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List of superparticular intervals/31-limit - Revision history
2026-07-01T15:44:59Z
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Fredg999: Split from List of superparticular intervals, as discussed on the talk page
2025-07-22T20:16:27Z
<p>Split from <a href="/w/List_of_superparticular_intervals" title="List of superparticular intervals">List of superparticular intervals</a>, as discussed on the talk page</p>
<p><b>New page</b></p><div>{{Breadcrumb}}<br />
== 31-limit ==<br />
{| class="wikitable center-6" style="width:100%"<br />
! width="10%" | [[Ratio]]<br />
! width="10%" | [[Cent]]s<br />
! width="15%" | Factorization<br />
! width="15%" | [[Monzo]]<br />
! width="45%" | Name(s)<br />
! width="5%" | Meta<ref name="ssp">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See [[square superparticular]] for details.</ref><br />
|-<br />
| [[31/30]]<br />
| 56.767<br />
| 31/(2×3×5)<br />
| 2.3.5.31 {{monzo| -1 -1 -1 1 }}<br />
| Large tricesimoprimal 1/4-tone<br />
| <br />
|-<br />
| [[32/31]]<br />
| 54.964<br />
| 2<sup>5</sup>/31<br />
| 2.31 {{monzo| 5 -1 }}<br />
| Small tricesimoprimal 1/4-tone, octave-reduced 31st subharmonic<br />
| <br />
|-<br />
| [[63/62]]<br />
| 27.700<br />
| (3<sup>2</sup>×7)/(2×31)<br />
| 2.3.7.31 {{monzo| -1 2 1 -1 }}<br />
| Tricesimoprimal 1/8-tone, co-archyta comma<br />
| <br />
|-<br />
| [[93/92]]<br />
| 18.716<br />
| (3×31)/(2<sup>2</sup>×23)<br />
| 2.3.23.31 {{monzo| -2 1 -1 1 }}<br />
| Tricema<br />
| <br />
|-<br />
| [[125/124]]<br />
| 13.906<br />
| 5<sup>3</sup>/(2<sup>2</sup>×31)<br />
| 2.5.31 {{monzo| -2 3 -1 }}<br />
| Twizzler<br />
| <br />
|-<br />
| [[155/154]]<br />
| 11.205<br />
| (5×31)/(2×7×11)<br />
| 2.5.7.11.31 {{monzo| -1 1 -1 -1 1 }}<br />
| Scyllisma<br />
| <br />
|-<br />
| [[156/155]]<br />
| 11.133<br />
| (2<sup>2</sup>×3×13)/(5×31)<br />
| 2.3.5.13.31 {{monzo| 2 1 -1 1 -1 }}<br />
| Xanthippisma<br />
| <br />
|-<br />
| [[187/186]]<br />
| 9.2828<br />
| (11×17)/(2×3×31)<br />
| 2.3.11.17.31 {{monzo| -1 -1 1 1 -1 }}<br />
| Lambertisma<br />
| <br />
|-<br />
| [[217/216]]<br />
| 7.9965<br />
| (7×31)/(2×3)<sup>3</sup><br />
| 2.3.7.31 {{monzo| -3 -3 1 1 }}<br />
| Eudorisma, tricesimoprimal kleisma<br />
| <br />
|-<br />
| [[248/247]]<br />
| 6.9949<br />
| (2<sup>3</sup>×31)/(13×19)<br />
| 2.13.19.31 {{monzo| 3 -1 -1 1 }}<br />
| Lameisma<br />
| <br />
|-<br />
| [[280/279]]<br />
| 6.1940<br />
| (2<sup>3</sup>×5×7)/(3<sup>2</sup>×31)<br />
| 2.3.5.7.31 {{monzo| 3 -2 1 1 -1 }}<br />
| Tricetone comma<br />
| <br />
|-<br />
| [[341/340]]<br />
| 5.0844<br />
| (11×31)/(2<sup>2</sup>×5×17)<br />
| 2.5.11.17.31 {{monzo| -2 -1 1 -1 1 }}<br />
| Californisma<br />
| <br />
|-<br />
| [[342/341]]<br />
| 5.0695<br />
| (2×3<sup>2</sup>×19)/(11×31)<br />
| 2.3.11.19.31 {{monzo| 1 2 -1 1 -1 }}<br />
| Endymisma<br />
| <br />
|-<br />
| [[435/434]]<br />
| 3.9844<br />
| (3×5×29)/(2×7×31)<br />
| 2.3.5.7.29.31 {{monzo| -1 1 1 -1 1 -1 }}<br />
| Chinthisma<br />
| <br />
|-<br />
| [[465/464]]<br />
| 3.7271<br />
| (3×5×31)/(2<sup>4</sup>×29)<br />
| 2.3.5.29.31 {{monzo| -4 1 1 -1 1 }}<br />
| Alektisma<br />
| <br />
|-<br />
| [[496/495]]<br />
| 3.4939<br />
| (2<sup>4</sup>×31)/(3<sup>2</sup>×5×11)<br />
| 2.3.5.11.31 {{monzo| 4 -2 -1 -1 1 }}<br />
| Navatonisma<br />
| <br />
|-<br />
| [[528/527]]<br />
| 3.2820<br />
| (2<sup>4</sup>×3×11)/(17×31)<br />
| 2.3.11.17.31 {{monzo| 4 1 1 -1 -1 }}<br />
| Rezisma<br />
| <br />
|-<br />
| [[589/588]]<br />
| 2.9418<br />
| (19×31)/(2<sup>2</sup>×3×7<sup>2</sup>)<br />
| 2.3.7.19.31 {{monzo| -2 -1 -2 1 1 }}<br />
| Croatisma<br />
| <br />
|-<br />
| [[621/620]]<br />
| 2.7901<br />
| (3<sup>3</sup>×23)/(2<sup>2</sup>×5×31)<br />
| 2.3.5.23.31 {{monzo| -2 3 -1 1 -1 }}<br />
| Owowhatsthisma<br />
| <br />
|-<br />
| [[651/650]]<br />
| 2.6614<br />
| (3×7×31)/(2×5<sup>2</sup>×13)<br />
| 2.3.5.7.13.31 {{monzo| -1 1 -2 1 -1 1 }}<br />
| Antiklisma<br />
| <br />
|-<br />
| [[714/713]]<br />
| 2.4264<br />
| (2×3×7×17)/(23×31)<br />
| 2.3.7.17.23.31 {{monzo| 1 1 1 1 -1 -1 }}<br />
| Ululisma<br />
| <br />
|-<br />
| [[806/805]]<br />
| 2.1493<br />
| (2×13×31)/(5×7×23)<br />
| 2.5.7.13.23.31 {{monzo| 1 -1 -1 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[837/836]]<br />
| 2.0696<br />
| (3<sup>3</sup>×31)/(2<sup>2</sup>×11×19)<br />
| 2.3.11.19.31 {{monzo| -2 3 -1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[868/867]]<br />
| 1.9957<br />
| (2<sup>2</sup>×7×31)/(3×17<sup>2</sup>)<br />
| 2.3.7.17.31 {{monzo| 2 -1 1 -2 1 }}<br />
| <br />
| <br />
|- <br />
| [[900/899]]<br />
| 1.9247<br />
| (2×3×5)<sup>2</sup>/(29×31)<br />
| 2.3.5.29.31 {{monzo| 2 2 2 -1 -1 }}<br />
| <br />
| S30<br />
|-<br />
| [[931/930]]<br />
| 1.8605<br />
| (7<sup>2</sup>×19)/(2×3×5×31)<br />
| 2.3.5.7.19.31 {{monzo| -1 -1 -1 2 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[961/960]]<br />
| 1.8024<br />
| 31<sup>2</sup>/(2<sup>6</sup>×3×5)<br />
| 2.3.5.31 {{monzo| -6 -1 -1 2 }}<br />
| <br />
| S31<br />
|- <br />
| [[1024/1023]]<br />
| 1.6915<br />
| 2<sup>10</sup>/(3×11×31)<br />
| 2.3.11.31 {{monzo| 10 -1 -1 -1 }}<br />
| Kibisma<br />
| S32<br />
|-<br />
| [[1054/1053]]<br />
| 1.6433<br />
| (2×17×31)/(3<sup>4</sup>×13)<br />
| 2.3.13.17.31 {{monzo| 1 -4 -1 1 1 }}<br />
| <br />
| <br />
|-<br />
| [[1210/1209]]<br />
| 1.4314<br />
| (2×5×11<sup>2</sup>)/(3×13×31)<br />
| 2.3.5.11.13.31 {{monzo| 1 -1 1 2 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[1365/1364]]<br />
| 1.2688<br />
| (3×5×7×13)/(2<sup>2</sup>×11×31)<br />
| 2.3.5.7.11.13.31 {{monzo| -2 1 1 1 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[1426/1425]]<br />
| 1.2145<br />
| (2×23×31)/(3×5<sup>2</sup>×19)<br />
| 2.3.5.19.23.31 {{monzo| 1 -1 -2 -1 1 1 }}<br />
| <br />
| <br />
|-<br />
| [[1519/1518]]<br />
| 1.1401<br />
| (7<sup>2</sup>×31)/(2×3×11×23)<br />
| 2.3.7.11.23.31 {{monzo| -1 -1 2 -1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[1520/1519]]<br />
| 1.1393<br />
| (2<sup>4</sup>×5×19)/(7<sup>2</sup>×31)<br />
| 2.5.7.19.31 {{monzo| 4 1 -2 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[1768/1767]]<br />
| 0.97948<br />
| (2<sup>3</sup>×13×17)/(3×19×31)<br />
| 2.3.13.17.19.31 {{monzo| 3 -1 1 1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[1860/1859]]<br />
| 0.93102<br />
| (2<sup>2</sup>×3×5×31)/(11×13<sup>2</sup>)<br />
| 2.3.5.11.13.31 {{monzo| 2 1 1 -1 -2 1 }}<br />
| <br />
| <br />
|-<br />
| [[2016/2015]]<br />
| 0.85896<br />
| (2<sup>5</sup>×3<sup>2</sup>×7)/(5×13×31)<br />
| 2.3.5.7.13.31 {{monzo| 5 2 -1 1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[2233/2232]]<br />
| 0.77547<br />
| (7×11×29)/(2<sup>3</sup>×3<sup>2</sup>×31)<br />
| 2.3.7.11.29.31 {{monzo| -3 -2 1 1 1 -1 }}<br />
| Kuznetsovisma<br />
| <br />
|-<br />
| [[2945/2944]]<br />
| 0.58796<br />
| (5×19×31)/(2<sup>7</sup>×23)<br />
| 2.5.19.23.31 {{monzo| -7 1 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[2976/2975]]<br />
| 0.58183<br />
| (2<sup>5</sup>×3×31)/(5<sup>2</sup>×7×17)<br />
| 2.3.5.7.17.31 {{monzo| 5 1 -2 -1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[3565/3564]]<br />
| 0.48569<br />
| (5×23×31)/((2×3<sup>2</sup>)<sup>2</sup>×11)<br />
| 2.3.5.11.23.31 {{monzo| -2 -4 1 -1 1 1 }}<br />
| <br />
| <br />
|-<br />
| [[3751/3750]]<br />
| 0.46160<br />
| (11<sup>2</sup>×31)/(2×3×5<sup>4</sup>)<br />
| 2.3.5.11.31 {{monzo| -1 -1 -4 2 1 }}<br />
| <br />
| <br />
|-<br />
| [[3876/3875]]<br />
| 0.44671<br />
| (2<sup>2</sup>×3×17×19)/(5<sup>3</sup>×31)<br />
| 2.3.5.17.19.31 {{monzo| 2 1 -3 1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[3969/3968]]<br />
| 0.43624<br />
| (3<sup>2</sup>×7)<sup>2</sup>/(2<sup>7</sup>×31)<br />
| 2.3.7.31 {{monzo| -7 4 2 -1 }}<br />
| Yunzee comma<br />
| S63<br />
|-<br />
| [[4186/4185]]<br />
| 0.41363<br />
| (2×7×13×23)/(3<sup>3</sup>×5×31)<br />
| 2.3.5.7.13.23.31 {{monzo| 1 -3 -1 1 1 1 -1 }}<br />
| Tamashimisma<br />
| <br />
|-<br />
| [[4960/4959]]<br />
| 0.34907<br />
| (2<sup>5</sup>×5×31)/(3<sup>2</sup>×19×29)<br />
| 2.3.5.19.29.31 {{monzo| 5 -2 1 -1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[4992/4991]]<br />
| 0.34684<br />
| (2<sup>7</sup>×3×13)/(7×23×31)<br />
| 2.3.7.13.23.31 {{monzo| 7 1 -1 1 -1 -1 }}<br />
| Kalmanisma<br />
| <br />
|-<br />
| [[5643/5642]]<br />
| 0.30682<br />
| (3<sup>3</sup>×11×19)/(2×7×13×31)<br />
| 2.3.7.11.13.19.31 {{monzo| -1 3 -1 1 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[5797/5796]]<br />
| 0.29867<br />
| (11×17×31)/((2×3)<sup>2</sup>×7×23)<br />
| 2.3.7.11.17.23.31 {{monzo| -2 -2 -1 1 1 -1 1 }}<br />
| Bivojisma<br />
| <br />
|-<br />
| [[6076/6075]]<br />
| 0.28495<br />
| ((2×7)<sup>2</sup>×31)/(3<sup>5</sup>×5<sup>2</sup>)<br />
| 2.3.5.7.31 {{monzo| 2 -5 -2 2 1 }}<br />
| Large ricegrain comma<br />
| <br />
|-<br />
| [[6138/6137]]<br />
| 0.28207<br />
| (2×3<sup>2</sup>×11×31)/(17×19<sup>2</sup>)<br />
| 2.3.11.17.19.31 {{monzo| 1 2 1 -1 -2 1 }}<br />
| <br />
| <br />
|-<br />
| [[6293/6292]]<br />
| 0.27513<br />
| (7×29×31)/((2×11)<sup>2</sup>×13)<br />
| 2.7.11.13.29.31 {{monzo| -2 1 -2 -1 1 1 }}<br />
| <br />
| <br />
|-<br />
| [[6325/6324]]<br />
| 0.27373<br />
| (5<sup>2</sup>×11×23)/(2<sup>2</sup>×3×17×31)<br />
| 2.3.5.11.17.23.31 {{monzo| -2 -1 2 1 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[6480/6479]]<br />
| 0.26719<br />
| ((2×3)<sup>4</sup>×5)/(11×19×31)<br />
| 2.3.5.11.19.31 {{monzo| 4 4 1 -1 -1 -1 }}<br />
| Scarlattisma<br />
| <br />
|-<br />
| [[6728/6727]]<br />
| 0.25734<br />
| (2<sup>3</sup>×29<sup>2</sup>)/(7×31<sup>2</sup>)<br />
| 2.7.29.31 {{monzo| 3 -1 2 -2 }}<br />
| Sushi comma<br />
| <br />
|-<br />
| [[7657/7656]]<br />
| 0.22611<br />
| (13×19×31)/(2<sup>3</sup>×3×11×29)<br />
| 2.3.11.13.19.29.31 {{monzo| -3 -1 -1 1 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[7905/7904]]<br />
| 0.21902<br />
| (3×5×17×31)/(2<sup>5</sup>×13×19)<br />
| 2.3.5.13.17.19.31 {{monzo| -5 1 1 -1 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[7936/7935]]<br />
| 0.21816<br />
| (2<sup>8</sup>×31)/(3×5×23<sup>2</sup>)<br />
| 2.3.5.23.31 {{monzo| 8 -1 -1 -2 1 }}<br />
| <br />
| <br />
|-<br />
| [[8092/8091]]<br />
| 0.21396<br />
| ((2×17)<sup>2</sup>×7)/(3<sup>2</sup>×29×31)<br />
| 2.3.7.17.29.31 {{monzo| 2 -2 1 2 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[8464/8463]]<br />
| 0.20455<br />
| (2<sup>2</sup>×23)<sup>2</sup>/(3×7×13×31)<br />
| 2.3.7.13.23.31 {{monzo| 4 -1 -1 -1 2 -1 }}<br />
| Polishookisma<br />
| S92<br />
|-<br />
| [[8526/8525]]<br />
| 0.20307<br />
| (2×3×7<sup>2</sup>×29)/(5<sup>2</sup>×11×31)<br />
| 2.3.5.7.11.29.31 {{monzo| 1 1 -2 2 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[8960/8959]]<br />
| 0.19323<br />
| (2<sup>8</sup>×5×7)/(17<sup>2</sup>×31)<br />
| 2.5.7.17.31 {{monzo| 8 1 1 -2 -1 }}<br />
| Small ricegrain comma<br />
| <br />
|-<br />
| [[9425/9424]]<br />
| 0.18370<br />
| (5<sup>2</sup>×13×29)/(2<sup>4</sup>×19×31)<br />
| 2.5.13.19.29.31 {{monzo| -4 2 1 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 10881/10880<br />
| 0.15911<br />
| (3<sup>3</sup>×13×31)/(2<sup>7</sup>×5×17)<br />
| 2.3.5.13.17.31 {{monzo| -7 3 -1 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| 11781/11780<br />
| 0.14696<br />
| (3<sup>2</sup>×7×11×17)/(2<sup>2</sup>×5×19×31)<br />
| 2.3.5.7.11.17.19.31 {{monzo| -2 2 -1 1 1 1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| 11935/11934<br />
| 0.14506<br />
| (5×7×11×31)/(2×3<sup>3</sup>×13×17)<br />
| 2.3.5.7.11.13.17.31 {{monzo| -1 -3 1 1 1 -1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| 12122/12121<br />
| 0.14282<br />
| (2×11×19×29)/(17×23×31)<br />
| 2.11.17.19.23.29.31 {{monzo| 1 1 -1 1 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 13300/13299<br />
| 0.13017<br />
| ((2×5)<sup>2</sup>×7×19)/(3×11×13×31)<br />
| 2.3.5.7.11.13.19.31 {{monzo| 2 -1 2 1 -1 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 13455/13454<br />
| 0.12867<br />
| (3<sup>2</sup>×5×13×23)/(2×7×31<sup>2</sup>)<br />
| 2.3.5.7.13.23.31 {{monzo| -1 2 1 -1 1 1 -2 }}<br />
| <br />
| <br />
|-<br />
| 15625/15624<br />
| 0.11080<br />
| 5<sup>6</sup>/(2<sup>3</sup>×3<sup>2</sup>×7×31)<br />
| 2.3.5.7.31 {{monzo| -3 -2 6 -1 -1 }}<br />
| <br />
| S125<br />
|-<br />
| [[Acronymisma|17577/17576]]<br />
| 0.098497<br />
| (3<sup>4</sup>×7×31)/(2<sup>3</sup>×13<sup>3</sup>)<br />
| 2.3.7.13.31 {{monzo| -3 4 1 -3 1 }}<br />
| Acronymisma<br />
| <br />
|-<br />
| [[Totziensisma|19251/19250]]<br />
| 0.089931<br />
| (3<sup>3</sup>×23×31)/(2×5<sup>3</sup>×7×11)<br />
| 2.3.5.7.11.23.31 {{monzo| -1 3 -3 -1 -1 1 1}}<br />
| Totziensisma<br />
| <br />
|-<br />
| [[Honeybrookisma|19344/19343]]<br />
| 0.089500<br />
| (2<sup>4</sup>×3×13×31)/(23×29<sup>2</sup>)<br />
| 2.3.13.23.29.31 {{monzo| 4 1 1 -1 -2 1 }}<br />
| Honeybrookisma<br />
| <br />
|-<br />
| 19965/19964<br />
| 0.086716<br />
| (3×5×11<sup>3</sup>)/(2<sup>2</sup>×7×23×31)<br />
| 2.3.5.7.11.23.31 {{monzo| -2 1 1 -1 3 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| 21142/21141<br />
| 0.081888<br />
| (2×11×31<sup>2</sup>)/(3<sup>6</sup>×29)<br />
| 2.3.11.29.31 {{monzo| 1 -6 1 -1 2 }}<br />
| <br />
| <br />
|-<br />
| 22816/22815<br />
| 0.075880<br />
| (2<sup>5</sup>×23×31)/(3<sup>3</sup>×5×13<sup>2</sup>)<br />
| 2.3.5.13.23.31 {{monzo| 5 -3 -1 -2 1 1 }}<br />
| <br />
| <br />
|-<br />
| 23375/23374<br />
| 0.074065<br />
| (5<sup>3</sup>×11×17)/(2×13×29×31)<br />
| 2.5.11.13.17.29.31 {{monzo| -1 3 1 -1 1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| 23716/23715<br />
| 0.073000<br />
| (2×7×11)<sup>2</sup>/(3<sup>2</sup>×5×17×31)<br />
| 2.3.5.7.11.17.31 {{monzo| 2 -2 -1 2 2 -1 -1 }}<br />
| <br />
| S154<br />
|-<br />
| 24025/24024<br />
| 0.072061<br />
| (5×31)<sup>2</sup>/(2<sup>3</sup>×3×7×11×13)<br />
| 2.3.5.7.11.13.31 {{monzo| -3 -1 2 -1 -1 -1 2 }}<br />
| <br />
| S155<br />
|-<br />
| 27405/27404<br />
| 0.063173<br />
| (3<sup>3</sup>×5×7×29)/(2<sup>2</sup>×13×17×31)<br />
| 2.3.5.7.13.17.29.31 {{monzo| -2 3 1 1 -1 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[Tricecubisma|29792/29791]]<br />
| 0.058112<br />
| (2<sup>5</sup>×7<sup>2</sup>×19)/31<sup>3</sup><br />
| 2.7.19.31 {{monzo| 5 2 1 -3 }}<br />
| Tricecubisma<br />
| <br />
|-<br />
| 31465/31464<br />
| 0.055022<br />
| (5×7×29×31)/(2<sup>3</sup>×3<sup>2</sup>×19×23)<br />
| 2.3.5.7.19.23.29.31 {{monzo| -3 -2 1 1 -1 -1 1 1 }}<br />
| <br />
| <br />
|-<br />
| 31900/31899<br />
| 0.054272<br />
| ((2×5)<sup>2</sup>×11×29)/(3×7<sup>3</sup>×31)<br />
| 2.3.5.7.11.29.31 {{monzo| 2 -1 2 -3 1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 32799/32798<br />
| 0.052784<br />
| (3×13×29<sup>2</sup>)/(2×23<sup>2</sup>×31)<br />
| 2.3.13.23.29.31 {{monzo| -1 1 1 -2 2 -1 }}<br />
| <br />
| <br />
|-<br />
| 41262/41261<br />
| 0.041958<br />
| (2×3×13×23<sup>2</sup>)/(11<sup>3</sup>×31)<br />
| 2.3.11.13.23.31 {{monzo| 1 1 -3 1 2 -1 }}<br />
| <br />
| <br />
|-<br />
| 42688/42687<br />
| 0.040556<br />
| (2<sup>6</sup>×23×29)/(3<sup>4</sup>×17×31)<br />
| 2.3.17.23.29.31 {{monzo| 6 -4 -1 1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 49011/49010<br />
| 0.035324<br />
| (3×17×31<sup>2</sup>)/(2×5×13<sup>2</sup>×29)<br />
| 2.3.5.13.17.29.31 {{monzo| -1 1 -1 -2 1 -1 2 }}<br />
| <br />
| <br />
|-<br />
| 58311/58310<br />
| 0.029690<br />
| (3<sup>2</sup>×11×19×31)/(2×5×7<sup>3</sup>×17)<br />
| 2.3.5.7.11.17.19.31 {{monzo| -1 2 -1 -3 1 -1 1 1 }}<br />
| <br />
| <br />
|-<br />
| 78337/78336<br />
| 0.022100<br />
| (7×19<sup>2</sup>×31)/(2<sup>9</sup>×3<sup>2</sup>×17)<br />
| 2.3.7.17.19.31 {{monzo| -9 -2 1 -1 2 1 }}<br />
| <br />
| <br />
|-<br />
| 96876/96875<br />
| 0.017871<br />
| (2<sup>2</sup>×3<sup>4</sup>×13×23)/(5<sup>5</sup>×31)<br />
| 2.3.5.13.23.31 {{monzo| 2 4 -5 1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 98736/98735<br />
| 0.017534<br />
| (2<sup>4</sup>×3×11<sup>2</sup>×17)/(5×7<sup>2</sup>×13×31)<br />
| 2.3.5.7.11.13.17.31 {{monzo| 4 1 -1 -2 2 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 102487/102486<br />
| 0.016892<br />
| (7×11<sup>4</sup>)/(2×3×19×29×31)<br />
| 2.3.7.11.19.29.31 {{monzo| -1 -1 1 4 -1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| 108376/108375<br />
| 0.015974<br />
| (2<sup>3</sup>×19×23×31)/(3×5<sup>3</sup>×17<sup>2</sup>)<br />
| 2.3.5.17.19.23.31 {{monzo| 3 -1 -3 -2 1 1 1 }}<br />
| <br />
| <br />
|-<br />
| 111321/111320<br />
| 0.015552<br />
| (3<sup>3</sup>×7×19×31)/(2<sup>3</sup>×5×11<sup>2</sup>×23)<br />
| 2.3.5.7.11.19.23.31 {{monzo| -3 3 -1 1 -2 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| 111476/111475<br />
| 0.015530<br />
| (2<sup>2</sup>×29×31<sup>2</sup>)/(5<sup>2</sup>×7<sup>3</sup>×13)<br />
| 2.5.7.13.29.31 {{monzo| 2 -2 -3 -1 1 2 }}<br />
| <br />
| <br />
|-<br />
| 116281/116280<br />
| 0.014888<br />
| (11×31)<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×5×17×19)<br />
| 2.3.5.11.17.19.31 {{monzo| -3 -2 -1 2 -1 -1 2 }}<br />
| <br />
| S341<br />
|-<br />
| 116964/116963<br />
| 0.014801<br />
| (2×3<sup>2</sup>×19)<sup>2</sup>/(7<sup>3</sup>×11×31)<br />
| 2.3.7.11.19.31 {{monzo| 2 4 -3 -1 2 -1 }}<br />
| <br />
| S342<br />
|-<br />
| 122265/122264<br />
| 0.014160<br />
| (3<sup>2</sup>×5×11×13×19)/(2<sup>3</sup>×17×29×31)<br />
| 2.3.5.11.13.17.19.29.31 {{monzo| -3 2 1 1 1 -1 1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| 174097/174096<br />
| 0.0099441<br />
| (7<sup>2</sup>×11×17×19)/(2<sup>4</sup>×3<sup>3</sup>×13×31)<br />
| 2.3.7.11.13.17.19.31 {{monzo| -4 -3 2 1 -1 1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 175770/175769<br />
| 0.0098495<br />
| (2×3<sup>4</sup>×5×7×31)/(11×19×29<sup>2</sup>)<br />
| 2.3.5.7.11.19.29.31 {{monzo| 1 4 1 1 -1 -1 -2 1 }}<br />
| <br />
| <br />
|-<br />
| 178126/178125<br />
| 0.0097192<br />
| (2×13<sup>2</sup>×17×31)/(3×5<sup>5</sup>×19)<br />
| 2.3.5.13.17.19.31 {{monzo| 1 -1 -5 2 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| 190464/190463<br />
| 0.0090896<br />
| (2<sup>11</sup>×3×31)/((7×13)<sup>2</sup>×23)<br />
| 2.3.7.13.23.31 {{monzo| 11 1 -2 -2 -1 1 }}<br />
| <br />
| <br />
|-<br />
| 207576/207575<br />
| 0.0083403<br />
| ((2×3)<sup>3</sup>×31<sup>2</sup>)/((5×19)<sup>2</sup>×23)<br />
| 2.3.5.19.23.31 {{monzo| 3 3 -2 -2 -1 2 }}<br />
| <br />
| <br />
|-<br />
| 212382/212381<br />
| 0.0081515<br />
| (2×3<sup>5</sup>×19×23)/(13×17×31<sup>2</sup>)<br />
| 2.3.13.17.19.23.31 {{monzo| 1 5 -1 -1 1 1 -2 }}<br />
| <br />
| <br />
|-<br />
| 227448/227447<br />
| 0.0076116<br />
| (2<sup>3</sup>×3<sup>7</sup>×13)/(11×23×29×31)<br />
| 2.3.11.13.23.29.31 {{monzo| 3 7 -1 1 -1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| 240065/240064<br />
| 0.0072115<br />
| (5×7×19<sup>3</sup>)/(2<sup>6</sup>×11<sup>2</sup>×31)<br />
| 2.5.7.11.19.31 {{monzo| -6 1 1 -2 3 -1 }}<br />
| <br />
| <br />
|-<br />
| 245025/245024<br />
| 0.0070656<br />
| (3<sup>2</sup>×5×11)<sup>2</sup>/(2<sup>5</sup>×13×19×31)<br />
| 2.3.5.11.13.19.31 {{monzo| -5 4 2 2 -1 -1 -1 }}<br />
| <br />
| S495<br />
|-<br />
| 260338/260337<br />
| 0.0066500<br />
| (2×13×17×19×31)/(3×7<sup>3</sup>×11×23)<br />
| 2.3.7.11.13.17.19.23.31 {{monzo| 1 -1 -3 -1 1 1 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| 268801/268800<br />
| 0.0064406<br />
| (13×23×29×31)/(2<sup>9</sup>×3×5<sup>2</sup>×7)<br />
| 2.3.5.7.13.23.29.31 {{monzo| -9 -1 -2 -1 1 1 1 1 }}<br />
| <br />
| <br />
|-<br />
| 278784/278783<br />
| 0.0062010<br />
| (2<sup>4</sup>×3×11)<sup>2</sup>/(17×23<sup>2</sup>×31)<br />
| 2.3.11.17.23.31 {{monzo| 8 2 2 -1 -2 -1 }}<br />
| <br />
| S528<br />
|-<br />
| 288145/288144<br />
| 0.0060082<br />
| (5×11×13<sup>2</sup>×31)/(2<sup>4</sup>×3×<sup>3</sup>×23×29)<br />
| 2.3.5.11.13.23.29.31 {{monzo| -4 -3 1 1 2 -1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| 314433/314432<br />
| 0.0055059<br />
| ((3×7)<sup>2</sup>×23×31)/(2<sup>2</sup>×17)<sup>3</sup><br />
| 2.3.7.17.23.31 {{monzo| -6 2 2 -3 1 1 }}<br />
| <br />
| <br />
|-<br />
| 453376/453375<br />
| 0.0038185<br />
| (2<sup>8</sup>×7×11×23)/(3<sup>2</sup>×5<sup>3</sup>×13×31)<br />
| 2.3.5.7.11.13.23.31 {{monzo| 8 -2 -3 1 1 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 459173/459172<br />
| 0.0037703<br />
| (11×13<sup>3</sup>×19)/(2<sup>2</sup>×7×23<sup>2</sup>×31)<br />
| 2.7.11.13.19.23.31 {{monzo| -2 -1 1 3 1 -2 -1 }}<br />
| <br />
| <br />
|-<br />
| 509796/509795<br />
| 0.0033959<br />
| (2×3×7×17)<sup>2</sup>/(5×11×13×23×31)<br />
| 2.3.5.7.11.13.17.23.31 {{monzo| 2 2 -1 2 -1 -1 2 -1 -1 }}<br />
| <br />
| S714<br />
|-<br />
| 773605/773604<br />
| 0.0022379<br />
| (5×7×23×31<sup>2</sup>)/(2<sup>2</sup>×3<sup>3</sup>×13×19×29)<br />
| 2.3.5.7.13.19.23.29.31 {{monzo| -2 -3 1 1 -1 -1 1 -1 2 }}<br />
| <br />
| <br />
|-<br />
| 863940/863939<br />
| 0.0020039<br />
| (2<sup>2</sup>×3×5×7×11<sup>2</sup>×17)/(29×31<sup>3</sup>)<br />
| 2.3.5.7.11.17.29.31 {{monzo| 2 1 1 1 2 1 -1 -3 }}<br />
| <br />
| <br />
|-<br />
| 912951/912950<br />
| 0.0018963<br />
| (3<sup>5</sup>×13×17<sup>2</sup>)/(2×5<sup>2</sup>×19×31<sup>2</sup>)<br />
| 2.3.5.13.17.19.31 {{monzo| -1 5 -2 1 2 -1 -2 }}<br />
| <br />
| <br />
|-<br />
| 1147125/1147124<br />
| 0.0015092<br />
| (3×5<sup>3</sup>×7×19×23)/(2<sup>2</sup>×11×29<sup>2</sup>×31)<br />
| 2.3.5.7.11.19.23.29.31 {{monzo| -2 1 3 1 -1 1 1 -2 -1 }}<br />
| <br />
| <br />
|-<br />
| 1154440/1154439<br />
| 0.0014996<br />
| (2<sup>3</sup>×5×7<sup>2</sup>×19×31)/(3<sup>3</sup>×11×13<sup>2</sup>×23)<br />
| 2.3.5.7.11.13.19.23.31 {{monzo| 3 -3 1 2 -1 -2 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| 1255501/1255500<br />
| 0.0013789<br />
| (13<sup>2</sup>×17×19×23)/(2<sup>2</sup>×3<sup>4</sup>×5<sup>3</sup>×31)<br />
| 2.3.5.13.17.19.23.31 {{monzo| -2 -4 -3 2 1 1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 1594176/1594175<br />
| 0.0010860<br />
| (2<sup>6</sup>×3×19<sup>2</sup>×23)/((5×11)<sup>2</sup>×17×31)<br />
| 2.3.5.11.17.19.23.31 {{monzo| 6 1 -2 -2 -1 2 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 2307361/2307360<br />
| 0.00075031<br />
| (7<sup>2</sup>×31)<sup>2</sup>/(2<sup>5</sup>×3×5×11×19×23)<br />
| 2.3.5.7.11.19.23.31 {{monzo| -5 -1 -1 4 -1 -1 -1 2 }}<br />
| <br />
| S1519<br />
|-<br />
| 2310400/2310399<br />
| 0.00074932<br />
| ((2<sup>4</sup>×5×19)/(3×7×13))<sup>2</sup>/31<br />
| 2.3.5.7.13.19.31 {{monzo| 8 -2 2 -2 -2 2 -1 }}<br />
| <br />
| S1520<br />
|-<br />
| 2345057/2345056<br />
| 0.00073825<br />
| (11×13×23<sup>2</sup>×31)/(2<sup>5</sup>×7×19<sup>2</sup>×29)<br />
| 2.7.11.13.19.23.29.31 {{monzo| -5 -1 1 1 -2 2 -1 1 }}<br />
| <br />
| <br />
|-<br />
| 3206269/3206268<br />
| 0.00053995<br />
| (11×19×23<sup>2</sup>×29)/((2×3×13)<sup>2</sup>×17×31)<br />
| 2.3.11.13.17.19.23.29.31 {{monzo| -2 -2 1 -2 -1 1 2 1 -1 }}<br />
| <br />
| <br />
|-<br />
| 3301376/3301375<br />
| 0.00052440<br />
| (2<sup>13</sup>×13×31)/(5<sup>3</sup>×7<sup>4</sup>×11)<br />
| 2.5.7.11.13.31 {{monzo| 13 -3 -4 -1 1 1 }}<br />
| <br />
| <br />
|-<br />
| 3346110/3346109<br />
| 0.00051739<br />
| (2×3<sup>9</sup>×5×17)/(13×19<sup>2</sup>×23×31)<br />
| 2.3.5.13.17.19.23.31 {{monzo| 1 9 1 -1 1 -2 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| 3897166/3897165<br />
| 0.00044423<br />
| (2×7<sup>3</sup>×13×19×23)/(3×5×17<sup>2</sup>×29×31)<br />
| 2.3.5.7.13.17.19.23.29.31 {{monzo| 1 -1 -1 3 1 -2 1 1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| <font style="font-size:0.88em">14753025/14753024</font><br />
| 0.00011735<br />
| ((3×5)<sup>2</sup>×7×17×19×29)/(2<sup>8</sup>×11×13<sup>2</sup>×31)<br />
| 2.3.5.7.11.13.17.19.29.31 {{monzo| -8 2 2 1 -1 -2 1 1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| <font style="font-size:0.88em">16093000/16092999</font><br />
| 0.00010758<br />
| ((2×5)<sup>3</sup>×7×11<sup>2</sup>×19)/(3<sup>4</sup>×13×17×29×31)<br />
| 2.3.5.7.11.13.17.19.29.31 {{monzo| 3 -4 3 1 2 -1 -1 1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| <font style="font-size:0.88em">76271625/76271624</font><br />
| 2.2698×10<sup>-5</sup><br />
| (3<sup>9</sup>×5<sup>3</sup>×31)/((2×11)<sup>3</sup>×13×19×29)<br />
| 2.3.5.11.13.19.29.31 {{monzo| -3 9 3 -3 -1 -1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| <font style="font-size:0.88em">80061345/80061344</font><br />
| 2.1624×10<sup>-5</sup><br />
| (3<sup>3</sup>×5×7<sup>4</sup>×13×19)/(2<sup>5</sup>×11<sup>2</sup>×23×29×31)<br />
| 2.3.5.7.11.13.19.23.29.31 {{monzo| -5 3 1 4 -2 1 1 -1 -1 -1 }}<br />
| <br />
| <br />
|-<br />
| <font style="font-size:0.79em">133920000/133919999</font><br />
| 1.2927×10<sup>-5</sup><br />
| (2<sup>8</sup>×3<sup>3</sup>×5<sup>4</sup>×31)/(17<sup>2</sup>×19×29<sup>3</sup>)<br />
| 2.3.5.17.19.29.31 {{monzo| 8 3 4 -2 -1 -3 1 }}<br />
| <br />
| <br />
|-<br />
| <font style="font-size:0.79em">181037025/181037024</font><br />
| 9.5629×10<sup>-6</sup><br />
| (3<sup>2</sup>×5×13×23)<sup>2</sup>/(2<sup>5</sup>×7×(29×31)<sup>2</sup>)<br />
| 2.3.5.7.13.23.29.31 {{monzo| -5 4 2 -1 2 2 -2 -2 }}<br />
| <br />
| S13455<br />
|-<br />
| <font style="font-size:0.79em">370256250/370256249</font><br />
| 4.6758×10<sup>-6</sup><br />
| (2×3×5<sup>5</sup>×7<sup>2</sup>×13×31)/(11<sup>7</sup>×19)<br />
| 2.3.5.7.11.13.19.31 {{monzo| 1 1 5 2 -7 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| <font style="font-size:0.72em">1611308700/1611308699</font><br />
| 1.0744×10<sup>-6</sup><br />
| ((2×3<sup>3</sup>×5×31)/(7<sup>2</sup>×13×19))<sup>2</sup>×(23/11)<br />
| 2.3.5.7.11.13.19.23.31 {{monzo| 2 6 2 -4 -1 -2 -2 1 2 }}<br />
| <br />
| <br />
|}<br />
<br />
== Notes ==<br />
<references/><br />
<br />
[[Category:Lists of intervals]]<br />
[[Category:Superparticular ratios|*]]</div>
Fredg999