List of superparticular intervals

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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) 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
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 (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) 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)
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)
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