List of superparticular intervals

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This is a list of superparticular intervals ordered by prime limit. It reaches to the 107-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 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 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 S65
4225/4224 0.40981 (5×13)2/(27×3×11) [-7 -1 2 0 -1 2 Leprechaun comma S66
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 Diasemisma, septendecimal kleisma, octave-reduced 255th subharmonic 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
37180/37179 0.046564 (22×5×11×132)/(37×17) [2 -7 1 0 1 2 -1
194481/194480 0.008902 (3×7)4/(24×5×11×13×17) [-4 4 -1 4 -1 -1 -1 Scintillisma S441
336141/336140 0.005150 (32×133×17)/(22×5×75) [-2 2 -1 -5 0 3 1

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
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 S39
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)/(22×3)3 [-6 -3 0 1 0 1 0 1 Ramanujanisma
2376/2375 0.7288 (23×33×11)/(53×19) [3 3 -3 0 1 0 0 -1
2432/2431 0.7120 (27×19)/(11×13×17) [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 (23×7)2/(3×5×11×19) [6 -1 -1 2 -1 0 0 -1 S56
3250/3249 0.5328 (2×53×13)/(3×19)2 [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 (22×19)2/(3×52×7×11) [4 -1 -2 -1 -1 0 0 2 S76
5929/5928 0.2920 (7×11)2/(23×3×13×19) [-3 -1 0 2 2 -1 0 -1 S77
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 2 1 -1
23409/23408 0.07396 (32×17)2/(24×7×11×19) [-4 4 0 -1 -1 0 1 -1 S153
27456/27455 0.06306 (26×3×11)/(5×172×19) [6 1 -1 0 1 0 -2 -1
28900/28899 0.05991 (2×5×17)2/(32×132×19) [2 -2 2 0 0 -2 2 -1 S170
43681/43680 0.03963 (11×19)2/(25×3×5×7×13) [-5 -1 -1 -1 2 -1 0 2 S209
89376/89375 0.01937 (25×3×72×19)/(54×11×13) [5 1 -4 2 -1 -1 0 1
104976/104975 0.01649 (2×32)4/(52×13×17×19) [4 8 -2 0 0 0 -1 -1 -1 S324
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) [1 -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 Devicisma
709632/709631 0.002440 (210×32×7×11)/(133×17×19) [10 2 0 1 1 -3 -1 -1
5909761/5909760 0.0002929 (11×13×17)2/(28×35×5×19) [-8 -5 -1 0 2 2 2 -1 S2431
11859211/11859210 0.0001460 (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
115/114 15.120 (5×23)/(2×3×19) [-1 -1 1 0 0 0 0 -1 1
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
231/230 7.5108 (3×7×11)/(2×5×23) [-1 1 -1 1 1 0 0 0 -1
253/252 6.8564 (11×23)/((2×3)2×7) [-2 -2 0 -1 1 0 0 0 1
276/275 6.2840 (22×3×23)/(52×11) [2 1 -2 0 -1 0 0 0 1
300/299 5.7804 ((2×5)2×3)/(13×23) [2 1 2 0 0 -1 0 0 -1
323/322 5.3682 (17×19)/(2×7×23) [-1 0 0 -1 0 0 1 1 -1
391/390 4.4334 (17×23)/(2×3×5×13) [-1 -1 -1 0 0 -1 1 0 1
392/391 4.4221 (23×72)/(17×23) [3 0 0 2 0 0 -1 0 -1
460/459 3.7676 (22×5×23)/(33×17) [2 -3 1 0 0 0 -1 0 1
484/483 3.5806 (2×11)2/(3×7×23) [2 -1 0 -1 2 0 0 0 -1 S22
507/506 3.4180 (3×132)/(2×11×23) [-1 1 0 0 -1 2 0 0 -1
529/528 3.2758 232/(24×3×11) [-4 -1 0 0 -1 0 0 0 2 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
760/759 2.2794 (23×5×19)/(3×11×23) [3 -1 1 0 -1 0 0 1 -1
875/874 1.9797 (53×7)/(2×19×23) [-1 0 3 1 0 0 0 -1 -1
897/896 1.9311 (3×13×23)/(27×7) [-7 1 0 -1 0 1 0 0 1
1105/1104 1.5674 (5×13×17)/(24×3×23) [-4 -1 1 0 0 1 1 0 -1
1197/1196 1.4469 (32×17×19)/(22×13×23) [-2 2 0 0 0 -1 1 1 -1
1288/1287 1.3446 (23×7×23)/(32×11×13) [3 -2 0 1 -1 -1 0 0 1
1496/1495 1.1576 (23×11×17)/(5×13×23) [3 0 -1 0 1 -1 1 0 -1
1863/1862 0.92952 (34×23)/(2×72×19) [-1 4 0 -2 0 0 0 -1 1
2024/2023 0.85556 (23×11×23)/(7×172) [3 0 0 -1 1 0 -2 0 1
2025/2024 0.85514 (32×5)2/(23×11×23) [-3 4 2 0 -1 0 0 0 -1 S45
2185/2184 0.79251 (5×19×23)/(23×3×7×13) [-3 -1 1 -1 0 -1 0 1 1
2300/2299 0.75287 (22×52×23)/(112×19) [2 0 2 0 -2 0 0 -1 1
2646/2645 0.65441 (2×33×72)/(5×232) [1 3 -1 2 0 0 0 0 -2
2737/2736 0.63265 (7×17×23)/(24×32×19) [-4 -2 0 1 0 0 1 -1 1
3060/3059 0.56586 (22×32×5×17)/(7×19×23) [2 2 1 -1 0 0 1 -1 -1
3381/3380 0.51212 (3×72×23)/(22×5×132) [-2 1 -1 2 0 -2 0 0 1
3520/3519 0.49190 (26×5×11)/(32×17×23) [6 -2 1 0 1 0 -1 0 -1
3888/3887 0.44533 (24×35)/(132×23) [4 5 0 0 0 -2 0 0 -1
4693/4692 0.36893 (13×192)/(22×3×17×23) [-2 -1 0 0 0 1 -1 2 -1
4761/4760 0.36367 (3×23)2/(23×5×7×17) [-3 2 -1 -1 0 0 -1 0 2 S69
5083/5082 0.34063 (13×17×23)/(2×3×7×112) [-1 -1 0 -1 -2 1 1 0 1
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
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 Large vicesimononal 1/4-tone
30/29 58.692 (2×3×5)/29 2.3.5.29 [1 1 1 -1 Small vicesimononal 1/4-tone
58/57 30.109 (2×29)/(3×19) 2.3.19.29 [1 -1 -1 1
88/87 19.786 (23×11)/(3×29) 2.3.11.29 [3 -1 1 -1
116/115 14.989 (22×29)/(5×23) 2.5.23.29 [2 -1 -1 1
117/116 14.860 (33×13)/(22×29) 2.3.13.29 [-2 3 1 -1
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
204/203 8.5073 (22×3×17)/(7×29) 2.3.7.17.29 [2 1 -1 1 -1
232/231 7.4783 (23×29)/(3×7×11) 2.3.7.11.29 [3 -1 -1 -1 1
261/260 6.6458 (32×29)/(22×5×13) 2.3.5.13.29 [-2 2 -1 -1 1
290/289 5.9801 (2×5×29)/172 2.5.17.29 [1 1 -2 1
320/319 5.4186 (26×5)/(11×29) 2.5.11.29 [6 1 -1 -1
378/377 4.5861 (2×33×7)/(13×29) 2.3.7.13.29 [1 3 1 -1 -1
406/405 4.2694 (2×7×29)/(34×5) 2.3.5.7.29 [1 -4 -1 1 1
494/493 3.5081 (2×13×19)/(17×29) 2.13.17.19.29 [1 1 -1 1 -1
551/550 3.1448 (19×29)/(2×52×11) 2.5.11.19.29 [-1 -2 -1 1 1
552/551 3.1391 (23×3×23)/(19×29) 2.3.19.23.29 [3 1 -1 1 -1 Marmosarubra
609/608 2.8451 (3×7×19)/(25×29) 2.3.7.19.29 [-5 1 1 1 -1
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 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 S28
841/840 2.0598 292/(23×3×5×7) 2.3.5.7.29 [-3 -1 -1 -1 2 S29
1015/1014 1.7065 2.3.5.7.13.29 [-1 -1 1 1 -2 1
1045/1044 1.6575 2.3.5.11.19.29 [-2 -2 1 1 1 -1
1276/1275 1.3573 2.3.5.11.17.29 [2 -1 -2 1 -1 1
1450/1449 1.1944 2.3.5.7.23.29 [1 -2 2 -1 -1 1
1596/1595 1.0851 2.3.5.7.11.19.29 [2 1 -1 1 -1 1 -1
1625/1624 1.0657 2.5.7.13.29 [-3 3 -1 1 -1
1683/1682 1.0290 2.3.11.17.29 [-1 2 1 1 -2
2001/2000 0.86540 2.3.5.23.29 [-4 1 -3 1 1
2002/2001 0.86497 2.3.7.11.13.23.29 [1 -1 1 1 1 -1 -1
2176/2175 0.79579 2.3.5.17.29 [7 -1 -2 1 -1
2205/2204 0.78532 2.3.5.7.19.29 [-2 2 1 2 -1 -1
2262/2261 0.76552 2.3.7.13.17.19.29 [1 1 -1 1 -1 -1 1
2465/2464 0.70247 2.5.7.11.17.29 [-5 1 -1 -1 1 1}
2640/2639 0.65589 2.3.5.7.11.13.29 [4 1 1 -1 1 -1 -1
2755/2754 0.62851 2.3.5.17.19.29 [-1 -4 1 -1 1 1
2784/2783 0.62196 2.3.11.23.29 [5 1 -2 -1 1
3249/3248 0.53293 2.3.7.19.29 [-4 2 -1 2 -1 S57
3451/3450 0.50173 2.3.5.7.17.23.29 [-1 -1 -2 1 1 -1 1
3510/3509 0.49330 2.3.5.11.13.29 [1 3 1 -2 1 -1
4641/4640 0.37307 2.3.5.7.13.17.29 [-5 1 -1 1 1 1 -1
4785/4784 0.36184 2.3.5.11.13.23.29 [-4 1 1 1 -1 -1 1
4901/4900 0.35328 2.5.7.13.29 [-2 -2 -2 2 1
5104/5103 0.33922 2.3.7.11.29 [4 -6 -1 1 1
5888/5887 0.29405 2.7.23.29 [8 -1 1 -2
5916/5915 0.29266 2.3.5.7.13.17.29 [2 1 -1 -1 -2 1 1
6670/6669 0.25957 2.3.5.13.19.23.29 [1 -3 1 -1 -1 1 1
7106/7105 0.24365 2.5.7.11.17.19.29 [1 -1 -2 1 1 1 -1
7425/7424 0.23318 2.3.5.11.29 [-8 3 2 1 -1
7889/7888 0.21946 2.7.17.23.29 [-4 3 -1 1 -1
8671/8670 0.19967 2.3.5.13.17.23.29 [-1 -1 -1 1 -2 1 1
9802/9801 0.17663 2.3.11.13.29 [1 -4 -2 2 1
10557/10556 0.16400 2.3.7.13.17.23.29 [-2 3 -1 -1 1 1 -1
11340/11339 0.15267 2.3.5.7.17.23.29 [2 4 1 1 -1 -1 -1
12006/12005 0.14420 2.3.5.7.23.29 [1 2 -1 -4 1 1
12673/12672 0.13661 2.3.11.19.23.29 [-7 -2 -1 1 1 1
13225/13224 0.13091 2.3.5.19.23.29 [-3 -1 2 -1 2 -1 S115
13311/13310 0.13007 2.3.5.11.17.29 [-1 3 -1 -3 1 1
13312/13311 0.13006 2.3.13.17.29 [10 -3 1 -1 -1
13456/13455 0.12866 2.3.5.13.23.29 [4 -2 -1 -1 -1 2 S116
19228/19227 0.090039 2.3.11.13.17.19.23.29 [2 -1 1 -1 -1 1 1 -1
20736/20735 0.083491 2.3.5.11.13.29 [8 4 -1 -1 -1 -1 S144
23751/23750 0.072893 2.3.5.7.13.19.29 [-1 2 -4 1 1 -1 1
24795/24794 0.069823 2.3.5.7.11.19.23.29 [-1 2 1 -2 -1 1 -1 1
25840/25839 0.067000 2.3.5.11.17.19.29 [4 -4 1 -1 1 1 -1
27000/26999 0.064121 2.3.5.7.19.29 [3 3 3 -2 -1 -1
30625/30624 0.056531 2.3.5.7.11.20 [-5 -1 4 2 -1 -1 S175
30856/30855 0.056108 2.3.5.7.11.17.19.29 [3 -1 -1 1 -2 -1 1 1
35322/35321 0.049014 2.3.7.11.13.19.29 [1 1 1 -1 -2 -1 2
47125/47124 0.036737 2.3.5.7.11.13.17.29 [-2 -2 3 -1 -1 1 -1 1
53361/53360 0.032444 2.3.5.7.11.23.29 [-4 2 -1 2 2 -1 -1 S231
72501/72500 0.023879 2.3.5.11.13.29 [-2 1 -4 1 3 -1
83521/83520 0.020728 2.3.5.17.29 [-6 -2 -1 4 -1 S289
87465/87464 0.019794 2.3.5.7.13.17.29 [-3 1 1 3 -1 1 -2
136851/136850 0.012651 2.3.5.7.11.13.17.23.29 [-1 1 -2 -1 2 1 -1 -1 1
158950/158949 0.010892 2.3.5.7.11.17.29 [1 -3 2 -1 1 2 -2
166635/166634 0.010389 2.3.5.7.13.17.23.29 [-1 2 1 1 -2 -1 2 -1
168751/168750 0.010259 2.3.5.11.23.29 [-1 -3 -5 1 2 1
176001/176000 0.0098365 2.3.5.7.11.17.29 [-7 1 -3 1 -1 2 1
176176/176175 0.0098268 2.3.5.7.11.13.29 [4 -5 -2 1 2 1 -1
184093/184092 0.0094042 2.3.7.13.17.23.29 [-2 -1 2 1 2 -2 -1
240787/240786 0.0071899 2.3.7.13.19.23.29 [-1 -3 -3 -1 2 1 1
244036/244035 0.0070942 2.3.5.11.13.17.19.29 [2 -2 -1 -1 2 -1 2 -1 S494
303601/303600 0.0057023 2.3.5.11.19.23.29 [-4 -1 -2 -1 2 -1 2 S551
410670/410669 0.0042156 2.3.5.7.13.17.29 [1 5 1 -2 2 -2 -1
418761/418760 0.0041342 2.3.5.7.17.19.23.29 [-3 2 -1 1 2 -2 1 -1
613089/613088 0.0028238 2.3.7.17.23.29 [-5 6 -2 -1 -1 2 S783
949026/949025 0.0018242 2.3.5.7.11.13.17.23.29 [1 1 -2 -1 -1 1 -1 3 -1
1163800/1163799 0.0014876 2.3.5.7.11.13.23.29 [3 -2 2 -3 1 -1 2 -1
1235169/1235168 0.0014016 2.3.11.13.17.23.29 [-5 5 -3 1 1 1 -1
1243840/1243839 0.0013918 2.3.5.13.17.23.29 [6 -1 1 2 -1 1 -3
1625625/1625624 0.0010650 2.3.5.7.11.13.17.29 [-3 2 4 -2 -1 -1 2 -1 S1275
1852201/1852200 0.00093469 2.3.5.7.13.17.29 [-3 -3 -2 -3 1 3 1
2697696/2697695 0.00064175 2.3.5.7.11.13.17.19.29 [5 2 -1 -3 -2 -1 1 1 1
4004001/4004000 0.00043238 2.3.5.7.11.13.23.29 [-5 2 -3 -1 -1 -1 2 2 S2001
4090625/4090624 0.00042322 2.5.7.11.17.19.29 [-8 5 1 1 1 -1 -2
8268800/8268799 0.00020937 2.5.7.11.17.19.23.29 [10 2 -2 -1 1 1 -2 -1
10556001/10556000 0.00016400 2.3.5.7.13.19.29 [-5 4 -3 -1 -1 4 -1 S3249
18085705/18085704 9.5724×10-5 2.3.5.7.11.13.17.23.29 [-3 -1 1 -3 1 -3 1 1 2
96059601/96059600 1.8022×10-5 2.3.5.7.11.13.29 [-4 8 -2 -2 4 -2 -1 S9801
177182721/177182720 9.7709×10-6 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
900/899 1.9247 (2×3×5)2/(29×31) 2.3.5.29.31 [2 2 2 -1 -1 S30
961/960 1.8024 312/(26×3×5) 2.3.5.31 [-6 -1 -1 2 S31
1024/1023 1.9247 210/(3×11×31) 2.3.11.31 [10 -1 -1 -1 S32
3969/3968 0.43624 (32×7)2/(27×31) 2.3.7.31 [-7 4 2 -1 Yunzee comma S63

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
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
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
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

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
87/86 20.014 (3×29)/(2×43) 2.3.29.43 [-1 1 1 -1
129/128 13.473 (3×43)/27 2.3.43 [-7 1 1 43rd-partial chroma
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
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
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
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
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

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

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