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This is a list of [[superparticular]] [[interval]]s ordered by [[prime limit]]. It reaches to the 127-limit and is complete up to the [[31-limit]].
This is a list of [[superparticular]] [[interval]]s ordered by [[prime limit]]. It reaches to the 127-limit and is complete up to the [[37-limit]].


[[Wikipedia: Størmer's theorem|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).
[[Wikipedia: Størmer's theorem|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).
Line 160: Line 160:
| 7<sup>2</sup>/(2<sup>4</sup>×3)
| 7<sup>2</sup>/(2<sup>4</sup>×3)
| {{Monzo| -4 -1 0 2 }}
| {{Monzo| -4 -1 0 2 }}
| Slendro diesis, large septimal diesis, <br>large septimal 1/6-tone
| Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma
| S7
| S7
|-
|-
Line 167: Line 167:
| 2×(5/7)<sup>2</sup>
| 2×(5/7)<sup>2</sup>
| {{Monzo| 1 0 2 -2 }}
| {{Monzo| 1 0 2 -2 }}
| Jubilisma, tritonic diesis, <br>small septimal diesis, small septimal 1/6-tone
| Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma
|  
|  
|-
|-
Line 1,134: Line 1,134:
|  
|  
|-
|-
| 12636/12635
| [[12636/12635]]
| 0.13701
| 0.13701
| (2<sup>2</sup>×3<sup>5</sup>×13)/(5×7×19<sup>2</sup>)
| (2<sup>2</sup>×3<sup>5</sup>×13)/(5×7×19<sup>2</sup>)
| {{Monzo| 2 5 -1 -1 0 1 0 -2 }}
| {{Monzo| 2 5 -1 -1 0 1 0 -2 }}
|  
| Padriellisma
|  
|  
|-
|-
Line 1,456: Line 1,456:
| (3<sup>2</sup>×7×19)/(2<sup>2</sup>×13×23)
| (3<sup>2</sup>×7×19)/(2<sup>2</sup>×13×23)
| {{Monzo| -2 2 0 1 0 -1 0 1 -1 }}
| {{Monzo| -2 2 0 1 0 -1 0 1 -1 }}
| Rhodesisma
| Rodessisma
|  
|  
|-
|-
Line 1,783: Line 1,783:


=== 29-limit ===
=== 29-limit ===
{{Main|List of superparticular intervals/29-limit}}
=== 31-limit ===
{{Main|List of superparticular intervals/31-limit}}
=== 37-limit ===
{{Main|List of superparticular intervals/37-limit}}
=== 41-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Ratio]]
Line 1,791: Line 1,800:
! width="5%" | Meta<ref name="ssp"/>
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[29/28]]
| [[41/40]]
| 60.751
| 42.749
| 29/(2<sup>2</sup>×7)
| 41/(2<sup>3</sup>×5)
| 2.7.29 {{monzo| -2 -1 1 }}
| 2.5.41 {{monzo| -3 -1 1 }}
| Vicesimononal thirdtone, vicesimononal subchroma, large vicesimononal quartertone, large vicesimononal 2/7-tone
| Large quadracesimoprimal 1/5-tone
|  
|  
|-
|-
| [[30/29]]
| [[42/41]]
| 58.692
| 41.719
| (2×3×5)/29
| (2×3×7)/41
| 2.3.5.29 {{monzo| 1 1 1 -1 }}
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| Small vicesimononal quartertone, small vicesimononal 2/7-tone
| Small quadracesimoprimal 1/5-tone
|  
|  
|-
|-
| [[58/57]]
| [[82/81]]
| 30.109
| 21.242
| (2×29)/(3×19)
| (2×41)/3<sup>4</sup>
| 2.3.19.29 {{monzo| 1 -1 -1 1 }}
| 2.3.41 {{monzo| 1 -4 1 }}
| Vicesimononal 1/7-tone
| 41st-partial chroma
|  
|  
|-
|-
| [[88/87]]
| [[124/123]]
| 19.786
| 14.018
| (2<sup>3</sup>×11)/(3×29)
| (2<sup>2</sup>×31)/(3×41)
| 2.3.11.29 {{monzo| 3 -1 1 -1 }}
| 2.3.31.41 {{monzo| 2 -1 1 -1 }}
| Vicesimononal 1/10-tone, farewell comma
|  
|  
|-
| [[116/115]]
| 14.989
| (2<sup>2</sup>×29)/(5×23)
| 2.5.23.29 {{monzo| 2 -1 -1 1 }}
| Sironisma
|  
|  
|-
|-
| [[117/116]]
| [[165/164]]
| 14.860
| 10.524
| (3<sup>2</sup>×13)/(2<sup>2</sup>×29)
| (3×5×11)/(2<sup>2</sup>×41)
| 2.3.13.29 {{monzo| -2 2 1 -1 }}
| 2.3.5.11.41 {{monzo| -2 1 1 1 -1 }}
| Lomisma
|  
|  
|-
| [[145/144]]
| 11.981
| (5×29)/(2<sup>2</sup>×3)<sup>2</sup>
| 2.3.5.29 {{monzo| -4 -2 1 1 }}
| Adeonisma, 29th-partial chroma
|  
|  
|-
|-
| [[175/174]]
| [[205/204]]
| 9.9211
| 8.4657
| (5<sup>2</sup>×7)/(2×3×29)
| (5×41)/(2<sup>2</sup>×3×17)
| 2.3.5.7.29 {{monzo| -1 -1 2 1 -1 }}
| 2.3.5.17.41 {{monzo| -2 -1 1 -1 1 }}
| Major chthonovinema
|  
|  
|-
| [[204/203]]
| 8.5073
| (2<sup>2</sup>×3×17)/(7×29)
| 2.3.7.17.29 {{monzo| 2 1 -1 1 -1 }}
| Kallistisma
|  
|  
|-
|-
| [[232/231]]
| [[246/245]]
| 7.4783
| 7.0519
| (2<sup>3</sup>×29)/(3×7×11)
| (2×3×41)/(5×7<sup>2</sup>)
| 2.3.7.11.29 {{monzo| 3 -1 -1 -1 1 }}
| 2.3.5.7.41 {{monzo| 1 1 -1 -2 1 }}
| Major paravinema
|  
|  
|-
| [[261/260]]
| 6.6458
| (3<sup>2</sup>×29)/(2<sup>2</sup>×5×13)
| 2.3.5.13.29 {{monzo| -2 2 -1 -1 1 }}
| Major vinetonema
|  
|  
|-
|-
| [[290/289]]
| [[247/246]]
| 5.9801
| 7.0233
| (2×5×29)/17<sup>2</sup>
| (13×19)/(2×3×41)
| 2.5.17.29 {{monzo| 1 1 -2 1 }}
| 2.3.13.19.41 {{monzo| -1 -1 1 1 -1 }}
| Brunisma
|  
|  
|-
| [[320/319]]
| 5.4186
| (2<sup>6</sup>×5)/(11×29)
| 2.5.11.29 {{monzo| 6 1 -1 -1 }}
| Minor paravinema
|  
|  
|-
|-
| [[378/377]]
| [[287/286]]
| 4.5861
| 6.0427
| (2×3<sup>3</sup>×7)/(13×29)
| (7×41)/(2×11×13)
| 2.3.7.13.29 {{monzo| 1 3 1 -1 -1 }}
| 2.7.11.13.41 {{monzo| -1 1 -1 -1 1 }}
| Major semivinema
|  
|  
|-
| [[406/405]]
| 4.2694
| (2×7×29)/(3<sup>4</sup>×5)
| 2.3.5.7.29 {{monzo| 1 -4 -1 1 1 }}
| Minor semivinema
|  
|  
|-
|-
| [[494/493]]
| [[288/287]]
| 3.5081
| 6.0217
| (2×13×19)/(17×29)
| (2<sup>5</sup>×3<sup>2</sup>)/(7×41)
| 2.13.17.19.29 {{monzo| 1 1 -1 1 -1 }}
| 2.3.7.41 {{monzo| 5 2 -1 -1 }}
| Minor vinetonema
|  
|  
|-
| [[551/550]]
| 3.1448
| (19×29)/(2×5<sup>2</sup>×11)
| 2.5.11.19.29 {{monzo| -1 -2 -1 1 1 }}
| Minor chthonovinema
|  
|  
|-
|-
| [[552/551]]
| [[369/368]]
| 3.1391
| 4.6981
| (2<sup>3</sup>×3×23)/(19×29)
| (3<sup>2</sup>×41)/(2<sup>4</sup>×23)
| 2.3.19.23.29 {{monzo| 3 1 -1 1 -1 }}
| 2.3.23.41 {{monzo| -4 2 -1 1 }}
| Sigelindisma
|  
|  
|-
| [[609/608]]
| 2.8451
| (3×7×29)/(2<sup>5</sup>×19)
| 2.3.7.19.29 {{monzo| -5 1 1 -1 1 }}
| Vineyard comma
|  
|  
|-
|-
| [[638/637]]
| [[370/369]]
| 2.7157
| 4.6853
| (2×11×29)/(7<sup>2</sup>×13)
| (2×5×37)/(3<sup>2</sup>×41)
| 2.7.11.13.29 {{monzo| 1 -2 1 -1 1 }}
| 2.3.5.37.41 {{monzo| 1 -2 1 1 -1 }}
| Moirisma
|  
|  
|-
| [[726/725]]
| 2.3863
| (2×3×11<sup>2</sup>)/(5<sup>2</sup>×29)
| 2.3.5.11.29 {{monzo| 1 1 -2 2 -1 }}
| Joellisma
|  
|  
|-
|-
| [[783/782]]
| [[451/450]]
| 2.2124
| 3.8429
| (3<sup>3</sup>×29)/(2×17×23)
| (11×41)/(2×(3×5)<sup>2</sup>)
| 2.3.17.23.29 {{monzo| -1 3 -1 -1 1 }}
| 2.3.5.11.41 {{monzo| -1 -2 -2 1 1 }}
| Norisma
|  
|  
|-
| [[784/783]]
| 2.2096
| (2<sup>2</sup>×7)<sup>2</sup>/(3<sup>3</sup>×29)
| 2.3.7.29 {{monzo| 4 -3 2 -1 }}
| Biminorisma, spoogalactic comma
| S28
|-
| [[841/840]]
| 2.0598
| 29<sup>2</sup>/(2<sup>3</sup>×3×5×7)
| 2.3.5.7.29 {{monzo| -3 -1 -1 -1 2 }}
| Arabellisma
| S29
|-
| [[1015/1014]]
| 1.7065
| (5×7×29)/(2×3×13<sup>2</sup>)
| 2.3.5.7.13.29 {{monzo| -1 -1 1 1 -2 1 }}
| Christisma
|  
|  
|-
|-
| [[1045/1044]]
| [[493/492]]
| 1.6575
| 3.5152
| (5×11×19)/((2×3)<sup>2</sup>×29)
| (17×29)/(2<sup>2</sup>×3×41)
| 2.3.5.11.19.29 {{monzo| -2 -2 1 1 1 -1 }}
| 2.3.17.29.41 {{monzo| -2 -1 1 1 -1 }}
| Michelisma
|  
|  
|-
| [[1276/1275]]
| 1.3573
| (2<sup>2</sup>×11×29)/(3×5<sup>2</sup>×17)
| 2.3.5.11.17.29 {{monzo| 2 -1 -2 1 -1 1 }}
| Ucclisma
|  
|  
|-
|-
| [[1450/1449]]
| [[533/532]]
| 1.1944
| 3.2511
| (2×5<sup>2</sup>×29)/(3<sup>2</sup>×7×23)
| (13×41)/(2<sup>2</sup>×7×19)
| 2.3.5.7.23.29 {{monzo| 1 -2 2 -1 -1 1 }}
| 2.7.13.19.41 {{monzo| -2 -1 1 -1 1 }}
| Raimondisma
|  
|  
|-
| [[1596/1595]]
| 1.0851
| (2<sup>2</sup>×3×7×19)/(5×11×29)
| 2.3.5.7.11.19.29 {{monzo| 2 1 -1 1 -1 1 -1 }}
| Itzigsohnisma
|  
|  
|-
|-
| [[1625/1624]]
| [[575/574]]
| 1.0657
| 3.0135
| (5<sup>3</sup>×13)/(2<sup>3</sup>×7×29)
| (5<sup>2</sup>×23)/(2×7×41)
| 2.5.7.13.29 {{monzo| -3 3 -1 1 -1 }}
| 2.5.7.23.41 {{monzo| -1 2 -1 1 -1 }}
| Norcma
| Renatisma
|  
|  
|-
|-
| [[1683/1682]]
| [[616/615]]
| 1.0290
| 2.8127
| (3<sup>2</sup>×11×17)/(2×29<sup>2</sup>)
| (2<sup>3</sup>×7×11)/(3×5×41)
| 2.3.11.17.29 {{monzo| -1 2 1 1 -2 }}
| 2.3.5.7.11.41 {{monzo| 3 -1 -1 1 1 -1 }}
| Castafiorisma
| Ellisma
|  
|  
|-
|-
| [[2001/2000]]
| [[697/696]]
| 0.86540
| 2.4856
| (3×23×29)/(2<sup>4</sup>×5<sup>3</sup>)
| (17×41)/(2<sup>3</sup>×3×29)
| 2.3.5.23.29 {{monzo| -4 1 -3 1 1 }}
| 2.3.17.29.41 {{monzo| -3 -1 1 -1 1 }}
| Major discoverisma
|  
|  
|-
| [[2002/2001]]
| 0.86497
| (2×7×11×13)/(3×23×29)
| 2.3.7.11.13.23.29 {{monzo| 1 -1 1 1 1 -1 -1 }}
| Minor discoverisma
|  
|  
|-
|-
| [[2176/2175]]
| [[780/779]]
| 0.79579
| 2.2210
| (2<sup>7</sup>×17)/(3×5<sup>2</sup>×29)
| (2<sup>2</sup>×3×5×13)/(19×41)
| 2.3.5.17.29 {{monzo| 7 -1 -2 1 -1 }}
| 2.3.5.13.19.41 {{monzo| 2 1 1 1 -1 -1 }}
| Donarisma
| Wiesentisma
|  
|  
|-
|-
| [[2205/2204]]
| [[820/819]]
| 0.78532
| 2.1125
| ((3×7)/2)<sup>2</sup>×(5/(19×29))
| (2<sup>2</sup>×5×41)/(3<sup>2</sup>×7×13)
| 2.3.5.7.19.29 {{monzo| -2 2 1 2 -1 -1 }}
| 2.3.5.7.13.41 {{monzo| 2 -2 1 -1 -1 1 }}
| Glinkisma
|  
|  
|-
| [[2262/2261]]
| 0.76552
| (2×3×13×29)/(7×17×19)
| 2.3.7.13.17.19.29 {{monzo| 1 1 -1 1 -1 -1 1 }}
| Mitidikisma
|  
|  
|-
|-
| [[2465/2464]]
| [[1025/1024]]
| 0.70247
| 1.6898
| (5×17×29)/(2<sup>5</sup>×7×11)
| (5<sup>2</sup>×41)/2<sup>10</sup>
| 2.5.7.11.17.29 {{monzo| -5 1 -1 -1 1 1 }}
| 2.5.41 {{monzo| -10 2 1 }}
| Laservine comma
| Kilobytisma
|  
|  
|-
|-
| [[2640/2639]]
| [[1026/1025]]
| 0.65589
| 1.6882
| (2<sup>4</sup>×3×5×11)/(7×13×29)
| (2×3<sup>3</sup>×19)/(5<sup>2</sup>×41)
| 2.3.5.7.11.13.29 {{monzo| 4 1 1 -1 1 -1 -1 }}
| 2.3.5.19.41 {{monzo| 1 3 -2 1 -1 }}
| Hällströmisma
| Ingridisma
|  
|  
|-
|-
| [[2755/2754]]
| [[1148/1147]]
| 0.62851
| 1.5087
| (5×19×29)/(2×3<sup>4</sup>×17)
| (2<sup>2</sup>×7×41)/(31×37)
| 2.3.5.17.19.29 {{monzo| -1 -4 1 -1 1 1 }}
| 2.7.31.37.41 {{monzo| 2 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[2784/2783]]
| [[1189/1188]]
| 0.62196
| 1.4567
| (2<sup>5</sup>×3×29)/(11<sup>2</sup>×23)
| (29×41)/(2<sup>2</sup>×3<sup>3</sup>×11)
| 2.3.11.23.29 {{monzo| 5 1 -2 -1 1 }}
| 2.3.11.29.41 {{monzo| -2 -3 -1 1 1 }}
| Domeykisma
|  
|  
|-
| [[3249/3248]]
| 0.53293
| (3×19)<sup>2</sup>/(2<sup>4</sup>×7×29)
| 2.3.7.19.29 {{monzo| -4 2 -1 2 -1 }}
| Musashinisma, Musashino comma
| S57
|-
| [[3451/3450]]
| 0.50173
| (7×17×29)/(2×3×5<sup>2</sup>×23)
| 2.3.5.7.17.23.29 {{monzo| -1 -1 -2 1 1 -1 1 }}
| Mentorisma
|  
|  
|-
|-
| [[3510/3509]]
| [[1190/1189]]
| 0.49330
| 1.4554
| (2×3<sup>3</sup>×5×13)/(11<sup>2</sup>×29)
| (2×5×7×17)/(29×41)
| 2.3.5.11.13.29 {{monzo| 1 3 1 -2 1 -1 }}
| 2.5.7.17.29.41 {{monzo| 1 1 1 1 -1 -1 }}
| Veederisma
| Pelagisma
|  
|  
|-
|-
| [[4641/4640]]
| [[1312/1311]]
| 0.37307
| 1.3200
| (3×7×13×17)/(2<sup>5</sup>×5×29)
| (2<sup>5</sup>×41)/(3×19×23)
| 2.3.5.7.13.17.29 {{monzo| -5 1 -1 1 1 1 -1 }}
| 2.3.19.23.41 {{monzo| 5 -1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[4785/4784]]
| [[1353/1352]]
| 0.36184
| 1.2800
| (3×5×11×29)/(2<sup>4</sup>×13×23)
| (3×11×41)/(2<sup>3</sup>×13<sup>2</sup>)
| 2.3.5.11.13.23.29 {{monzo| -4 1 1 1 -1 -1 1 }}
| 2.3.11.13.41 {{monzo| -3 1 1 -2 1 }}
| Petrovsma
|  
|  
|-
| [[4901/4900]]
| 0.35328
| (13/(2×5×7))<sup>2</sup>×29
| 2.5.7.13.29 {{monzo| -2 -2 -2 2 1 }}
| Large grapevine comma
|  
|  
|-
|-
| [[5104/5103]]
| [[1395/1394]]
| 0.33922
| 1.2415
| (2<sup>4</sup>×11×29)/(3<sup>6</sup>×7)
| (3<sup>2</sup>×5×31)/(2×17×41)
| 2.3.7.11.29 {{monzo| 4 -6 -1 1 1 }}
| 2.3.5.17.31.41 {{monzo| -1 2 1 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[5888/5887]]
| [[1518/1517]]
| 0.29405
| 1.1408
| (2<sup>8</sup>×23)/(7×29<sup>2</sup>)
| (2×3×11×23)/(37×41)
| 2.7.23.29 {{monzo| 8 -1 1 -2 }}
| 2.3.11.23.37.41 {{monzo| 1 1 1 1 -1 -1 }}
|  
| Rovaniemisma
|  
|  
|-
|-
| [[5916/5915]]
| [[1600/1599]]
| 0.29266
| 1.0824
| (2<sup>2</sup>×3×17×29)/(5×7×13<sup>2</sup>)
| (2<sup>3</sup>×5)<sup>2</sup>/(3×13×41)
| 2.3.5.7.13.17.29 {{monzo| 2 1 -1 -1 -2 1 1 }}
| 2.3.5.13.41 {{monzo| 6 -1 2 -1 -1 }}
| Woudisma
|
|  
| S40
|-
|-
| [[6670/6669]]  
| [[1681/1680]]
| 0.25957
| 1.0302
| (2×5×23×29)/(3<sup>3</sup>×13×19)
| 41<sup>2</sup>/(2<sup>4</sup>×3×5×7)
| 2.3.5.13.19.23.29 {{monzo| 1 -3 1 -1 -1 1 1 }}
| 2.3.5.7.41 {{monzo| -4 -1 -1 -1 2 }}
|  
|
|  
| S41
|-
|-
| [[7106/7105]]
| [[1682/1681]]
| 0.24365
| 1.0296
| (2×11×17×19)/(5×7<sup>2</sup>×29)
| (2×29<sup>2</sup>)/41<sup>2</sup>
| 2.5.7.11.17.19.29 {{monzo| 1 -1 -2 1 1 1 -1 }}
| 2.29.41 {{monzo| 1 2 -2 }}
| Shaftesburisma
|  
|  
|-
| [[1805/1804]]
| 0.95940
| (5×19<sup>2</sup>)/(2<sup>2</sup>×11×41)
| 2.5.11.19.41 {{monzo| -2 1 -1 2 -1 }}
|  
|  
|-
| [[7425/7424]]
| 0.23318
| (3<sup>3</sup>×5<sup>2</sup>×11)/(2<sup>8</sup>×29)
| 2.3.5.11.29 {{monzo| -8 3 2 1 -1 }}
| Small grapevine comma
|  
|  
|-
|-
| [[7889/7888]]
| [[1886/1885]]
| 0.21946
| 0.91818
| (7<sup>3</sup>×23)/(2<sup>4</sup>×17×29)
| (2×23×41)/(5×13×29)
| 2.7.17.23.29 {{monzo| -4 3 -1 1 -1 }}
| 2.5.13.23.29.41 {{monzo| 1 -1 -1 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[8671/8670]]
| [[1887/1886]]
| 0.19967
| 0.91770
| (13×23×29)/(2×3×5×17<sup>2</sup>)
| (3×17×37)/(2×23×41)
| 2.3.5.13.17.23.29 {{monzo| -1 -1 -1 1 -2 1 1 }}
| 2.3.17.23.37.41 {{monzo| -1 1 1 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[9802/9801]]
| [[2091/2090]]
| 0.17663
| 0.82814
| (2×13<sup>2</sup>×29)/(3<sup>2</sup>×11)<sup>2</sup>
| (3×17×41)/(2×5×11×19)
| 2.3.11.13.29 {{monzo| 1 -4 -2 2 1 }}
| 2.3.5.11.17.19.41 {{monzo| -1 1 -1 -1 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[10557/10556]]
| [[2255/2254]]
| 0.16400
| 0.76790
| (3<sup>3</sup>×17×23)/(2<sup>2</sup>×7×13×29)
| (5×11×41)/(2×7<sup>2</sup>×23)
| 2.3.7.13.17.23.29 {{monzo| -2 3 -1 -1 1 1 -1 }}
| 2.5.7.11.23.41 {{monzo| -1 1 -2 1 -1 1 }}
| Rowlandisma
| Qinghaisma
|  
|  
|-
|-
| 11340/11339
| [[2296/2295]]
| 0.15267
| 0.75419
| (2<sup>2</sup>×3<sup>4</sup>×5×7)/(17×23×29)
| (2<sup>3</sup>×7×41)/(3<sup>3</sup>×5×17)
| 2.3.5.7.17.23.29 {{monzo| 2 4 1 1 -1 -1 -1 }}
| 2.3.5.7.17.41 {{monzo| 3 -3 -1 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[Uma|12006/12005]]
| [[2542/2541]]
| 0.14420
| 0.68119
| (2×3<sup>2</sup>×23×29)/(5×7<sup>4</sup>)
| (2×31×41)/(3×7×11<sup>2</sup>)
| 2.3.5.7.23.29 {{monzo| 1 2 -1 -4 1 1 }}
| 2.3.7.11.31.41 {{monzo| 1 -1 -1 -2 1 1 }}
| Uma, umic comma
|
|-
| 12673/12672
| 0.13661
| (19×23×29)/(2<sup>7</sup>×3<sup>2</sup>×11)
| 2.3.11.19.23.29 {{monzo| -7 -2 -1 1 1 1 }}
|  
|  
|  
|  
|-
|-
| 13225/13224
| [[2584/2583]]
| 0.13091
| 0.67011
| (5×23)<sup>2</sup>/(2<sup>3</sup>×3×19×29)
| (2<sup>3</sup>×17×19)/(3<sup>2</sup>×7×41)
| 2.3.5.19.23.29 {{monzo| -3 -1 2 -1 2 -1 }}
| 2.3.7.17.19.41 {{monzo| 3 -2 -1 1 1 -1 }}
|
| S115
|-
| 13311/13310
| 0.13007
| (3<sup>3</sup>×17×29)/(2×5×11<sup>3</sup>)
| 2.3.5.11.17.29 {{monzo| -1 3 -1 -3 1 1 }}
|  
|  
|  
|  
|-
|-
| 13312/13311
| [[2625/2624]]
| 0.13006
| 0.65964
| (2<sup>10</sup>×13)/(3<sup>3</sup>×17×29)
| (3×5<sup>3</sup>×7)/(2<sup>6</sup>×41)
| 2.3.13.17.29 {{monzo| 10 -3 1 -1 -1 }}
| 2.3.5.7.41 {{monzo| -6 1 3 1 -1 }}
|  
|  
|  
|  
|-
|-
| 13456/13455
| [[2665/2664]]
| 0.12866
| 0.64974
| (2<sup>2</sup>×29)<sup>2</sup>/(3<sup>2</sup>×5×13×23)
| (5×13×41)/(2<sup>3</sup>×3<sup>2</sup>×37)
| 2.3.5.13.23.29 {{monzo| 4 -2 -1 -1 -1 2 }}
| 2.3.5.13.37.41 {{monzo| -3 -2 1 1 -1 1 }}
|
| S116
|-
| 19228/19227
| 0.090039
| (2<sup>2</sup>×11×19×23)/(3×13×17×29)
| 2.3.11.13.17.19.23.29 {{monzo| 2 -1 1 -1 -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 20736/20735
| [[2871/2870]]
| 0.083491
| 0.60311
| (2<sup>2</sup>×3)<sup>4</sup>/(5×11×13×29)
| (3<sup>2</sup>×11×29)/(2×5×7×41)
| 2.3.5.11.13.29 {{monzo| 8 4 -1 -1 -1 -1 }}
| 2.3.5.7.11.29.41 {{monzo| -1 2 -1 -1 1 1 -1 }}
| Schoberisma
|  
|  
| S144
|-
|-
| 23751/23750
| [[3690/3689]]
| 0.072893
| 0.46923
| (3<sup>2</sup>×7×13×29)/(2×5<sup>4</sup>×19)
| (2×3<sup>2</sup>×5×41)/(7×17×31)
| 2.3.5.7.13.19.29 {{monzo| -1 2 -4 1 1 -1 1 }}
| 2.3.5.7.17.31.41 {{monzo| 1 2 1 -1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 24795/24794
| [[3773/3772]]
| 0.069823
| 0.45891
| (3<sup>2</sup>×5×19×29)/(2×7<sup>2</sup>×11×23)
| (7<sup>3</sup>×11)/(2<sup>2</sup>×23×41)
| 2.3.5.7.11.19.23.29 {{monzo| -1 2 1 -2 -1 1 -1 1 }}
| 2.7.11.23.41 {{monzo| -2 3 1 -1 -1 }}
|  
| Smithsonianisma
|  
|  
|-
|-
| [[Vuillafansisma|25840/25839]]
| [[4060/4059]]
| 0.067000
| 0.42646
| (2<sup>4</sup>×5×17×19)/(3<sup>4</sup>×11×29)
| (2<sup>2</sup>×5×7×29)/(3<sup>2</sup>×11×41)
| 2.3.5.11.17.19.29 {{monzo| 4 -4 1 -1 1 1 -1 }}
| 2.3.5.7.11.29.41 {{monzo| 2 -2 1 1 -1 1 -1 }}
| Vuillafansisma
| Deipylosisma
|  
|  
|-
|-
| 27000/26999
| [[4264/4263]]
| 0.064121
| 0.40606
| (2×3×5)<sup>3</sup>/(7<sup>2</sup>×19×29)
| (2<sup>3</sup>×13×41)/(3×7<sup>2</sup>×29)
| 2.3.5.7.19.29 {{monzo| 3 3 3 -2 -1 -1 }}
| 2.3.7.13.29.41 {{monzo| 3 -1 -2 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 30625/30624
| [[4551/4550]]
| 0.056531
| 0.38045
| (5<sup>2</sup>×7)<sup>2</sup>/(2<sup>5</sup>×3×11×29)
| (3×37×41)/(2×5<sup>2</sup>×7×13)
| 2.3.5.7.11.29 {{monzo| -5 -1 4 2 -1 -1 }}
| 2.3.5.7.13.37.41 {{monzo| -1 1 -2 -1 -1 1 1 }}
|
|  
|  
| S175
|-
|-
| 30856/30855
| [[4675/4674]]
| 0.056108
| 0.37036
| (2<sup>3</sup>×7×19×29)/(3×5×11<sup>2</sup>×17)
| (5<sup>2</sup>×11×17)/(2×3×19×41)
| 2.3.5.7.11.17.19.29 {{monzo| 3 -1 -1 1 -2 -1 1 1 }}
| 2.3.5.11.17.19.41 {{monzo| -1 -1 2 1 1 -1 -1 }}
|  
| Ohbokisma
|  
|  
|-
|-
| 35322/35321
| [[4921/4920]]
| 0.049014
| 0.35184
| (2×3×7×29<sup>2</sup>)/(11×13<sup>2</sup>×19)
| (7×19×37)/(2<sup>3</sup>×3×5×41)
| 2.3.7.11.13.19.29 {{monzo| 1 1 1 -1 -2 -1 2 }}
| 2.3.5.7.19.37.41 {{monzo| -3 -1 -1 1 1 1 -1 }}
|  
| Volontisma
|  
|  
|-
|-
| 47125/47124
| [[4961/4960]]
| 0.036737
| 0.34900
| (5<sup>3</sup>×13×29)/((2×3)<sup>2</sup>×7×11×17)
| (11<sup>2</sup>×41)/(2<sup>5</sup>×5×31)
| 2.3.5.7.11.13.17.29 {{monzo| -2 -2 3 -1 -1 1 -1 1 }}
| 2.5.11.31.41 {{monzo| -5 -1 2 -1 1 }}
|  
|  
|  
|  
|-
|-
| 53361/53360
| [[5084/5083]]
| 0.032444
| 0.34056
| (3×7×11)<sup>2</sup>/(2<sup>4</sup>×5×23×29)
| (2<sup>2</sup>×31×41)/(13×17×23)
| 2.3.5.7.11.23.29 {{monzo| -4 2 -1 2 2 -1 -1 }}
| 2.13.17.23.31.41 {{monzo| 2 -1 -1 -1 1 1 }}
|
| S231
|-
| 72501/72500
| 0.023879
| (3×11×13<sup>3</sup>)/((2×5<sup>2</sup>)<sup>2</sup>×29)
| 2.3.5.11.13.29 {{monzo| -2 1 -4 1 3 -1 }}
|  
|  
|  
|  
|-
|-
| 83521/83520
| [[5577/5576]]
| 0.020728
| 0.31045
| 17<sup>4</sup>/((2<sup>3</sup>×3)<sup>2</sup>×5×29)
| (3×11×13<sup>2</sup>)/(2<sup>3</sup>×17×41)
| 2.3.5.17.29 {{monzo| -6 -2 -1 4 -1 }}
| 2.3.11.13.17.41 {{monzo| -3 1 1 2 -1 -1 }}
| Priestlisma
|  
|  
| S289
|-
|-
| 87465/87464
| [[6069/6068]]
| 0.019794
| 0.28528
| (3×5×7<sup>3</sup>×17)/(2<sup>3</sup>×13×29<sup>2</sup>)
| (3×7×17<sup>2</sup>)/(2<sup>2</sup>×37×41)
| 2.3.5.7.13.17.29 {{monzo| -3 1 1 3 -1 1 -2 }}
| 2.3.7.17.37.41 {{monzo| -2 1 1 2 -1 -1 }}
|  
| Cevolanisma
|  
|  
|-
|-
| 136851/136850
| [[6273/6272]]
| 0.012651
| 0.27600
| (3×11<sup>2</sup>×13×29)/(2×5<sup>2</sup>×7×17×23)
| (3<sup>2</sup>×17×41)/(2<sup>7</sup>×7<sup>2</sup>)
| 2.3.5.7.11.13.17.23.29 {{monzo| -1 1 -2 -1 2 1 -1 -1 1 }}
| 2.3.7.17.41 {{monzo| -7 2 -2 1 1 }}
|  
|  
|  
|  
|-
|-
| 158950/158949
| [[6561/6560]]
| 0.010892
| 0.26389
| (2×(5×17)<sup>2</sup>×11)/(3<sup>3</sup>×7×29<sup>2</sup>)
| 3<sup>8</sup>/(2<sup>5</sup>×5×41)
| 2.3.5.7.11.17.29 {{monzo| 1 -3 2 -1 1 2 -2 }}
| 2.3.5.41 {{monzo| -5 8 -1 -1 }}
|
|  
|  
| S81
|-
|-
| 166635/166634
| [[6601/6600]]
| 0.010389
| 0.26229
| ((3×23)<sup>2</sup>×5×7)/(2×13<sup>2</sup>×17×29)
| (7×23×41)/(2<sup>3</sup>×3×5<sup>2</sup>×11)
| 2.3.5.7.13.17.23.29 {{monzo| -1 2 1 1 -2 -1 2 -1 }}
| 2.3.5.7.11.23.41 {{monzo| -3 -1 -2 1 -1 1 1 }}
|  
|  
|  
|  
|-
|-
| 168751/168750
| [[6930/6929]]
| 0.010259
| 0.24984
| (11×23<sup>2</sup>×29)/(2×3<sup>3</sup>×5<sup>5</sup>)
| (2×3<sup>2</sup>×5×7×11)/(13<sup>2</sup>×41)
| 2.3.5.11.23.29 {{monzo| -1 -3 -5 1 2 1 }}
| 2.3.5.7.11.13.41 {{monzo| 1 2 1 1 1 -2 -1 }}
|  
| Bedanisma
|  
|  
|-
|-
| 176001/176000
| [[7176/7175]]
| 0.0098365
| 0.24127
| (3×7×17<sup>2</sup>×29)/(2<sup>7</sup>×5<sup>3</sup>×11)
| (2<sup>3</sup>×3×13×23)/(5<sup>2</sup>×7×41)
| 2.3.5.7.11.17.29 {{monzo| -7 1 -3 1 -1 2 1 }}
| 2.3.5.7.13.23.41 {{monzo| 3 1 -2 -1 1 1 -1 }}
|  
| Kunijisma
|  
|  
|-
|-
| 176176/176175
| [[7216/7215]]
| 0.0098268
| 0.23993
| (2<sup>4</sup>×7×11<sup>2</sup>×13)/(3<sup>5</sup>×5<sup>2</sup>×29)
| (2<sup>4</sup>×11×41)/(3×5×13×37)
| 2.3.5.7.11.13.29 {{monzo| 4 -5 -2 1 2 1 -1 }}
| 2.3.5.11.13.37.41 {{monzo| 4 -1 -1 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 184093/184092
| [[7750/7749]]
| 0.0094042
| 0.22340
| ((7×17)<sup>2</sup>×13)/((2×23)<sup>2</sup>×3×29)
| (2×5<sup>3</sup>×31)/(3<sup>3</sup>×7×41)
| 2.3.7.13.17.23.29 {{monzo| -2 -1 2 1 2 -2 -1 }}
| 2.3.5.7.31.41 {{monzo| 1 -3 3 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 240787/240786
| [[8569/8568]]
| 0.0071899
| 0.20205
| (19<sup>2</sup>×23×29)/(2×(3×7)<sup>3</sup>×13)
| (11×19×41)/(2<sup>3</sup>×3<sup>2</sup>×7×17)
| 2.3.7.13.19.23.29 {{monzo| -1 -3 -3 -1 2 1 1 }}
| 2.3.7.11.17.19.41 {{monzo| -3 -2 -1 1 -1 1 1 }}
|  
| Mamelisma
|  
|  
|-
|-
| 244036/244035
| [[8856/8855]]
| 0.0070942
| 0.19550
| (2×13×19)<sup>2</sup>/(3<sup>2</sup>×5×11×17×29)
| ((2×3)<sup>3</sup>×41)/(5×7×11×23)
| 2.3.5.11.13.17.19.29 {{monzo| 2 -2 -1 -1 2 -1 2 -1 }}
| 2.3.5.7.11.23.41 {{monzo| 3 3 -1 -1 -1 -1 1 }}
|  
|  
| S494
|-
| 303601/303600
| 0.0057023
| ((19×29)/(2<sup>2</sup>×5))<sup>2</sup>/(3×11×23)
| 2.3.5.11.19.23.29 {{monzo| -4 -1 -2 -1 2 -1 2 }}
|  
|  
| S551
|-
|-
| 410670/410669
| [[9472/9471]]
| 0.0042156
| 0.18278
| (2×3<sup>5</sup>×5×13<sup>2</sup>)/((7×17)<sup>2</sup>×29)
| (2<sup>8</sup>×37)/(3×7×11×41)
| 2.3.5.7.13.17.29 {{monzo| 1 5 1 -2 2 -2 -1 }}
| 2.3.7.11.37.41 {{monzo| 8 -1 -1 -1 1 -1 }}
|  
| Brugesisma
|  
|  
|-
|-
| 418761/418760
| 10045/10044
| 0.0041342
| 0.17236
| ((3×17)<sup>2</sup>×7×23)/(2<sup>3</sup>×5×19<sup>2</sup>×29)
| (5×7<sup>2</sup>×41)/(2<sup>2</sup>×3<sup>4</sup>×31)
| 2.3.5.7.17.19.23.29 {{monzo| -3 2 -1 1 2 -2 1 -1 }}
| 2.3.5.7.31.41 {{monzo| -2 -4 1 2 -1 1 }}
|  
|  
|  
|  
|-
|-
| 613089/613088
| [[10374/10373]]
| 0.0028238
| 0.16689
| (3<sup>3</sup>×29)<sup>2</sup>/(2<sup>5</sup>×7<sup>2</sup>×17×23)
| (2×3×7×13×19)/(11×23×41)
| 2.3.7.17.23.29 {{monzo| -5 6 -2 -1 -1 2 }}
| 2.3.7.11.13.19.23.41 {{monzo| 1 1 1 -1 1 1 -1 -1}}
| Etampesisma
|  
|  
| S783
|-
|-
| 949026/949025
| 10660/10659
| 0.0018242
| 0.16241
| (2×3×13×23<sup>3</sup>)/(5<sup>2</sup>×7×11×17×29)
| (2<sup>2</sup>×5×13×41)/(3×11×17×19)
| 2.3.5.7.11.13.17.23.29 {{monzo| 1 1 -2 -1 -1 1 -1 3 -1 }}
| 2.3.5.11.13.17.19.41 {{monzo| 2 -1 1 -1 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 1163800/1163799
| [[11440/11439]]
| 0.0014876
| 0.15134
| (2<sup>3</sup>×(5×23)<sup>2</sup>×11)/(3<sup>2</sup>×7<sup>3</sup>×13×29)
| (2<sup>4</sup>×5×11×13)/(3<sup>2</sup>×31×41)
| 2.3.5.7.11.13.23.29 {{monzo| 3 -2 2 -3 1 -1 2 -1 }}
| 2.3.5.11.13.31.41 {{monzo| 4 -2 1 1 1 -1 -1 }}
|  
| Massironisma
|  
|  
|-
|-
| 1235169/1235168
| 13776/13775
| 0.0014016
| 0.12567
| (3<sup>5</sup>×13×17×23)/(2<sup>5</sup>×11<sup>3</sup>×29)
| (2<sup>4</sup>×3×7×41)/(5<sup>2</sup>×19×29)
| 2.3.11.13.17.23.29 {{monzo| -5 5 -3 1 1 1 -1 }}
| 2.3.5.7.19.29.41 {{monzo| 4 1 -2 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 1243840/1243839
| 14145/14144
| 0.0013918
| 0.12240
| ((2<sup>3</sup>×13)<sup>2</sup>×5×23)/(3×17×29<sup>3</sup>)
| (3×5×23×41)/(2<sup>6</sup>×13×17)
| 2.3.5.13.17.23.29 {{monzo| 6 -1 1 2 -1 1 -3 }}
| 2.3.5.13.17.23.41 {{monzo| -6 1 1 -1 -1 1 1 }}
|  
|  
|  
|  
|-
|-
| 1625625/1625624
| 14801/14800
| 0.0010650
| 0.11697
| (3×5<sup>2</sup>×17)<sup>2</sup>/(2<sup>3</sup>×7<sup>2</sup>×11×13×29)
| (19<sup>2</sup>×41)/(2<sup>4</sup>×5<sup>2</sup>×37)
| 2.3.5.7.11.13.17.29 {{monzo| -3 2 4 -2 -1 -1 2 -1 }}
| 2.5.19.37.41 {{monzo| -4 -2 2 -1 1 }}
|
| S1275
|-
| 1852201/1852200
| 0.00093469
| (13×17<sup>3</sup>×29)/((2×3×7)<sup>3</sup>×5<sup>2</sup>)
| 2.3.5.7.13.17.29 {{monzo| -3 -3 -2 -3 1 3 1 }}
|  
|  
|  
|  
|-
|-
| 2697696/2697695
| [[15376/15375]]
| 0.00064175
| 0.11260
| (2<sup>5</sup>×3<sup>2</sup>×17×19×29)/(5×7<sup>3</sup>×11<sup>2</sup>×13)
| (2<sup>2</sup>×31)<sup>2</sup>/(3×5<sup>3</sup>×41)
| 2.3.5.7.11.13.17.19.29 {{monzo| 5 2 -1 -3 -2 -1 1 1 1 }}
| 2.3.5.31.41 {{monzo| 4 -1 -3 2 -1 }}
|  
| Martakisma
| S124
|-
| 15457/15456
| 0.11201
| (13×29×41)/(2<sup>5</sup>×3×7×23)
| 2.3.7.13.23.29.41 {{monzo| -5 -1 -1 1 -1 1 1 }}
|  
|  
|  
|-
|-
| [[Odyssey comma|4004001/4004000]]
| 16400/16399
| 0.00043238
| 0.10557
| (3×23×29)<sup>2</sup>/(2<sup>5</sup>×5<sup>3</sup>×7×11×13)
| (2<sup>4</sup>×5<sup>2</sup>×41)/(23<sup>2</sup>×31)
| 2.3.5.7.11.13.23.29 {{monzo| -5 2 -3 -1 -1 -1 2 2 }}
| 2.5.23.31.41 {{monzo| 4 2 -2 -1 1 }}
| Odyssey comma
| S2001
|-
| 4090625/4090624
| 0.00042322
| (5<sup>5</sup>×7×11×17)/((2<sup>4</sup>×29)<sup>2</sup>×19)
| 2.5.7.11.17.19.29 {{monzo| -8 5 1 1 1 -1 -2 }}
|  
|  
|  
|  
|-
|-
| 8268800/8268799
| 16524/16523
| 0.00020937
| 0.10477
| ((2<sup>5</sup>×5)<sup>2</sup>×17×19)/((7×23)<sup>2</sup>×11×29)
| (2<sup>2</sup>×3<sup>5</sup>×17)/(13×31×41)
| 2.5.7.11.17.19.23.29 {{monzo| 10 2 -2 -1 1 1 -2 -1 }}
| 2.3.13.17.31.41 {{monzo| 2 5 -1 1 -1 -1 }}
|  
|  
|  
|  
|-
|-
| <font style="font-size:0.88em">10556001/10556000</font>
| 16606/16605
| 0.00016400
| 0.10426
| (3×19)<sup>4</sup>/(2<sup>5</sup>×5<sup>3</sup>×7×13×29)
| (2×19<sup>2</sup>×23)/(3<sup>4</sup>×5×41)
| 2.3.5.7.13.19.29 {{monzo| -5 4 -3 -1 -1 4 -1 }}
| 2.3.5.19.23.41 {{monzo| 1 -4 -1 2 1 -1 }}
|
|  
|  
| S3249
|-
|-
| <font style="font-size:0.88em">18085705/18085704</font>
| 17425/17424
| 9.5724×10<sup>-5</sup>
| 0.099356
| (5×11×17×23×29<sup>2</sup>)/((2×7×13)<sup>3</sup>×3)
| (5<sup>2</sup>×17×41)/(2<sup>2</sup>×3×11)<sup>2</sup>
| 2.3.5.7.11.13.17.23.29 {{monzo| -3 -1 1 -3 1 -3 1 1 2 }}
| 2.3.5.11.17.41 {{monzo| -4 -2 2 -2 1 1 }}
|  
|  
|  
|  
|-
|-
| <font style="font-size:0.88em">96059601/96059600</font>
| [[17836/17835]]
| 1.8022×10<sup>-5</sup>
| 0.097067
| (3<sup>2</sup>×11)<sup>4</sup>/((2<sup>2</sup>×5×7×13)<sup>2</sup>×29)
| (2<sup>2</sup>×7<sup>3</sup>×13)/(3×5×29×41)
| 2.3.5.7.11.13.29 {{monzo| -4 8 -2 -2 4 -2 -1 }}
| 2.3.5.7.13.29.41 {{monzo| 2 -1 -1 3 1 -1 -1 }}
| Canupisma
|  
|  
| S9801
|-
|-
| <font style="font-size:0.79em">177182721/177182720</font>
| 17918/17917
| 9.7709×10<sup>-6</sup>
| 0.096623
| (3<sup>3</sup>×17×29)<sup>2</sup>/(2<sup>11</sup>×5×11<sup>3</sup>×13)
| (2×17<sup>2</sup>×31)/(19×23×41)
| 2.3.5.11.13.17.29 {{monzo| -11 6 -1 -3 -1 2 2 }}
| 2.17.19.23.31.41 {{monzo| 1 2 -1 -1 1 -1 }}
|  
|  
| S13311
|  
|}
|-
 
| 19721/19720
=== 31-limit ===
| 0.087789
| (13×37×41)/(2<sup>3</sup>×5×17×29)
| 2.5.13.17.29.37.41 {{monzo| -3 -1 1 -1 -1 1 1 }}
|
|
|-
| 19845/19844
| 0.087240
| (3<sup>4</sup>×5×7<sup>2</sup>)/((2×11)<sup>2</sup>×41)
| 2.3.5.7.11.41 {{monzo| -2 4 1 2 -2 -1 }}
|
|
|-
| [[76384/76383]]
| 0.022665
| (2<sup>5</sup>×7×11×31)/(3<sup>4</sup>×23×41)
| 2.3.7.11.23.31.41 {{monzo| 5 -4 1 1 -1 1 -1 }}
| Vernonisma
|
|-
| [[Mebisma|1048576/1048575]]
| 0.0016510
| 2<sup>20</sup>/(3×5<sup>2</sup>×11×31×41)
| 2.3.5.11.31.41 {{monzo| 20 -1 -2 -1 -1 -1 }}
| Mebisma
| S1024
|}
 
=== 43-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Ratio]]
Line 2,529: Line 2,391:
! width="5%" | Meta<ref name="ssp"/>
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[31/30]]
| [[43/42]]
| 56.767
| 40.737
| 31/(2×3×5)
| 43/(2×3×7)
| 2.3.5.31 {{monzo| -1 -1 -1 1 }}
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| Large tricesimoprimal 1/4-tone
| Large quadracesimotertial 1/5-tone
|  
|  
|-
|-
| [[32/31]]
| [[44/43]]
| 54.964
| 39.800
| 2<sup>5</sup>/31
| (2<sup>2</sup>×11)/43
| 2.31 {{monzo| 5 -1 }}
| 2.11.43 {{monzo| 2 1 -1 }}
| Small tricesimoprimal 1/4-tone, octave-reduced 31st subharmonic
| Small quadracesimotertial 1/5-tone
|
|-
| [[63/62]]
| 27.700
| (3<sup>2</sup>×7)/(2×31)
| 2.3.7.31 {{monzo| -1 2 1 -1 }}
| Tricesimoprimal 1/8-tone, co-archyta comma
|  
|  
|-
|-
| [[93/92]]
| [[86/85]]
| 18.716
| 20.249
| (3×31)/(2<sup>2</sup>×23)
| (2×43)/(5×17)
| 2.3.23.31 {{monzo| -2 1 -1 1 }}
| 2.5.17.43 {{monzo| 1 -1 -1 1 }}
| Large quadracesimotertial 1/10-tone
|  
|  
|-
| [[87/86]]
| 20.014
| (3×29)/(2×43)
| 2.3.29.43 {{monzo| -1 1 1 -1 }}
| Small quadracesimotertial 1/10-tone
|  
|  
|-
|-
| [[125/124]]
| [[129/128]]
| 13.906
| 13.473
| 5<sup>3</sup>/(2<sup>2</sup>×31)
| (3×43)/2<sup>7</sup>
| 2.5.31 {{monzo| -2 3 -1 }}
| 2.3.43 {{monzo| -7 1 1 }}
| Twizzler
| 43rd-partial chroma
|  
|  
|-
|-
| [[155/154]]
| [[130/129]]
| 11.205
| 13.369
| (5×31)/(2×7×11)
| (2×5×13)/(3×43)
| 2.5.7.11.31 {{monzo| -1 1 -1 -1 1 }}
| 2.3.5.13.43 {{monzo| 1 -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[156/155]]
| [[172/171]]
| 11.133
| 10.095
| (2<sup>2</sup>×3×13)/(5×31)
| (2<sup>2</sup>×43)/(3<sup>2</sup>×19)
| 2.3.5.13.31 {{monzo| 2 1 -1 1 -1 }}
| 2.3.19.43 {{monzo| 2 -2 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[187/186]]
| [[216/215]]
| 9.2828
| 8.0336
| (11×17)/(2×3×31)
| (2×3)<sup>3</sup>/(5×43)
| 2.3.11.17.31 {{monzo| -1 -1 1 1 -1 }}
| 2.3.5.43 {{monzo| 3 3 -1 -1 }}
|  
|  
|  
|  
|-
|-
| [[217/216]]
| [[259/258]]
| 7.9965
| 6.6972
| (7×31)/(2×3)<sup>3</sup>
| (7×37)/(2×3×43)
| 2.3.7.31 {{monzo| -3 -3 1 1 }}
| 2.3.7.37.43 {{monzo| -1 -1 1 1 -1 }}
| Tricesimoprimal kleisma
|  
|  
|  
|-
|-
| [[248/247]]
| [[301/300]]
| 6.9949
| 5.7612
| (2<sup>3</sup>×31)/(13×19)
| (7×43)/((2×5)<sup>2</sup>×3)
| 2.13.19.31 {{monzo| 3 -1 -1 1 }}
| 2.3.5.7.43 {{monzo| -2 -1 -2 1 1 }}
|  
|  
|  
|  
|-
|-
| [[280/279]]
| [[344/343]]
| 6.1940
| 5.0400
| (2<sup>3</sup>×5×7)/(3<sup>2</sup>×31)
| (2<sup>3</sup>×43)/7<sup>3</sup>
| 2.3.5.7.31 {{monzo| 3 -2 1 1 -1 }}
| 2.7.43 {{monzo| 3 -3 1 }}
| Tricetone comma
|
|-
| [[341/340]]
| 5.0844
| (11×31)/(2<sup>2</sup>×5×17)
| 2.5.11.17.31 {{monzo| -2 -1 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[342/341]]
| [[345/344]]
| 5.0695
| 5.0254
| (2×3<sup>2</sup>×19)/(11×31)
| (3×5×23)/(2<sup>3</sup>×43)
| 2.3.11.19.31 {{monzo| 1 2 -1 1 -1 }}
| 2.3.5.23.43 {{monzo| -3 1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[435/434]]
| [[430/429]]
| 3.9844
| 4.0308
| (3×5×29)/(2×7×31)
| (2×5×43)/(3×11×13)
| 2.3.5.7.29.31 {{monzo| -1 1 1 -1 1 -1 }}
| 2.3.5.11.13.43 {{monzo| 1 -1 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[465/464]]
| [[559/558]]
| 3.7271
| 3.0998
| (3×5×31)/(2<sup>4</sup>×29)
| (13×43)/(2×3<sup>2</sup>×31)
| 2.3.5.29.31 {{monzo| -4 1 1 -1 1 }}
| 2.3.13.31.43 {{monzo| -1 -2 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[496/495]]
| [[560/559]]
| 3.4939
| 3.0943
| (2<sup>4</sup>×31)/(3<sup>2</sup>×5×11)
| (2<sup>4</sup>×5×7)/(13×43)
| 2.3.5.11.31 {{monzo| 4 -2 -1 -1 1 }}
| 2.5.7.13.43 {{monzo| 4 1 1 -1 -1 }}
| Navatonisma
|
|-
| [[528/527]]
| 3.2820
| (2<sup>4</sup>×3×11)/(17×31)
| 2.3.11.17.31 {{monzo| 4 1 1 -1 -1 }}
|  
|  
|  
|  
|-
|-
| [[589/588]]
| [[645/644]]
| 2.9418
| 2.6862
| (19×31)/(2<sup>2</sup>×3×7<sup>2</sup>)
| (3×5×43)/(2<sup>2</sup>×7×23)
| 2.3.7.19.31 {{monzo| -2 -1 -2 1 1 }}
| 2.3.5.7.23.43 {{monzo| -2 1 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[621/620]]
| [[646/645]]
| 2.7901
| 2.6820
| (3<sup>3</sup>×23)/(2<sup>2</sup>×5×31)
| (2×17×19)/(3×5×43)
| 2.3.5.23.31 {{monzo| -2 3 -1 1 -1 }}
| 2.3.5.17.19.43 {{monzo| 1 -1 -1 1 1 -1 }}
| Owowhatsthisma
| Kastalisma
|  
|  
|-
|-
| [[651/650]]
| [[775/774]]
| 2.6614
| 2.2353
| (3×7×31)/(2×5<sup>2</sup>×13)
| (5<sup>2</sup>×31)/(2×3<sup>2</sup>×43)
| 2.3.5.7.13.31 {{monzo| -1 1 -2 1 -1 1 }}
| 2.3.5.31.43 {{monzo| -1 -2 2 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[714/713]]
| [[817/816]]
| 2.4264
| 2.1203
| (2×3×7×17)/(23×31)
| (19×43)/(2<sup>4</sup>×3×17)
| 2.3.7.17.23.31 {{monzo| 1 1 1 1 -1 -1 }}
| 2.3.17.19.43 {{monzo| -4 -1 -1 1 1 }}
|  
|  
|  
|  
|-
|-
| [[806/805]]
| [[861/860]]
| 2.1493
| 2.0119
| (2×13×31)/(5×7×23)
| (3×7×41)/(2<sup>2</sup>×5×43)
| 2.5.7.13.23.31 {{monzo| 1 -1 -1 1 -1 1 }}
| 2.3.5.7.41.43 {{monzo| -2 1 -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[837/836]]
| [[903/902]]
| 2.0696
| 1.9183
| (3<sup>3</sup>×31)/(2<sup>2</sup>×11×19)
| (3×7×43)/(2×11×41)
| 2.3.11.19.31 {{monzo| -2 3 -1 -1 1 }}
| 2.3.7.11.41.43 {{monzo| -1 1 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[868/867]]
| [[946/945]]
| 1.9957
| 1.8310
| (2<sup>2</sup>×7×31)/(3×17<sup>2</sup>)
| (2×11×43)/(3<sup>3</sup>×5×7)
| 2.3.7.17.31 {{monzo| 2 -1 1 -2 1 }}
| 2.3.5.7.11.43 {{monzo| 1 -3 -1 -1 1 1 }}
|  
|  
|  
|  
|-
| [[900/899]]
| 1.9247
| (2×3×5)<sup>2</sup>/(29×31)
| 2.3.5.29.31 {{monzo| 2 2 2 -1 -1 }}
|
| S30
|-
|-
| [[931/930]]
| [[989/988]]
| 1.8605
| 1.7514
| (7<sup>2</sup>×19)/(2×3×5×31)
| (23×43)/(2<sup>2</sup>×13×19)
| 2.3.5.7.19.31 {{monzo| -1 -1 -1 2 1 -1 }}
| 2.13.19.23.43 {{monzo| -2 -1 -1 1 1 }}
|  
|  
|  
|  
|-
|-
| [[961/960]]
| [[990/989]]
| 1.8024
| 1.7496
| 31<sup>2</sup>/(2<sup>6</sup>×3×5)
| (2×3<sup>2</sup>×5×11)/(23×43)
| 2.3.5.31 {{monzo| -6 -1 -1 2 }}
| 2.3.5.11.23.43 {{monzo| 1 2 1 1 -1 -1 }}
| Yerkesisma
|  
|  
| S31
|-
| [[1024/1023]]
| 1.6915
| 2<sup>10</sup>/(3×11×31)
| 2.3.11.31 {{monzo| 10 -1 -1 -1 }}
| Kibisma
| S32
|-
|-
| [[1054/1053]]
| [[1161/1160]]
| 1.6433
| 1.4918
| (2×17×31)/(3<sup>4</sup>×13)
| (3<sup>3</sup>×43)/(2<sup>3</sup>×5×29)
| 2.3.13.17.31 {{monzo| 1 -4 -1 1 1 }}
| 2.3.5.29.43 {{monzo| -3 3 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[1210/1209]]
| [[1248/1247]]
| 1.4314
| 1.3878
| (2×5×11<sup>2</sup>)/(3×13×31)
| (2<sup>5</sup>×3×13)/(29×43)
| 2.3.5.11.13.31 {{monzo| 1 -1 1 2 -1 -1 }}
| 2.3.13.29.43 {{monzo| 5 1 1 -1 -1 }}
|  
|  
|  
|  
|-
|-
| [[1365/1364]]
| [[1333/1332]]
| 1.2688
| 1.2992
| (3×5×7×13)/(2<sup>2</sup>×11×31)
| (31×43)/((2×3)<sup>2</sup>×37)
| 2.3.5.7.11.13.31 {{monzo| -2 1 1 1 -1 1 -1 }}
| 2.3.31.37.43 {{monzo| -2 -2 1 -1 1 }}
|  
| Cevenolisma
|  
|  
|-
|-
| [[1426/1425]]
| [[1334/1333]]
| 1.2145
| 1.2983
| (2×23×31)/(3×5<sup>2</sup>×19)
| (2×23×29)/(31×43)
| 2.3.5.19.23.31 {{monzo| 1 -1 -2 -1 1 1 }}
| 2.23.29.31.43 {{monzo| 1 1 1 -1 -1 }}
|  
|  
|  
|  
|-
|-
| [[1519/1518]]
| [[1376/1375]]
| 1.1401
| 1.2586
| (7<sup>2</sup>×31)/(2×3×11×23)
| (2<sup>5</sup>×43)/(5<sup>3</sup>×11)
| 2.3.7.11.23.31 {{monzo| -1 -1 2 -1 -1 1 }}
| 2.5.11.43 {{monzo| 5 -3 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[1520/1519]]
| [[1377/1376]]
| 1.1393
| 1.2577
| (2<sup>4</sup>×5×19)/(7<sup>2</sup>×31)
| (3<sup>4</sup>×17)/(2<sup>5</sup>×43)
| 2.5.7.19.31 {{monzo| 4 1 -2 1 -1 }}
| 2.3.17.43 {{monzo| -5 4 1 -1 }}
| Roberbauxisma
|  
|  
|-
| [[1463/1462]]
| 1.1838
| (7×11×19)/(2×17×43)
| 2.7.11.17.19.43 {{monzo| -1 1 1 -1 1 -1 }}
| Nordenmarkisma
|  
|  
|-
|-
| [[1768/1767]]
| [[1548/1547]]
| 0.97948
| 1.1187
| (2<sup>3</sup>×13×17)/(3×19×31)
| (2<sup>2</sup>×3<sup>2</sup>×43)/(7×13×17)
| 2.3.13.17.19.31 {{monzo| 3 -1 1 1 -1 -1 }}
| 2.3.7.13.17.43 {{monzo| 2 2 -1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[1860/1859]]
| [[1764/1763]]
| 0.93102
| 0.98170
| (2<sup>2</sup>×3×5×31)/(11×13<sup>2</sup>)
| (2×3×7)<sup>2</sup>/(41×43)
| 2.3.5.11.13.31 {{monzo| 2 1 1 -1 -2 1 }}
| 2.3.7.41.43 {{monzo| 2 2 2 -1 -1 }}
|  
|
|  
| S42
|-
|-
| [[2016/2015]]
| [[1806/1805]]
| 0.85896
| 0.95887
| (2<sup>5</sup>×3<sup>2</sup>×7)/(5×13×31)
| (2×3×7×43)/(5×19<sup>2</sup>)
| 2.3.5.7.13.31 {{monzo| 5 2 -1 1 -1 -1 }}
| 2.3.5.7.19.43 {{monzo| 1 1 -1 1 -2 1 }}
|  
|
|  
|  
|-
|-
| [[2233/2232]]
| [[1849/1848]]
| 0.77547
| 0.93656
| (7×11×29)/(2<sup>3</sup>×3<sup>2</sup>×31)
| 43<sup>2</sup>/(2<sup>3</sup>×3×7×11)
| 2.3.7.11.29.31 {{monzo| -3 -2 1 1 1 -1 }}
| 2.3.7.11.43 {{monzo| -3 -1 -1 -1 2 }}
| Kuznetsovisma
|  
|  
| S43
|-
|-
| [[2945/2944]]
| [[1850/1849]]
| 0.58796
| 0.93606
| (5×19×31)/(2<sup>7</sup>×23)
| (2×5<sup>2</sup>×37)/43<sup>2</sup>
| 2.5.19.23.31 {{monzo| -7 1 1 -1 1 }}
| 2.5.37.43 {{monzo| 1 2 1 -2 }}
|  
|  
|  
|  
|-
|-
| [[2976/2975]]
| [[1936/1935]]
| 0.58183
| 0.89446
| (2<sup>5</sup>×3×31)/(5<sup>2</sup>×7×17)
| (2<sup>2</sup>×11)<sup>2</sup>/(3<sup>2</sup>×5×43)
| 2.3.5.7.17.31 {{monzo| 5 1 -2 -1 -1 1 }}
| 2.3.5.11.43 {{monzo| 4 -2 -1 2 -1 }}
|  
|
|  
| S44
|-
|-
| [[3565/3564]]
| [[2925/2924]]
| 0.48569
| 0.59198
| (5×23×31)/((2×3<sup>2</sup>)<sup>2</sup>×11)
| (3<sup>2</sup>×5<sup>2</sup>×13)/(2<sup>2</sup>×17×43)
| 2.3.5.11.23.31 {{monzo| -2 -4 1 -1 1 1 }}
| 2.3.5.13.17.43 {{monzo| -2 2 2 1 -1 -1 }}
|  
| Beattisma
|  
|  
|-
|-
| [[3751/3750]]
| [[3312/3311]]
| 0.46160
| 0.52279
| (11<sup>2</sup>×31)/(2×3×5<sup>4</sup>)
| (2<sup>4</sup>×3<sup>2</sup>×23)/(7×11×43)
| 2.3.5.11.31 {{monzo| -1 -1 -4 2 1 }}
| 2.3.7.11.23.43 {{monzo| 4 2 -1 -1 1 -1 }}
| Pedersenisma
|  
|  
|-
| [[4000/3999]]
| 0.43286
| (2<sup>5</sup>×5<sup>3</sup>)/(3×31×43)
| 2.3.5.31.43 {{monzo| 5 -1 3 -1 -1 }}
| Hipparchusisma
|  
|  
|-
|-
| [[3876/3875]]
| [[4301/4300]]
| 0.44671
| 0.40257
| (2<sup>2</sup>×3×17×19)/(5<sup>3</sup>×31)
| (11×17×23)/(2<sup>2</sup>×5<sup>2</sup>×43)
| 2.3.5.17.19.31 {{monzo| 2 1 -3 1 1 -1 }}
| 2.5.11.17.23.43 {{monzo| -2 -2 1 1 1 -1 }}
|  
| Boydenisma
|  
|  
|-
|-
| [[3969/3968]]
| [[4774/4773]]
| 0.43624
| 0.36268
| (3<sup>2</sup>×7)<sup>2</sup>/(2<sup>7</sup>×31)
| (2×7×11×31)/(3×37×43)
| 2.3.7.31 {{monzo| -7 4 2 -1 }}
| 2.3.7.11.31.37.43 {{monzo| 1 -1 1 1 1 -1 -1 }}
| Yunzee comma
| Hobetsisma
| S63
|
|-
|-
| [[4186/4185]]
| [[5720/5719]]
| 0.41363
| 0.30269
| (2×7×13×23)/(3<sup>3</sup>×5×31)
| (2<sup>3</sup>×5×11×13)/(7×19×43)
| 2.3.5.7.13.23.31 {{monzo| 1 -3 -1 1 1 1 -1 }}
| 2.5.7.11.13.19.43 {{monzo| 3 1 -1 1 1 -1 -1 }}
| Tamashimisma
| Halweaverisma
|  
|  
|-
|-
| [[4960/4959]]
| [[7225/7224]]
| 0.34907
| 0.23963
| (2<sup>5</sup>×5×31)/(3<sup>2</sup>×19×29)
| (5×17)<sup>2</sup>/(2<sup>3</sup>×3×7×43)
| 2.3.5.19.29.31 {{monzo| 5 -2 1 -1 -1 1 }}
| 2.3.5.7.17.43 {{monzo| -3 -1 2 -1 2 -1 }}
|  
| Huntressisma
|  
| S85
|-
|-
| [[4992/4991]]
| [[7956/7955]]
| 0.34684
| 0.21761
| (2<sup>7</sup>×3×13)/(7×23×31)
| (2<sup>2</sup>×3<sup>2</sup>×13×17)/(5×37×43)
| 2.3.7.13.23.31 {{monzo| 7 1 -1 1 -1 -1 }}
| 2.3.5.13.17.37.43 {{monzo| 2 2 -1 1 1 -1 -1 }}
| Kalmanisma
| Yajinisma
|  
|  
|-
|-
| [[5643/5642]]
| [[9504/9503]]
| 0.30682
| 0.18217
| (3<sup>3</sup>×11×19)/(2×7×13×31)
| (2<sup>5</sup>×3<sup>3</sup>×11)/(13×17×43)
| 2.3.7.11.13.19.31 {{monzo| -1 3 -1 1 -1 1 -1 }}
| 2.3.11.13.17.43 {{monzo| 5 3 1 -1 -1 -1 }}
|  
| Lionelisma
|  
|  
|-
|-
| [[5797/5796]]
| [[9633/9632]]
| 0.29867
| 0.17973
| (11×17×31)/((2×3)<sup>2</sup>×7×23)
| (3×13<sup>2</sup>×19)/(2<sup>5</sup>×7×43)
| 2.3.7.11.17.23.31 {{monzo| -2 -2 -1 1 1 -1 1 }}
| 2.3.7.13.19.43 {{monzo| -5 1 -1 2 1 -1 }}
| Bivojisma
| Coturisma
|  
|  
|-
|-
| [[6076/6075]]
| [[10450/10449]]
| 0.28495
| 0.16568
| ((2×7)<sup>2</sup>×31)/(3<sup>5</sup>×5<sup>2</sup>)
| (2×5<sup>2</sup>×11×19)/(3<sup>5</sup>×43)
| 2.3.5.7.31 {{monzo| 2 -5 -2 2 1 }}
| 2.3.5.11.19.43 {{monzo| 1 -5 2 1 1 -1}}
|  
| Girardisma
|  
|  
|-
|-
| [[6138/6137]]
| [[10880/10879]]
| 0.28207
| 0.15912
| (2×3<sup>2</sup>×11×31)/(17×19<sup>2</sup>)
| (2<sup>7</sup>×5×17)/(11×23×43)
| 2.3.11.17.19.31 {{monzo| 1 2 1 -1 -2 1 }}
| 2.5.11.17.23.43 {{monzo| 7 1 -1 1 -1 -1 }}
|  
| Kaguyisma
|  
|  
|-
|-
| [[6293/6292]]
| [[17545/17544]]
| 0.27513
| 0.098677
| (7×29×31)/((2×11)<sup>2</sup>×13)
| (5×11<sup>2</sup>×29)/(2<sup>3</sup>×3×17×43)
| 2.7.11.13.29.31 {{monzo| -2 1 -2 -1 1 1 }}
| 2.3.5.11.17.29.43 {{monzo| -3 -1 1 2 -1 1 -1 }}
|  
| Manheimisma
|  
|  
|-
|-
| [[6325/6324]]
| [[27048/27047]]
| 0.27373
| 0.064007
| (5<sup>2</sup>×11×23)/(2<sup>2</sup>×3×17×31)
| (2<sup>3</sup>×3×7<sup>2</sup>×23)/(17×37×43)
| 2.3.5.11.17.23.31 {{monzo| -2 -1 2 1 -1 1 -1 }}
| 2.3.7.17.23.37.43 {{monzo| 3 1 2 -1 1 -1 -1 }}
|  
| Jangongisma
|  
|  
|-
|-
| [[6480/6479]]
| [[29241/29240]]
| 0.26719
| 0.059207
| ((2×3)<sup>4</sup>×5)/(11×19×31)
| (3<sup>2</sup>×19)<sup>2</sup>/(2<sup>3</sup>×5×17×43)
| 2.3.5.11.19.31 {{monzo| 4 4 1 -1 -1 -1 }}
| 2.3.5.17.19.43 {{monzo| -3 4 -1 -1 2 -1 }}
| Scarlattisma
| Locquirecisma
|  
| S171
|-
|}
| [[6728/6727]]
 
| 0.25734
=== 47-limit (incomplete) ===
| (2<sup>3</sup>×29<sup>2</sup>)/(7×31<sup>2</sup>)
{| class="wikitable center-6" style="width:100%"
| 2.7.29.31 {{monzo| 3 -1 2 -2 }}
! width="10%" | [[Ratio]]
|  
! width="10%" | [[Cent]]s
|  
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[7657/7656]]
| [[47/46]]
| 0.22611
| 37.232
| (13×19×31)/(2<sup>3</sup>×3×11×29)
| 47/(2×23)
| 2.3.11.13.19.29.31 {{monzo| -3 -1 -1 1 1 -1 1 }}
| 2.23.47 {{monzo| -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[7905/7904]]
| [[48/47]]
| 0.21902
| 36.448
| (3×5×17×31)/(2<sup>5</sup>×13×19)
| (2<sup>4</sup>×3)/47
| 2.3.5.13.17.19.31 {{monzo| -5 1 1 -1 1 -1 1 }}
| 2.3.47 {{monzo| 4 1 -1 }}
|  
| 47th-partial chroma
|  
|  
|-
|-
| [[7936/7935]]
| [[94/93]]
| 0.21816
| 18.516
| (2<sup>8</sup>×31)/(3×5×23<sup>2</sup>)
| (2×47)/(3×31)
| 2.3.5.23.31 {{monzo| 8 -1 -1 -2 1 }}
| 2.3.31.47 {{monzo| 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[8092/8091]]
| [[95/94]]
| 0.21396
| 18.320
| ((2×17)<sup>2</sup>×7)/(3<sup>2</sup>×29×31)
| (5×19)/(2×47)
| 2.3.7.17.29.31 {{monzo| 2 -2 1 2 -1 -1 }}
| 2.5.19.47 {{monzo| -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[8464/8463]]
| [[141/140]]
| 0.20455
| 12.322
| (2<sup>2</sup>×23)<sup>2</sup>/(3×7×13×31)
| (3×47)/(2<sup>2</sup>×5×7)
| 2.3.7.13.23.31 {{monzo| 4 -1 -1 -1 2 -1 }}
| 2.3.5.7.47 {{monzo| -2 1 -1 -1 1 }}
| Polishookisma
| S92
|-
| [[8526/8525]]
| 0.20307
| (2×3×7<sup>2</sup>×29)/(5<sup>2</sup>×11×31)
| 2.3.5.7.11.29.31 {{monzo| 1 1 -2 2 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[8960/8959]]
| [[188/187]]
| 0.19323
| 9.2333
| (2<sup>8</sup>×5×7)/(17<sup>2</sup>×31)
| (2<sup>2</sup>×47)/(11×17)
| 2.5.7.17.31 {{monzo| 8 1 1 -2 -1 }}
| 2.11.37.47 {{monzo| 2 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[9425/9424]]
| [[189/188]]
| 0.18370
| 9.1843
| (5<sup>2</sup>×13×29)/(2<sup>4</sup>×19×31)
| (3<sup>3</sup>×7)/(2<sup>2</sup>×47)
| 2.5.13.19.29.31 {{monzo| -4 2 1 -1 1 -1 }}
| 2.3.7.47 {{monzo| -2 3 1 -1 }}
|  
|  
|  
|  
|-
|-
| 10881/10880
| [[235/234]]
| 0.15911
| 7.3827
| (3<sup>3</sup>×13×31)/(2<sup>7</sup>×5×17)
| (5×47)/(2×3<sup>2</sup>×13)
| 2.3.5.13.17.31 {{monzo| -7 3 -1 1 -1 1 }}
| 2.3.5.13.47 {{monzo| -1 -2 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 11781/11780
| [[329/328]]
| 0.14696
| 5.2701
| (3<sup>2</sup>×7×11×17)/(2<sup>2</sup>×5×19×31)
| (7×47)/(2<sup>3</sup>×41)
| 2.3.5.7.11.17.19.31 {{monzo| -2 2 -1 1 1 1 -1 -1 }}
| 2.7.41.47 {{monzo| -3 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 11935/11934
| [[330/329]]
| 0.14506
| 5.2541
| (5×7×11×31)/(2×3<sup>3</sup>×13×17)
| (2×3×5×11)/(7×47)
| 2.3.5.7.11.13.17.31 {{monzo| -1 -3 1 1 1 -1 -1 1 }}
| 2.3.5.7.11.47 {{monzo| 1 1 1 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 12122/12121
| [[376/375]]
| 0.14282
| 4.6105
| (2×11×19×29)/(17×23×31)
| (2<sup>3</sup>×47)/(3×5<sup>3</sup>)
| 2.11.17.19.23.29.31 {{monzo| 1 1 -1 1 -1 1 -1 }}
| 2.3.5.47 {{monzo| 3 -1 -3 1 }}
|  
|  
|  
|  
|-
|-
| 13300/13299
| [[377/376]]
| 0.13017
| 4.5982
| ((2×5)<sup>2</sup>×7×19)/(3×11×13×31)
| (13×29)/(2<sup>3</sup>×47)
| 2.3.5.7.11.13.19.31 {{monzo| 2 -1 2 1 -1 -1 1 -1 }}
| 2.13.29.47 {{monzo| -3 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 13455/13454
| [[1176/1175]]
| 0.12867
| 1.4728
| (3<sup>2</sup>×5×13×23)/(2×7×31<sup>2</sup>)
| (2<sup>3</sup>×3×7<sup>2</sup>)/(5<sup>2</sup>×47)
| 2.3.5.7.13.23.31 {{monzo| -1 2 1 -1 1 1 -2 }}
| 2.3.5.7.47 {{monzo| 3 1 -2 2 -1 }}
|  
| Lucidorisma
|  
|  
|-
|-
| 15625/15624
| [[2116/2115]]
| 0.11080
| 0.81836
| 5<sup>6</sup>/(2<sup>3</sup>×3<sup>2</sup>×7×31)
| (2×23)<sup>2</sup>/(3<sup>2</sup>×5×47)
| 2.3.5.7.31 {{monzo| -3 -2 6 -1 -1 }}
| 2.3.5.23.47 {{monzo| 2 -2 -1 2 -1 }}
|  
|
| S125
| S46
|-
|-
| [[Acronymisma|17577/17576]]
| [[2209/2208]]
| 0.098497
| 0.78390
| (3<sup>4</sup>×7×31)/(2<sup>3</sup>×13<sup>3</sup>)
| 47<sup>2</sup>/(2<sup>5</sup>×3×5)
| 2.3.7.13.31 {{monzo| -3 4 1 -3 1 }}
| 2.3.23.47 {{monzo| -5 -1 -1 2 }}
| Acronymisma
|  
|  
| S47
|-
|-
| [[Totziensisma|19251/19250]]
| [[2304/2303]]
| 0.089931
| 0.75157
| (3<sup>3</sup>×23×31)/(2×5<sup>3</sup>×7×11)
| (2<sup>4</sup>×3)<sup>2</sup>/(7<sup>2</sup>×47)
| 2.3.5.7.11.23.31 {{monzo| -1 3 -3 -1 -1 1 1}}
| 2.3.7.47 {{monzo| 8 2 -2 -1 }}
| Totziensisma
|  
|  
| S48
|}
=== 53-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[Honeybrookisma|19344/19343]]
| [[53/52]]
| 0.089500
| 32.977
| (2<sup>4</sup>×3×13×31)/(23×29<sup>2</sup>)
| 53/(2<sup>2</sup>×13)
| 2.3.13.23.29.31 {{monzo| 4 1 1 -1 -2 1 }}
| 2.13.53 {{monzo| -2 -1 1 }}
| Honeybrookisma
|  
|  
|  
|-
|-
| 19965/19964
| [[54/53]]
| 0.086716
| 32.360
| (3×5×11<sup>3</sup>)/(2<sup>2</sup>×7×23×31)
| (2×3<sup>3</sup>)/53
| 2.3.5.7.11.23.31 {{monzo| -2 1 1 -1 3 -1 -1 }}
| 2.3.53 {{monzo| 1 3 -1 }}
|  
|  
|  
|  
|-
|-
| 21142/21141
| [[106/105]]
| 0.081888
| 16.410
| (2×11×31<sup>2</sup>)/(3<sup>6</sup>×29)
| (2×53)/(3×5×7)
| 2.3.11.29.31 {{monzo| 1 -6 1 -1 2 }}
| 2.3.5.7.53 {{monzo| 1 -1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 22816/22815
| [[160/159]]
| 0.075880
| 10.854
| (2<sup>5</sup>×23×31)/(3<sup>3</sup>×5×13<sup>2</sup>)
| (2<sup>5</sup>×5)/(3×53)
| 2.3.5.13.23.31 {{monzo| 5 -3 -1 -2 1 1 }}
| 2.3.5.53 {{monzo| 5 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 23375/23374
| [[265/264]]
| 0.074065
| 6.5453
| (5<sup>3</sup>×11×17)/(2×13×29×31)
| (5×53)/(2<sup>3</sup>×3×11)
| 2.5.11.13.17.29.31 {{monzo| -1 3 1 -1 1 -1 -1 }}
| 2.3.5.11.53 {{monzo| -3 -1 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 23716/23715
| [[266/265]]
| 0.073000
| 6.5207
| (2×7×11)<sup>2</sup>/(3<sup>2</sup>×5×17×31)
| (2×7×19)/(5×53)
| 2.3.5.7.11.17.31 {{monzo| 2 -2 -1 2 2 -1 -1 }}
| 2.5.7.19.53 {{monzo| 1 -1 1 1 -1 }}
|  
|  
| S154
|-
| 24025/24024
| 0.072061
| (5×31)<sup>2</sup>/(2<sup>3</sup>×3×7×11×13)
| 2.3.5.7.11.13.31 {{monzo| -3 -1 2 -1 -1 -1 2 }}
|  
|  
| S155
|-
|-
| 27405/27404
| [[319/318]]
| 0.063173
| 5.4356
| (3<sup>3</sup>×5×7×29)/(2<sup>2</sup>×13×17×31)
| (11×29)/(2×3×53)
| 2.3.5.7.13.17.29.31 {{monzo| -2 3 1 1 -1 -1 1 -1 }}
| 2.3.11.29.53 {{monzo| -1 -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[Tricecubisma|29792/29791]]
| [[371/370]]
| 0.058112
| 4.6727
| (2<sup>5</sup>×7<sup>2</sup>×19)/31<sup>3</sup>
| (7×53)/(2×5×37)
| 2.7.19.31 {{monzo| 5 2 1 -3 }}
| 2.5.7.37.53 {{monzo| -1 -1 1 -1 1 }}
| Tricecubisma
|
|-
| 31465/31464
| 0.055022
| (5×7×29×31)/(2<sup>3</sup>×3<sup>2</sup>×19×23)
| 2.3.5.7.19.23.29.31 {{monzo| -3 -2 1 1 -1 -1 1 1 }}
|  
|  
|  
|  
|-
|-
| 31900/31899
| [[372/371]]
| 0.054272
| 4.6601
| ((2×5)<sup>2</sup>×11×29)/(3×7<sup>3</sup>×31)
| (2<sup>2</sup>×3×31)/(7×53)
| 2.3.5.7.11.29.31 {{monzo| 2 -1 2 -3 1 1 -1 }}
| 2.3.7.31.53 {{monzo| 2 1 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 32799/32798
| [[424/423]]
| 0.052784
| 4.0879
| (3×13×29<sup>2</sup>)/(2×23<sup>2</sup>×31)
| (2<sup>3</sup>×53)/(3<sup>2</sup>×47)
| 2.3.13.23.29.31 {{monzo| -1 1 1 -2 2 -1 }}
| 2.3.47.53 {{monzo| 3 -2 -1 1 }}
|  
|  
|  
|  
|-
|-
| 41262/41261
| [[425/424]]
| 0.041958
| 4.0783
| (2×3×13×23<sup>2</sup>)/(11<sup>3</sup>×31)
| (5<sup>2</sup>×17)/(2<sup>3</sup>×53)
| 2.3.11.13.23.31 {{monzo| 1 1 -3 1 2 -1 }}
| 2.5.17.53 {{monzo| -3 2 1 -1 }}
|  
|  
|  
|  
|-
|-
| 42688/42687
| [[477/476]]
| 0.040556
| 3.6332
| (2<sup>6</sup>×23×29)/(3<sup>4</sup>×17×31)
| (3<sup>2</sup>×53)/(2<sup>2</sup>×7×17)
| 2.3.17.23.29.31 {{monzo| 6 -4 -1 1 1 -1 }}
| 2.3.7.17.53 {{monzo| -2 2 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 49011/49010
| [[2809/2808]]
| 0.035324
| 0.61643
| (3×17×31<sup>2</sup>)/(2×5×13<sup>2</sup>×29)
| 53<sup>2</sup>/(2<sup>3</sup>×3<sup>3</sup>×13)
| 2.3.5.13.17.29.31 {{monzo| -1 1 -1 -2 1 -1 2 }}
| 2.3.13.53 {{monzo| -3 -3 -1 2 }}
|
|  
|  
| S53
|-
|-
| 58311/58310
| [[4081/4080]]
| 0.029690
| 0.42427
| (3<sup>2</sup>×11×19×31)/(2×5×7<sup>3</sup>×17)
| (7×11×53)/(2<sup>4</sup>×3×5×17)
| 2.3.5.7.11.17.19.31 {{monzo| -1 2 -1 -3 1 -1 1 1 }}
| 2.3.5.7.11.17.53 {{monzo| -4 -1 -1 1 1 -1 1 }}
|
|
|-
| 78337/78336
| 0.022100
| (7×19<sup>2</sup>×31)/(2<sup>9</sup>×3<sup>2</sup>×17)
| 2.3.7.17.19.31 {{monzo| -9 -2 1 -1 2 1 }}
|  
|  
|  
|  
|}
=== 59-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| 96876/96875
| [[59/58]]
| 0.017871
| 29.594
| (2<sup>2</sup>×3<sup>4</sup>×13×23)/(5<sup>5</sup>×31)
| 59/(2×29)
| 2.3.5.13.23.31 {{monzo| 2 4 -5 1 1 -1 }}
| 2.29.59 {{monzo| -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 98736/98735
| [[60/59]]
| 0.017534
| 29.097
| (2<sup>4</sup>×3×11<sup>2</sup>×17)/(5×7<sup>2</sup>×13×31)
| (2<sup>2</sup>×3×5)/59
| 2.3.5.7.11.13.17.31 {{monzo| 4 1 -1 -2 2 -1 1 -1 }}
| 2.3.5.59 {{monzo| 2 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 102487/102486
| [[118/117]]
| 0.016892
| 14.734
| (7×11<sup>4</sup>)/(2×3×19×29×31)
| (2×59)/(3<sup>2</sup>×13)
| 2.3.7.11.19.29.31 {{monzo| -1 -1 1 4 -1 -1 -1 }}
| 2.3.13.59 {{monzo| 1 -2 -1 1 }}
|  
|  
|  
|  
|-
|-
| 108376/108375
| [[119/118]]
| 0.015974
| 14.610
| (2<sup>3</sup>×19×23×31)/(3×5<sup>3</sup>×17<sup>2</sup>)
| (7×17)/(2×59)
| 2.3.5.17.19.23.31 {{monzo| 3 -1 -3 -2 1 1 1 }}
| 2.7.17.59 {{monzo| -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 111321/111320
| [[177/176]]
| 0.015552
| 9.8087
| (3<sup>3</sup>×7×19×31)/(2<sup>3</sup>×5×11<sup>2</sup>×23)
| (3×59)/(2<sup>4</sup>×11)
| 2.3.5.7.11.19.23.31 {{monzo| -3 3 -1 1 -2 1 -1 1 }}
| 2.3.11.59 {{monzo| -4 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 111476/111475
| [[236/235]]
| 0.015530
| 7.3513
| (2<sup>2</sup>×29×31<sup>2</sup>)/(5<sup>2</sup>×7<sup>3</sup>×13)
| (2<sup>2</sup>×59)/(5×47)
| 2.5.7.13.29.31 {{monzo| 2 -2 -3 -1 1 2 }}
| 2.5.47.59 {{monzo| 2 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 116281/116280
| [[295/294]]
| 0.014888
| 5.8786
| (11×31)<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×5×17×19)
| (5×59)/(2×3×7<sup>2</sup>)
| 2.3.5.11.17.19.31 {{monzo| -3 -2 -1 2 -1 -1 2 }}
| 2.3.5.7.59 {{monzo| -1 -1 1 -2 1 }}
|  
|  
| S341
|-
| 116964/116963
| 0.014801
| (2×3<sup>2</sup>×19)<sup>2</sup>/(7<sup>3</sup>×11×31)
| 2.3.7.11.19.31 {{monzo| 2 4 -3 -1 2 -1 }}
|  
|  
| S342
|-
|-
| 122265/122264
| [[296/295]]
| 0.014160
| 5.8587
| (3<sup>2</sup>×5×11×13×19)/(2<sup>3</sup>×17×29×31)
| (2<sup>3</sup>×37)/(5×59)
| 2.3.5.11.13.17.19.29.31 {{monzo| -3 2 1 1 1 -1 1 -1 -1 }}
| 2.5.37.59 {{monzo| 3 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 174097/174096
| [[414/413]]
| 0.0099441
| 4.1868
| (7<sup>2</sup>×11×17×19)/(2<sup>4</sup>×3<sup>3</sup>×13×31)
| (2×3<sup>2</sup>×23)/(7×59)
| 2.3.7.11.13.17.19.31 {{monzo| -4 -3 2 1 -1 1 1 -1 }}
| 2.3.7.23.59 {{monzo| 1 2 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 175770/175769
| [[473/472]]
| 0.0098495
| 3.6640
| (2×3<sup>4</sup>×5×7×31)/(11×19×29<sup>2</sup>)
| (11×43)/(2<sup>3</sup>×59)
| 2.3.5.7.11.19.29.31 {{monzo| 1 4 1 1 -1 -1 -2 1 }}
| 2.11.43.59 {{monzo| -3 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 178126/178125
| [[1121/1120]]
| 0.0097192
| 1.5451
| (2×13<sup>2</sup>×17×31)/(3×5<sup>5</sup>×19)
| (19×59)/(2<sup>5</sup>×5×7)
| 2.3.5.13.17.19.31 {{monzo| 1 -1 -5 2 1 -1 1 }}
| 2.5.7.19.59 {{monzo| -5 -1 -1 1 1 }}
|  
|  
|  
|  
|-
|-
| 190464/190463
| [[1122/1121]]
| 0.0090896
| 1.5437
| (2<sup>11</sup>×3×31)/((7×13)<sup>2</sup>×23)
| (2×3×11×17)/(19×59)
| 2.3.7.13.23.31 {{monzo| 11 1 -2 -2 -1 1 }}
| 2.3.11.17.19.59 {{monzo| 1 1 1 1 -1 -1 }}
|  
|  
|  
|  
|-
|-
| 207576/207575
| [[3481/3480]]
| 0.0083403
| 0.49741
| ((2×3)<sup>3</sup>×31<sup>2</sup>)/((5×19)<sup>2</sup>×23)
| 59<sup>2</sup>/(2<sup>3</sup>×3×5×29)
| 2.3.5.19.23.31 {{monzo| 3 3 -2 -2 -1 2 }}
| 2.3.5.29.59 {{monzo| -3 -1 -1 -1 2}}
|
|  
|  
| S59
|}
=== 61-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| 212382/212381
| [[61/60]]
| 0.0081515
| 28.616
| (2×3<sup>5</sup>×19×23)/(13×17×31<sup>2</sup>)
| 61/(2<sup>2</sup>×3×5)
| 2.3.13.17.19.23.31 {{monzo| 1 5 -1 -1 1 1 -2 }}
| 2.3.5.61 {{monzo| -2 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 227448/227447
| [[62/61]]
| 0.0076116
| 28.151
| (2<sup>3</sup>×3<sup>7</sup>×13)/(11×23×29×31)
| (2×31)/61
| 2.3.11.13.23.29.31 {{monzo| 3 7 -1 1 -1 -1 -1 }}
| 2.31.61 {{monzo| 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 240065/240064
| [[122/121]]
| 0.0072115
| 14.249
| (5×7×19<sup>3</sup>)/(2<sup>6</sup>×11<sup>2</sup>×31)
| (2×61)/(11<sup>2</sup>)
| 2.5.7.11.19.31 {{monzo| -6 1 1 -2 3 -1 }}
| 2.11.61 {{monzo| 1 -2 1 }}
|  
|  
|  
|  
|-
|-
| 245025/245024
| [[123/122]]
| 0.0070656
| 14.133
| (3<sup>2</sup>×5×11)<sup>2</sup>/(2<sup>5</sup>×13×19×31)
| (3×41)/(2×61)
| 2.3.5.11.13.19.31 {{monzo| -5 4 2 2 -1 -1 -1 }}
| 2.3.41.61 {{monzo| -1 1 1 -1 }}
|
|  
|  
| S495
|-
|-
| 260338/260337
| [[183/182]]
| 0.0066500
| 9.4862
| (2×13×17×19×31)/(3×7<sup>3</sup>×11×23)
| (3×61)/(2×7×13)
| 2.3.7.11.13.17.19.23.31 {{monzo| 1 -1 -3 -1 1 1 1 -1 1 }}
| 2.3.7.13.61 {{monzo| -1 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 268801/268800
| [[184/183]]
| 0.0064406
| 9.4345
| (13×23×29×31)/(2<sup>9</sup>×3×5<sup>2</sup>×7)
| (2<sup>3</sup>×23)/(3×61)
| 2.3.5.7.13.23.29.31 {{monzo| -9 -1 -2 -1 1 1 1 1 }}
| 2.3.23.61 {{monzo| 3 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 278784/278783
| [[244/243]]
| 0.0062010
| 7.1098
| (2<sup>4</sup>×3×11)<sup>2</sup>/(17×23<sup>2</sup>×31)
| (2<sup>2</sup>×61)/3<sup>5</sup>
| 2.3.11.17.23.31 {{monzo| 8 2 2 -1 -2 -1 }}
| 2.3.61 {{monzo| 2 -5 1 }}
|
| S528
|-
| 288145/288144
| 0.0060082
| (5×11×13<sup>2</sup>×31)/(2<sup>4</sup>×3×<sup>3</sup>×23×29)
| 2.3.5.11.13.23.29.31 {{monzo| -4 -3 1 1 2 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 314433/314432
| [[245/244]]
| 0.0055059
| 7.0807
| ((3×7)<sup>2</sup>×23×31)/(2<sup>2</sup>×17)<sup>3</sup>
| (5×7<sup>2</sup>)/(2<sup>2</sup>×61)
| 2.3.7.17.23.31 {{monzo| -6 2 2 -3 1 1 }}
| 2.5.7.61 {{monzo| -2 1 2 -1 }}
|  
|  
|  
|  
|-
|-
| 453376/453375
| [[305/304]]
| 0.0038185
| 5.6855
| (2<sup>8</sup>×7×11×23)/(3<sup>2</sup>×5<sup>3</sup>×13×31)
| (5×61)/(2<sup>4</sup>×19)
| 2.3.5.7.11.13.23.31 {{monzo| 8 -2 -3 1 1 -1 1 -1 }}
| 2.5.19.61 {{monzo| -4 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 459173/459172
| [[306/305]]
| 0.0037703
| 5.6669
| (11×13<sup>3</sup>×19)/(2<sup>2</sup>×7×23<sup>2</sup>×31)
| (2×3<sup>2</sup>×17)/(5×61)
| 2.7.11.13.19.23.31 {{monzo| -2 -1 1 3 1 -2 -1 }}
| 2.3.5.17.61 {{monzo| 1 2 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 509796/509795
| [[672/671]]
| 0.0033959
| 2.5782
| (2×3×7×17)<sup>2</sup>/(5×11×13×23×31)
| (2<sup>5</sup>×3×7)/(11×61)
| 2.3.5.7.11.13.17.23.31 {{monzo| 2 2 -1 2 -1 -1 2 -1 -1 }}
| 2.3.7.11.61 {{monzo| 5 1 1 -1 -1 }}
|
| S714
|-
| 773605/773604
| 0.0022379
| (5×7×23×31<sup>2</sup>)/(2<sup>2</sup>×3<sup>3</sup>×13×19×29)
| 2.3.5.7.13.19.23.29.31 {{monzo| -2 -3 1 1 -1 -1 1 -1 2 }}
|  
|  
|  
|  
|-
|-
| 863940/863939
| [[1404/1403]]
| 0.0020039
| 1.2335
| (2<sup>2</sup>×3×5×7×11<sup>2</sup>×17)/(29×31<sup>3</sup>)
| (2<sup>2</sup>×3<sup>3</sup>×13)/(23×61)
| 2.3.5.7.11.17.29.31 {{monzo| 2 1 1 1 2 1 -1 -3 }}
| 2.3.13.23.61 {{monzo| 2 3 1 -1 -1 }}
|  
|  
|  
|  
|-
|-
| 912951/912950
| [[3721/3720]]
| 0.0018963
| 0.46532
| (3<sup>5</sup>×13×17<sup>2</sup>)/(2×5<sup>2</sup>×19×31<sup>2</sup>)
| 61<sup>2</sup>/(2<sup>3</sup>×3×5×31)
| 2.3.5.13.17.19.31 {{monzo| -1 5 -2 1 2 -1 -2 }}
| 2.3.5.31.61 {{monzo| -3 -1 -1 -1 2 }}
|
|  
|  
| S61
|}
=== 67-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| 1147125/1147124
| [[67/66]]
| 0.0015092
| 26.034
| (3×5<sup>3</sup>×7×19×23)/(2<sup>2</sup>×11×29<sup>2</sup>×31)
| 67/(2×3×11)
| 2.3.5.7.11.19.23.29.31 {{monzo| -2 1 3 1 -1 1 1 -2 -1 }}
| 2.3.11.67 {{monzo| -1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 1154440/1154439
| [[68/67]]
| 0.0014996
| 25.648
| (2<sup>3</sup>×5×7<sup>2</sup>×19×31)/(3<sup>3</sup>×11×13<sup>2</sup>×23)
| (2<sup>2</sup>×17)/67
| 2.3.5.7.11.13.19.23.31 {{monzo| 3 -3 1 2 -1 -2 1 -1 1 }}
| 2.17.67 {{monzo| 2 1 -1 }}
|  
|  
|  
|  
|-
|-
| 1255501/1255500
| [[134/133]]
| 0.0013789
| 12.968
| (13<sup>2</sup>×17×19×23)/(2<sup>2</sup>×3<sup>4</sup>×5<sup>3</sup>×31)
| (2×67)/(7×19)
| 2.3.5.13.17.19.23.31 {{monzo| -2 -4 -3 2 1 1 1 -1 }}
| 2.7.19.67 {{monzo| 1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 1594176/1594175
| [[135/134]]
| 0.0010860
| 12.872
| (2<sup>6</sup>×3×19<sup>2</sup>×23)/((5×11)<sup>2</sup>×17×31)
| (3<sup>3</sup>×5)/(2×67)
| 2.3.5.11.17.19.23.31 {{monzo| 6 1 -2 -2 -1 2 1 -1 }}
| 2.3.5.67 {{monzo| -1 3 1 -1 }}
|  
|  
|  
|  
|-
|-
| 2307361/2307360
| [[201/200]]
| 0.00075031
| 8.6346
| (7<sup>2</sup>×31)<sup>2</sup>/(2<sup>5</sup>×3×5×11×19×23)
| (3×67)/(2<sup>3</sup>×5<sup>2</sup>)
| 2.3.5.7.11.19.23.31 {{monzo| -5 -1 -1 4 -1 -1 -1 2 }}
| 2.3.5.67 {{monzo| -3 1 -2 1 }}
|  
|  
| S1519
|-
| 2310400/2310399
| 0.00074932
| ((2<sup>4</sup>×5×19)/(3×7×13))<sup>2</sup>/31
| 2.3.5.7.13.19.31 {{monzo| 8 -2 2 -2 -2 2 -1 }}
|  
|  
| S1520
|-
|-
| 2345057/2345056
| [[336/335]]
| 0.00073825
| 5.1602
| (11×13×23<sup>2</sup>×31)/(2<sup>5</sup>×7×19<sup>2</sup>×29)
| (2<sup>4</sup>×3×7)/(5×67)
| 2.7.11.13.19.23.29.31 {{monzo| -5 -1 1 1 -2 2 -1 1 }}
| 2.3.5.7.67 {{monzo| 4 1 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 3206269/3206268
| [[671/670]]
| 0.00053995
| 2.5820
| (11×19×23<sup>2</sup>×29)/((2×3×13)<sup>2</sup>×17×31)
| (11×61)/(2×5×67)
| 2.3.11.13.17.19.23.29.31 {{monzo| -2 -2 1 -2 -1 1 2 1 -1 }}
| 2.5.11.61.67 {{monzo| -1 -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 3301376/3301375
| [[4489/4488]]
| 0.00052440
| 0.38570
| (2<sup>13</sup>×13×31)/(5<sup>3</sup>×7<sup>4</sup>×11)
| 67<sup>2</sup>/(2<sup>3</sup>×3×11×17)
| 2.5.7.11.13.31 {{monzo| 13 -3 -4 -1 1 1 }}
| 2.3.11.17.67 {{monzo| -3 -1 -1 -1 2 }}
|
|
|-
| 3346110/3346109
| 0.00051739
| (2×3<sup>9</sup>×5×17)/(13×19<sup>2</sup>×23×31)
| 2.3.5.13.17.19.23.31 {{monzo| 1 9 1 -1 1 -2 -1 -1 }}
|
|
|-
| 3897166/3897165
| 0.00044423
| (2×7<sup>3</sup>×13×19×23)/(3×5×17<sup>2</sup>×29×31)
| 2.3.5.7.13.17.19.23.29.31 {{monzo| 1 -1 -1 3 1 -2 1 1 -1 -1 }}
|
|
|-
| <font style="font-size:0.88em">14753025/14753024</font>
| 0.00011735
| ((3×5)<sup>2</sup>×7×17×19×29)/(2<sup>8</sup>×11×13<sup>2</sup>×31)
| 2.3.5.7.11.13.17.19.29.31 {{monzo| -8 2 2 1 -1 -2 1 1 1 -1 }}
|
|
|-
| <font style="font-size:0.88em">16093000/16092999</font>
| 0.00010758
| ((2×5)<sup>3</sup>×7×11<sup>2</sup>×19)/(3<sup>4</sup>×13×17×29×31)
| 2.3.5.7.11.13.17.19.29.31 {{monzo| 3 -4 3 1 2 -1 -1 1 -1 -1 }}
|
|
|-
| <font style="font-size:0.88em">76271625/76271624</font>
| 2.2698×10<sup>-5</sup>
| (3<sup>9</sup>×5<sup>3</sup>×31)/((2×11)<sup>3</sup>×13×19×29)
| 2.3.5.11.13.19.29.31 {{monzo| -3 9 3 -3 -1 -1 -1 1 }}
|
|
|-
| <font style="font-size:0.88em">80061345/80061344</font>
| 2.1624×10<sup>-5</sup>
| (3<sup>3</sup>×5×7<sup>4</sup>×13×19)/(2<sup>5</sup>×11<sup>2</sup>×23×29×31)
| 2.3.5.7.11.13.19.23.29.31 {{monzo| -5 3 1 4 -2 1 1 -1 -1 -1 }}
|
|
|-
| <font style="font-size:0.79em">133920000/133919999</font>
| 1.2927×10<sup>-5</sup>
| (2<sup>8</sup>×3<sup>3</sup>×5<sup>4</sup>×31)/(17<sup>2</sup>×19×29<sup>3</sup>)
| 2.3.5.17.19.29.31 {{monzo| 8 3 4 -2 -1 -3 1 }}
|
|
|-
| <font style="font-size:0.79em">181037025/181037024</font>
| 9.5629×10<sup>-6</sup>
| (3<sup>2</sup>×5×13×23)<sup>2</sup>/(2<sup>5</sup>×7×(29×31)<sup>2</sup>)
| 2.3.5.7.13.23.29.31 {{monzo| -5 4 2 -1 2 2 -2 -2 }}
|
| S13455
|-
| <font style="font-size:0.79em">370256250/370256249</font>
| 4.6758×10<sup>-6</sup>
| (2×3×5<sup>5</sup>×7<sup>2</sup>×13×31)/(11<sup>7</sup>×19)
| 2.3.5.7.11.13.19.31 {{monzo| 1 1 5 2 -7 1 -1 1 }}
|
|
|-
| <font style="font-size:0.72em">1611308700/1611308699</font>
| 1.0744×10<sup>-6</sup>
| ((2×3<sup>3</sup>×5×31)/(7<sup>2</sup>×13×19))<sup>2</sup>×(23/11)
| 2.3.5.7.11.13.19.23.31 {{monzo| 2 6 2 -4 -1 -2 -2 1 2 }}
|
|  
|  
| S67
|}
|}


=== 37-limit (incomplete) ===
=== 71-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Ratio]]
Line 3,498: Line 3,263:
! width="5%" | Meta<ref name="ssp"/>
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[37/36]]
| [[71/70]]
| 47.434
| 24.557
| 37/(2×3)<sup>2</sup>
| 71/(2×5×7)
| 2.3.37 {{monzo| -2 -2 1 }}
| 2.5.7.71 {{monzo| -1 -1 -1 1 }}
| Large tricesimoseptimal 1/4-tone, 37th-partial chroma
|  
|  
|-
| [[38/37]]
| 46.169
| (2×19)/37
| 2.19.37 {{monzo| 1 1 -1 }}
| Small tricesimoseptimal 1/4-tone
|  
|  
|-
|-
| [[75/74]]
| [[72/71]]
| 23.238
| 24.213
| (3×5<sup>2</sup>)/(2×37)
| (2<sup>3</sup>×3<sup>2</sup>)/71
| 2.3.5.37 {{monzo| -1 1 2 -1 }}
| 2.3.71 {{monzo| 3 2 -1 }}
|  
|  
|  
|  
|-
|-
| [[111/110]]
| [[5041/5040]]
| 15.667
| 0.34346
| (3×37)/(2×5×11)
| 71<sup>2</sup>/(2<sup>4</sup>×3<sup>2</sup>×5×7)
| 2.3.5.11.37 {{monzo| -1 1 -1 -1 1 }}
| 2.3.5.7.71 {{monzo| -4 -2 -1 -1 2 }}
|  
| Third brown pair comma
|  
| S71
|-
|-
| [[112/111]]
| <font style="font-size:0.85em">[[Borcherdsma|160561400000 / 160561399999]]</font>
| 15.527
| 1.0783×10<sup>-8</sup>
| (2<sup>4</sup>×7)/(3×37)
| (2<sup>6</sup>×5<sup>5</sup>×19×29×31×47) / (7×11<sup>2</sup>×13×59<sup>3</sup>×71)
| 2.3.7.37 {{monzo| 4 -1 1 -1 }}
| 2.5.7.11.13.19.29.31.47.59.71 {{monzo| 6 5 -1 -2 -1 1 1 1 1 -3 -1 }}
|  
| Borcherdsma
|  
|  
|}
=== 73-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[148/147]]
| [[73/72]]
| 11.737
| 23.879
| (2<sup>2</sup>×37)/(3×7<sup>2</sup>)
| 73/(2<sup>3</sup>×3<sup>2</sup>)
| 2.3.7.37 {{monzo| 2 -1 -2 1 }}
| 2.3.73 {{monzo| -3 -2 1 }}
|  
|  
|  
|  
|-
|-
| [[185/184]]
| [[74/73]]
| 9.3834
| 23.555
| (5×37)/(2<sup>3</sup>×23)
| (2×37)/73
| 2.5.23.37 {{monzo| -3 1 -1 1 }}
| 2.37.73 {{monzo| 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[186/185]]
| [[366/365]]
| 9.3328
| 4.737
| (2×3×31)/(5×37)
| (2×3×61)/(5×73)
| 2.3.5.31.37 {{monzo| 1 1 -1 1 -1 }}
| 2.3.5.61.73 [1 1 -1 1 -1⟩
|  
| Sidereal comma
|  
|
|-
|}
| [[222/221]]
 
| 7.8160
=== 79-limit (incomplete) ===
| (2×3×37)/(13×17)
{| class="wikitable center-6" style="width:100%"
| 2.3.13.17.37 {{monzo| 1 1 -1 -1 1 }}
! width="10%" | [[Ratio]]
|  
! width="10%" | [[Cent]]s
|  
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[260/259]]
| [[79/78]]
| 6.6714
| 22.054
| (2<sup>2</sup>×5×13)/(7×37)
| 79/(2×3×13)
| 2.5.7.13.37 {{monzo| 2 1 -1 1 -1 }}
| 2.3.13.79 {{monzo| -1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[297/296]]
| [[80/79]]
| 5.8389
| 21.777
| (3<sup>3</sup>×11)/(2<sup>3</sup>×37)
| (2<sup>4</sup>×5)/79
| 2.3.11.37 {{monzo| -3 3 1 -1 }}
| 2.5.79 {{monzo| 4 1 -1 }}
|  
|  
|  
|  
|}
=== 83-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[407/406]]
| [[83/82]]
| 4.2589
| 20.985
| (11×37)/(2×7×29)
| 83/(2×41)
| 2.7.11.29.37 {{monzo| -1 -1 1 -1 1 }}
| 2.41.83 {{monzo| -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| [[408/407]]
| [[84/83]]
| 4.2484
| 20.734
| (2<sup>3</sup>×3×17)/(11×37)
| (2<sup>2</sup>×3×7)/83
| 2.3.11.17.37 {{monzo| 3 1 -1 1 -1 }}
| 2.3.7.83 {{monzo| 2 1 1 -1 }}
|  
|  
|  
|  
|}
=== 89-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[481/480]]
| [[89/88]]
| 3.6030
| 19.562
| (13×37)/(2<sup>5</sup>×3×5)
| 89/(2<sup>3</sup>×11)
| 2.3.5.13.37 {{monzo| -5 -1 -1 1 1 }}
| 2.11.89 {{monzo| -3 -1 1 }}
| Semaphorisma
| Tailwind comma{{idiosyncratic}}
|  
|  
|-
|-
| [[630/629]]
| [[90/89]]
| 2.7502
| 19.344
| (2×3<sup>2</sup>×5×7)/(17×37)
| (2×3<sup>2</sup>×5)/89
| 2.3.5.7.17.37 {{monzo| 1 2 1 1 -1 -1 }}
| 2.3.5.89 {{monzo| 1 2 1 -1 }}
|  
|  
|  
|  
|}
=== 97-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[666/665]]
| [[97/96]]
| 2.6014
| 17.940
| (2×3<sup>2</sup>×37)/(5×7×19)
| 97/(2<sup>5</sup>×3)
| 2.3.5.7.19.37 {{monzo| 1 2 -1 -1 -1 1 }}
| 2.3.97 {{monzo| -5 -1 1 }}
| Beastisma
|  
|  
|-
| [[667/666]]
| 2.5975
| (23×29)/(2×3<sup>2</sup>×37)
| 2.3.23.29.37 {{monzo| -1 -2 1 1 -1 }}
| Denisisma
|  
|  
|-
|-
| [[703/702]]
| [[98/97]]
| 2.4644
| 17.756
| (19×37)/(2×3<sup>3</sup>×13)
| (2×7<sup>2</sup>)/97
| 2.3.13.19.37 {{monzo| -1 -3 -1 1 1 }}
| 2.7.97 {{monzo| 1 2 -1 }}
| Noemisma
|  
|  
|-
| [[704/703]]
| 2.4609
| (2<sup>6</sup>×11)/(19×37)
| 2.11.19.37 {{monzo| 6 1 -1 -1 }}
| Minimyna
|
|-
| [[741/740]]
| 2.3379
| (3×13×19)/(2<sup>2</sup>×5×37)
| 2.3.5.13.19.37 {{monzo| -2 1 -1 1 1 -1 }}
| Botolphisma
|  
|  
|}
=== 101-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[851/850]]
| [[101/100]]
| 2.0355
| 17.226
| (23×37)/(2×5<sup>2</sup>×17)
| 101/(2×5)<sup>2</sup>
| 2.5.17.23.37 {{monzo| -1 -2 -1 1 1 }}
| 2.5.101 {{monzo| -2 -2 1 }}
| Zeissisma
|  
|  
|-
| [[925/924]]
| 1.8726
| (5<sup>2</sup>×37)/(2<sup>2</sup>×3×7×11)
| 2.3.5.7.11.37 {{monzo| -2 -1 2 -1 -1 1 }}
| Alphonsinisma
|  
|  
|-
|-
| [[962/961]]
| [[102/101]]
| 1.8006
| 17.057
| (2×13×37)/31<sup>2</sup>
| (2×3×17)/101
| 2.13.31.37 {{monzo| 1 1 -2 1 }}
| 2.3.17.101 {{monzo| 1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[1000/999]]
| [[7777/7776]]
| 1.7321
| 0.223
| (2×5)<sup>3</sup>/(3<sup>3</sup>×37)
| 7×11×101/(2×3)<sup>5</sup>
| 2.3.5.37 {{monzo| 3 -3 3 -1 }}
| 2.3.7.11.101 {{monzo| -5 -5 1 1 1 }}
|  
| Pulsar comma
|  
|  
|}
=== 103-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[1036/1035]]
| [[103/102]]
| 1.6719
| 16.890
| (2<sup>2</sup>×7×37)/(3<sup>2</sup>×5×23)
| 103/(2×3×17)
| 2.3.5.7.23.37 {{monzo| 2 -2 -1 1 -1 1 }}
| 2.3.17.103 {{monzo| -1 -1 -1 1 }}
| Ganymedisma
|  
|  
|-
| [[1184/1183]]
| 1.4628
| (2<sup>5</sup>×37)/(7×13<sup>2</sup>)
| 2.7.13.37 {{monzo| 5 -1 -2 1 }}
| Gaeisma
|  
|  
|-
|-
| [[1296/1295]]
| [[104/103]]
| 1.3363
| 16.727
| (2×3)<sup>4</sup>/(5×7×37)
| (2<sup>3</sup>×13)/103
| 2.3.5.7.37 {{monzo| 4 4 -1 -1 -1 }}
| 2.13.103 {{monzo| 3 1 -1 }}
|  
|  
| S36
|-
| [[1332/1331]]
| 1.3002
| (2<sup>2</sup>×3<sup>2</sup>×37)/11<sup>3</sup>
| 2.3.11.37 {{monzo| 2 2 -3 1 }}
| Marconisma
|  
|  
|}
=== 107-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[1369/1368]]
| [[107/106]]
| 1.2651
| 16.256
| 37<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×19)
| 107/(2×53)
| 2.3.19.37 {{monzo| -3 -2 -1 2 }}
| 2.53.107 {{monzo| -1 -1 1 }}
|  
|  
| S37
|-
| [[1444/1443]]
| 1.1993
| (2×19)<sup>2</sup>/(3×13×37)
| 2.3.13.19.37 {{monzo| 2 -1 -1 2 -1 }}
|  
|  
| S38
|-
|-
| [[1480/1479]]
| [[108/107]]
| 1.1701
| 16.105
| (2<sup>3</sup>×5×37)/(3×17×29)
| (2<sup>2</sup>×3<sup>3</sup>)/107
| 2.3.5.17.29.37 {{monzo| 3 -1 1 -1 -1 1 }}
| 2.3.107 {{monzo| 2 3 -1 }}
| Aunusisma
|  
|  
|-
| [[1665/1664]]
| 1.0401
| (3<sup>2</sup>×5×37)/(2<sup>7</sup>×13)
| 2.3.5.13.37 {{monzo| -7 2 1 -1 1 }}
| Gabisma
|  
|  
|-
|-
| [[1666/1665]]
| [[750/749]]
| 1.0395
| 2.3099
| (2×7<sup>2</sup>×17)/(3<sup>2</sup>×5×37)
| (2×3×5<sup>3</sup>)/(7×107)
| 2.3.5.7.17.37 {{monzo| 1 -2 -1 2 1 -1 }}
| 2.3.5.7.107 {{monzo| 1 1 3 -1 -1 }}
| Gentisma
| Ancient Chinese tempering comma
|  
|  
|}
=== 109-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[1702/1701]]
| [[109/108]]
| 1.0175
| (2×23×37)/(3<sup>5</sup>×7)
| 2.3.7.23.37 {{monzo| 1 -5 -1 1 1}}
| Kalaharisma
|
|-
| [[1925/1924]]
| 0.89958
| (5<sup>2</sup>×7×11)/(2<sup>2</sup>×13×37)
| 2.5.7.11.13.37 {{monzo| -2 2 1 1 -1 -1 }}
| Misericorde
|
|-
| [[2109/2108]]
| 0.82107
| (3×19×37)/(2<sup>2</sup>×17×31)
| 2.3.17.19.31.37 {{monzo| -2 1 -1 1 -1 1 }}
| Dhotelisma
|
|-
| [[2146/2145]]
| 0.80691
| (2×29×37)/(3×5×11×13)
| 2.3.5.11.13.29.37 {{monzo| 1 -1 -1 -1 -1 1 1 }}
| Stentorisma
|
|-
| [[2295/2294]]
| 0.75451
| (3<sup>3</sup>×5×17)/(2×31×37)
| 2.3.5.17.31.37 {{monzo| -1 3 1 1 -1 -1 }}
|
|
|-
| [[2553/2552]]
| 0.67825
| (3×23×37)/(2<sup>3</sup>×11×29)
| 2.3.11.23.29.37 {{monzo| -3 1 -1 1 -1 1 }}
| Viljevisma
|
|-
| [[2738/2737]]
| 0.63241
| (2×37<sup>2</sup>)/(7×17×23)
| 2.7.17.23.37 {{monzo| 1 -1 -1 -1 2 }}
|
|
|-
| [[2850/2849]]
| 0.60756
| (2×3×5<sup>2</sup>×19)/(7×11×37)
| 2.3.5.7.11.19.37 {{monzo| 1 1 2 -1 -1 1 -1 }}
| Mozhaiskisma
|
|-
| [[3146/3145]]
| 0.55038
| (2×11<sup>2</sup>×13)/(5×17×37)
| 2.5.11.13.17.37 {{monzo| 1 -1 2 1 -1 -1 }}
| Datonisma
|
|-
| [[3220/3219]]
| 0.53773
| (2<sup>2</sup>×5×7×23)/(3×29×37)
| 2.3.5.7.23.29.37 {{monzo| 2 -1 1 1 1 -1 -1 }}
| Murayamisma
|
|-
| [[3256/3255]]
| 0.53179
| (2<sup>3</sup>×11×37)/(3×5×7×31)
| 2.3.5.7.11.31.37 {{monzo| 3 -1 -1 -1 1 -1 1 }}
| Daguerrisma
|
|-
| [[3367/3366]]
| 0.51425
| (7×13×37)/(2×3<sup>2</sup>×11×17)
| 2.3.7.11.13.17.37 {{monzo| -1 -2 1 -1 1 -1 1 }}
| Alexisma
|
|-
| [[3553/3552]]
| 0.48733
| (11×17×19)/(2<sup>5</sup>×3×37)
| 2.3.11.17.19.37 {{monzo| -5 -1 1 1 1 -1 }}
| Meranisma
|
|-
| [[3626/3625]]
| 0.47752
| (2×7<sup>2</sup>×37)/(5<sup>3</sup>×29)
| 2.5.7.29.37 {{monzo| 1 -3 2 -1 1 }}
| Ohsakisma
|
|-
| [[3627/3626]]
| 0.47738
| (3<sup>2</sup>×13×31)/(2×7<sup>2</sup>×37)
| 2.3.7.13.31.37 {{monzo| -1 2 -2 1 1 -1 }}
| Sayersisma
|
|-
| [[3774/3773]]
| 0.45879
| (2×3×17×37)/(7<sup>3</sup>×11)
| 2.3.7.11.17.37 {{monzo| 1 1 -3 -1 1 1 }}
| Megumisma
|
|-
| [[4256/4255]]
| 0.40682
| (2<sup>5</sup>×7×19)/(5×23×37)
| 2.5.7.19.23.37 {{monzo| 5 -1 1 1 -1 -1 }}
|
|
|-
| [[4625/4624]]
| 0.37436
| (5<sup>3</sup>×37)/(2<sup>4</sup>×17<sup>2</sup>)
| 2.5.17.37 {{monzo| -4 3 -2 1 }}
| Shchedrinisma
|
|-
| [[5291/5290]]
| 0.32723
| (11×13×37)/(2×5×23<sup>2</sup>)
| 2.5.11.13.23.37 {{monzo| -1 -1 1 1 -2 1 }}
|
|
|-
| [[5292/5291]]
| 0.32717
| (2<sup>2</sup>×3<sup>3</sup>×7<sup>2</sup>)/(11×13×37)
| 2.3.7.11.13.37 {{monzo| 2 3 2 -1 -1 -1 }}
| Bullionisma
|
|-
| [[5440/5439]]
| 0.31827
| (2<sup>6</sup>×5×17)/(3×7<sup>2</sup>×37)
| 2.3.5.7.17.37 {{monzo| 6 -1 1 -2 1 -1 }}
| Teraosma
|
|-
| [[5625/5624]]
| 0.30780
| (3×5<sup>2</sup>)<sup>2</sup>/(2<sup>3</sup>×19×37)
| 2.3.5.19.37 {{monzo| -3 2 4 -1 -1 }}
|
| S75
|-
| [[6993/6992]]
| 0.24758
| (3<sup>3</sup>×7×37)/(2<sup>4</sup>×19×23)
| 2.3.7.19.23.37 {{monzo| -4 3 1 -1 -1 1 }}
|
|
|-
| [[7105/7104]]
| 0.24368
| (5×7<sup>2</sup>×29)/(2<sup>6</sup>×3×37)
| 2.3.5.7.29.37 {{monzo| -6 -1 1 2 1 -1 }}
| Yousyozanisma
|
|-
| [[7696/7695]]
| 0.22497
| (2<sup>4</sup>×13×37)/(3<sup>4</sup>×5×19)
| 2.3.5.13.19.37 {{monzo| 4 -4 -1 1 -1 1 }}
| Liebisma
|
|-
| [[8991/8990]]
| 0.19256
| (3<sup>5</sup>×37)/(2×5×29×31)
| 2.3.5.29.31.37 {{monzo| -1 5 -1 -1 -1 1 }}
| Solidaritisma, solidarity comma
|
|-
| [[9177/9176]]
| 0.18866
| (3×7×19×23)/(2<sup>3</sup>×31×37)
| 2.3.7.19.23.31.37 {{monzo| -3 1 1 1 1 -1 -1 }}
| Donsaarisma
|
|-
| [[9251/9250]]
| 0.18715
| (11×29<sup>2</sup>)/(2×5<sup>3</sup>×37)
| 2.5.11.29.37 {{monzo| -1 -3 1 2 -1 }}
| Harchisma
|
|-
| [[9361/9360]]
| 0.18495
| (11×23×37)/(2<sup>4</sup>×3<sup>2</sup>×5×13)
| 2.3.5.11.13.23.37 {{monzo| -4 -2 -1 1 -1 1 1 }}
| Friesachisma
|
|-
| [[Zangarisma|10693/10692]]
| 0.16191
| (17<sup>2</sup>×37)/(2<sup>2</sup>×3<sup>5</sup>×11)
| 2.3.11.17.37 {{monzo| -2 -5 -1 2 1 }}
| Zangarisma
|
|-
| [[Sinachopoulosisma|11914/11913]]
| 0.14532
| (2×7×23×37)/(3×11×19<sup>2</sup>)
| 2.3.7.11.19.23.37 {{monzo| 1 -1 1 -1 -2 1 1 }}
| Sinachopoulosisma
|
|-
| [[12321/12320]]
| 0.14052
| (3<sup>2</sup>×37<sup>2</sup>)/(2<sup>5</sup>×5×7×11)
| 2.3.5.7.11.37 {{monzo| -5 2 -1 -1 -1 2 }}
| Zurakowskisma
| S111
|-
| 13690/13689
| 0.12646
| (2×5×37<sup>2</sup>)/(3<sup>2</sup>×13)<sup>2</sup>
| 2.3.5.13.37 {{monzo| 1 -4 1 -2 2 }}
|
|
|-
| 13950/13949
| 0.12411
| (2×(3×5)<sup>2</sup>×31)/(13×29×37)
| 2.3.5.13.29.31.37 {{monzo| 1 2 2 -1 -1 1 -1 }}
|
|
|-
| 14652/14651
| 0.11816
| ((2×3)<sup>2</sup>×11×37)/(7<sup>2</sup>×13×23)
| 2.3.7.11.13.23.37 {{monzo| 2 2 -2 1 -1 -1 1 }}
|
|
|-
| 15873/15872
| 0.10907
| (3×11×13×37)/(2<sup>9</sup>×31)
| 2.3.11.13.31.37 {{monzo| -9 1 1 1 -1 1 }}
|
|
|-
| 16170/16169
| 0.10707
| (2×3×5×7<sup>2</sup>×11)/(19×23×37)
| 2.3.5.7.11.19.23.37 {{monzo| 1 1 1 2 1 -1 -1 -1 }}
|
|
|-
| 16576/16575
| 0.10445
| (2<sup>6</sup>×7×37)/(3×5<sup>2</sup>×13×17)
| 2.3.5.7.13.17.37 {{monzo| 6 -1 -2 1 -1 -1 1 }}
|
|
|-
| 17205/17204
| 0.10063
| (3×5×31×37)/(2<sup>2</sup>×11×17×23)
| 2.3.5.11.17.23.31.37 {{monzo| -2 1 1 -1 -1 -1 1 1 }}
|
|
|-
| 17576/17575
| 0.098503
| (2×13)<sup>3</sup>/(5<sup>2</sup>×19×37)
| 2.5.13.19.37 {{monzo| 3 -2 3 -1 -1 }}
|
|
|-
| [[Genzelisma|18241/18240]]
| 0.094912
| (17×29×37)/(2<sup>6</sup>×3×5×19)
| 2.3.5.17.19.29.37 {{monzo| -6 -1 -1 1 -1 1 1 }}
| Genzelisma
|
|-
| 19500/19499
| 0.088784
| (2<sup>2</sup>×3×5<sup>3</sup>×13)/(17×31×37)
| 2.3.5.13.17.31.37 {{monzo| 2 1 3 1 -1 -1 -1 }}
|
|
|-
| 19684/19683
| 0.087954
| (2<sup>2</sup>×7×19×37)/3<sup>9</sup>
| 2.3.7.19.37 {{monzo| 2 -9 1 1 1 }}
|
|
|-
| 20350/20349
| 0.085075
| (2×5<sup>2</sup>×11×37)/(3<sup>2</sup>×7×17×19)
| 2.3.5.7.11.17.19.37 {{monzo| 1 -2 2 -1 1 -1 -1 1 }}
|
|
|-
| 23200/23199
| 0.074624
| (2<sup>5</sup>×5<sup>2</sup>×29)/(3×11×19×37)
| 2.3.5.11.19.29.37 {{monzo| 5 -1 2 -1 -1 1 -1 }}
|
|
|-
| 26011/26010
| 0.066559
| (19×37<sup>2</sup>)/(2×3<sup>2</sup>×5×17<sup>2</sup>)
| 2.3.5.17.19.37 {{monzo| -1 -2 -1 -2 1 2 }}
|
|
|-
| 28750/28749
| 0.060218
| (2×5<sup>4</sup>×23)/(3×7×37<sup>2</sup>)
| 2.3.5.7.23.37 {{monzo| 1 -1 4 -1 1 -2 }}
|
|
|-
| 28861/28860
| 0.059986
| (7<sup>2</sup>×19×31)/(2<sup>2</sup>×3×5×13×37)
| 2.3.5.7.13.19.31.37 {{monzo| -2 -1 -1 2 -1 1 1 -1 }}
|
|
|-
| 29601/29600
| 0.058487
| (3<sup>2</sup>×11×13×23)/(2<sup>5</sup>×5<sup>2</sup>×37)
| 2.3.5.11.13.23.37 {{monzo| -5 2 -2 1 1 1 -1 }}
|
|
|-
| [[33264/33263]]
| 0.052046
| (2<sup>4</sup>×3<sup>3</sup>×7×11)/(29×31×37)
| 2.3.7.11.29.31.37 {{monzo| 4 3 1 1 -1 -1 -1 }}
| Maryrogersisma
|
|-
| 34225/34224
| 0.050585
| (5×37)<sup>2</sup>/(2<sup>4</sup>×3×23×31)
| 2.3.5.23.31.37 {{monzo| -4 -1 2 -1 -1 2 }}
|
| S185
|-
| 34596/34595
| 0.050042
| (2×3×31)<sup>2</sup>/(5×11×17×37)
| 2.3.5.11.17.31.37 {{monzo| 2 2 -1 -1 -1 2 -1 }}
|
| S186
|-
| 35816/35815
| 0.048338
| (2<sup>3</sup>×11<sup>2</sup>×37)/(5×13×19×29)
| 2.5.11.13.19.29.37 {{monzo| 3 -1 2 -1 -1 -1 1 }}
|
|
|-
| 37962/37961
| 0.045605
| (2×3<sup>3</sup>×19×37)/(7×11×17×29)
| 2.3.7.11.17.19.29.37 {{monzo| 1 3 -1 -1 -1 1 -1 1 }}
|
|
|-
| 38962/38961
| 0.044434
| (2×7×11<sup>2</sup>×23)/(3<sup>4</sup>×13×37)
| 2.3.7.11.13.23.37 {{monzo| 1 -4 1 2 -1 1 -1 }}
|
|
|-
| 41515/41514
| 0.041702
| (5×19<sup>2</sup>×23)/(2×3×11×17×37)
| 2.3.5.11.17.19.23.37 {{monzo| -1 -1 1 -1 -1 2 1 -1 }}
|
|
|-
| 42625/42624
| 0.040616
| (5<sup>3</sup>×11×31)/(2<sup>7</sup>×3<sup>2</sup>×37)
| 2.3.5.11.31.37 {{monzo| -7 -2 3 1 1 -1 }}
|
|
|-
| 43401/43400
| 0.039890
| (3×17×23×37)/(2<sup>3</sup>×5<sup>2</sup>×7×31)
| 2.3.5.7.17.23.31.37 {{monzo| -3 1 -2 -1 1 1 -1 1 }}
|
|
|-
| 44955/44954
| 0.038511
| (3<sup>5</sup>×5×37)/(2×7×13<sup>2</sup>×19)
| 2.3.5.7.13.19.37 {{monzo| -1 5 1 -1 -2 -1 1 }}
|
|
|-
| 45696/45695
| 0.037886
| (2<sup>7</sup>×3×7×17)/(5×13×19×37)
| 2.3.5.7.13.17.19.37 {{monzo| 7 1 -1 1 -1 1 -1 -1 }}
|
|
|-
| 47916/47915
| 0.036131
| ((2×3)<sup>2</sup>×11<sup>3</sup>)/(5×7×37<sup>2</sup>)
| 2.3.5.7.11.37 {{monzo| 2 2 -1 -1 3 -2 }}
|
|
|-
| 48841/48840
| 0.035447
| (13×17)<sup>2</sup>/(2<sup>3</sup>×3×5×11×37)
| 2.3.5.11.13.17.37 {{monzo| -3 -1 -1 -1 2 2 -1 }}
|
| S221
|-
| 49248/49247
| 0.035154
| (2<sup>5</sup>×3<sup>4</sup>×19)/(11<sup>3</sup>×37)
| 2.3.11.19.37 {{monzo| 5 4 -3 1 -1 }}
|
|
|-
| 50025/50024
| 0.034608
| (3×5<sup>2</sup>×23×29)/(2<sup>3</sup>×13<sup>2</sup>×37)
| 2.3.5.13.23.29.37 {{monzo| -3 1 2 -2 1 1 -1 }}
|
|
|-
| 55056/55055
| 0.031445
| (2<sup>4</sup>×3×31×37)/(5×7×11<sup>2</sup>×13)
| 2.3.5.7.11.13.31.37 {{monzo| 4 1 -1 -1 -2 -1 1 1 }}
|
|
|-
| 56203/56202
| 0.030804
| (7<sup>2</sup>×31×37)/(2×3×17×19×29)
| 2.3.7.17.19.29.31.37 {{monzo| -1 -1 2 -1 -1 -1 1 1 }}
|
|
|-
| 60606/60605
| 0.028566
| (2×3<sup>2</sup>×7×13×37)/(5×17×23×31)
| 2.3.5.7.13.17.23.31.37 {{monzo| 1 2 -1 1 1 -1 -1 -1 1 }}
|
|
|-
| 67600/67599
| 0.025610
| (2<sup>2</sup>×5×13)<sup>2</sup>/(3<sup>2</sup>×7×29×37)
| 2.3.5.7.13.29.37 {{monzo| 4 -2 2 -1 2 -1 -1 }}
|
| S260
|-
| 68783/68782
| 0.025170
| (11×13<sup>2</sup>×37)/(2×7×17<sup>3</sup>)
| 2.7.11.13.17.37 {{monzo| -1 -1 1 2 -3 1 }}
|
|
|-
| 71485/71484
| 0.024218
| (5×17×29<sup>2</sup>)/(2<sup>2</sup>×3×7×23×37)
| 2.3.5.7.17.23.29.37 {{monzo| -2 -1 1 -1 1 -1 2 -1 }}
|
|
|-
| [[Jouvisma|77441/77440]]
| 0.022356
| (7×13×23×37)/(2<sup>7</sup>×5×11<sup>2</sup>)
| 2.5.7.11.13.23.37 {{monzo| -7 -1 1 -2 1 1 1 }}
| Jouvisma
|
|-
| 78625/78624
| 0.022019
| (5<sup>3</sup>×17×37)/(2<sup>5</sup>×3<sup>3</sup>×7×13)
| 2.3.5.7.13.17.37 {{monzo| -5 -3 3 -1 -1 1 1 }}
|
|
|-
| 80920/80919
| 0.021395
| (2<sup>3</sup>×5×7×17<sup>2</sup>)/(3<sup>7</sup>×37)
| 2.3.5.7.17.37 {{monzo| 3 -7 1 1 2 -1 }}
|
|
|-
| 82621/82620
| 0.020954
| (7×11×29×37)/(2<sup>2</sup>×3<sup>5</sup>×5×17)
| 2.3.5.7.11.17.29.37 {{monzo| -2 -5 -1 1 1 -1 1 1 }}
|
|
|-
| 85064/85063
| 0.020352
| ((2×7)<sup>3</sup>×31)/(11<sup>2</sup>×19×37)
| 2.7.11.19.31.37 {{monzo| 3 3 -2 -1 1 -1 }}
|
|
|-
| 88320/88319
| 0.019602
| (2<sup>8</sup>×3×5×23)/(7×11×31×37)
| 2.3.5.7.11.23.31.37 {{monzo| 8 1 1 -1 -1 1 -1 -1 }}
|
|
|-
| 93093/93092
| 0.018597
| (3×7×11×13×31)/(2<sup>2</sup>×17×37<sup>2</sup>)
| 2.3.7.11.13.17.31.37 {{monzo| -2 1 1 1 1 -1 1 -2 }}
|
|
|-
| [[93500/93499]]
| 0.018516
| (2<sup>2</sup>×5<sup>3</sup>×11×17)/(7×19<sup>2</sup>×37)
| 2.5.7.11.17.19.37 {{monzo| 2 3 -1 1 1 -2 -1 }}
|
|
|-
| 108780/108779
| 0.015915
| (2<sup>2</sup>×3×5×7<sup>2</sup>×37)/(11<sup>2</sup>×29×31)
| 2.3.5.7.11.29.31.37 {{monzo| 2 1 1 2 -2 -1 -1 1 }}
|
|
|-
| 208495/208494
| 0.0083035
| (5×7<sup>2</sup>×23×37)/(2×3<sup>6</sup>×11×13)
| 2.3.5.7.11.13.23.37 {{monzo| -1 -6 1 2 -1 -1 1 1 }}
|
|
|-
| 443556/443555
| 0.0039031
| (2×3<sup>2</sup>×37)<sup>2</sup>/(5×7×19×23×29)
| 2.3.5.7.19.23.29.37 {{monzo| 2 4 -1 -1 -1 -1 -1 2 }}
|
| S666
|-
| 466830/466829
| 0.0037085
| (2×3<sup>3</sup>×5×7×13×19)/(11×31×37<sup>2</sup>)
| 2.3.5.7.11.13.19.31.37 {{monzo| 1 3 1 1 -1 1 1 -1 -2 }}
|
|
|-
| 1055241/1055240
| 0.0016406
| (3<sup>3</sup>×11<sup>2</sup>×17×19)/(2<sup>3</sup>×5×23×31×37)
| 2.3.5.11.17.19.23.31.37 {{monzo| -3 3 -1 2 1 1 -1 -1 -1 }}
|
|
|-
| 1763125/1763124
| 9.8191×10<sup>-4</sup>
| (5<sup>4</sup>×7×13×31)/(2<sup>2</sup>×3×11×19<sup>2</sup>×37)
| 2.3.5.7.11.13.19.31.37 {{monzo| -2 -1 4 1 -1 1 -2 1 -1 }}
|
|
|-
| <font style="font-size:0.88em">50481025/50481024</font>
| 3.4295×10<sup>-5</sup>
| (5×7<sup>2</sup>×29)<sup>2</sup>/(2<sup>7</sup>×3×11×17×19×37)
| 2.3.5.7.11.17.19.29.37 {{monzo| -7 -1 2 4 -1 -1 -1 2 -1 }}
|
| S7105
|}
 
=== 41-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[41/40]]
| 42.749
| 41/(2<sup>3</sup>×5)
| 2.5.41 {{monzo| -3 -1 1 }}
| Large quadracesimoprimal 1/5-tone
|
|-
| [[42/41]]
| 41.719
| (2×3×7)/41
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| Small quadracesimoprimal 1/5-tone
|
|-
| [[82/81]]
| 21.242
| (2×41)/3<sup>4</sup>
| 2.3.41 {{monzo| 1 -4 1 }}
| 41st-partial chroma
|
|-
| [[124/123]]
| 14.018
| (2<sup>2</sup>×31)/(3×41)
| 2.3.31.41 {{monzo| 2 -1 1 -1 }}
|
|
|-
| [[165/164]]
| 10.524
| (3×5×11)/(2<sup>2</sup>×41)
| 2.3.5.11.41 {{monzo| -2 1 1 1 -1 }}
|
|
|-
| [[205/204]]
| 8.4657
| (5×41)/(2<sup>2</sup>×3×17)
| 2.3.5.17.41 {{monzo| -2 -1 1 -1 1 }}
|
|
|-
| [[246/245]]
| 7.0519
| (2×3×41)/(5×7<sup>2</sup>)
| 2.3.5.7.41 {{monzo| 1 1 -1 -2 1 }}
|
|
|-
| [[247/246]]
| 7.0233
| (13×19)/(2×3×41)
| 2.3.13.19.41 {{monzo| -1 -1 1 1 -1 }}
|
|
|-
| [[287/286]]
| 6.0427
| (7×41)/(2×11×13)
| 2.7.11.13.41 {{monzo| -1 1 -1 -1 1 }}
|
|
|-
| [[288/287]]
| 6.0217
| (2<sup>5</sup>×3<sup>2</sup>)/(7×41)
| 2.3.7.41 {{monzo| 5 2 -1 -1 }}
|
|
|-
| [[369/368]]
| 4.6981
| (3<sup>2</sup>×41)/(2<sup>4</sup>×23)
| 2.3.23.41 {{monzo| -4 2 -1 1 }}
|
|
|-
| [[370/369]]
| 4.6853
| (2×5×37)/(3<sup>2</sup>×41)
| 2.3.5.37.41 {{monzo| 1 -2 1 1 -1 }}
|
|
|-
| [[451/450]]
| 3.8429
| (11×41)/(2×(3×5)<sup>2</sup>)
| 2.3.5.11.41 {{monzo| -1 -2 -2 1 1 }}
|
|
|-
| [[493/492]]
| 3.5152
| (17×29)/(2<sup>2</sup>×3×41)
| 2.3.17.29.41 {{monzo| -2 -1 1 1 -1 }}
|
|
|-
| [[533/532]]
| 3.2511
| (13×41)/(2<sup>2</sup>×7×19)
| 2.7.13.19.41 {{monzo| -2 -1 1 -1 1 }}
|
|
|-
| [[575/574]]
| 3.0135
| (5<sup>2</sup>×23)/(2×7×41)
| 2.5.7.23.41 {{monzo| -1 2 -1 1 -1 }}
| Renatisma
|
|-
| [[616/615]]
| 2.8127
| (2<sup>3</sup>×7×11)/(3×5×41)
| 2.3.5.7.11.41 {{monzo| 3 -1 -1 1 1 -1 }}
| Ellisma
|
|-
| [[697/696]]
| 2.4856
| (17×41)/(2<sup>3</sup>×3×29)
| 2.3.17.29.41 {{monzo| -3 -1 1 -1 1 }}
|
|
|-
| [[780/779]]
| 2.2210
| (2<sup>2</sup>×3×5×13)/(19×41)
| 2.3.5.13.19.41 {{monzo| 2 1 1 1 -1 -1 }}
| Wiesentisma
|
|-
| [[820/819]]
| 2.1125
| (2<sup>2</sup>×5×41)/(3<sup>2</sup>×7×13)
| 2.3.5.7.13.41 {{monzo| 2 -2 1 -1 -1 1 }}
|
|
|-
| [[1025/1024]]
| 1.6898
| (5<sup>2</sup>×41)/2<sup>10</sup>
| 2.5.41 {{monzo| -10 2 1 }}
| Kilobytisma
|
|-
| [[1026/1025]]
| 1.6882
| (2×3<sup>3</sup>×19)/(5<sup>2</sup>×41)
| 2.3.5.19.41 {{monzo| 1 3 -2 1 -1 }}
| Ingridisma
|
|-
| [[1148/1147]]
| 1.5087
| (2<sup>2</sup>×7×41)/(31×37)
| 2.7.31.37.41 {{monzo| 2 1 -1 -1 1 }}
|
|
|-
| [[1189/1188]]
| 1.4567
| (29×41)/(2<sup>2</sup>×3<sup>3</sup>×11)
| 2.3.11.29.41 {{monzo| -2 -3 -1 1 1 }}
|
|
|-
| [[1190/1189]]
| 1.4554
| (2×5×7×17)/(29×41)
| 2.5.7.17.29.41 {{monzo| 1 1 1 1 -1 -1 }}
| Pelagisma
|
|-
| [[1312/1311]]
| 1.3200
| (2<sup>5</sup>×41)/(3×19×23)
| 2.3.19.23.41 {{monzo| 5 -1 -1 -1 1 }}
|
|
|-
| [[1353/1352]]
| 1.2800
| (3×11×41)/(2<sup>3</sup>×13<sup>2</sup>)
| 2.3.11.13.41 {{monzo| -3 1 1 -2 1 }}
|
|
|-
| [[1395/1394]]
| 1.2415
| (3<sup>2</sup>×5×31)/(2×17×41)
| 2.3.5.17.31.41 {{monzo| -1 2 1 -1 1 -1 }}
|
|
|-
| [[1518/1517]]
| 1.1408
| (2×3×11×23)/(37×41)
| 2.3.11.23.37.41 {{monzo| 1 1 1 1 -1 -1 }}
| Rovaniemisma
|
|-
| [[1600/1599]]
| 1.0824
| (2<sup>3</sup>×5)<sup>2</sup>/(3×13×41)
| 2.3.5.13.41 {{monzo| 6 -1 2 -1 -1 }}
|
| S40
|-
| [[1681/1680]]
| 1.0302
| 41<sup>2</sup>/(2<sup>4</sup>×3×5×7)
| 2.3.5.7.41 {{monzo| -4 -1 -1 -1 2 }}
|
| S41
|-
| [[1682/1681]]
| 1.0296
| (2×29<sup>2</sup>)/41<sup>2</sup>
| 2.29.41 {{monzo| 1 2 -2 }}
| Shaftesburisma
|
|-
| [[1805/1804]]
| 0.95940
| (5×19<sup>2</sup>)/(2<sup>2</sup>×11×41)
| 2.5.11.19.41 {{monzo| -2 1 -1 2 -1 }}
|
|
|-
| [[1886/1885]]
| 0.91818
| (2×23×41)/(5×13×29)
| 2.5.13.23.29.41 {{monzo| 1 -1 -1 1 -1 1 }}
|
|
|-
| [[1887/1886]]
| 0.91770
| (3×17×37)/(2×23×41)
| 2.3.17.23.37.41 {{monzo| -1 1 1 -1 1 -1 }}
|
|
|-
| [[2091/2090]]
| 0.82814
| (3×17×41)/(2×5×11×19)
| 2.3.5.11.17.19.41 {{monzo| -1 1 -1 -1 1 -1 1 }}
|
|
|-
| [[2255/2254]]
| 0.76790
| (5×11×41)/(2×7<sup>2</sup>×23)
| 2.5.7.11.23.41 {{monzo| -1 1 -2 1 -1 1 }}
| Qinghaisma
|
|-
| [[2296/2295]]
| 0.75419
| (2<sup>3</sup>×7×41)/(3<sup>3</sup>×5×17)
| 2.3.5.7.17.41 {{monzo| 3 -3 -1 1 -1 1 }}
|
|
|-
| [[2542/2541]]
| 0.68119
| (2×31×41)/(3×7×11<sup>2</sup>)
| 2.3.7.11.31.41 {{monzo| 1 -1 -1 -2 1 1 }}
|
|
|-
| [[2584/2583]]
| 0.67011
| (2<sup>3</sup>×17×19)/(3<sup>2</sup>×7×41)
| 2.3.7.17.19.41 {{monzo| 3 -2 -1 1 1 -1 }}
|
|
|-
| [[2625/2624]]
| 0.65964
| (3×5<sup>3</sup>×7)/(2<sup>6</sup>×41)
| 2.3.5.7.41 {{monzo| -6 1 3 1 -1 }}
|
|
|-
| [[2665/2664]]
| 0.64974
| (5×13×41)/(2<sup>3</sup>×3<sup>2</sup>×37)
| 2.3.5.13.37.41 {{monzo| -3 -2 1 1 -1 1 }}
|
|
|-
| [[2871/2870]]
| 0.60311
| (3<sup>2</sup>×11×29)/(2×5×7×41)
| 2.3.5.7.11.29.41 {{monzo| -1 2 -1 -1 1 1 -1 }}
| Schoberisma
|
|-
| [[3690/3689]]
| 0.46923
| (2×3<sup>2</sup>×5×41)/(7×17×31)
| 2.3.5.7.17.31.41 {{monzo| 1 2 1 -1 -1 -1 1 }}
|
|
|-
| [[3773/3772]]
| 0.45891
| (7<sup>3</sup>×11)/(2<sup>2</sup>×23×41)
| 2.7.11.23.41 {{monzo| -2 3 1 -1 -1 }}
| Smithsonianisma
|
|-
| [[4060/4059]]
| 0.42646
| (2<sup>2</sup>×5×7×29)/(3<sup>2</sup>×11×41)
| 2.3.5.7.11.29.41 {{monzo| 2 -2 1 1 -1 1 -1 }}
| Deipylosisma
|
|-
| [[4264/4263]]
| 0.40606
| (2<sup>3</sup>×13×41)/(3×7<sup>2</sup>×29)
| 2.3.7.13.29.41 {{monzo| 3 -1 -2 1 -1 1 }}
|
|
|-
| [[4551/4550]]
| 0.38045
| (3×37×41)/(2×5<sup>2</sup>×7×13)
| 2.3.5.7.13.37.41 {{monzo| -1 1 -2 -1 -1 1 1 }}
|
|
|-
| [[4675/4674]]
| 0.37036
| (5<sup>2</sup>×11×17)/(2×3×19×41)
| 2.3.5.11.17.19.41 {{monzo| -1 -1 2 1 1 -1 -1 }}
| Ohbokisma
|
|-
| [[4921/4920]]
| 0.35184
| (7×19×37)/(2<sup>3</sup>×3×5×41)
| 2.3.5.7.19.37.41 {{monzo| -3 -1 -1 1 1 1 -1 }}
| Volontisma
|
|-
| [[4961/4960]]
| 0.34900
| (11<sup>2</sup>×41)/(2<sup>5</sup>×5×31)
| 2.5.11.31.41 {{monzo| -5 -1 2 -1 1 }}
|
|
|-
| [[5084/5083]]
| 0.34056
| (2<sup>2</sup>×31×41)/(13×17×23)
| 2.13.17.23.31.41 {{monzo| 2 -1 -1 -1 1 1 }}
|
|
|-
| [[5577/5576]]
| 0.31045
| (3×11×13<sup>2</sup>)/(2<sup>3</sup>×17×41)
| 2.3.11.13.17.41 {{monzo| -3 1 1 2 -1 -1 }}
| Priestlisma
|
|-
| [[6069/6068]]
| 0.28528
| (3×7×17<sup>2</sup>)/(2<sup>2</sup>×37×41)
| 2.3.7.17.37.41 {{monzo| -2 1 1 2 -1 -1 }}
| Cevolanisma
|
|-
| [[6273/6272]]
| 0.27600
| (3<sup>2</sup>×17×41)/(2<sup>7</sup>×7<sup>2</sup>)
| 2.3.7.17.41 {{monzo| -7 2 -2 1 1 }}
|
|
|-
| [[6561/6560]]
| 0.26389
| 3<sup>8</sup>/(2<sup>5</sup>×5×41)
| 2.3.5.41 {{monzo| -5 8 -1 -1 }}
|
| S81
|-
| [[6601/6600]]
| 0.26229
| (7×23×41)/(2<sup>3</sup>×3×5<sup>2</sup>×11)
| 2.3.5.7.11.23.41 {{monzo| -3 -1 -2 1 -1 1 1 }}
|
|
|-
| [[6930/6929]]
| 0.24984
| (2×3<sup>2</sup>×5×7×11)/(13<sup>2</sup>×41)
| 2.3.5.7.11.13.41 {{monzo| 1 2 1 1 1 -2 -1 }}
| Bedanisma
|
|-
| [[7176/7175]]
| 0.24127
| (2<sup>3</sup>×3×13×23)/(5<sup>2</sup>×7×41)
| 2.3.5.7.13.23.41 {{monzo| 3 1 -2 -1 1 1 -1 }}
| Kunijisma
|
|-
| [[7216/7215]]
| 0.23993
| (2<sup>4</sup>×11×41)/(3×5×13×37)
| 2.3.5.11.13.37.41 {{monzo| 4 -1 -1 1 -1 -1 1 }}
|
|
|-
| [[7750/7749]]
| 0.22340
| (2×5<sup>3</sup>×31)/(3<sup>3</sup>×7×41)
| 2.3.5.7.31.41 {{monzo| 1 -3 3 -1 1 -1 }}
|
|
|-
| [[8569/8568]]
| 0.20205
| (11×19×41)/(2<sup>3</sup>×3<sup>2</sup>×7×17)
| 2.3.7.11.17.19.41 {{monzo| -3 -2 -1 1 -1 1 1 }}
| Mamelisma
|
|-
| [[8856/8855]]
| 0.19550
| ((2×3)<sup>3</sup>×41)/(5×7×11×23)
| 2.3.5.7.11.23.41 {{monzo| 3 3 -1 -1 -1 -1 1 }}
|
|
|-
| [[9472/9471]]
| 0.18278
| (2<sup>8</sup>×37)/(3×7×11×41)
| 2.3.7.11.37.41 {{monzo| 8 -1 -1 -1 1 -1 }}
| Brugesisma
|
|-
| 10045/10044
| 0.17236
| (5×7<sup>2</sup>×41)/(2<sup>2</sup>×3<sup>4</sup>×31)
| 2.3.5.7.31.41 {{monzo| -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 {{monzo| 1 1 1 -1 1 1 -1 -1}}
| Etampesisma
|
|-
| 10660/10659
| 0.16241
| (2<sup>2</sup>×5×13×41)/(3×11×17×19)
| 2.3.5.11.13.17.19.41 {{monzo| 2 -1 1 -1 1 -1 -1 1 }}
|
|
|-
| [[11440/11439]]
| 0.15134
| (2<sup>4</sup>×5×11×13)/(3<sup>2</sup>×31×41)
| 2.3.5.11.13.31.41 {{monzo| 4 -2 1 1 1 -1 -1 }}
| Massironisma
|
|-
| 13776/13775
| 0.12567
| (2<sup>4</sup>×3×7×41)/(5<sup>2</sup>×19×29)
| 2.3.5.7.19.29.41 {{monzo| 4 1 -2 1 -1 -1 1 }}
|
|
|-
| 14145/14144
| 0.12240
| (3×5×23×41)/(2<sup>6</sup>×13×17)
| 2.3.5.13.17.23.41 {{monzo| -6 1 1 -1 -1 1 1 }}
|
|
|-
| 14801/14800
| 0.11697
| (19<sup>2</sup>×41)/(2<sup>4</sup>×5<sup>2</sup>×37)
| 2.5.19.37.41 {{monzo| -4 -2 2 -1 1 }}
|
|
|-
| [[15376/15375]]
| 0.11260
| (2<sup>2</sup>×31)<sup>2</sup>/(3×5<sup>3</sup>×41)
| 2.3.5.31.41 {{monzo| 4 -1 -3 2 -1 }}
| Martakisma
| S124
|-
| 15457/15456
| 0.11201
| (13×29×41)/(2<sup>5</sup>×3×7×23)
| 2.3.7.13.23.29.41 {{monzo| -5 -1 -1 1 -1 1 1 }}
|
|
|-
| 16400/16399
| 0.10557
| (2<sup>4</sup>×5<sup>2</sup>×41)/(23<sup>2</sup>×31)
| 2.5.23.31.41 {{monzo| 4 2 -2 -1 1 }}
|
|
|-
| 16524/16523
| 0.10477
| (2<sup>2</sup>×3<sup>5</sup>×17)/(13×31×41)
| 2.3.13.17.31.41 {{monzo| 2 5 -1 1 -1 -1 }}
|
|
|-
| 16606/16605
| 0.10426
| (2×19<sup>2</sup>×23)/(3<sup>4</sup>×5×41)
| 2.3.5.19.23.41 {{monzo| 1 -4 -1 2 1 -1 }}
|
|
|-
| 17425/17424
| 0.099356
| (5<sup>2</sup>×17×41)/(2<sup>2</sup>×3×11)<sup>2</sup>
| 2.3.5.11.17.41 {{monzo| -4 -2 2 -2 1 1 }}
|
|
|-
| [[17836/17835]]
| 0.097067
| (2<sup>2</sup>×7<sup>3</sup>×13)/(3×5×29×41)
| 2.3.5.7.13.29.41 {{monzo| 2 -1 -1 3 1 -1 -1 }}
| Canupisma
|
|-
| 17918/17917
| 0.096623
| (2×17<sup>2</sup>×31)/(19×23×41)
| 2.17.19.23.31.41 {{monzo| 1 2 -1 -1 1 -1 }}
|
|
|-
| 19721/19720
| 0.087789
| (13×37×41)/(2<sup>3</sup>×5×17×29)
| 2.5.13.17.29.37.41 {{monzo| -3 -1 1 -1 -1 1 1 }}
|
|
|-
| 19845/19844
| 0.087240
| (3<sup>4</sup>×5×7<sup>2</sup>)/((2×11)<sup>2</sup>×41)
| 2.3.5.7.11.41 {{monzo| -2 4 1 2 -2 -1 }}
|
|
|-
| [[76384/76383]]
| 0.022665
| (2<sup>5</sup>×7×11×31)/(3<sup>4</sup>×23×41)
| 2.3.7.11.23.31.41 {{monzo| 5 -4 1 1 -1 1 -1 }}
| Vernonisma
|
|-
| [[Mebisma|1048576/1048575]]
| 0.0016510
| 2<sup>20</sup>/(3×5<sup>2</sup>×11×31×41)
| 2.3.5.11.31.41 {{monzo| 20 -1 -2 -1 -1 -1 }}
| Mebisma
| S1024
|}
 
=== 43-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[43/42]]
| 40.737
| 43/(2×3×7)
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| Large quadracesimotertial 1/5-tone
|
|-
| [[44/43]]
| 39.800
| (2<sup>2</sup>×11)/43
| 2.11.43 {{monzo| 2 1 -1 }}
| Small quadracesimotertial 1/5-tone
|
|-
| [[86/85]]
| 20.249
| (2×43)/(5×17)
| 2.5.17.43 {{monzo| 1 -1 -1 1 }}
| Large quadracesimotertial 1/10-tone
|
|-
| [[87/86]]
| 20.014
| (3×29)/(2×43)
| 2.3.29.43 {{monzo| -1 1 1 -1 }}
| Small quadracesimotertial 1/10-tone
|
|-
| [[129/128]]
| 13.473
| (3×43)/2<sup>7</sup>
| 2.3.43 {{monzo| -7 1 1 }}
| 43rd-partial chroma
|
|-
| [[130/129]]
| 13.369
| (2×5×13)/(3×43)
| 2.3.5.13.43 {{monzo| 1 -1 1 1 -1 }}
|
|
|-
| [[172/171]]
| 10.095
| (2<sup>2</sup>×43)/(3<sup>2</sup>×19)
| 2.3.19.43 {{monzo| 2 -2 -1 1 }}
|
|
|-
| [[216/215]]
| 8.0336
| (2×3)<sup>3</sup>/(5×43)
| 2.3.5.43 {{monzo| 3 3 -1 -1 }}
|
|
|-
| [[259/258]]
| 6.6972
| (7×37)/(2×3×43)
| 2.3.7.37.43 {{monzo| -1 -1 1 1 -1 }}
|
|
|-
| [[301/300]]
| 5.7612
| (7×43)/((2×5)<sup>2</sup>×3)
| 2.3.5.7.43 {{monzo| -2 -1 -2 1 1 }}
|
|
|-
| [[344/343]]
| 5.0400
| (2<sup>3</sup>×43)/7<sup>3</sup>
| 2.7.43 {{monzo| 3 -3 1 }}
|
|
|-
| [[345/344]]
| 5.0254
| (3×5×23)/(2<sup>3</sup>×43)
| 2.3.5.23.43 {{monzo| -3 1 1 1 -1 }}
|
|
|-
| [[430/429]]
| 4.0308
| (2×5×43)/(3×11×13)
| 2.3.5.11.13.43 {{monzo| 1 -1 1 -1 -1 1 }}
|
|
|-
| [[559/558]]
| 3.0998
| (13×43)/(2×3<sup>2</sup>×31)
| 2.3.13.31.43 {{monzo| -1 -2 1 -1 1 }}
|
|
|-
| [[560/559]]
| 3.0943
| (2<sup>4</sup>×5×7)/(13×43)
| 2.5.7.13.43 {{monzo| 4 1 1 -1 -1 }}
|
|
|-
| [[645/644]]
| 2.6862
| (3×5×43)/(2<sup>2</sup>×7×23)
| 2.3.5.7.23.43 {{monzo| -2 1 1 -1 -1 1 }}
|
|
|-
| [[646/645]]
| 2.6820
| (2×17×19)/(3×5×43)
| 2.3.5.17.19.43 {{monzo| 1 -1 -1 1 1 -1 }}
| Kastalisma
|
|-
| [[990/989]]
| 1.7496
| (2×3<sup>2</sup>×5×11)/(23×43)
| 2.3.5.11.23.43 {{monzo| 1 2 1 1 -1 -1 }}
| Yerkesisma
|
|-
| [[1333/1332]]
| 1.2992
| (31×43)/(2<sup>2</sup>×3<sup>2</sup>×37)
| 2.3.31.37.43 {{monzo| -2 -2 1 -1 1 }}
| Cevenolisma
|
|-
| [[1377/1376]]
| 1.2577
| (3<sup>4</sup>×17)/(2<sup>5</sup>×43)
| 2.3.17.43 {{monzo| -5 4 1 -1 }}
| Roberbauxisma
|
|-
| [[1463/1462]]
| 1.1838
| (7×11×19)/(2×17×43)
| 2.7.11.17.19.43 {{monzo| -1 1 1 -1 1 -1 }}
| Nordenmarkisma
|
|-
| [[1764/1763]]
| 0.98170
| (2×3×7)<sup>2</sup>/(41×43)
| 2.3.7.41.43 {{monzo| 2 2 2 -1 -1 }}
|
| S42
|-
| [[1849/1848]]
| 0.93656
| 43<sup>2</sup>/(2<sup>3</sup>×3×7×11)
| 2.3.7.11.43 {{monzo| -3 -1 -1 -1 2 }}
|
| S43
|-
| [[1936/1935]]
| 0.98170
| (2<sup>2</sup>×11)<sup>2</sup>/(3<sup>2</sup>×5×43)
| 2.3.5.11.43 {{monzo| 4 -2 -1 2 -1 }}
|
| S44
|-
| [[2925/2924]]
| 0.59198
| (3<sup>2</sup>×5<sup>2</sup>×13)/(2<sup>2</sup>×17×43)
| 2.3.5.13.17.43 {{monzo| -2 2 2 1 -1 -1 }}
| Beattisma
|
|-
| [[3312/3311]]
| 0.52279
| (2<sup>4</sup>×3<sup>2</sup>×23)/(7×11×43)
| 2.3.7.11.23.43 {{monzo| 4 2 -1 -1 1 -1 }}
| Pedersenisma
|
|-
| [[4000/3999]]
| 0.43286
| (2<sup>5</sup>×5<sup>3</sup>)/(3×31×43)
| 2.3.5.31.43 {{monzo| 5 -1 3 -1 -1 }}
| Hipparchusisma
|
|-
| [[4301/4300]]
| 0.40257
| (11×17×23)/(2<sup>2</sup>×5<sup>2</sup>×43)
| 2.5.11.17.23.43 {{monzo| -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 {{monzo| 1 -1 1 1 1 -1 -1 }}
| Hobetsisma
|
|-
| [[5720/5719]]
| 0.30269
| (2<sup>3</sup>×5×11×13)/(7×19×43)
| 2.5.7.11.13.19.43 {{monzo| 3 1 -1 1 1 -1 -1 }}
| Halweaverisma
|
|-
| [[7225/7224]]
| 0.23963
| (5×17)<sup>2</sup>/(2<sup>3</sup>×3×7×43)
| 2.3.5.7.17.43 {{monzo| -3 -1 2 -1 2 -1 }}
| Huntressisma
| S85
|-
| [[7956/7955]]
| 0.21761
| (2<sup>2</sup>×3<sup>2</sup>×13×17)/(5×37×43)
| 2.3.5.13.17.37.43 {{monzo| 2 2 -1 1 1 -1 -1 }}
| Yajinisma
|
|-
| [[9504/9503]]
| 0.18217
| (2<sup>5</sup>×3<sup>3</sup>×11)/(13×17×43)
| 2.3.11.13.17.43 {{monzo| 5 3 1 -1 -1 -1 }}
| Lionelisma
|
|-
| [[9633/9632]]
| 0.17973
| (3×13<sup>2</sup>×19)/(2<sup>5</sup>×7×43)
| 2.3.7.13.19.43 {{monzo| -5 1 -1 2 1 -1 }}
| Coturisma
|
|-
| [[10450/10449]]
| 0.16568
| (2×5<sup>2</sup>×11×19)/(3<sup>5</sup>×43)
| 2.3.5.11.19.43 {{monzo| 1 -5 2 1 1 -1}}
| Girardisma
|
|-
| [[10880/10879]]
| 0.15912
| (2<sup>7</sup>×5×17)/(11×23×43)
| 2.5.11.17.23.43 {{monzo| 7 1 -1 1 -1 -1 }}
| Kaguyisma
|
|-
| [[17545/17544]]
| 0.098677
| (5×11<sup>2</sup>×29)/(2<sup>3</sup>×3×17×43)
| 2.3.5.11.17.29.43 {{monzo| -3 -1 1 2 -1 1 -1 }}
| Manheimisma
|
|-
| [[27048/27047]]
| 0.064007
| (2<sup>3</sup>×3×7<sup>2</sup>×23)/(17×37×43)
| 2.3.7.17.23.37.43 {{monzo| 3 1 2 -1 1 -1 -1 }}
| Jangongisma
|
|-
| [[29241/29240]]
| 0.059207
| (3<sup>2</sup>×19)<sup>2</sup>/(2<sup>3</sup>×5×17×43)
| 2.3.5.17.19.43 {{monzo| -3 4 -1 -1 2 -1 }}
| Locquirecisma
| S171
|}
 
=== 47-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[47/46]]
| 37.232
| 47/(2×23)
| 2.23.47 {{monzo| -1 -1 1 }}
|
|
|-
| [[48/47]]
| 36.448
| (2<sup>4</sup>×3)/47
| 2.3.47 {{monzo| 4 1 -1 }}
| 47th-partial chroma
|
|-
| [[94/93]]
| 18.516
| (2×47)/(3×31)
| 2.3.31.47 {{monzo| 1 -1 -1 1 }}
|
|
|-
| [[95/94]]
| 18.320
| (5×19)/(2×47)
| 2.5.19.47 {{monzo| -1 1 1 -1 }}
|
|
|-
| [[141/140]]
| 12.322
| (3×47)/(2<sup>2</sup>×5×7)
| 2.3.5.7.47 {{monzo| -2 1 -1 -1 1 }}
|
|
|-
| [[188/187]]
| 9.2333
| (2<sup>2</sup>×47)/(11×17)
| 2.11.37.47 {{monzo| 2 -1 -1 1 }}
|
|
|-
| [[189/188]]
| 9.1843
| (3<sup>3</sup>×7)/(2<sup>2</sup>×47)
| 2.3.7.47 {{monzo| -2 3 1 -1 }}
|
|
|-
| [[235/234]]
| 7.3827
| (5×47)/(2×3<sup>2</sup>×13)
| 2.3.5.13.47 {{monzo| -1 -2 1 -1 1 }}
|
|
|-
| [[329/328]]
| 5.2701
| (7×47)/(2<sup>3</sup>×41)
| 2.7.41.47 {{monzo| -3 1 -1 1 }}
|
|
|-
| [[330/329]]
| 5.2541
| (2×3×5×11)/(7×47)
| 2.3.5.7.11.47 {{monzo| 1 1 1 -1 1 -1 }}
|
|
|-
| [[376/375]]
| 4.6105
| (2<sup>3</sup>×47)/(3×5<sup>3</sup>)
| 2.3.5.47 {{monzo| 3 -1 -3 1 }}
|
|
|-
| [[377/376]]
| 4.5982
| (13×29)/(2<sup>3</sup>×47)
| 2.13.29.47 {{monzo| -3 1 1 -1 }}
|
|
|-
| [[1176/1175]]
| 1.4728
| (2<sup>3</sup>×3×7<sup>2</sup>)/(5<sup>2</sup>×47)
| 2.3.5.7.47 {{monzo| 3 1 -2 2 -1 }}
|
|
|-
| [[2116/2115]]
| 0.81836
| (2×23)<sup>2</sup>/(3<sup>2</sup>×5×47)
| 2.3.5.23.47 {{monzo| 2 -2 -1 2 -1 }}
|
| S46
|-
| [[2209/2208]]
| 0.78390
| 47<sup>2</sup>/(2<sup>5</sup>×3×5)
| 2.3.23.47 {{monzo| -5 -1 -1 2 }}
|
| S47
|-
| [[2304/2303]]
| 0.75157
| (2<sup>4</sup>×3)<sup>2</sup>/(7<sup>2</sup>×47)
| 2.3.7.47 {{monzo| 8 2 -2 -1 }}
|
| S48
|}
 
=== 53-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[53/52]]
| 32.977
| 53/(2<sup>2</sup>×13)
| 2.13.53 {{monzo| -2 -1 1 }}
|
|
|-
| [[54/53]]
| 32.360
| (2×3<sup>3</sup>)/53
| 2.3.53 {{monzo| 1 3 -1 }}
|
|
|-
| [[106/105]]
| 16.410
| (2×53)/(3×5×7)
| 2.3.5.7.53 {{monzo| 1 -1 -1 -1 1 }}
|
|
|-
| [[160/159]]
| 10.854
| (2<sup>5</sup>×5)/(3×53)
| 2.3.5.53 {{monzo| 5 -1 1 -1 }}
|
|
|-
| [[265/264]]
| 6.5453
| (5×53)/(2<sup>3</sup>×3×11)
| 2.3.5.11.53 {{monzo| -3 -1 1 -1 1 }}
|
|
|-
| [[266/265]]
| 6.5207
| (2×7×19)/(5×53)
| 2.5.7.19.53 {{monzo| 1 -1 1 1 -1 }}
|
|
|-
| [[319/318]]
| 5.4356
| (11×29)/(2×3×53)
| 2.3.11.29.53 {{monzo| -1 -1 1 1 -1 }}
|
|
|-
| [[371/370]]
| 4.6727
| (7×53)/(2×5×37)
| 2.5.7.37.53 {{monzo| -1 -1 1 -1 1 }}
|
|
|-
| [[372/371]]
| 4.6601
| (2<sup>2</sup>×3×31)/(7×53)
| 2.3.7.31.53 {{monzo| 2 1 -1 1 -1 }}
|
|
|-
| [[424/423]]
| 4.0879
| (2<sup>3</sup>×53)/(3<sup>2</sup>×47)
| 2.3.47.53 {{monzo| 3 -2 -1 1 }}
|
|
|-
| [[425/424]]
| 4.0783
| (5<sup>2</sup>×17)/(2<sup>3</sup>×53)
| 2.5.17.53 {{monzo| -3 2 1 -1 }}
|
|
|-
| [[477/476]]
| 3.6332
| (3<sup>2</sup>×53)/(2<sup>2</sup>×7×17)
| 2.3.7.17.53 {{monzo| -2 2 -1 -1 1 }}
|
|
|-
| [[2809/2808]]
| 0.61643
| 53<sup>2</sup>/(2<sup>3</sup>×3<sup>3</sup>×13)
| 2.3.13.53 {{monzo| -3 -3 -1 2 }}
|
| S53
|-
| [[4081/4080]]
| 0.42427
| (7×11×53)/(2<sup>4</sup>×3×5×17)
| 2.3.5.7.11.17.53 {{monzo| -4 -1 -1 1 1 -1 1 }}
|
|
|}
 
=== 59-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[59/58]]
| 29.594
| 59/(2×29)
| 2.29.59 {{monzo| -1 -1 1 }}
|
|
|-
| [[60/59]]
| 29.097
| (2<sup>2</sup>×3×5)/59
| 2.3.5.59 {{monzo| 2 1 1 -1 }}
|
|
|-
| [[118/117]]
| 14.734
| (2×59)/(3<sup>2</sup>×13)
| 2.3.13.59 {{monzo| 1 -2 -1 1 }}
|
|
|-
| [[119/118]]
| 14.610
| (7×17)/(2×59)
| 2.7.17.59 {{monzo| -1 1 1 -1 }}
|
|
|-
| [[177/176]]
| 9.8087
| (3×59)/(2<sup>4</sup>×11)
| 2.3.11.59 {{monzo| -4 1 -1 1 }}
|
|
|-
| [[236/235]]
| 7.3513
| (2<sup>2</sup>×59)/(5×47)
| 2.5.47.59 {{monzo| 2 -1 -1 1 }}
|
|
|-
| [[295/294]]
| 5.8786
| (5×59)/(2×3×7<sup>2</sup>)
| 2.3.5.7.59 {{monzo| -1 -1 1 -2 1 }}
|
|
|-
| [[296/295]]
| 5.8587
| (2<sup>3</sup>×37)/(5×59)
| 2.5.37.59 {{monzo| 3 -1 1 -1 }}
|
|
|-
| [[414/413]]
| 4.1868
| (2×3<sup>2</sup>×23)/(7×59)
| 2.3.7.23.59 {{monzo| 1 2 -1 1 -1 }}
|
|
|-
| [[473/472]]
| 3.6640
| (11×43)/(2<sup>3</sup>×59)
| 2.11.43.59 {{monzo| -3 1 1 -1 }}
|
|
|-
| [[3481/3480]]
| 0.49741
| 59<sup>2</sup>/(2<sup>3</sup>×3×5×29)
| 2.3.5.29.59 {{monzo| -3 -1 -1 -1 2}}
|
| S59
|}
 
=== 61-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[61/60]]
| 28.616
| 61/(2<sup>2</sup>×3×5)
| 2.3.5.61 {{monzo| -2 -1 -1 1 }}
|
|
|-
| [[62/61]]
| 28.151
| (2×31)/61
| 2.31.61 {{monzo| 1 1 -1 }}
|
|
|-
| [[122/121]]
| 14.249
| (2×61)/(11<sup>2</sup>)
| 2.11.61 {{monzo| 1 -2 1 }}
|
|
|-
| [[123/122]]
| 14.133
| (3×41)/(2×61)
| 2.3.41.61 {{monzo| -1 1 1 -1 }}
|
|
|-
| [[183/182]]
| 9.4862
| (3×61)/(2×7×13)
| 2.3.7.13.61 {{monzo| -1 1 -1 -1 1 }}
|
|
|-
| [[184/183]]
| 9.4345
| (2<sup>3</sup>×23)/(3×61)
| 2.3.23.61 {{monzo| 3 -1 1 -1 }}
|
|
|-
| [[244/243]]
| 7.1098
| (2<sup>2</sup>×61)/3<sup>5</sup>
| 2.3.61 {{monzo| 2 -5 1 }}
|
|
|-
| [[245/244]]
| 7.0807
| (5×7<sup>2</sup>)/(2<sup>2</sup>×61)
| 2.5.7.61 {{monzo| -2 1 2 -1 }}
|
|
|-
| [[305/304]]
| 5.6855
| (5×61)/(2<sup>4</sup>×19)
| 2.5.19.61 {{monzo| -4 1 -1 1 }}
|
|
|-
| [[306/305]]
| 5.6669
| (2×3<sup>2</sup>×17)/(5×61)
| 2.3.5.17.61 {{monzo| 1 2 -1 1 -1 }}
|
|
|-
| [[672/671]]
| 2.5782
| (2<sup>5</sup>×3×7)/(11×61)
| 2.3.7.11.61 {{monzo| 5 1 1 -1 -1 }}
|
|
|-
| [[1404/1403]]
| 1.2335
| (2<sup>2</sup>×3<sup>3</sup>×13)/(23×61)
| 2.3.13.23.61 {{monzo| 2 3 1 -1 -1 }}
|
|
|-
| [[3721/3720]]
| 0.46532
| 61<sup>2</sup>/(2<sup>3</sup>×3×5×31)
| 2.3.5.31.61 {{monzo| -3 -1 -1 -1 2 }}
|
| S61
|}
 
=== 67-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[67/66]]
| 26.034
| 67/(2×3×11)
| 2.3.11.67 {{monzo| -1 -1 -1 1 }}
|
|
|-
| [[68/67]]
| 25.648
| (2<sup>2</sup>×17)/67
| 2.17.67 {{monzo| 2 1 -1 }}
|
|
|-
| [[134/133]]
| 12.968
| (2×67)/(7×19)
| 2.7.19.67 {{monzo| 1 -1 -1 1 }}
|
|
|-
| [[135/134]]
| 12.872
| (3<sup>3</sup>×5)/(2×67)
| 2.3.5.67 {{monzo| -1 3 1 -1 }}
|
|
|-
| [[201/200]]
| 8.6346
| (3×67)/(2<sup>3</sup>×5<sup>2</sup>)
| 2.3.5.67 {{monzo| -3 1 -2 1 }}
|
|
|-
| [[336/335]]
| 5.1602
| (2<sup>4</sup>×3×7)/(5×67)
| 2.3.5.7.67 {{monzo| 4 1 -1 1 -1 }}
|
|
|-
| [[671/670]]
| 2.5820
| (11×61)/(2×5×67)
| 2.5.11.61.67 {{monzo| -1 -1 1 1 -1 }}
|
|
|-
| [[4489/4488]]
| 0.38570
| 67<sup>2</sup>/(2<sup>3</sup>×3×11×17)
| 2.3.11.17.67 {{monzo| -3 -1 -1 -1 2 }}
|
| S67
|}
 
=== 71-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[71/70]]
| 24.557
| 71/(2×5×7)
| 2.5.7.71 {{monzo| -1 -1 -1 1 }}
|
|
|-
| [[72/71]]
| 24.213
| (2<sup>3</sup>×3<sup>2</sup>)/71
| 2.3.71 {{monzo| 3 2 -1 }}
|
|
|-
| [[5041/5040]]
| 0.34346
| 71<sup>2</sup>/(2<sup>4</sup>×3<sup>2</sup>×5×7)
| 2.3.5.7.71 {{monzo| -4 -2 -1 -1 2 }}
| Third brown pair comma
| S71
|-
| <font style="font-size:0.85em">[[Borcherdsma|160561400000 / 160561399999]]</font>
| 1.0783×10<sup>-8</sup>
| (2<sup>6</sup>×5<sup>5</sup>×19×29×31×47) / (7×11<sup>2</sup>×13×59<sup>3</sup>×71)
| 2.5.7.11.13.19.29.31.47.59.71 {{monzo| 6 5 -1 -2 -1 1 1 1 1 -3 -1 }}
| Borcherdsma
|
|}
 
=== 73-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[73/72]]
| 23.879
| 73/(2<sup>3</sup>×3<sup>2</sup>)
| 2.3.73 {{monzo| -3 -2 1 }}
|
|
|-
| [[74/73]]
| 23.555
| (2×37)/73
| 2.37.73 {{monzo| 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) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[79/78]]
| 22.054
| 79/(2×3×13)
| 2.3.13.79 {{monzo| -1 -1 -1 1 }}
|
|
|-
| [[80/79]]
| 21.777
| (2<sup>4</sup>×5)/79
| 2.5.79 {{monzo| 4 1 -1 }}
|
|
|}
 
=== 83-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[83/82]]
| 20.985
| 83/(2×41)
| 2.41.83 {{monzo| -1 -1 1 }}
|
|
|-
| [[84/83]]
| 20.734
| (2<sup>2</sup>×3×7)/83
| 2.3.7.83 {{monzo| 2 1 1 -1 }}
|
|
|}
 
=== 89-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[89/88]]
| 19.562
| 89/(2<sup>3</sup>×11)
| 2.11.89 {{monzo| -3 -1 1 }}
| Tailwind comma{{idiosyncratic}}
|
|-
| [[90/89]]
| 19.344
| (2×3<sup>2</sup>×5)/89
| 2.3.5.89 {{monzo| 1 2 1 -1 }}
|
|
|}
 
=== 97-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[97/96]]
| 17.940
| 97/(2<sup>5</sup>×3)
| 2.3.97 {{monzo| -5 -1 1 }}
|
|
|-
| [[98/97]]
| 17.756
| (2×7<sup>2</sup>)/97
| 2.7.97 {{monzo| 1 2 -1 }}
|
|
|}
 
=== 101-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[101/100]]
| 17.226
| 101/(2×5)<sup>2</sup>
| 2.5.101 {{monzo| -2 -2 1 }}
|
|
|-
| [[102/101]]
| 17.057
| (2×3×17)/101
| 2.3.17.101 {{monzo| 1 1 1 -1 }}
|
|
|-
| [[7777/7776]]
| 0.223
| 7×11×101/(2×3)<sup>5</sup>
| 2.3.7.11.101 {{monzo| -5 -5 1 1 1 }}
| Pulsar comma
|
|}
 
=== 103-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[103/102]]
| 16.890
| 103/(2×3×17)
| 2.3.17.103 {{monzo| -1 -1 -1 1 }}
|
|
|-
| [[104/103]]
| 16.727
| (2<sup>3</sup>×13)/103
| 2.13.103 {{monzo| 3 1 -1 }}
|
|
|}
 
=== 107-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[107/106]]
| 16.256
| 107/(2×53)
| 2.53.107 {{monzo| -1 -1 1 }}
|
|
|-
| [[108/107]]
| 16.105
| (2<sup>2</sup>×3<sup>3</sup>)/107
| 2.3.107 {{monzo| 2 3 -1 }}
|
|
|-
| [[750/749]]
| 2.3099
| (2×3×5<sup>3</sup>)/(7×107)
| 2.3.5.7.107 {{monzo| 1 1 3 -1 -1 }}
| Ancient Chinese tempering comma
|
|}
 
=== 109-limit (incomplete) ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
| [[109/108]]
| 15.956
| 15.956
| 109/(2<sup>2</sup>×3<sup>3</sup>)
| 109/(2<sup>2</sup>×3<sup>3</sup>)
Line 5,978: Line 3,550:
| 2.3.19.113 {{monzo| 1 1 1 -1 }}
| 2.3.19.113 {{monzo| 1 1 1 -1 }}
|  
|  
|
|-
| [[226/225]]
| 7.6773
| (2×113)/(3×5)<sup>2</sup>
| 2.3.5.113 {{monzo| 1 -2 -2 1 }}
| Reversed marvel comma
|  
|  
|}
|}
Retrieved from "https://en.xen.wiki/w/List_of_superparticular_intervals"