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 19-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)
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
9/8	203.910	32/23	[-3 2⟩	(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)
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
25/24	70.672	52/(23*3)	[-3 -1 2⟩	classic chromatic semitone, chroma, Zarlinian semitone
81/80	21.506	(3/2)4/5	[-4 4 -1⟩	syntonic comma, Didymus comma
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
49/48	35.697	72/(24*3)	[-4 -1 0 2⟩	slendro diesis, large septimal diesis, large septimal 1/6-tone
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
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
2401/2400	0.72120	74/(25*3*52)	[-5 -1 -2 4⟩	breedsma
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
121/120	14.376	112/(23*3*5)	[-3 -1 -1 0 2⟩	biyatisma, undecimal seconds comma
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
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
9801/9800	0.17665	(11/(5*7))2*34/23	[-3 4 -2 -2 2⟩	kalisma, Gauss comma
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
169/168	10.274	132/(23*3*7)	[-3 -1 0 -1 0 2⟩	buzurgisma, dhanvantarisma
196/195	8.8554	(2*7)2/(3*5*13)	[2 -1 -1 2 0 -1⟩	mynucuma
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
676/675	2.5629	(2*13/5)2/33	[2 -3 -2 0 0 2⟩	island comma
729/728	2.3764	(32/2)3/(7*13)	[-3 6 0 -1 0 -1⟩	squbema
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
4225/4224	0.40981	(5*13)2/(27*3*11)	[-7 -1 2 0 -1 2⟩	leprechaun comma
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
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⟩
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
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
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
1156/1155	1.4983	(22*172)/(3*5*7*11)	[2 -1 -1 -1 -1 0 2⟩	septendecimal 1/4-tones comma
1225/1224	1.4138	(52*72)/(23*32*17)	[-3 -2 2 2 0 0 -1⟩	noema
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⟩
2601/2600	0.66573	(32*172)/(23*52*13)	[-3 2 -2 0 0 -1 2⟩	septendecimal 1/6-tones comma
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
28561/28560	0.060616	(134)/(24*3*5*7*17)	[-4 -1 -1 -1 0 4 -1⟩
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
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
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
400/399	4.3335	(24*52)/(3*7*19)	[4 -1 2 -1 0 0 0 -1⟩
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
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	(53*19)/(23*33*11)	[-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⟩
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⟩
5929/5928	0.2920	(72*112)/(23*3*13*19)	[-3 -1 0 2 2 -1 0 -1⟩
5985/5984	0.2893	(25*11*17)/(32*5*7*19)	[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⟩
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⟩
43681/43680	0.03963	(112*192)/(25*3*5*7*13)	[-5 -1 -1 -1 2 -1 0 2⟩
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⟩
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⟩
11859211/11859210	0.0001460	(7*13*194)/(2*34*5*114)	[-1 -4 -1 1 -4 1 0 4⟩
23-limit (incomplete)
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)
507/506	3.4180	(3*132)/(2*11*23)
529/528	3.2758	232/(24*3*11)
576/575	3.0082	(26*32)/(23*52)
29-limit (incomplete)
29/28	60.751	29/(22*7)
30/29	58.692	(2*3*5)/29
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)
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
37-limit (incomplete)
37/36	47.434	37/(22*32)
38/37	46.169	(2*19)/37
75/74	23.238	(3*52)/(2*37)
41-limit (incomplete)
41/40	42.749	41/(23*5)
42/41	41.719	(2*3*7)/41
82/81	21.242	(2*41)/34
43-limit (incomplete)
43/42	40.737	43/(2*3*7)
44/43	39.800	(22*11)/43
86/85	20.249	(2*43)/(5*17)
87/86	20.014	(3*29)/(2*43)
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