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 37-limit.

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

List of superparticular intervals

2-limit

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

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, 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 (2×3)2/(5×7) [2 2 -1 -1⟩ Septimal 1/4-tone, mint comma S6
49/48 35.697 72/(24×3) [-4 -1 0 2⟩ Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma S7
50/49 34.976 2×(5/7)2 [1 0 2 -2⟩ Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma
64/63 27.264 26/(32×7) [6 -2 0 -1⟩ Septimal comma, Archytas' comma S8
126/125 13.795 (2×32×7)/53 [1 2 -3 1⟩ Starling comma, septimal semicomma
225/224 7.7115 (3×5)2/(25×7) [-5 2 2 -1⟩ Marvel comma, septimal kleisma S15
2401/2400 0.72120 74/(25×3×52) [-5 -1 -2 4⟩ Breedsma S49
4375/4374 0.39576 (54×7)/(2×37) [-1 -7 4 1⟩ Ragisma

11-limit

Ratio Cents Factorization Monzo Name(s) Meta[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, cake comma
55/54 31.767 (5×11)/(2×33) [-1 -3 1 0 1⟩ Telepathma, eleventyfive comma,
undecimal diasecundal comma
56/55 31.194 (23×7)/(5×11) [3 0 -1 1 -1⟩ Undecimal tritonic comma, konbini comma
99/98 17.576 (3/7)2×(11/2) [-1 2 0 -2 1⟩ Mothwellsma, small undecimal comma
100/99 17.399 ((2×5)/3)2/11 [2 -2 2 0 -1⟩ Ptolemisma, Ptolemy's comma S10
121/120 14.376 112/(23×3×5) [-3 -1 -1 0 2⟩ Biyatisma, undecimal seconds comma S11
176/175 9.8646 (24×11)/(52×7) [4 0 -2 -1 1⟩ Valinorsma
243/242 7.1391 35/(2×112) [-1 5 0 0 -2⟩ Rastma, neutral thirds comma
385/384 4.5026 (5×7×11)/(27×3) [-7 -1 1 1 1⟩ Keenanisma
441/440 3.9302 (3×7)2/(23×5×11) [-3 2 -1 2 -1⟩ Werckisma, Werckmeister's undecimal septenarian schisma S21
540/539 3.2090 (2/7)2×((33×5)/11) [2 3 1 -2 -1⟩ Swetisma, Swets' comma
3025/3024 0.57240 (5×11)2/(24×33×7) [-4 -3 2 -1 2⟩ Lehmerisma S55
9801/9800 0.17665 ((32×11)/(5×7))2/23 [-3 4 -2 -2 2⟩ Kalisma, Gauss comma S99

13-limit

Ratio Cents Factorization Monzo Name(s) Meta[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 (5/(2×32))2×13 [-2 -4 2 0 0 1⟩ Marveltwin comma
351/350 4.9393 (33×13)/(2×52×7) [-1 3 -2 -1 0 1⟩ Ratwolfsma
352/351 4.9253 (25×11)/(33×13) [5 -3 0 0 1 -1⟩ Major minthma, major gentle comma
364/363 4.7627 (2/11)2×((7×13)/3) [2 -1 0 1 -2 1⟩ Minor minthma, minor gentle comma
625/624 2.7722 (5/2)4/(3×13) [-4 -1 4 0 0 -1⟩ Tunbarsma S25
676/675 2.5629 ((2×13)/5)2/33 [2 -3 -2 0 0 2⟩ Island comma S26
729/728 2.3764 (32/2)3/(7×13) [-3 6 0 -1 0 -1⟩ Squbema S27
1001/1000 1.7304 (7×11×13)/(2×5)3 [-3 0 -3 1 1 1⟩ Sinbadma
1716/1715 1.0092 (22×3×11×13)/(5×73) [2 1 -1 -3 1 1⟩ Lummic comma
2080/2079 0.83252 (25×5×13)/(33×7×11) [5 -3 1 -1 -1 1⟩ Ibnsinma
4096/4095 0.42272 (26/3)2/(5×7×13) [12 -2 -1 -1 0 -1⟩ Schismina, tridecimal schisma S64
4225/4224 0.40981 (5×13)2/(27×3×11) [-7 -1 2 0 -1 2⟩ Leprechaun comma S65
6656/6655 0.26012 (23/11)3×(13/5) [9 0 -1 0 -3 1⟩ Jacobin comma
10648/10647 0.16260 (2×11)3/((3×13)2×7) [3 -2 0 -1 3 -2⟩ Harmonisma
123201/123200 0.014052 (3/2)6×(13/5)2/(7×11) [-6 6 -2 -1 -1 2⟩ Chalmersia S351

17-limit

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

19-limit

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

23-limit

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

29-limit

Main article: List of superparticular intervals/29-limit

31-limit

Main article: List of superparticular intervals/31-limit

37-limit

Main article: List of superparticular intervals/37-limit

41-limit (incomplete)

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

43-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[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⟩
559/558 3.0998 (13×43)/(2×32×31) 2.3.13.31.43 [-1 -2 1 -1 1⟩
560/559 3.0943 (24×5×7)/(13×43) 2.5.7.13.43 [4 1 1 -1 -1⟩
645/644 2.6862 (3×5×43)/(22×7×23) 2.3.5.7.23.43 [-2 1 1 -1 -1 1⟩
646/645 2.6820 (2×17×19)/(3×5×43) 2.3.5.17.19.43 [1 -1 -1 1 1 -1⟩ Kastalisma
775/774 2.2353 (52×31)/(2×32×43) 2.3.5.31.43 [-1 -2 2 1 -1⟩
817/816 2.1203 (19×43)/(24×3×17) 2.3.17.19.43 [-4 -1 -1 1 1⟩
861/860 2.0119 (3×7×41)/(22×5×43) 2.3.5.7.41.43 [-2 1 -1 1 1 -1⟩
903/902 1.9183 (3×7×43)/(2×11×41) 2.3.7.11.41.43 [-1 1 1 -1 -1 1⟩
946/945 1.8310 (2×11×43)/(33×5×7) 2.3.5.7.11.43 [1 -3 -1 -1 1 1⟩
989/988 1.7514 (23×43)/(22×13×19) 2.13.19.23.43 [-2 -1 -1 1 1⟩
990/989 1.7496 (2×32×5×11)/(23×43) 2.3.5.11.23.43 [1 2 1 1 -1 -1⟩ Yerkesisma
1161/1160 1.4918 (33×43)/(23×5×29) 2.3.5.29.43 [-3 3 -1 -1 1⟩
1248/1247 1.3878 (25×3×13)/(29×43) 2.3.13.29.43 [5 1 1 -1 -1⟩
1333/1332 1.2992 (31×43)/((2×3)2×37) 2.3.31.37.43 [-2 -2 1 -1 1⟩ Cevenolisma
1334/1333 1.2983 (2×23×29)/(31×43) 2.23.29.31.43 [1 1 1 -1 -1⟩
1376/1375 1.2586 (25×43)/(53×11) 2.5.11.43 [5 -3 -1 1⟩
1377/1376 1.2577 (34×17)/(25×43) 2.3.17.43 [-5 4 1 -1⟩ Roberbauxisma
1463/1462 1.1838 (7×11×19)/(2×17×43) 2.7.11.17.19.43 [-1 1 1 -1 1 -1⟩ Nordenmarkisma
1548/1547 1.1187 (22×32×43)/(7×13×17) 2.3.7.13.17.43 [2 2 -1 -1 -1 1⟩
1764/1763 0.98170 (2×3×7)2/(41×43) 2.3.7.41.43 [2 2 2 -1 -1⟩ S42
1806/1805 0.95887 (2×3×7×43)/(5×192) 2.3.5.7.19.43 [1 1 -1 1 -2 1⟩
1849/1848 0.93656 432/(23×3×7×11) 2.3.7.11.43 [-3 -1 -1 -1 2⟩ S43
1850/1849 0.93606 (2×52×37)/432 2.5.37.43 [1 2 1 -2⟩
1936/1935 0.89446 (22×11)2/(32×5×43) 2.3.5.11.43 [4 -2 -1 2 -1⟩ S44
2925/2924 0.59198 (32×52×13)/(22×17×43) 2.3.5.13.17.43 [-2 2 2 1 -1 -1⟩ Beattisma
3312/3311 0.52279 (24×32×23)/(7×11×43) 2.3.7.11.23.43 [4 2 -1 -1 1 -1⟩ Pedersenisma
4000/3999 0.43286 (25×53)/(3×31×43) 2.3.5.31.43 [5 -1 3 -1 -1⟩ Hipparchusisma
4301/4300 0.40257 (11×17×23)/(22×52×43) 2.5.11.17.23.43 [-2 -2 1 1 1 -1⟩ Boydenisma
4774/4773 0.36268 (2×7×11×31)/(3×37×43) 2.3.7.11.31.37.43 [1 -1 1 1 1 -1 -1⟩ Hobetsisma
5720/5719 0.30269 (23×5×11×13)/(7×19×43) 2.5.7.11.13.19.43 [3 1 -1 1 1 -1 -1⟩ Halweaverisma
7225/7224 0.23963 (5×17)2/(23×3×7×43) 2.3.5.7.17.43 [-3 -1 2 -1 2 -1⟩ Huntressisma S85
7956/7955 0.21761 (22×32×13×17)/(5×37×43) 2.3.5.13.17.37.43 [2 2 -1 1 1 -1 -1⟩ Yajinisma
9504/9503 0.18217 (25×33×11)/(13×17×43) 2.3.11.13.17.43 [5 3 1 -1 -1 -1⟩ Lionelisma
9633/9632 0.17973 (3×132×19)/(25×7×43) 2.3.7.13.19.43 [-5 1 -1 2 1 -1⟩ Coturisma
10450/10449 0.16568 (2×52×11×19)/(35×43) 2.3.5.11.19.43 [1 -5 2 1 1 -1⟩ Girardisma
10880/10879 0.15912 (27×5×17)/(11×23×43) 2.5.11.17.23.43 [7 1 -1 1 -1 -1⟩ Kaguyisma
17545/17544 0.098677 (5×112×29)/(23×3×17×43) 2.3.5.11.17.29.43 [-3 -1 1 2 -1 1 -1⟩ Manheimisma
27048/27047 0.064007 (23×3×72×23)/(17×37×43) 2.3.7.17.23.37.43 [3 1 2 -1 1 -1 -1⟩ Jangongisma
29241/29240 0.059207 (32×19)2/(23×5×17×43) 2.3.5.17.19.43 [-3 4 -1 -1 2 -1⟩ Locquirecisma S171

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

53-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[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⟩
1121/1120 1.5451 (19×59)/(25×5×7) 2.5.7.19.59 [-5 -1 -1 1 1⟩
1122/1121 1.5437 (2×3×11×17)/(19×59) 2.3.11.17.19.59 [1 1 1 1 -1 -1⟩
3481/3480 0.49741 592/(23×3×5×29) 2.3.5.29.59 [-3 -1 -1 -1 2⟩ S59

61-limit (incomplete)

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

71-limit (incomplete)

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

73-limit (incomplete)

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

97-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[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⟩
226/225 7.6773 (2×113)/(3×5)2 2.3.5.113 [1 -2 -2 1⟩ Reversed marvel comma

127-limit (incomplete)

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

See also

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 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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