*11)
68/67	25.648	(22*17)/67
71-limit (incomplete)
71/70	24.557	71/(2*5*7)
72/71	24.213	(23*32)/71
73-limit (incomplete)
73/72	23.879	73/(23*32)
74/73	23.555	(2*37)/73
79-limit (incomplete)
79/78	22.054	79/(2*3*13)
80/79	21.777	(24*5)/79
83-limit (incomplete)
83/82	20.985	83/(2*41)
84/83	20.734	(22*3*7)/83
89-limit (incomplete)
89/88	19.562	89/(23*11)
90/89	19.344	(2*32*5)/89
97-limit (incomplete)
97/96	17.940	97/(25*3)
98/97	17.756	(2*72)/97
101-limit (incomplete)
101/100	17.226	101/(22*52)
102/101	17.057	(2*3*17)/101
7777/7776	0.223	7*11*101/(25*35)