List of superparticular intervals

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This is a list of superparticular intervals ordered by prime limit. It reaches to the 127-limit and is complete up to the 29-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[1]
2/1 1200.000 2/1 [1⟩ Octave, duple

3-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
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 or harmonic ninth S3

5-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
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[1]
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 (22×32)/(5×7) [2 2 -1 -1⟩ Septimal 1/4-tone, septimal diesis S6
49/48 35.697 72/(24×3) [-4 -1 0 2⟩ Slendro diesis, large septimal diesis, large septimal 1/6-tone S7
50/49 34.976 2×(5/7)2 [1 0 2 -2⟩ Jubilisma, tritonic diesis, small septimal diesis, small septimal 1/6-tone
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[1]
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
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/(24×32×7) [-4 -3 2 -1 2⟩ Lehmerisma S55
9801/9800 0.17665 (11/(5×7))2×34/23 [-3 4 -2 -2 2⟩ Kalisma, Gauss comma S99

13-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
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 (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⟩ 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[1]
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⟩ Diatonisma, 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⟩ Char comma, charisma, 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 134/(24×3×5×7×17) [-4 -1 -1 -1 0 4 -1⟩ Neuseisma 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[1]
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 (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⟩ Buddhisma
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 (23×33×11)/(53×19) [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)/(32×52×13) [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⟩ 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⟩
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⟩
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 (32×17)2/(24×7×11×19) [-4 4 0 -1 -1 0 1 -1⟩ S153
27456/27455 0.063056 (26×3×11)/(5×172×19) [6 1 -1 0 1 0 -2 -1⟩
28900/28899 0.059905 (2×5×17)2/(32×132×19) [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 0 -1 -1 -1⟩ S324
165376/165375 0.010469 (29×17×19)/(33×53×72) [9 -3 -3 -2 0 0 1 1⟩ Decimillisma
228096/228095 0.0075900 (28×34×11)/(5×74×19) [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 (7×13×194)/(2×34×5×114) [-1 -4 -1 1 -4 1 0 4⟩

23-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
23/22 76.956 23/(2×11) [-1 0 0 0 -1 0 0 0 1⟩ Greater 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)2/(23×52) [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⟩ Rhodesisma
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⟩ Insincere comma
2025/2024 0.85514 (32×5)2/(23×11×23) [-3 4 2 0 -1 0 0 0 -1⟩ Fokkerisma 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 (22×52×23)/(112×19) [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
2737/2736 0.63265 (7×17×23)/(24×32×19) [-4 -2 0 1 0 0 1 -1 1⟩ Kotkisma
3060/3059 0.56586 (22×32×5×17)/(7×19×23) [2 2 1 -1 0 0 1 -1 -1⟩ Vicious comma
3381/3380 0.51212 (3×72×23)/(22×5×132) [-2 1 -1 2 0 -2 0 0 1⟩ Seminaiadvice comma
3520/3519 0.49190 (26×5×11)/(32×17×23) [6 -2 1 0 1 0 -1 0 -1⟩ Vicedim comma
3888/3887 0.44533 (24×35)/(132×23) [4 5 0 0 0 -2 0 0 -1⟩ Vicetride comma
4693/4692 0.36893 (13×192)/(22×3×17×23) [-2 -1 0 0 0 1 -1 2 -1⟩ Viceaug comma
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⟩
10626/10625 0.16293 (2×3×7×11×23)/(54×17) [1 1 -4 1 1 0 -1 0 1⟩
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 0 0 3 0 -2 1 0 -1⟩
12168/12167 0.14228 (23×32×132)/233 [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 (22×11×232)/(52×72×19) [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⟩
25921/25920 0.066790 (7×23)2/(26×34×5) [-6 -4 -1 2 0 0 0 0 2⟩ 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)/(2×33×113) [-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 -1 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 0 -3⟩
2023425/2023424 0.00085560 (32×52×17×232)/(213×13×19) [-13 2 2 0 0 -1 1 -1 2⟩
4096576/4096575 0.00042261 (23×11×23)2/(34×52×7×172) [6 -4 -2 -1 2 0 -2 0 2⟩ S2024
5142501/5142500 0.00033665 (33×72×132×23)/(22×54×112×17) [-2 3 -4 2 -2 2 -1 0 1⟩

29-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
29/28 60.751 29/(22×7) 2.7.29 [-2 -1 1⟩ Vicesimononal thirdtone, vicesimononal subchroma, large vicesimononal quartertone, large vicesimononal 2/7-tone
30/29 58.692 (2×3×5)/29 2.3.5.29 [1 1 1 -1⟩ Small vicesimononal quartertone, small vicesimononal 2/7-tone
58/57 30.109 (2×29)/(3×19) 2.3.19.29 [1 -1 -1 1⟩ Vicesimononal 1/7-tone
88/87 19.786 (23×11)/(3×29) 2.3.11.29 [3 -1 1 -1⟩ Vicesimononal 1/10-tone
116/115 14.989 (22×29)/(5×23) 2.5.23.29 [2 -1 -1 1⟩ Sironisma
117/116 14.860 (32×13)/(22×29) 2.3.13.29 [-2 2 1 -1⟩ Lomisma
145/144 11.981 (5×29)/(22×3)2 2.3.5.29 [-4 -2 1 1⟩ 29th-partial chroma
175/174 9.9211 (52×7)/(2×3×29) 2.3.5.7.29 [-1 -1 2 1 -1⟩ Major chthonovinema
204/203 8.5073 (22×3×17)/(7×29) 2.3.7.17.29 [2 1 -1 1 -1⟩ Kallistisma
232/231 7.4783 (23×29)/(3×7×11) 2.3.7.11.29 [3 -1 -1 -1 1⟩ Major paravinema
261/260 6.6458 (32×29)/(22×5×13) 2.3.5.13.29 [-2 2 -1 -1 1⟩ Major vinetonema
290/289 5.9801 (2×5×29)/172 2.5.17.29 [1 1 -2 1⟩ Brunisma
320/319 5.4186 (26×5)/(11×29) 2.5.11.29 [6 1 -1 -1⟩ Minor paravinema
378/377 4.5861 (2×33×7)/(13×29) 2.3.7.13.29 [1 3 1 -1 -1⟩ Major semivinema
406/405 4.2694 (2×7×29)/(34×5) 2.3.5.7.29 [1 -4 -1 1 1⟩ Minor semivinema
494/493 3.5081 (2×13×19)/(17×29) 2.13.17.19.29 [1 1 -1 1 -1⟩ Minor vinetonema
551/550 3.1448 (19×29)/(2×52×11) 2.5.11.19.29 [-1 -2 -1 1 1⟩ Minor chthonovinema
552/551 3.1391 (23×3×23)/(19×29) 2.3.19.23.29 [3 1 -1 1 -1⟩ Marmosarubra
609/608 2.8451 (3×7×29)/(25×19) 2.3.7.19.29 [-5 1 1 -1 1⟩ Vineyard comma
638/637 2.7157 (2×11×29)/(72×13) 2.7.11.13.29 [1 -2 1 -1 1⟩
726/725 2.3863 (2×3×112)/(52×29) 2.3.5.11.29 [1 1 -2 2 -2⟩
783/782 2.2124 (33×29)/(2×17×23) 2.3.17.23.29 [-1 3 -1 -1 1⟩
784/783 2.2096 (22×7)2/(33×29) 2.3.7.29 [4 -3 2 -1⟩ Biminorisma, Spoogalactic comma S28
841/840 2.0598 292/(23×3×5×7) 2.3.5.7.29 [-3 -1 -1 -1 2⟩ Arabellisma S29
1015/1014 1.7065 (5×7×29)/(2×3×132) 2.3.5.7.13.29 [-1 -1 1 1 -2 1⟩
1045/1044 1.6575 (5×11×19)/((2×3)2×29) 2.3.5.11.19.29 [-2 -2 1 1 1 -1⟩
1276/1275 1.3573 (22×11×29)/(3×52×17) 2.3.5.11.17.29 [2 -1 -2 1 -1 1⟩
1450/1449 1.1944 (2×52×29)/(32×7×23) 2.3.5.7.23.29 [1 -2 2 -1 -1 1⟩
1596/1595 1.0851 (22×3×7×19)/(5×11×29) 2.3.5.7.11.19.29 [2 1 -1 1 -1 1 -1⟩
1625/1624 1.0657 (53×13)/(23×7×29) 2.5.7.13.29 [-3 3 -1 1 -1⟩
1683/1682 1.0290 (32×11×17)/(2×292) 2.3.11.17.29 [-1 2 1 1 -2⟩
2001/2000 0.86540 (3×23×29)/(24×53) 2.3.5.23.29 [-4 1 -3 1 1⟩
2002/2001 0.86497 (2×7×11×13)/(3×23×29) 2.3.7.11.13.23.29 [1 -1 1 1 1 -1 -1⟩
2176/2175 0.79579 (27×17)/(3×52×29) 2.3.5.17.29 [7 -1 -2 1 -1⟩
2205/2204 0.78532 ((3×7)2×5)/(22×19×29) 2.3.5.7.19.29 [-2 2 1 2 -1 -1⟩
2262/2261 0.76552 (2×3×13×29)/(7×17×19) 2.3.7.13.17.19.29 [1 1 -1 1 -1 -1 1⟩
2465/2464 0.70247 (5×17×29)/(25×7×11) 2.5.7.11.17.29 [-5 1 -1 -1 1 1⟩
2640/2639 0.65589 (24×3×5×11)/(7×13×29) 2.3.5.7.11.13.29 [4 1 1 -1 1 -1 -1⟩
2755/2754 0.62851 (5×19×29)/(2×34×17) 2.3.5.17.19.29 [-1 -4 1 -1 1 1⟩
2784/2783 0.62196 (25×3×29)/(112×23) 2.3.11.23.29 [5 1 -2 -1 1⟩
3249/3248 0.53293 (3×19)2/(24×7×29) 2.3.7.19.29 [-4 2 -1 2 -1⟩ S57
3451/3450 0.50173 (7×17×29)/(2×3×52×23) 2.3.5.7.17.23.29 [-1 -1 -2 1 1 -1 1⟩
3510/3509 0.49330 (2×33×5×13)/(112×29) 2.3.5.11.13.29 [1 3 1 -2 1 -1⟩
4641/4640 0.37307 (3×7×13×17)/(25×5×29) 2.3.5.7.13.17.29 [-5 1 -1 1 1 1 -1⟩
4785/4784 0.36184 (3×5×11×29)/(25×13×23) 2.3.5.11.13.23.29 [-4 1 1 1 -1 -1 1⟩
4901/4900 0.35328 (13/(2×5×7))2×29 2.5.7.13.29 [-2 -2 -2 2 1⟩ Large grapevine comma
5104/5103 0.33922 (24×11×29)/(36×7) 2.3.7.11.29 [4 -6 -1 1 1⟩
5888/5887 0.29405 (28×23)/(7×292) 2.7.23.29 [8 -1 1 -2⟩
5916/5915 0.29266 (22×3×17×29)/(5×7×132) 2.3.5.7.13.17.29 [2 1 -1 -1 -2 1 1⟩
6670/6669 0.25957 (2×5×23×29)/(33×13×19) 2.3.5.13.19.23.29 [1 -3 1 -1 -1 1 1⟩
7106/7105 0.24365 (2×11×17×19)/(5×72×29) 2.5.7.11.17.19.29 [1 -1 -2 1 1 1 -1⟩
7425/7424 0.23318 (33×52×11)/(28×29) 2.3.5.11.29 [-8 3 2 1 -1⟩ Small grapevine comma
7889/7888 0.21946 (73×23)/(24×17×29) 2.7.17.23.29 [-4 3 -1 1 -1⟩
8671/8670 0.19967 (13×23×29)/(2×3×5×172) 2.3.5.13.17.23.29 [-1 -1 -1 1 -2 1 1⟩
9802/9801 0.17663 (2×132×29)/(32×11)2 2.3.11.13.29 [1 -4 -2 2 1⟩
10557/10556 0.16400 (33×17×23)/(22×7×13×29) 2.3.7.13.17.23.29 [-2 3 -1 -1 1 1 -1⟩
11340/11339 0.15267 (22×34×5×7)/(17×23×29) 2.3.5.7.17.23.29 [2 4 1 1 -1 -1 -1⟩
12006/12005 0.14420 (2×32×23×29)/(5×74) 2.3.5.7.23.29 [1 2 -1 -4 1 1⟩ Uma, umic comma
12673/12672 0.13661 (19×23×29)/(27×32×11) 2.3.11.19.23.29 [-7 -2 -1 1 1 1⟩
13225/13224 0.13091 (5×23)2/(23×3×19×29) 2.3.5.19.23.29 [-3 -1 2 -1 2 -1⟩ S115
13311/13310 0.13007 (33×17×29)/(2×5×113) 2.3.5.11.17.29 [-1 3 -1 -3 1 1⟩
13312/13311 0.13006 (210×13)/(33×17×29) 2.3.13.17.29 [10 -3 1 -1 -1⟩
13456/13455 0.12866 (22×29)2/(32×5×13×23) 2.3.5.13.23.29 [4 -2 -1 -1 -1 2⟩ S116
19228/19227 0.090039 (22×11×19×23)/(3×13×17×29) 2.3.11.13.17.19.23.29 [2 -1 1 -1 -1 1 1 -1⟩
20736/20735 0.083491 (22×3)4/(5×11×13×29) 2.3.5.11.13.29 [8 4 -1 -1 -1 -1⟩ S144
23751/23750 0.072893 (32×7×13×29)/(2×54×19) 2.3.5.7.13.19.29 [-1 2 -4 1 1 -1 1⟩
24795/24794 0.069823 (32×5×19×29)/(2×72×11×23) 2.3.5.7.11.19.23.29 [-1 2 1 -2 -1 1 -1 1⟩
25840/25839 0.067000 (24×5×17×19)/(34×11×29) 2.3.5.11.17.19.29 [4 -4 1 -1 1 1 -1⟩
27000/26999 0.064121 (2×3×5)3/(72×19×29) 2.3.5.7.19.29 [3 3 3 -2 -1 -1⟩
30625/30624 0.056531 (52×7)2/(25×3×11×29) 2.3.5.7.11.29 [-5 -1 4 2 -1 -1⟩ S175
30856/30855 0.056108 (23×7×19×29)/(3×5×112×17) 2.3.5.7.11.17.19.29 [3 -1 -1 1 -2 -1 1 1⟩
35322/35321 0.049014 (2×3×7×292)/(11×132×19) 2.3.7.11.13.19.29 [1 1 1 -1 -2 -1 2⟩
47125/47124 0.036737 (53×13×29)/((2×3)2×7×11×17) 2.3.5.7.11.13.17.29 [-2 -2 3 -1 -1 1 -1 1⟩
53361/53360 0.032444 (3×7×11)2/(24×5×23×29) 2.3.5.7.11.23.29 [-4 2 -1 2 2 -1 -1⟩ S231
72501/72500 0.023879 (3×11×133)/((2×52)2×29) 2.3.5.11.13.29 [-2 1 -4 1 3 -1⟩
83521/83520 0.020728 174/((23×3)2×5×29) 2.3.5.17.29 [-6 -2 -1 4 -1⟩ S289
87465/87464 0.019794 (3×5×73×17)/(23×13×292) 2.3.5.7.13.17.29 [-3 1 1 3 -1 1 -2⟩
136851/136850 0.012651 (3×112×13×29)/(2×52×7×17×23) 2.3.5.7.11.13.17.23.29 [-1 1 -2 -1 2 1 -1 -1 1⟩
158950/158949 0.010892 (2×(5×17)2×11)/(33×7×292) 2.3.5.7.11.17.29 [1 -3 2 -1 1 2 -2⟩
166635/166634 0.010389 ((3×23)2×5×7)/(2×132×17×29) 2.3.5.7.13.17.23.29 [-1 2 1 1 -2 -1 2 -1⟩
168751/168750 0.010259 (11×232×29)/(2×33×55) 2.3.5.11.23.29 [-1 -3 -5 1 2 1⟩
176001/176000 0.0098365 (3×7×172×29)/(27×53×11) 2.3.5.7.11.17.29 [-7 1 -3 1 -1 2 1⟩
176176/176175 0.0098268 (24×7×112×13)/(35×52×29) 2.3.5.7.11.13.29 [4 -5 -2 1 2 1 -1⟩
184093/184092 0.0094042 ((7×17)2×13)/((2×23)2×3×29) 2.3.7.13.17.23.29 [-2 -1 2 1 2 -2 -1⟩
240787/240786 0.0071899 (192×23×29)/(2×(3×7)3×13) 2.3.7.13.19.23.29 [-1 -3 -3 -1 2 1 1⟩
244036/244035 0.0070942 (2×13×19)2/(32×5×11×17×29) 2.3.5.11.13.17.19.29 [2 -2 -1 -1 2 -1 2 -1⟩ S494
303601/303600 0.0057023 (19×29)2/((22×5)2×3×11×23) 2.3.5.11.19.23.29 [-4 -1 -2 -1 2 -1 2⟩ S551
410670/410669 0.0042156 (2×35×5×132)/((7×17)2×29) 2.3.5.7.13.17.29 [1 5 1 -2 2 -2 -1⟩
418761/418760 0.0041342 ((3×17)2×7×23)/(23×5×192×29) 2.3.5.7.17.19.23.29 [-3 2 -1 1 2 -2 1 -1⟩
613089/613088 0.0028238 (33×29)2/(25×72×17×23) 2.3.7.17.23.29 [-5 6 -2 -1 -1 2⟩ S783
949026/949025 0.0018242 (2×3×13×233)/(52×7×11×17×29) 2.3.5.7.11.13.17.23.29 [1 1 -2 -1 -1 1 -1 3 -1⟩
1163800/1163799 0.0014876 (23×(5×23)2×11)/(32×73×13×29) 2.3.5.7.11.13.23.29 [3 -2 2 -3 1 -1 2 -1⟩
1235169/1235168 0.0014016 (35×13×17×23)/(25×113×29) 2.3.11.13.17.23.29 [-5 5 -3 1 1 1 -1⟩
1243840/1243839 0.0013918 ((23×13)2×5×23)/(3×17×293) 2.3.5.13.17.23.29 [6 -1 1 2 -1 1 -3⟩
1625625/1625624 0.0010650 (3×52×17)2/(23×72×11×13×29) 2.3.5.7.11.13.17.29 [-3 2 4 -2 -1 -1 2 -1⟩ S1275
1852201/1852200 0.00093469 (13×173×29)/((2×3×7)3×52) 2.3.5.7.13.17.29 [-3 -3 -2 -3 1 3 1⟩
2697696/2697695 0.00064175 (25×32×17×19×29)/(5×73×112×13) 2.3.5.7.11.13.17.19.29 [5 2 -1 -3 -2 -1 1 1 1⟩
4004001/4004000 0.00043238 (3×23×29)2/(25×53×7×11×13) 2.3.5.7.11.13.23.29 [-5 2 -3 -1 -1 -1 2 2⟩ Odyssey comma S2001
4090625/4090624 0.00042322 (55×7×11×17)/((24×29)2×19) 2.5.7.11.17.19.29 [-8 5 1 1 1 -1 -2⟩
8268800/8268799 0.00020937 ((25×5)2×17×19)/((7×23)2×11×29) 2.5.7.11.17.19.23.29 [10 2 -2 -1 1 1 -2 -1⟩
10556001/10556000 0.00016400 (3×19)4/(25×53×7×13×29) 2.3.5.7.13.19.29 [-5 4 -3 -1 -1 4 -1⟩ S3249
18085705/18085704 9.5724×10-5 (5×11×17×23×292)/((2×7×13)3×3) 2.3.5.7.11.13.17.23.29 [-3 -1 1 -3 1 -3 1 1 2⟩
96059601/96059600 1.8022×10-5 (32×11)4/((22×5×7×13)2×29) 2.3.5.7.11.13.29 [-4 8 -2 -2 4 -2 -1⟩ S9801
177182721/177182720 9.7709×10-6 (33×17×29)2/(211×5×113×13) 2.3.5.11.13.17.29 [-11 6 -1 -3 -1 2 2⟩ S13311

31-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
31/30 56.767 31/(2×3×5) 2.3.5.31 [-1 -1 -1 1⟩ Large tricesimoprimal 1/4-tone
32/31 54.964 25/31 2.31 [5 -1⟩ Small tricesimoprimal 1/4-tone, octave-reduced 31st subharmonic
63/62 27.700 (32×7)/(2×31) 2.3.7.31 [-1 2 1 -1⟩ tricesimoprimal 1/8-tone
93/92 18.716 (3×31)/(22×23) 2.3.23.31 [-2 1 -1 1⟩
125/124 13.906 53/(22×31) 2.5.31 [-2 3 -1⟩ Twizzler
155/154 11.205 (5×31)/(2×7×11) 2.5.7.11.31 [-1 1 -1 -1 1⟩
156/155 11.133 (22×3×13)/(5×31) 2.3.5.13.31 [2 1 -1 1 -1⟩
187/186 9.2828 (11×17)/(2×3×31) 2.3.11.17.31 [-1 -1 1 1 -1⟩
217/216 7.9965 (7×31)/(2×3)3 2.3.7.31 [-3 -3 1 1⟩
248/247 6.9949 (23×31)/(13×19) 2.13.19.31 [3 -1 -1 1⟩
280/279 6.1940 (23×5×7)/(32×31) 2.3.5.7.31 [3 -2 1 1 -1⟩
341/340 5.0844 (11×31)/(22×5×17) 2.5.11.17.31 [-2 -1 1 -1 1⟩
342/341 5.0695 (2×32×19)/(11×31) 2.3.11.19.31 [1 2 -1 1 -1⟩
435/434 3.9844 (3×5×29)/(2×7×31) 2.3.5.7.29.31 [-1 1 1 -1 1 -1⟩
465/464 3.7271 (3×5×31)/(24×29) 2.3.5.29.31 [-4 1 1 -1 -1⟩
496/495 3.4939 (24×31)/(32×5×11) 2.3.5.11.31 [4 -2 -1 -1 1⟩
528/527 3.2820 (24×3×11)/(17×31) 2.3.11.17.31 [4 1 1 -1 -1⟩
589/588 2.9418 (19×31)/(22×3×72) 2.3.7.19.31 [-2 -1 -2 1 1⟩
621/620 2.7901 (33×23)/(22×5×31) 2.3.5.23.31 [-2 3 -1 1 -1⟩ Owowhatsthisma
651/650 2.6614 (3×7×31)/(2×52×13) 2.3.5.7.13.31 [-1 1 -2 1 -1 1⟩
714/713 2.4264 (2×3×7×17)/(23×31) 2.3.7.17.23.31 [1 1 1 1 -1 -1⟩
806/805 2.1493 (2×13×31)/(5×7×23) 2.5.7.13.23.31 [1 -1 -1 1 -1 1⟩
837/836 2.0696 (33×31)/(22×11×19) 2.3.11.19.31 [-2 3 -1 -1 1⟩
868/867 1.9957 (22×7×31)/(3×172) 2.3.7.17.31 [2 -1 1 -2 1⟩
900/899 1.9247 (2×3×5)2/(29×31) 2.3.5.29.31 [2 2 2 -1 -1⟩ S30
931/930 1.8605 (72×19)/(2×3×5×31) 2.3.5.7.19.31 [-1 -1 -1 2 1 -1⟩
961/960 1.8024 312/(26×3×5) 2.3.5.31 [-6 -1 -1 2⟩ S31
1024/1023 1.6915 210/(3×11×31) 2.3.11.31 [10 -1 -1 -1⟩ Kilobyte comma S32
1054/1053 1.6433 (2×17×31)/(34×13) 2.3.13.17.31 [1 -4 -1 1 1⟩
1210/1209 1.4314 (2×5×112)/(3×13×31) 2.3.5.11.13.31 [1 -1 1 2 -1 -1⟩
1365/1364 1.2688 (3×5×7×13)/(22×11×31) 2.3.5.7.11.13.31 [-2 1 1 1 -1 1 -1⟩
1426/1425 1.2145 (2×23×31)/(3×52×19) 2.3.5.19.23.31 [1 -1 -2 -1 1 1⟩
1519/1518 1.1401 (72×31)/(2×3×11×23) 2.3.7.11.23.31 [-1 -1 2 -1 -1 1⟩
1520/1519 1.1393 (24×5×19)/(72×31) 2.5.7.19.31 [4 1 -2 1 -1⟩
1768/1767 0.97948 (23×13×17)/(3×19×31) 2.3.13.17.19.31 [3 -1 1 1 -1 -1⟩
1860/1859 0.93102 (22×3×5×31)/(11×132) 2.3.5.11.13.31 [2 1 1 -1 -2 1⟩
2016/2015 0.85896 (25×32×7)/(5×13×31) 2.3.5.7.13.31 [5 2 -1 1 -1 -1⟩
2233/2232 0.77547 (7×11×29)/(23×32×31) 2.3.7.11.29.31 [-3 -2 1 1 1 -1⟩
2945/2944 0.58796 (5×19×31)/(27×23) 2.5.19.23.31 [-7 1 1 -1 1⟩
2976/2975 0.58183 (25×3×31)/(52×7×17) 2.3.5.7.17.31 [5 1 -2 -1 -1 1⟩
3565/3564 0.48569 (5×23×31)/((2×32)2×11) 2.3.5.11.23.31 [-2 -4 1 -1 1 1⟩
3751/3750 0.46160 (112×31)/(2×3×54) 2.3.5.11.31 [-1 -1 -4 2 1⟩
3876/3875 0.44671 (22×3×17×19)/(53×31) 2.3.5.17.19.31 [2 1 -3 1 1 -1⟩
3969/3968 0.43624 (32×7)2/(27×31) 2.3.7.31 [-7 4 2 -1⟩ Yunzee comma S63
4186/4185 0.41363 (2×7×13×23)/(33×5×31) 2.3.5.7.13.23.31 [1 -3 -1 1 1 1 -1⟩
4960/4959 0.34907 (25×5×31)/(32×19×29) 2.3.5.19.29.31 [5 -2 1 -1 -1 1⟩
4992/4991 0.34684 (27×3×13)/(7×23×31) 2.3.7.13.23.31 [7 1 -1 1 -1 -1⟩
5643/5642 0.30682 (33×11×19)/(2×7×13×31) 2.3.7.11.13.19.31 [-1 3 -1 1 -1 1 -1⟩
5797/5796 0.29867 (11×17×31)/((2×3)2×7×23) 2.3.7.11.17.23.31 [-2 -2 -1 1 1 -1 1⟩
6076/6075 0.28495 ((2×7)2×31)/(35×52) 2.3.5.7.31 [2 -5 -2 2 1⟩
6138/6137 0.28207 (2×32×11×31)/(17×192) 2.3.11.17.19.31 [1 2 1 -1 -2 1⟩
6293/6292 0.27513 (7×29×31)/((2×11)2×13) 2.7.11.13.29.31 [-2 1 -2 -1 1 1⟩
6325/6324 0.27373 (52×11×23)/(22×3×17×31) 2.3.5.11.17.23.31 [-2 -1 2 1 -1 1 -1⟩
6480/6479 0.26719 ((2×3)4×5)/(11×19×31) 2.3.5.11.19.31 [4 4 1 -1 -1 -1⟩
6728/6727 0.25734 (23×292)/(7×312) 2.7.29.31 [3 -1 2 -2⟩
7657/7656 0.22611 (13×19×31)/(23×3×11×29) 2.3.11.13.19.29.31 [-3 -1 -1 1 1 -1 1⟩
7905/7904 0.21902 (3×5×17×31)/(25×13×19) 2.3.5.13.17.19.31 [-5 1 1 -1 1 -1 1⟩
7936/7935 0.21816 (28×31)/(3×5×232) 2.3.5.23.31 [8 -1 -1 -2 1⟩
8092/8091 0.21396 ((2×17)2×7)/(32×29×31) 2.3.7.17.29.31 [2 -2 1 2 -1 -1⟩
8464/8463 0.20455 (22×23)2/(3×7×13×31) 2.3.7.13.23.31 [4 -1 -1 -1 2 -1⟩ S92
29792/29791 0.058112 (25×72×19)/313 2.7.19.31 [5 2 1 -3⟩ Tricetertisma

37-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
37/36 47.434 37/(22×32) 2.3.37 [-2 -2 1⟩ Large tricesimoseptimal 1/4-tone, 37th-partial chroma
38/37 46.169 (2×19)/37 2.19.37 [1 1 -1⟩ Small tricesimoseptimal 1/4-tone
75/74 23.238 (3×52)/(2×37) 2.3.5.37 [-1 1 2 -1⟩
111/110 15.667 (3×37)/(2×5×11) 2.3.5.11.37 [-1 1 -1 -1 1⟩
112/111 15.527 (24×7)/(3×37) 2.3.7.37 [4 -1 1 -1⟩
148/147 11.737 (22×37)/(3×72) 2.3.7.37 [2 -1 -2 1⟩
185/184 9.3834 (5×37)/(23×23) 2.5.23.37 [-3 1 -1 1⟩
186/185 9.3328 (2×3×31)/(5×37) 2.3.5.31.37 [1 1 -1 1 -1⟩
222/221 7.8160 (2×3×37)/(13×17) 2.3.13.17.37 [1 1 -1 -1 1⟩
260/259 6.6714 (22×5×13)/(7×37) 2.5.7.13.37 [2 1 -1 1 -1⟩
297/296 5.8389 (33×11)/(23×37) 2.3.11.37 [-3 3 1 -1⟩
407/406 4.2589 (11×37)/(2×7×29) 2.7.11.29.37 [-1 -1 1 -1 1⟩
408/407 4.2484 (23×3×17)/(11×37) 2.3.11.17.37 [3 1 -1 1 -1⟩
481/480 3.6030 (13×37)/(25×3×5) 2.3.5.13.37 [-5 -1 -1 1 1⟩ Semaphorisma
704/703 2.4609 (26×11)/(19×37) 2.11.19.37 [6 1 -1 -1⟩ Minimyna
1296/1295 1.3363 (2×3)4/(5×7×37) 2.3.5.7.37 [4 4 -1 -1 -1⟩ S36
1369/1368 1.2651 372/(23×32×19) 2.3.19.37 [-3 -2 -1 2⟩ S37
1444/1443 1.1993 (2×19)2/(3×13×37) 2.3.13.19.37 [2 -1 -1 2 -1⟩ S38
1925/1924 0.89958 (52×7×11)/(22×13×37) 2.5.7.11.13.37 [-2 2 1 1 -1 -1⟩ Misericorde
5292/5291 0.32717 (22×33×72)/(11×13×37) 2.3.7.11.13.37 [2 3 2 -1 -1 -1⟩ Bullionisma

41-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
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⟩
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⟩
1025/1024 1.6898 (52×41)/210 2.5.41 [-10 2 1⟩
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
1048576/1048575 0.0016510 220/(3×52×11×31×41) 2.3.5.11.31.41 [20 -1 -2 -1 -1 -1⟩ Megabyte comma S1024

43-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
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⟩
1764/1763 0.98170 (2×3×7)2/(41×43) 2.3.7.41.43 [2 2 2 -1 -1⟩ S42
1849/1848 0.93656 432/(23×3×7×11) 2.3.7.11.43 [-3 -1 -1 -1 2⟩ S43
1936/1935 0.98170 (22×11)2/(32×5×43) 2.3.5.11.43 [4 -2 -1 2 -1⟩ S44

47-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
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⟩
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⟩
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[1]
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[1]
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⟩
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[1]
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[1]
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⟩

71-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
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⟩

73-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
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[1]
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[1]
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[1]
89/88 19.562 89/(23×11) 2.11.89 [-3 -1 1⟩ Sky comma
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[1]
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[1]
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[1]
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[1]
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[1]
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[1]
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⟩

127-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
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⟩

See also

Notes

  1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 Denoted by S-expressions, where sk is defined as (k/(k - 1))/((k + 1)/k). See square superparticular for details.

External links

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