List of superparticular intervals: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,012 edits
Tags: Mobile edit Mobile web edit
Eufalesio (talk | contribs)
autopatrolled
625 edits
 
(10 intermediate revisions by 4 users not shown)
Line 1: Line 1:
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 502: Line 502:
| (2<sup>5</sup>×5×13)/(3<sup>3</sup>×7×11)
| (2<sup>5</sup>×5×13)/(3<sup>3</sup>×7×11)
| {{Monzo| 5 -3 1 -1 -1 1 }}
| {{Monzo| 5 -3 1 -1 -1 1 }}
| Ibnsinma
| Ibnsinma, sinaisma
|  
|  
|-
|-
Line 509: Line 509:
| (2<sup>6</sup>/3)<sup>2</sup>/(5×7×13)
| (2<sup>6</sup>/3)<sup>2</sup>/(5×7×13)
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| Schismina, tridecimal schisma
| Minisma
| S64
| S64
|-
|-
Line 1,246: Line 1,246:
| S2431
| S2431
|-
|-
| <font style="font-size:0.88em">11859211/11859210</font>
| <font style="font-size:0.88em">[[11859211/11859210]]</font>
| 0.00014598
| 0.00014598
| (19/(3×11))<sup>4</sup>×((7×13)/(2×5))
| (19/(3×11))<sup>4</sup>×((7×13)/(2×5))
| {{Monzo| -1 -4 -1 1 -4 1 0 4 }}
| {{Monzo| -1 -4 -1 1 -4 1 0 4 }}
|  
| Tredekisma
|  
|  
|}
|}
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 1,782: Line 1,782:
|}
|}


=== 29-limit ===
=== Higher-limit ===
{| class="wikitable center-6" style="width:100%"
See:  
! width="10%" | [[Ratio]]
* [[List of superparticular intervals/29-limit]]
! width="10%" | [[Cent]]s
* [[List of superparticular intervals/31-limit]]
! width="15%" | Factorization
* [[List of superparticular intervals/37-limit]]
! width="15%" | [[Monzo]]
* [[List of superparticular intervals/41-limit]]
! width="45%" | Name(s)
* [[List of superparticular intervals/43-limit]]
! width="5%" | Meta<ref name="ssp"/>
* [[List of superparticular intervals/47-limit]]
|-
* [[List of superparticular intervals/53-limit]]
| [[29/28]]
* [[List of superparticular intervals/59-limit]]
| 60.751
* [[List of superparticular intervals/61-limit]]
| 29/(2<sup>2</sup>×7)
* [[List of superparticular intervals/67-limit]]
| 2.7.29 {{monzo| -2 -1 1 }}
* [[List of superparticular intervals/71-limit]]
| Vicesimononal thirdtone, vicesimononal subchroma, large vicesimononal quartertone, large vicesimononal 2/7-tone
* [[List of superparticular intervals/73-limit]]
|
* [[List of superparticular intervals/79-limit]]
|-
* [[List of superparticular intervals/83-limit]]
| [[30/29]]
* [[List of superparticular intervals/89-limit]]
| 58.692
* [[List of superparticular intervals/97-limit]]
| (2×3×5)/29
* [[List of superparticular intervals/101-limit]]
| 2.3.5.29 {{monzo| 1 1 1 -1 }}
* [[List of superparticular intervals/103-limit]]
| Small vicesimononal quartertone, small vicesimononal 2/7-tone
* [[List of superparticular intervals/107-limit]]
|
* [[List of superparticular intervals/109-limit]]
|-
* [[List of superparticular intervals/113-limit]]
| [[58/57]]
* [[List of superparticular intervals/127-limit]]
| 30.109
| (2×29)/(3×19)
| 2.3.19.29 {{monzo| 1 -1 -1 1 }}
| Vicesimononal 1/7-tone
|
|-
| [[88/87]]
| 19.786
| (2<sup>3</sup>×11)/(3×29)
| 2.3.11.29 {{monzo| 3 -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]]
| 14.860
| (3<sup>2</sup>×13)/(2<sup>2</sup>×29)
| 2.3.13.29 {{monzo| -2 2 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]]
| 9.9211
| (5<sup>2</sup>×7)/(2×3×29)
| 2.3.5.7.29 {{monzo| -1 -1 2 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]]
| 7.4783
| (2<sup>3</sup>×29)/(3×7×11)
| 2.3.7.11.29 {{monzo| 3 -1 -1 -1 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]]
| 5.9801
| (2×5×29)/17<sup>2</sup>
| 2.5.17.29 {{monzo| 1 1 -2 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]]
| 4.5861
| (2×3<sup>3</sup>×7)/(13×29)
| 2.3.7.13.29 {{monzo| 1 3 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]]
| 3.5081
| (2×13×19)/(17×29)
| 2.13.17.19.29 {{monzo| 1 1 -1 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]]
| 3.1391
| (2<sup>3</sup>×3×23)/(19×29)
| 2.3.19.23.29 {{monzo| 3 1 -1 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]]
| 2.7157
| (2×11×29)/(7<sup>2</sup>×13)
| 2.7.11.13.29 {{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]]
| 2.2124
| (3<sup>3</sup>×29)/(2×17×23)
| 2.3.17.23.29 {{monzo| -1 3 -1 -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]]
| 1.6575
| (5×11×19)/((2×3)<sup>2</sup>×29)
| 2.3.5.11.19.29 {{monzo| -2 -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]]
| 1.1944
| (2×5<sup>2</sup>×29)/(3<sup>2</sup>×7×23)
| 2.3.5.7.23.29 {{monzo| 1 -2 2 -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]]
| 1.0657
| (5<sup>3</sup>×13)/(2<sup>3</sup>×7×29)
| 2.5.7.13.29 {{monzo| -3 3 -1 1 -1 }}
| Norcma
|
|-
| [[1683/1682]]
| 1.0290
| (3<sup>2</sup>×11×17)/(2×29<sup>2</sup>)
| 2.3.11.17.29 {{monzo| -1 2 1 1 -2 }}
| Castafiorisma
|
|-
| [[2001/2000]]
| 0.86540
| (3×23×29)/(2<sup>4</sup>×5<sup>3</sup>)
| 2.3.5.23.29 {{monzo| -4 1 -3 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]]
| 0.79579
| (2<sup>7</sup>×17)/(3×5<sup>2</sup>×29)
| 2.3.5.17.29 {{monzo| 7 -1 -2 1 -1 }}
| Donarisma
|
|-
| [[2205/2204]]
| 0.78532
| ((3×7)/2)<sup>2</sup>×(5/(19×29))
| 2.3.5.7.19.29 {{monzo| -2 2 1 2 -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]]
| 0.70247
| (5×17×29)/(2<sup>5</sup>×7×11)
| 2.5.7.11.17.29 {{monzo| -5 1 -1 -1 1 1 }}
| Laservine comma
|
|-
| [[2640/2639]]
| 0.65589
| (2<sup>4</sup>×3×5×11)/(7×13×29)
| 2.3.5.7.11.13.29 {{monzo| 4 1 1 -1 1 -1 -1 }}
| Hällströmisma
|
|-
| [[2755/2754]]
| 0.62851
| (5×19×29)/(2×3<sup>4</sup>×17)
| 2.3.5.17.19.29 {{monzo| -1 -4 1 -1 1 1 }}
| Avicema
|
|-
| [[2784/2783]]
| 0.62196
| (2<sup>5</sup>×3×29)/(11<sup>2</sup>×23)
| 2.3.11.23.29 {{monzo| 5 1 -2 -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]]
| 0.49330
| (2×3<sup>3</sup>×5×13)/(11<sup>2</sup>×29)
| 2.3.5.11.13.29 {{monzo| 1 3 1 -2 1 -1 }}
| Veederisma
|
|-
| [[4641/4640]]
| 0.37307
| (3×7×13×17)/(2<sup>5</sup>×5×29)
| 2.3.5.7.13.17.29 {{monzo| -5 1 -1 1 1 1 -1 }}
| Vinecute comma
|
|-
| [[4785/4784]]
| 0.36184
| (3×5×11×29)/(2<sup>4</sup>×13×23)
| 2.3.5.11.13.23.29 {{monzo| -4 1 1 1 -1 -1 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]]
| 0.33922
| (2<sup>4</sup>×11×29)/(3<sup>6</sup>×7)
| 2.3.7.11.29 {{monzo| 4 -6 -1 1 1 }}
|
|
|-
| [[5888/5887]]
| 0.29405
| (2<sup>8</sup>×23)/(7×29<sup>2</sup>)
| 2.7.23.29 {{monzo| 8 -1 1 -2 }}
| Vinocular comma
|
|-
| [[5916/5915]]
| 0.29266
| (2<sup>2</sup>×3×17×29)/(5×7×13<sup>2</sup>)
| 2.3.5.7.13.17.29 {{monzo| 2 1 -1 -1 -2 1 1 }}
| Woudisma
|
|-
| [[6670/6669]]
| 0.25957
| (2×5×23×29)/(3<sup>3</sup>×13×19)
| 2.3.5.13.19.23.29 {{monzo| 1 -3 1 -1 -1 1 1 }}
|
|
|-
| [[7106/7105]]
| 0.24365
| (2×11×17×19)/(5×7<sup>2</sup>×29)
| 2.5.7.11.17.19.29 {{monzo| 1 -1 -2 1 1 1 -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]]
| 0.21946
| (7<sup>3</sup>×23)/(2<sup>4</sup>×17×29)
| 2.7.17.23.29 {{monzo| -4 3 -1 1 -1 }}
|
|
|-
| [[8671/8670]]
| 0.19967
| (13×23×29)/(2×3×5×17<sup>2</sup>)
| 2.3.5.13.17.23.29 {{monzo| -1 -1 -1 1 -2 1 1 }}
| Vinous comma, vinousma
|
|-
| [[9802/9801]]
| 0.17663
| (2×13<sup>2</sup>×29)/(3<sup>2</sup>×11)<sup>2</sup>
| 2.3.11.13.29 {{monzo| 1 -4 -2 2 1 }}
|
|
|-
| [[10557/10556]]
| 0.16400
| (3<sup>3</sup>×17×23)/(2<sup>2</sup>×7×13×29)
| 2.3.7.13.17.23.29 {{monzo| -2 3 -1 -1 1 1 -1 }}
| Rowlandisma
|
|-
| 11340/11339
| 0.15267
| (2<sup>2</sup>×3<sup>4</sup>×5×7)/(17×23×29)
| 2.3.5.7.17.23.29 {{monzo| 2 4 1 1 -1 -1 -1 }}
|
|
|-
| [[Uma|12006/12005]]
| 0.14420
| (2×3<sup>2</sup>×23×29)/(5×7<sup>4</sup>)
| 2.3.5.7.23.29 {{monzo| 1 2 -1 -4 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
| 0.13091
| (5×23)<sup>2</sup>/(2<sup>3</sup>×3×19×29)
| 2.3.5.19.23.29 {{monzo| -3 -1 2 -1 2 -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
| 0.13006
| (2<sup>10</sup>×13)/(3<sup>3</sup>×17×29)
| 2.3.13.17.29 {{monzo| 10 -3 1 -1 -1 }}
|
|
|-
| 13456/13455
| 0.12866
| (2<sup>2</sup>×29)<sup>2</sup>/(3<sup>2</sup>×5×13×23)
| 2.3.5.13.23.29 {{monzo| 4 -2 -1 -1 -1 2 }}
|
| 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
| 0.083491
| (2<sup>2</sup>×3)<sup>4</sup>/(5×11×13×29)
| 2.3.5.11.13.29 {{monzo| 8 4 -1 -1 -1 -1 }}
|
| S144
|-
| 23751/23750
| 0.072893
| (3<sup>2</sup>×7×13×29)/(2×5<sup>4</sup>×19)
| 2.3.5.7.13.19.29 {{monzo| -1 2 -4 1 1 -1 1 }}
|
|
|-
| 24795/24794
| 0.069823
| (3<sup>2</sup>×5×19×29)/(2×7<sup>2</sup>×11×23)
| 2.3.5.7.11.19.23.29 {{monzo| -1 2 1 -2 -1 1 -1 1 }}
|
|
|-
| [[Vuillafansisma|25840/25839]]
| 0.067000
| (2<sup>4</sup>×5×17×19)/(3<sup>4</sup>×11×29)
| 2.3.5.11.17.19.29 {{monzo| 4 -4 1 -1 1 1 -1 }}
| Vuillafansisma
|
|-
| 27000/26999
| 0.064121
| (2×3×5)<sup>3</sup>/(7<sup>2</sup>×19×29)
| 2.3.5.7.19.29 {{monzo| 3 3 3 -2 -1 -1 }}
|
|
|-
| 30625/30624
| 0.056531
| (5<sup>2</sup>×7)<sup>2</sup>/(2<sup>5</sup>×3×11×29)
| 2.3.5.7.11.29 {{monzo| -5 -1 4 2 -1 -1 }}
|
| S175
|-
| 30856/30855
| 0.056108
| (2<sup>3</sup>×7×19×29)/(3×5×11<sup>2</sup>×17)
| 2.3.5.7.11.17.19.29 {{monzo| 3 -1 -1 1 -2 -1 1 1 }}
|
|
|-
| 35322/35321
| 0.049014
| (2×3×7×29<sup>2</sup>)/(11×13<sup>2</sup>×19)
| 2.3.7.11.13.19.29 {{monzo| 1 1 1 -1 -2 -1 2 }}
|
|
|-
| 47125/47124
| 0.036737
| (5<sup>3</sup>×13×29)/((2×3)<sup>2</sup>×7×11×17)
| 2.3.5.7.11.13.17.29 {{monzo| -2 -2 3 -1 -1 1 -1 1 }}
|
|
|-
| 53361/53360
| 0.032444
| (3×7×11)<sup>2</sup>/(2<sup>4</sup>×5×23×29)
| 2.3.5.7.11.23.29 {{monzo| -4 2 -1 2 2 -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
| 0.020728
| 17<sup>4</sup>/((2<sup>3</sup>×3)<sup>2</sup>×5×29)
| 2.3.5.17.29 {{monzo| -6 -2 -1 4 -1 }}
|
| S289
|-
| 87465/87464
| 0.019794
| (3×5×7<sup>3</sup>×17)/(2<sup>3</sup>×13×29<sup>2</sup>)
| 2.3.5.7.13.17.29 {{monzo| -3 1 1 3 -1 1 -2 }}
|
|
|-
| 136851/136850
| 0.012651
| (3×11<sup>2</sup>×13×29)/(2×5<sup>2</sup>×7×17×23)
| 2.3.5.7.11.13.17.23.29 {{monzo| -1 1 -2 -1 2 1 -1 -1 1 }}
|
|
|-
| 158950/158949
| 0.010892
| (2×(5×17)<sup>2</sup>×11)/(3<sup>3</sup>×7×29<sup>2</sup>)
| 2.3.5.7.11.17.29 {{monzo| 1 -3 2 -1 1 2 -2 }}
|
|
|-
| 166635/166634
| 0.010389
| ((3×23)<sup>2</sup>×5×7)/(2×13<sup>2</sup>×17×29)
| 2.3.5.7.13.17.23.29 {{monzo| -1 2 1 1 -2 -1 2 -1 }}
|
|
|-
| 168751/168750
| 0.010259
| (11×23<sup>2</sup>×29)/(2×3<sup>3</sup>×5<sup>5</sup>)
| 2.3.5.11.23.29 {{monzo| -1 -3 -5 1 2 1 }}
|
|
|-
| 176001/176000
| 0.0098365
| (3×7×17<sup>2</sup>×29)/(2<sup>7</sup>×5<sup>3</sup>×11)
| 2.3.5.7.11.17.29 {{monzo| -7 1 -3 1 -1 2 1 }}
|
|
|-
| 176176/176175
| 0.0098268
| (2<sup>4</sup>×7×11<sup>2</sup>×13)/(3<sup>5</sup>×5<sup>2</sup>×29)
| 2.3.5.7.11.13.29 {{monzo| 4 -5 -2 1 2 1 -1 }}
|
|
|-
| 184093/184092
| 0.0094042
| ((7×17)<sup>2</sup>×13)/((2×23)<sup>2</sup>×3×29)
| 2.3.7.13.17.23.29 {{monzo| -2 -1 2 1 2 -2 -1 }}
|
|
|-
| 240787/240786
| 0.0071899
| (19<sup>2</sup>×23×29)/(2×(3×7)<sup>3</sup>×13)
| 2.3.7.13.19.23.29 {{monzo| -1 -3 -3 -1 2 1 1 }}
|
|
|-
| 244036/244035
| 0.0070942
| (2×13×19)<sup>2</sup>/(3<sup>2</sup>×5×11×17×29)
| 2.3.5.11.13.17.19.29 {{monzo| 2 -2 -1 -1 2 -1 2 -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
| 0.0042156
| (2×3<sup>5</sup>×5×13<sup>2</sup>)/((7×17)<sup>2</sup>×29)
| 2.3.5.7.13.17.29 {{monzo| 1 5 1 -2 2 -2 -1 }}
|
|
|-
| 418761/418760
| 0.0041342
| ((3×17)<sup>2</sup>×7×23)/(2<sup>3</sup>×5×19<sup>2</sup>×29)
| 2.3.5.7.17.19.23.29 {{monzo| -3 2 -1 1 2 -2 1 -1 }}
|
|
|-
| 613089/613088
| 0.0028238
| (3<sup>3</sup>×29)<sup>2</sup>/(2<sup>5</sup>×7<sup>2</sup>×17×23)
| 2.3.7.17.23.29 {{monzo| -5 6 -2 -1 -1 2 }}
|
| S783
|-
| 949026/949025
| 0.0018242
| (2×3×13×23<sup>3</sup>)/(5<sup>2</sup>×7×11×17×29)
| 2.3.5.7.11.13.17.23.29 {{monzo| 1 1 -2 -1 -1 1 -1 3 -1 }}
|
|
|-
| 1163800/1163799
| 0.0014876
| (2<sup>3</sup>×(5×23)<sup>2</sup>×11)/(3<sup>2</sup>×7<sup>3</sup>×13×29)
| 2.3.5.7.11.13.23.29 {{monzo| 3 -2 2 -3 1 -1 2 -1 }}
|
|
|-
| 1235169/1235168
| 0.0014016
| (3<sup>5</sup>×13×17×23)/(2<sup>5</sup>×11<sup>3</sup>×29)
| 2.3.11.13.17.23.29 {{monzo| -5 5 -3 1 1 1 -1 }}
|
|
|-
| 1243840/1243839
| 0.0013918
| ((2<sup>3</sup>×13)<sup>2</sup>×5×23)/(3×17×29<sup>3</sup>)
| 2.3.5.13.17.23.29 {{monzo| 6 -1 1 2 -1 1 -3 }}
|
|
|-
| 1625625/1625624
| 0.0010650
| (3×5<sup>2</sup>×17)<sup>2</sup>/(2<sup>3</sup>×7<sup>2</sup>×11×13×29)
| 2.3.5.7.11.13.17.29 {{monzo| -3 2 4 -2 -1 -1 2 -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
| 0.00064175
| (2<sup>5</sup>×3<sup>2</sup>×17×19×29)/(5×7<sup>3</sup>×11<sup>2</sup>×13)
| 2.3.5.7.11.13.17.19.29 {{monzo| 5 2 -1 -3 -2 -1 1 1 1 }}
|
|
|-
| [[Odyssey comma|4004001/4004000]]
| 0.00043238
| (3×23×29)<sup>2</sup>/(2<sup>5</sup>×5<sup>3</sup>×7×11×13)
| 2.3.5.7.11.13.23.29 {{monzo| -5 2 -3 -1 -1 -1 2 2 }}
| 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
| 0.00020937
| ((2<sup>5</sup>×5)<sup>2</sup>×17×19)/((7×23)<sup>2</sup>×11×29)
| 2.5.7.11.17.19.23.29 {{monzo| 10 2 -2 -1 1 1 -2 -1 }}
|
|
|-
| <font style="font-size:0.88em">10556001/10556000</font>
| 0.00016400
| (3×19)<sup>4</sup>/(2<sup>5</sup>×5<sup>3</sup>×7×13×29)
| 2.3.5.7.13.19.29 {{monzo| -5 4 -3 -1 -1 4 -1 }}
|
| S3249
|-
| <font style="font-size:0.88em">18085705/18085704</font>
| 9.5724×10<sup>-5</sup>
| (5×11×17×23×29<sup>2</sup>)/((2×7×13)<sup>3</sup>×3)
| 2.3.5.7.11.13.17.23.29 {{monzo| -3 -1 1 -3 1 -3 1 1 2 }}
|
|
|-
| <font style="font-size:0.88em">96059601/96059600</font>
| 1.8022×10<sup>-5</sup>
| (3<sup>2</sup>×11)<sup>4</sup>/((2<sup>2</sup>×5×7×13)<sup>2</sup>×29)
| 2.3.5.7.11.13.29 {{monzo| -4 8 -2 -2 4 -2 -1 }}
|
| S9801
|-
| <font style="font-size:0.79em">177182721/177182720</font>
| 9.7709×10<sup>-6</sup>
| (3<sup>3</sup>×17×29)<sup>2</sup>/(2<sup>11</sup>×5×11<sup>3</sup>×13)
| 2.3.5.11.13.17.29 {{monzo| -11 6 -1 -3 -1 2 2 }}
|
| S13311
|}
 
=== 31-limit ===
{| 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"/>
|-
| [[31/30]]
| 56.767
| 31/(2×3×5)
| 2.3.5.31 {{monzo| -1 -1 -1 1 }}
| Large tricesimoprimal 1/4-tone
|
|-
| [[32/31]]
| 54.964
| 2<sup>5</sup>/31
| 2.31 {{monzo| 5 -1 }}
| Small tricesimoprimal 1/4-tone, octave-reduced 31st subharmonic
|
|-
| [[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]]
| 18.716
| (3×31)/(2<sup>2</sup>×23)
| 2.3.23.31 {{monzo| -2 1 -1 1 }}
| Tricema
|
|-
| [[125/124]]
| 13.906
| 5<sup>3</sup>/(2<sup>2</sup>×31)
| 2.5.31 {{monzo| -2 3 -1 }}
| Twizzler
|
|-
| [[155/154]]
| 11.205
| (5×31)/(2×7×11)
| 2.5.7.11.31 {{monzo| -1 1 -1 -1 1 }}
| Scyllisma
|
|-
| [[156/155]]
| 11.133
| (2<sup>2</sup>×3×13)/(5×31)
| 2.3.5.13.31 {{monzo| 2 1 -1 1 -1 }}
| Xanthippisma
|
|-
| [[187/186]]
| 9.2828
| (11×17)/(2×3×31)
| 2.3.11.17.31 {{monzo| -1 -1 1 1 -1 }}
| Lambertisma
|
|-
| [[217/216]]
| 7.9965
| (7×31)/(2×3)<sup>3</sup>
| 2.3.7.31 {{monzo| -3 -3 1 1 }}
| Eudorisma, tricesimoprimal kleisma
|
|-
| [[248/247]]
| 6.9949
| (2<sup>3</sup>×31)/(13×19)
| 2.13.19.31 {{monzo| 3 -1 -1 1 }}
| Lameisma
|
|-
| [[280/279]]
| 6.1940
| (2<sup>3</sup>×5×7)/(3<sup>2</sup>×31)
| 2.3.5.7.31 {{monzo| 3 -2 1 1 -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 }}
| Californisma
|
|-
| [[342/341]]
| 5.0695
| (2×3<sup>2</sup>×19)/(11×31)
| 2.3.11.19.31 {{monzo| 1 2 -1 1 -1 }}
| Endymisma
|
|-
| [[435/434]]
| 3.9844
| (3×5×29)/(2×7×31)
| 2.3.5.7.29.31 {{monzo| -1 1 1 -1 1 -1 }}
| Chinthisma
|
|-
| [[465/464]]
| 3.7271
| (3×5×31)/(2<sup>4</sup>×29)
| 2.3.5.29.31 {{monzo| -4 1 1 -1 1 }}
| Alektisma
|
|-
| [[496/495]]
| 3.4939
| (2<sup>4</sup>×31)/(3<sup>2</sup>×5×11)
| 2.3.5.11.31 {{monzo| 4 -2 -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 }}
| Rezisma
|
|-
| [[589/588]]
| 2.9418
| (19×31)/(2<sup>2</sup>×3×7<sup>2</sup>)
| 2.3.7.19.31 {{monzo| -2 -1 -2 1 1 }}
| Croatisma
|
|-
| [[621/620]]
| 2.7901
| (3<sup>3</sup>×23)/(2<sup>2</sup>×5×31)
| 2.3.5.23.31 {{monzo| -2 3 -1 1 -1 }}
| Owowhatsthisma
|
|-
| [[651/650]]
| 2.6614
| (3×7×31)/(2×5<sup>2</sup>×13)
| 2.3.5.7.13.31 {{monzo| -1 1 -2 1 -1 1 }}
| Antiklisma
|
|-
| [[714/713]]
| 2.4264
| (2×3×7×17)/(23×31)
| 2.3.7.17.23.31 {{monzo| 1 1 1 1 -1 -1 }}
| Ululisma
|
|-
| [[806/805]]
| 2.1493
| (2×13×31)/(5×7×23)
| 2.5.7.13.23.31 {{monzo| 1 -1 -1 1 -1 1 }}
|
|
|-
| [[837/836]]
| 2.0696
| (3<sup>3</sup>×31)/(2<sup>2</sup>×11×19)
| 2.3.11.19.31 {{monzo| -2 3 -1 -1 1 }}
|
|
|-
| [[868/867]]
| 1.9957
| (2<sup>2</sup>×7×31)/(3×17<sup>2</sup>)
| 2.3.7.17.31 {{monzo| 2 -1 1 -2 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]]
| 1.8605
| (7<sup>2</sup>×19)/(2×3×5×31)
| 2.3.5.7.19.31 {{monzo| -1 -1 -1 2 1 -1 }}
|
|
|-
| [[961/960]]
| 1.8024
| 31<sup>2</sup>/(2<sup>6</sup>×3×5)
| 2.3.5.31 {{monzo| -6 -1 -1 2 }}
|
| 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]]
| 1.6433
| (2×17×31)/(3<sup>4</sup>×13)
| 2.3.13.17.31 {{monzo| 1 -4 -1 1 1 }}
|
|
|-
| [[1210/1209]]
| 1.4314
| (2×5×11<sup>2</sup>)/(3×13×31)
| 2.3.5.11.13.31 {{monzo| 1 -1 1 2 -1 -1 }}
|
|
|-
| [[1365/1364]]
| 1.2688
| (3×5×7×13)/(2<sup>2</sup>×11×31)
| 2.3.5.7.11.13.31 {{monzo| -2 1 1 1 -1 1 -1 }}
|
|
|-
| [[1426/1425]]
| 1.2145
| (2×23×31)/(3×5<sup>2</sup>×19)
| 2.3.5.19.23.31 {{monzo| 1 -1 -2 -1 1 1 }}
|
|
|-
| [[1519/1518]]
| 1.1401
| (7<sup>2</sup>×31)/(2×3×11×23)
| 2.3.7.11.23.31 {{monzo| -1 -1 2 -1 -1 1 }}
|
|
|-
| [[1520/1519]]
| 1.1393
| (2<sup>4</sup>×5×19)/(7<sup>2</sup>×31)
| 2.5.7.19.31 {{monzo| 4 1 -2 1 -1 }}
|
|
|-
| [[1768/1767]]
| 0.97948
| (2<sup>3</sup>×13×17)/(3×19×31)
| 2.3.13.17.19.31 {{monzo| 3 -1 1 1 -1 -1 }}
|
|
|-
| [[1860/1859]]
| 0.93102
| (2<sup>2</sup>×3×5×31)/(11×13<sup>2</sup>)
| 2.3.5.11.13.31 {{monzo| 2 1 1 -1 -2 1 }}
|
|
|-
| [[2016/2015]]
| 0.85896
| (2<sup>5</sup>×3<sup>2</sup>×7)/(5×13×31)
| 2.3.5.7.13.31 {{monzo| 5 2 -1 1 -1 -1 }}
|
|
|-
| [[2233/2232]]
| 0.77547
| (7×11×29)/(2<sup>3</sup>×3<sup>2</sup>×31)
| 2.3.7.11.29.31 {{monzo| -3 -2 1 1 1 -1 }}
| Kuznetsovisma
|
|-
| [[2945/2944]]
| 0.58796
| (5×19×31)/(2<sup>7</sup>×23)
| 2.5.19.23.31 {{monzo| -7 1 1 -1 1 }}
|
|
|-
| [[2976/2975]]
| 0.58183
| (2<sup>5</sup>×3×31)/(5<sup>2</sup>×7×17)
| 2.3.5.7.17.31 {{monzo| 5 1 -2 -1 -1 1 }}
|
|
|-
| [[3565/3564]]
| 0.48569
| (5×23×31)/((2×3<sup>2</sup>)<sup>2</sup>×11)
| 2.3.5.11.23.31 {{monzo| -2 -4 1 -1 1 1 }}
|
|
|-
| [[3751/3750]]
| 0.46160
| (11<sup>2</sup>×31)/(2×3×5<sup>4</sup>)
| 2.3.5.11.31 {{monzo| -1 -1 -4 2 1 }}
|
|
|-
| [[3876/3875]]
| 0.44671
| (2<sup>2</sup>×3×17×19)/(5<sup>3</sup>×31)
| 2.3.5.17.19.31 {{monzo| 2 1 -3 1 1 -1 }}
|
|
|-
| [[3969/3968]]
| 0.43624
| (3<sup>2</sup>×7)<sup>2</sup>/(2<sup>7</sup>×31)
| 2.3.7.31 {{monzo| -7 4 2 -1 }}
| Yunzee comma
| S63
|-
| [[4186/4185]]
| 0.41363
| (2×7×13×23)/(3<sup>3</sup>×5×31)
| 2.3.5.7.13.23.31 {{monzo| 1 -3 -1 1 1 1 -1 }}
| Tamashimisma
|
|-
| [[4960/4959]]
| 0.34907
| (2<sup>5</sup>×5×31)/(3<sup>2</sup>×19×29)
| 2.3.5.19.29.31 {{monzo| 5 -2 1 -1 -1 1 }}
|
|
|-
| [[4992/4991]]
| 0.34684
| (2<sup>7</sup>×3×13)/(7×23×31)
| 2.3.7.13.23.31 {{monzo| 7 1 -1 1 -1 -1 }}
| Kalmanisma
|
|-
| [[5643/5642]]
| 0.30682
| (3<sup>3</sup>×11×19)/(2×7×13×31)
| 2.3.7.11.13.19.31 {{monzo| -1 3 -1 1 -1 1 -1 }}
|
|
|-
| [[5797/5796]]
| 0.29867
| (11×17×31)/((2×3)<sup>2</sup>×7×23)
| 2.3.7.11.17.23.31 {{monzo| -2 -2 -1 1 1 -1 1 }}
| Bivojisma
|
|-
| [[6076/6075]]
| 0.28495
| ((2×7)<sup>2</sup>×31)/(3<sup>5</sup>×5<sup>2</sup>)
| 2.3.5.7.31 {{monzo| 2 -5 -2 2 1 }}
| Large ricegrain comma
|
|-
| [[6138/6137]]
| 0.28207
| (2×3<sup>2</sup>×11×31)/(17×19<sup>2</sup>)
| 2.3.11.17.19.31 {{monzo| 1 2 1 -1 -2 1 }}
|
|
|-
| [[6293/6292]]
| 0.27513
| (7×29×31)/((2×11)<sup>2</sup>×13)
| 2.7.11.13.29.31 {{monzo| -2 1 -2 -1 1 1 }}
|
|
|-
| [[6325/6324]]
| 0.27373
| (5<sup>2</sup>×11×23)/(2<sup>2</sup>×3×17×31)
| 2.3.5.11.17.23.31 {{monzo| -2 -1 2 1 -1 1 -1 }}
|
|
|-
| [[6480/6479]]
| 0.26719
| ((2×3)<sup>4</sup>×5)/(11×19×31)
| 2.3.5.11.19.31 {{monzo| 4 4 1 -1 -1 -1 }}
| Scarlattisma
|
|-
| [[6728/6727]]
| 0.25734
| (2<sup>3</sup>×29<sup>2</sup>)/(7×31<sup>2</sup>)
| 2.7.29.31 {{monzo| 3 -1 2 -2 }}
| Sushi comma
|
|-
| [[7657/7656]]
| 0.22611
| (13×19×31)/(2<sup>3</sup>×3×11×29)
| 2.3.11.13.19.29.31 {{monzo| -3 -1 -1 1 1 -1 1 }}
|
|
|-
| [[7905/7904]]
| 0.21902
| (3×5×17×31)/(2<sup>5</sup>×13×19)
| 2.3.5.13.17.19.31 {{monzo| -5 1 1 -1 1 -1 1 }}
|
|
|-
| [[7936/7935]]
| 0.21816
| (2<sup>8</sup>×31)/(3×5×23<sup>2</sup>)
| 2.3.5.23.31 {{monzo| 8 -1 -1 -2 1 }}
|
|
|-
| [[8092/8091]]
| 0.21396
| ((2×17)<sup>2</sup>×7)/(3<sup>2</sup>×29×31)
| 2.3.7.17.29.31 {{monzo| 2 -2 1 2 -1 -1 }}
|
|
|-
| [[8464/8463]]
| 0.20455
| (2<sup>2</sup>×23)<sup>2</sup>/(3×7×13×31)
| 2.3.7.13.23.31 {{monzo| 4 -1 -1 -1 2 -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]]
| 0.19323
| (2<sup>8</sup>×5×7)/(17<sup>2</sup>×31)
| 2.5.7.17.31 {{monzo| 8 1 1 -2 -1 }}
| Small ricegrain comma
|
|-
| [[9425/9424]]
| 0.18370
| (5<sup>2</sup>×13×29)/(2<sup>4</sup>×19×31)
| 2.5.13.19.29.31 {{monzo| -4 2 1 -1 1 -1 }}
|
|
|-
| 10881/10880
| 0.15911
| (3<sup>3</sup>×13×31)/(2<sup>7</sup>×5×17)
| 2.3.5.13.17.31 {{monzo| -7 3 -1 1 -1 1 }}
|
|
|-
| 11781/11780
| 0.14696
| (3<sup>2</sup>×7×11×17)/(2<sup>2</sup>×5×19×31)
| 2.3.5.7.11.17.19.31 {{monzo| -2 2 -1 1 1 1 -1 -1 }}
|
|
|-
| 11935/11934
| 0.14506
| (5×7×11×31)/(2×3<sup>3</sup>×13×17)
| 2.3.5.7.11.13.17.31 {{monzo| -1 -3 1 1 1 -1 -1 1 }}
|
|
|-
| 12122/12121
| 0.14282
| (2×11×19×29)/(17×23×31)
| 2.11.17.19.23.29.31 {{monzo| 1 1 -1 1 -1 1 -1 }}
|
|
|-
| 13300/13299
| 0.13017
| ((2×5)<sup>2</sup>×7×19)/(3×11×13×31)
| 2.3.5.7.11.13.19.31 {{monzo| 2 -1 2 1 -1 -1 1 -1 }}
|
|
|-
| 13455/13454
| 0.12867
| (3<sup>2</sup>×5×13×23)/(2×7×31<sup>2</sup>)
| 2.3.5.7.13.23.31 {{monzo| -1 2 1 -1 1 1 -2 }}
|
|
|-
| 15625/15624
| 0.11080
| 5<sup>6</sup>/(2<sup>3</sup>×3<sup>2</sup>×7×31)
| 2.3.5.7.31 {{monzo| -3 -2 6 -1 -1 }}
|
| S125
|-
| [[Acronymisma|17577/17576]]
| 0.098497
| (3<sup>4</sup>×7×31)/(2<sup>3</sup>×13<sup>3</sup>)
| 2.3.7.13.31 {{monzo| -3 4 1 -3 1 }}
| Acronymisma
|
|-
| [[Totziensisma|19251/19250]]
| 0.089931
| (3<sup>3</sup>×23×31)/(2×5<sup>3</sup>×7×11)
| 2.3.5.7.11.23.31 {{monzo| -1 3 -3 -1 -1 1 1}}
| Totziensisma
|
|-
| [[Honeybrookisma|19344/19343]]
| 0.089500
| (2<sup>4</sup>×3×13×31)/(23×29<sup>2</sup>)
| 2.3.13.23.29.31 {{monzo| 4 1 1 -1 -2 1 }}
| Honeybrookisma
|
|-
| 19965/19964
| 0.086716
| (3×5×11<sup>3</sup>)/(2<sup>2</sup>×7×23×31)
| 2.3.5.7.11.23.31 {{monzo| -2 1 1 -1 3 -1 -1 }}
|
|
|-
| 21142/21141
| 0.081888
| (2×11×31<sup>2</sup>)/(3<sup>6</sup>×29)
| 2.3.11.29.31 {{monzo| 1 -6 1 -1 2 }}
|
|
|-
| 22816/22815
| 0.075880
| (2<sup>5</sup>×23×31)/(3<sup>3</sup>×5×13<sup>2</sup>)
| 2.3.5.13.23.31 {{monzo| 5 -3 -1 -2 1 1 }}
|
|
|-
| 23375/23374
| 0.074065
| (5<sup>3</sup>×11×17)/(2×13×29×31)
| 2.5.11.13.17.29.31 {{monzo| -1 3 1 -1 1 -1 -1 }}
|
|
|-
| 23716/23715
| 0.073000
| (2×7×11)<sup>2</sup>/(3<sup>2</sup>×5×17×31)
| 2.3.5.7.11.17.31 {{monzo| 2 -2 -1 2 2 -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
| 0.063173
| (3<sup>3</sup>×5×7×29)/(2<sup>2</sup>×13×17×31)
| 2.3.5.7.13.17.29.31 {{monzo| -2 3 1 1 -1 -1 1 -1 }}
|
|
|-
| [[Tricecubisma|29792/29791]]
| 0.058112
| (2<sup>5</sup>×7<sup>2</sup>×19)/31<sup>3</sup>
| 2.7.19.31 {{monzo| 5 2 1 -3 }}
| 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
| 0.054272
| ((2×5)<sup>2</sup>×11×29)/(3×7<sup>3</sup>×31)
| 2.3.5.7.11.29.31 {{monzo| 2 -1 2 -3 1 1 -1 }}
|
|
|-
| 32799/32798
| 0.052784
| (3×13×29<sup>2</sup>)/(2×23<sup>2</sup>×31)
| 2.3.13.23.29.31 {{monzo| -1 1 1 -2 2 -1 }}
|
|
|-
| 41262/41261
| 0.041958
| (2×3×13×23<sup>2</sup>)/(11<sup>3</sup>×31)
| 2.3.11.13.23.31 {{monzo| 1 1 -3 1 2 -1 }}
|
|
|-
| 42688/42687
| 0.040556
| (2<sup>6</sup>×23×29)/(3<sup>4</sup>×17×31)
| 2.3.17.23.29.31 {{monzo| 6 -4 -1 1 1 -1 }}
|
|
|-
| 49011/49010
| 0.035324
| (3×17×31<sup>2</sup>)/(2×5×13<sup>2</sup>×29)
| 2.3.5.13.17.29.31 {{monzo| -1 1 -1 -2 1 -1 2 }}
|
|
|-
| 58311/58310
| 0.029690
| (3<sup>2</sup>×11×19×31)/(2×5×7<sup>3</sup>×17)
| 2.3.5.7.11.17.19.31 {{monzo| -1 2 -1 -3 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 }}
|
|
|-
| 96876/96875
| 0.017871
| (2<sup>2</sup>×3<sup>4</sup>×13×23)/(5<sup>5</sup>×31)
| 2.3.5.13.23.31 {{monzo| 2 4 -5 1 1 -1 }}
|
|
|-
| 98736/98735
| 0.017534
| (2<sup>4</sup>×3×11<sup>2</sup>×17)/(5×7<sup>2</sup>×13×31)
| 2.3.5.7.11.13.17.31 {{monzo| 4 1 -1 -2 2 -1 1 -1 }}
|
|
|-
| 102487/102486
| 0.016892
| (7×11<sup>4</sup>)/(2×3×19×29×31)
| 2.3.7.11.19.29.31 {{monzo| -1 -1 1 4 -1 -1 -1 }}
|
|
|-
| 108376/108375
| 0.015974
| (2<sup>3</sup>×19×23×31)/(3×5<sup>3</sup>×17<sup>2</sup>)
| 2.3.5.17.19.23.31 {{monzo| 3 -1 -3 -2 1 1 1 }}
|
|
|-
| 111321/111320
| 0.015552
| (3<sup>3</sup>×7×19×31)/(2<sup>3</sup>×5×11<sup>2</sup>×23)
| 2.3.5.7.11.19.23.31 {{monzo| -3 3 -1 1 -2 1 -1 1 }}
|
|
|-
| 111476/111475
| 0.015530
| (2<sup>2</sup>×29×31<sup>2</sup>)/(5<sup>2</sup>×7<sup>3</sup>×13)
| 2.5.7.13.29.31 {{monzo| 2 -2 -3 -1 1 2 }}
|
|
|-
| 116281/116280
| 0.014888
| (11×31)<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×5×17×19)
| 2.3.5.11.17.19.31 {{monzo| -3 -2 -1 2 -1 -1 2 }}
|
| 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
| 0.014160
| (3<sup>2</sup>×5×11×13×19)/(2<sup>3</sup>×17×29×31)
| 2.3.5.11.13.17.19.29.31 {{monzo| -3 2 1 1 1 -1 1 -1 -1 }}
|
|
|-
| 174097/174096
| 0.0099441
| (7<sup>2</sup>×11×17×19)/(2<sup>4</sup>×3<sup>3</sup>×13×31)
| 2.3.7.11.13.17.19.31 {{monzo| -4 -3 2 1 -1 1 1 -1 }}
|
|
|-
| 175770/175769
| 0.0098495
| (2×3<sup>4</sup>×5×7×31)/(11×19×29<sup>2</sup>)
| 2.3.5.7.11.19.29.31 {{monzo| 1 4 1 1 -1 -1 -2 1 }}
|
|
|-
| 178126/178125
| 0.0097192
| (2×13<sup>2</sup>×17×31)/(3×5<sup>5</sup>×19)
| 2.3.5.13.17.19.31 {{monzo| 1 -1 -5 2 1 -1 1 }}
|
|
|-
| 190464/190463
| 0.0090896
| (2<sup>11</sup>×3×31)/((7×13)<sup>2</sup>×23)
| 2.3.7.13.23.31 {{monzo| 11 1 -2 -2 -1 1 }}
|
|
|-
| 207576/207575
| 0.0083403
| ((2×3)<sup>3</sup>×31<sup>2</sup>)/((5×19)<sup>2</sup>×23)
| 2.3.5.19.23.31 {{monzo| 3 3 -2 -2 -1 2 }}
|
|
|-
| 212382/212381
| 0.0081515
| (2×3<sup>5</sup>×19×23)/(13×17×31<sup>2</sup>)
| 2.3.13.17.19.23.31 {{monzo| 1 5 -1 -1 1 1 -2 }}
|
|
|-
| 227448/227447
| 0.0076116
| (2<sup>3</sup>×3<sup>7</sup>×13)/(11×23×29×31)
| 2.3.11.13.23.29.31 {{monzo| 3 7 -1 1 -1 -1 -1 }}
|
|
|-
| 240065/240064
| 0.0072115
| (5×7×19<sup>3</sup>)/(2<sup>6</sup>×11<sup>2</sup>×31)
| 2.5.7.11.19.31 {{monzo| -6 1 1 -2 3 -1 }}
|
|
|-
| 245025/245024
| 0.0070656
| (3<sup>2</sup>×5×11)<sup>2</sup>/(2<sup>5</sup>×13×19×31)
| 2.3.5.11.13.19.31 {{monzo| -5 4 2 2 -1 -1 -1 }}
|
| S495
|-
| 260338/260337
| 0.0066500
| (2×13×17×19×31)/(3×7<sup>3</sup>×11×23)
| 2.3.7.11.13.17.19.23.31 {{monzo| 1 -1 -3 -1 1 1 1 -1 1 }}
|
|
|-
| 268801/268800
| 0.0064406
| (13×23×29×31)/(2<sup>9</sup>×3×5<sup>2</sup>×7)
| 2.3.5.7.13.23.29.31 {{monzo| -9 -1 -2 -1 1 1 1 1 }}
|
|
|-
| 278784/278783
| 0.0062010
| (2<sup>4</sup>×3×11)<sup>2</sup>/(17×23<sup>2</sup>×31)
| 2.3.11.17.23.31 {{monzo| 8 2 2 -1 -2 -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
| 0.0055059
| ((3×7)<sup>2</sup>×23×31)/(2<sup>2</sup>×17)<sup>3</sup>
| 2.3.7.17.23.31 {{monzo| -6 2 2 -3 1 1 }}
|
|
|-
| 453376/453375
| 0.0038185
| (2<sup>8</sup>×7×11×23)/(3<sup>2</sup>×5<sup>3</sup>×13×31)
| 2.3.5.7.11.13.23.31 {{monzo| 8 -2 -3 1 1 -1 1 -1 }}
|
|
|-
| 459173/459172
| 0.0037703
| (11×13<sup>3</sup>×19)/(2<sup>2</sup>×7×23<sup>2</sup>×31)
| 2.7.11.13.19.23.31 {{monzo| -2 -1 1 3 1 -2 -1 }}
|
|
|-
| 509796/509795
| 0.0033959
| (2×3×7×17)<sup>2</sup>/(5×11×13×23×31)
| 2.3.5.7.11.13.17.23.31 {{monzo| 2 2 -1 2 -1 -1 2 -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
| 0.0020039
| (2<sup>2</sup>×3×5×7×11<sup>2</sup>×17)/(29×31<sup>3</sup>)
| 2.3.5.7.11.17.29.31 {{monzo| 2 1 1 1 2 1 -1 -3 }}
|
|
|-
| 912951/912950
| 0.0018963
| (3<sup>5</sup>×13×17<sup>2</sup>)/(2×5<sup>2</sup>×19×31<sup>2</sup>)
| 2.3.5.13.17.19.31 {{monzo| -1 5 -2 1 2 -1 -2 }}
|
|
|-
| 1147125/1147124
| 0.0015092
| (3×5<sup>3</sup>×7×19×23)/(2<sup>2</sup>×11×29<sup>2</sup>×31)
| 2.3.5.7.11.19.23.29.31 {{monzo| -2 1 3 1 -1 1 1 -2 -1 }}
|
|
|-
| 1154440/1154439
| 0.0014996
| (2<sup>3</sup>×5×7<sup>2</sup>×19×31)/(3<sup>3</sup>×11×13<sup>2</sup>×23)
| 2.3.5.7.11.13.19.23.31 {{monzo| 3 -3 1 2 -1 -2 1 -1 1 }}
|
|
|-
| 1255501/1255500
| 0.0013789
| (13<sup>2</sup>×17×19×23)/(2<sup>2</sup>×3<sup>4</sup>×5<sup>3</sup>×31)
| 2.3.5.13.17.19.23.31 {{monzo| -2 -4 -3 2 1 1 1 -1 }}
|
|
|-
| 1594176/1594175
| 0.0010860
| (2<sup>6</sup>×3×19<sup>2</sup>×23)/((5×11)<sup>2</sup>×17×31)
| 2.3.5.11.17.19.23.31 {{monzo| 6 1 -2 -2 -1 2 1 -1 }}
|
|
|-
| 2307361/2307360
| 0.00075031
| (7<sup>2</sup>×31)<sup>2</sup>/(2<sup>5</sup>×3×5×11×19×23)
| 2.3.5.7.11.19.23.31 {{monzo| -5 -1 -1 4 -1 -1 -1 2 }}
|
| 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
| 0.00073825
| (11×13×23<sup>2</sup>×31)/(2<sup>5</sup>×7×19<sup>2</sup>×29)
| 2.7.11.13.19.23.29.31 {{monzo| -5 -1 1 1 -2 2 -1 1 }}
|
|
|-
| 3206269/3206268
| 0.00053995
| (11×19×23<sup>2</sup>×29)/((2×3×13)<sup>2</sup>×17×31)
| 2.3.11.13.17.19.23.29.31 {{monzo| -2 -2 1 -2 -1 1 2 1 -1 }}
|
|
|-
| 3301376/3301375
| 0.00052440
| (2<sup>13</sup>×13×31)/(5<sup>3</sup>×7<sup>4</sup>×11)
| 2.5.7.11.13.31 {{monzo| 13 -3 -4 -1 1 1 }}
|
|
|-
| 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 }}
|
|
|}
 
=== 37-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"/>
|-
| [[37/36]]
| 47.434
| 37/(2×3)<sup>2</sup>
| 2.3.37 {{monzo| -2 -2 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]]
| 23.238
| (3×5<sup>2</sup>)/(2×37)
| 2.3.5.37 {{monzo| -1 1 2 -1 }}
|
|
|-
| [[111/110]]
| 15.667
| (3×37)/(2×5×11)
| 2.3.5.11.37 {{monzo| -1 1 -1 -1 1 }}
|
|
|-
| [[112/111]]
| 15.527
| (2<sup>4</sup>×7)/(3×37)
| 2.3.7.37 {{monzo| 4 -1 1 -1 }}
|
|
|-
| [[148/147]]
| 11.737
| (2<sup>2</sup>×37)/(3×7<sup>2</sup>)
| 2.3.7.37 {{monzo| 2 -1 -2 1 }}
|
|
|-
| [[185/184]]
| 9.3834
| (5×37)/(2<sup>3</sup>×23)
| 2.5.23.37 {{monzo| -3 1 -1 1 }}
|
|
|-
| [[186/185]]
| 9.3328
| (2×3×31)/(5×37)
| 2.3.5.31.37 {{monzo| 1 1 -1 1 -1 }}
|
|
|-
| [[222/221]]
| 7.8160
| (2×3×37)/(13×17)
| 2.3.13.17.37 {{monzo| 1 1 -1 -1 1 }}
|
|
|-
| [[260/259]]
| 6.6714
| (2<sup>2</sup>×5×13)/(7×37)
| 2.5.7.13.37 {{monzo| 2 1 -1 1 -1 }}
|
|
|-
| [[297/296]]
| 5.8389
| (3<sup>3</sup>×11)/(2<sup>3</sup>×37)
| 2.3.11.37 {{monzo| -3 3 1 -1 }}
|
|
|-
| [[407/406]]
| 4.2589
| (11×37)/(2×7×29)
| 2.7.11.29.37 {{monzo| -1 -1 1 -1 1 }}
|
|
|-
| [[408/407]]
| 4.2484
| (2<sup>3</sup>×3×17)/(11×37)
| 2.3.11.17.37 {{monzo| 3 1 -1 1 -1 }}
|
|
|-
| [[481/480]]
| 3.6030
| (13×37)/(2<sup>5</sup>×3×5)
| 2.3.5.13.37 {{monzo| -5 -1 -1 1 1 }}
| Semaphorisma
|
|-
| [[630/629]]
| 2.7502
| (2×3<sup>2</sup>×5×7)/(17×37)
| 2.3.5.7.17.37 {{monzo| 1 2 1 1 -1 -1 }}
|
|
|-
| [[666/665]]
| 2.6014
| (2×3<sup>2</sup>×37)/(5×7×19)
| 2.3.5.7.19.37 {{monzo| 1 2 -1 -1 -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]]
| 2.4644
| (19×37)/(2×3<sup>3</sup>×13)
| 2.3.13.19.37 {{monzo| -1 -3 -1 1 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
|
|-
| [[851/850]]
| 2.0355
| (23×37)/(2×5<sup>2</sup>×17)
| 2.5.17.23.37 {{monzo| -1 -2 -1 1 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]]
| 1.8006
| (2×13×37)/31<sup>2</sup>
| 2.13.31.37 {{monzo| 1 1 -2 1 }}
|
|
|-
| [[1000/999]]
| 1.7321
| (2×5)<sup>3</sup>/(3<sup>3</sup>×37)
| 2.3.5.37 {{monzo| 3 -3 3 -1 }}
|
|
|-
| [[1036/1035]]
| 1.6719
| (2<sup>2</sup>×7×37)/(3<sup>2</sup>×5×23)
| 2.3.5.7.23.37 {{monzo| 2 -2 -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]]
| 1.3363
| (2×3)<sup>4</sup>/(5×7×37)
| 2.3.5.7.37 {{monzo| 4 4 -1 -1 -1 }}
|
| S36
|-
| [[1332/1331]]
| 1.3002
| ((2×3)<sup>2</sup>×37)/11<sup>3</sup>
| 2.3.11.37 {{monzo| 2 2 -3 1 }}
| Marconisma
|
|-
| [[1369/1368]]
| 1.2651
| 37<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×19)
| 2.3.19.37 {{monzo| -3 -2 -1 2 }}
|
| 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]]
| 1.1701
| (2<sup>3</sup>×5×37)/(3×17×29)
| 2.3.5.17.29.37 {{monzo| 3 -1 1 -1 -1 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]]
| 1.0395
| (2×7<sup>2</sup>×17)/(3<sup>2</sup>×5×37)
| 2.3.5.7.17.37 {{monzo| 1 -2 -1 2 1 -1 }}
| Gentisma
|
|-
| [[1702/1701]]
| 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 }}
| Lesleymartin comma
|
|-
| 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 }}
| Pantinisma
|
|-
| 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 }}
|
|
|-
| 108928/108927
| 0.015893
| (2<sup>7</sup>×23×37)/((3×7)<sup>2</sup>×13×19)
| 2.3.7.13.19.23.37 {{monzo| 7 -2 -2 -1 -1 1 1 }}
|
|
|-
| 117624/117623
| 0.014718
| (2<sup>3</sup>×3×13<sup>2</sup>×29)/(11×17<sup>2</sup>×37)
| 2.3.11.13.17.29.37 {{monzo| 3 1 -1 2 -2 1 -1 }}
|
|
|-
| 120176/120175
| 0.014406
| (2<sup>4</sup>×7×29×37)/(5<sup>2</sup>×11×19×23)
| 2.5.7.11.19.23.29.37 {{monzo| 4 -1 1 -1 -1 -1 1 1 }}
|
|
|-
| 143375/143374
| 0.012075
| (5<sup>3</sup>×31×37)/(2×7<sup>3</sup>×11×19)
| 2.5.7.11.19.31.37 {{monzo| -1 3 -3 -1 -1 1 1 }}
|
|
|-
| 155585/155584
| 0.011127
| (5×29<sup>2</sup>×37)/(2<sup>6</sup>×11×13×17)
| 2.5.11.13.17.29.37 {{monzo| -6 1 -1 -1 -1 2 1 }}
|
|
|-
| 156066/156065
| 0.011093
| (2×3×19×37<sup>2</sup>)/(5×7<sup>4</sup>×13)
| 2.3.5.7.13.19.37 {{monzo| 1 1 -1 -4 -1 1 2 }}
|
|
|-
| 161875/161874
| 0.010695
| (5<sup>4</sup>×7×37)/(2×3<sup>2</sup>×17×23<sup>2</sup>)
| 2.3.5.7.17.23.37 {{monzo| -1 -2 4 1 -1 -2 1 }}
|
|
|-
| 164836/164835
| 0.010503
| (2×7×29)<sup>2</sup>/(3<sup>4</sup>×5×11×37)
| 2.3.5.7.11.29.37 {{monzo| 2 -4 -1 2 -1 2 -1 }}
|
| S406
|-
| 165649/165648
| 0.010451
| (11×37)<sup>2</sup>/(2<sup>4</sup>×3×7×17×29)
| 2.3.7.11.17.29.37 {{monzo| -4 -1 -1 2 -1 -1 2 }}
|
| S407
|-
| 198912/198911
| 0.0087035
| (2<sup>8</sup>×3×7×37)/(19<sup>3</sup>×29)
| 2.3.7.19.29.37 {{monzo| 8 1 1 -3 -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 }}
|
|
|-
| 227070/227069
| 0.0076242
| (2×3<sup>3</sup>×5×29<sup>2</sup>)/(17×19<sup>2</sup>×37)
| 2.3.5.17.19.29.37 {{monzo| 1 3 1 -1 -2 2 -1 }}
|
|
|-
| 254449/254448
| 0.0068039
| (13×23<sup>2</sup>×37)/(2<sup>4</sup>×3<sup>3</sup>×19×31)
| 2.3.13.19.23.31.37 {{monzo| -4 -3 1 -1 2 -1 1 }}
|
|
|-
| 285418/285417
| 0.0060656
| (2×7×19×29×37)/(3<sup>3</sup>×11×31<sup>2</sup>)
| 2.3.7.11.19.29.31.37 {{monzo| 1 -3 1 -1 1 1 -2 1 }}
|
|
|-
| 319125/319124
| 0.0054249
| (3×5<sup>3</sup>×23×37)/(2<sup>2</sup>×13×17×19<sup>2</sup>)
| 2.3.5.13.17.19.23.37 {{monzo| -2 1 3 -1 -1 -2 1 1 }}
|
|
|-
| 348726/348725
| 0.0049645
| (2×3×7×19<sup>2</sup>×23)/(5<sup>2</sup>×13×29×37)
| 2.3.5.7.13.19.23.29.37 {{monzo| 1 1 -2 1 -1 2 1 -1 -1 }}
|
|
|-
| 360640/360639
| 0.0048005
| (2<sup>6</sup>×5×7<sup>2</sup>×23)/(3<sup>3</sup>×19<sup>2</sup>×37)
| 2.3.5.7.19.23.37 {{monzo| 6 -3 1 2 -2 1 -1 }}
|
|
|-
| 378880/378879
| 0.0045694
| (2<sup>11</sup>×5×37)/(3×17<sup>2</sup>×19×23)
| 2.3.5.17.19.23.37 {{monzo| 11 -1 1 -2 -1 -1 1 }}
|
|
|-
| 390166/390165
| 0.0044372
| (2×7×29×31<sup>2</sup>)/(3×5×19×37<sup>2</sup>)
| 2.3.5.7.19.29.31.37 {{monzo| 1 -1 -1 1 -1 1 2 -2 }}
|
|
|-
| 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
|-
| 446369/446368
| 0.0038785
| (7×11<sup>2</sup>×17×31)/(2<sup>5</sup>×13×29×37)
| 2.7.11.13.17.29.31.37 {{monzo| -5 1 2 -1 1 -1 1 -1 }}
|
|
|-
| 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 }}
|
|
|-
| 469568/469567
| 0.0036869
| (2<sup>6</sup>×11×23×29)/(7<sup>3</sup>×37<sup>2</sup>)
| 2.7.11.23.29.37 {{monzo| 6 -3 1 1 1 -2 }}
|
|
|-
| 494209/494208
| 0.0035030
| (19×37)<sup>2</sup>/(2<sup>7</sup>×3<sup>3</sup>×11×13)
| 2.3.11.13.19.37 {{monzo| -7 -3 -1 -1 2 2 }}
|
| S703
|-
| 675584/675583
| 0.0025626
| (2<sup>8</sup>×7×13×29)/(19×31<sup>2</sup>×37)
| 2.7.13.19.29.31.37 {{monzo| 8 1 1 -1 1 -2 -1 }}
|
|
|-
| 777925/777924
| 0.0022255
| ((5×29)<sup>2</sup>×37)/(2×(3×7)<sup>2</sup>)<sup>2</sup>
| 2.3.5.7.29.37 {{monzo| -2 -4 2 -4 2 1 }}
|
|
|-
| 787176/787175
| 0.0021993
| (2<sup>3</sup>×3<sup>2</sup>×13×29<sup>2</sup>)/(5<sup>2</sup>×23×37<sup>2</sup>)
| 2.3.5.13.23.29.37 {{monzo| 3 2 -2 1 -1 2 -2 }}
|
|
|-
| 812890/812889
| 0.0021297
| (2×5×13<sup>3</sup>×37)/(3<sup>3</sup>×7×11×17×23)
| 2.3.5.7.11.13.17.23.37 {{monzo| 1 -3 1 -1 -1 3 -1 -1 1 }}
|
|
|-
| 837200/837199
| 0.0020679
| (2<sup>4</sup>×5<sup>2</sup>×7×13×23)/(11<sup>3</sup>×17×37)
| 2.5.7.11.13.17.23.37 {{monzo| 4 2 1 -3 1 -1 1 -1 }}
|
|
|-
| 923521/923520
| 0.0018746
| 31<sup>4</sup>/(2<sup>7</sup>×3×5×13×37)
| 2.3.5.13.31.37 {{monzo| -7 -1 -1 -1 4 -1 }}
|
| S961
|-
| 986272/986271
| 0.0017553
| (2<sup>5</sup>×7<sup>2</sup>×17×37)/(3×11<sup>3</sup>×13×19)
| 2.3.7.11.13.17.19.37 {{monzo| 5 -1 2 -3 -1 1 -1 1 }}
|
|
|-
| 1000000/999999
| 0.0017312
| (2×5)<sup>6</sup>/(3<sup>3</sup>×7×11×13×37)
| 2.3.5.7.11.13.37 {{monzo| 6 -3 6 -1 -1 -1 -1 }}
|
| S1000
|-
| 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
|
|-
| [[775/774]]
| 2.2353
| (5<sup>2</sup>×31)/(2×3<sup>2</sup>×43)
| 2.3.5.31.43 {{monzo| -1 -2 2 1 -1 }}
|
|
|-
| [[817/816]]
| 2.1203
| (19×43)/(2<sup>4</sup>×3×17)
| 2.3.17.19.43 {{monzo| -4 -1 -1 1 1 }}
|
|
|-
| [[861/860]]
| 2.0119
| (3×7×41)/(2<sup>2</sup>×5×43)
| 2.3.5.7.41.43 {{monzo| -2 1 -1 1 1 -1 }}
|
|
|-
| [[903/902]]
| 1.9183
| (3×7×43)/(2×11×41)
| 2.3.7.11.41.43 {{monzo| -1 1 1 -1 -1 1 }}
|
|
|-
| [[946/945]]
| 1.8310
| (2×11×43)/(3<sup>3</sup>×5×7)
| 2.3.5.7.11.43 {{monzo| 1 -3 -1 -1 1 1 }}
|
|
|-
| [[989/988]]
| 1.7514
| (23×43)/(2<sup>2</sup>×13×19)
| 2.13.19.23.43 {{monzo| -2 -1 -1 1 1 }}
|
|
|-
| [[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
|
|-
| [[1161/1160]]
| 1.4918
| (3<sup>3</sup>×43)/(2<sup>3</sup>×5×29)
| 2.3.5.29.43 {{monzo| -3 3 -1 -1 1 }}
|
|
|-
| [[1248/1247]]
| 1.3878
| (2<sup>5</sup>×3×13)/(29×43)
| 2.3.13.29.43 {{monzo| 5 1 1 -1 -1 }}
|
|
|-
| [[1333/1332]]
| 1.2992
| (31×43)/((2×3)<sup>2</sup>×37)
| 2.3.31.37.43 {{monzo| -2 -2 1 -1 1 }}
| Cevenolisma
|
|-
| [[1334/1333]]
| 1.2983
| (2×23×29)/(31×43)
| 2.23.29.31.43 {{monzo| 1 1 1 -1 -1 }}
|
|
|-
| [[1376/1375]]
| 1.2586
| (2<sup>5</sup>×43)/(5<sup>3</sup>×11)
| 2.5.11.43 {{monzo| 5 -3 -1 1 }}
|
|
|-
| [[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
|
|-
| [[1548/1547]]
| 1.1187
| (2<sup>2</sup>×3<sup>2</sup>×43)/(7×13×17)
| 2.3.7.13.17.43 {{monzo| 2 2 -1 -1 -1 1 }}
|
|
|-
| [[1764/1763]]
| 0.98170
| (2×3×7)<sup>2</sup>/(41×43)
| 2.3.7.41.43 {{monzo| 2 2 2 -1 -1 }}
|
| S42
|-
| [[1806/1805]]
| 0.95887
| (2×3×7×43)/(5×19<sup>2</sup>)
| 2.3.5.7.19.43 {{monzo| 1 1 -1 1 -2 1 }}
|
|
|-
| [[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
|-
| [[1850/1849]]
| 0.93606
| (2×5<sup>2</sup>×37)/43<sup>2</sup>
| 2.5.37.43 {{monzo| 1 2 1 -2 }}
|
|
|-
| [[1936/1935]]
| 0.89446
| (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 }}
| Lucidorisma
|
|-
| [[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
| 109/(2<sup>2</sup>×3<sup>3</sup>)
| 2.3.109 {{monzo| -2 -3 1 }}
|
|
|-
| [[110/109]]
| 15.810
| (2×5×11)/109
| 2.5.11.109 {{monzo| 1 1 1 -1 }}
|
|
|}
 
=== 113-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"/>
|-
| [[113/112]]
| 15.389
| 113/(2<sup>4</sup>×7)
| 2.7.113 {{monzo| -4 -1 1 }}
|
|
|-
| [[114/113]]
| 15.253
| (2×3×19)/113
| 2.3.19.113 {{monzo| 1 1 1 -1 }}
|
|
|}
 
=== 127-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"/>
|-
| [[127/126]]
| 13.686
| 127/(2×3<sup>2</sup>×7)
| 2.3.7.127 {{monzo| -1 -2 -1 1 }}
|
|
|-
| [[128/127]]
| 13.578
| 2<sup>7</sup>/127
| 2.127 {{monzo| 7 -1 }}
|
|
|-
| [[381/380]]
| 4.5499
| (3×127)/(2<sup>2</sup>×5×19)
| 2.3.5.19.127 {{monzo| -2 1 -1 -1 1 }}
| Five feet comma
|
|-
| 500000/499999
| 0.0034625
| (2<sup>5</sup>×5<sup>6</sup>)/(31×127<sup>2</sup>)
| 2.5.31.127 {{monzo| 5 6 -1 -2 }}
|
|
|}


== See also ==
== See also ==

Latest revision as of 08:38, 28 March 2026

This is a list of superparticular intervals ordered by prime limit. It reaches to the 127-limit and is complete up to the 37-limit.

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

List of superparticular intervals

2-limit

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

3-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
3/2 701.955 3/2 [-1 1⟩ Perfect fifth, octave-reduced 3rd harmonic, diapente
4/3 498.045 22/3 [2 -1⟩ Perfect fourth, octave-reduced 3rd subharmonic, diatessaron S2
9/8 203.910 32/23 [-3 2⟩ Pythagorean whole tone, Pythagorean major second,
major whole tone, octave-reduced 9th harmonic, harmonic ninth 		S3

5-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
5/4 386.314 5/22 [-2 0 1⟩ Classic(al)/just major third, octave-reduced 5th harmonic
6/5 315.641 (2×3)/5 [1 1 -1⟩ Classic(al)/just minor third
10/9 182.404 (2×5)/32 [1 -2 1⟩ Classic(al) (whole) tone, classic major second, minor whole tone
16/15 111.731 24/(3×5) [4 -1 -1⟩ Classic(al)/just diatonic semitone, 15th subharmonic S4
25/24 70.672 52/(23×3) [-3 -1 2⟩ Classic(al)/just chromatic semitone, chroma, Zarlinian semitone S5
81/80 21.506 (3/2)4/5 [-4 4 -1⟩ Syntonic comma, Didymus comma S9

7-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
7/6 266.871 7/(2×3) [-1 -1 0 1⟩ (Septimal) subminor third, septimal minor third
8/7 231.174 23/7 [3 0 0 -1⟩ (Septimal) supermajor second, septimal whole tone,
octave-reduced 7th subharmonic
15/14 119.443 (3×5)/(2×7) [-1 1 1 -1⟩ Septimal major semitone, septimal diatonic semitone
21/20 84.467 (3×7)/(22×5) [-2 1 -1 1⟩ Septimal minor semitone, large septimal chroma
28/27 62.961 (22×7)/33 [2 -3 0 1⟩ Septimal 1/3-tone, small septimal chroma,
(septimal) subminor second, septimal minor second,
trienstonic comma
36/35 48.770 (2×3)2/(5×7) [2 2 -1 -1⟩ Septimal 1/4-tone, mint comma S6
49/48 35.697 72/(24×3) [-4 -1 0 2⟩ Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma S7
50/49 34.976 2×(5/7)2 [1 0 2 -2⟩ Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma
64/63 27.264 26/(32×7) [6 -2 0 -1⟩ Septimal comma, Archytas' comma S8
126/125 13.795 (2×32×7)/53 [1 2 -3 1⟩ Starling comma, septimal semicomma
225/224 7.7115 (3×5)2/(25×7) [-5 2 2 -1⟩ Marvel comma, septimal kleisma S15
2401/2400 0.72120 74/(25×3×52) [-5 -1 -2 4⟩ Breedsma S49
4375/4374 0.39576 (54×7)/(2×37) [-1 -7 4 1⟩ Ragisma

11-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
11/10 165.004 11/(2×5) [-1 0 -1 0 1⟩ Large undecimal neutral second,
undecimal submajor second, Ptolemy's second
12/11 150.637 (22×3)/11 [2 1 0 0 -1⟩ Small undecimal neutral second
22/21 80.537 (2×11)/(3×7) [1 -1 0 -1 1⟩ Undecimal minor semitone
33/32 53.273 (3×11)/25 [-5 1 0 0 1⟩ Undecimal 1/4-tone, undecimal diesis,
al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
45/44 38.906 (3/2)2×(5/11) [-2 2 1 0 -1⟩ Undecimal 1/5-tone, cake comma
55/54 31.767 (5×11)/(2×33) [-1 -3 1 0 1⟩ Telepathma, eleventyfive comma,
undecimal diasecundal comma
56/55 31.194 (23×7)/(5×11) [3 0 -1 1 -1⟩ Undecimal tritonic comma, konbini comma
99/98 17.576 (3/7)2×(11/2) [-1 2 0 -2 1⟩ Mothwellsma, small undecimal comma
100/99 17.399 ((2×5)/3)2/11 [2 -2 2 0 -1⟩ Ptolemisma, Ptolemy's comma S10
121/120 14.376 112/(23×3×5) [-3 -1 -1 0 2⟩ Biyatisma, undecimal seconds comma S11
176/175 9.8646 (24×11)/(52×7) [4 0 -2 -1 1⟩ Valinorsma
243/242 7.1391 35/(2×112) [-1 5 0 0 -2⟩ Rastma, neutral thirds comma
385/384 4.5026 (5×7×11)/(27×3) [-7 -1 1 1 1⟩ Keenanisma
441/440 3.9302 (3×7)2/(23×5×11) [-3 2 -1 2 -1⟩ Werckisma, Werckmeister's undecimal septenarian schisma S21
540/539 3.2090 (2/7)2×((33×5)/11) [2 3 1 -2 -1⟩ Swetisma, Swets' comma
3025/3024 0.57240 (5×11)2/(24×33×7) [-4 -3 2 -1 2⟩ Lehmerisma S55
9801/9800 0.17665 ((32×11)/(5×7))2/23 [-3 4 -2 -2 2⟩ Kalisma, Gauss comma S99

13-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
13/12 138.573 13/(22×3) [-2 -1 0 0 0 1⟩ Large tridecimal 2/3-tone,
tridecimal neutral second
14/13 128.298 (2×7)/13 [1 0 0 1 0 -1⟩ Small tridecimal 2/3-tone, trienthird
26/25 67.900 (2×13)/52 [1 0 -2 0 0 1⟩ Large tridecimal 1/3-tone
27/26 65.337 33/(2×13) [-1 3 0 0 0 -1⟩ Small tridecimal 1/3-tone
40/39 43.831 (23×5)/(3×13) [3 -1 1 0 0 -1⟩ Tridecimal minor diesis
65/64 26.841 (5×13)/26 [-6 0 1 0 0 1⟩ Wilsorma, 13th-partial chroma
66/65 26.432 (2×3×11)/(5×13) [1 1 -1 0 1 -1⟩ Winmeanma
78/77 22.339 (2×3×13)/(7×11) [1 1 0 -1 -1 1⟩ Negustma
91/90 19.130 (7×13)/(2×32×5) [-1 -2 -1 1 0 1⟩ Biome comma, superleap comma
105/104 16.567 (3×5×7)/(23×13) [-3 1 1 1 0 -1⟩ Animist comma, small tridecimal comma
144/143 12.064 (22×3)2/(11×13) [4 2 0 0 -1 -1⟩ Grossma S12
169/168 10.274 132/(23×3×7) [-3 -1 0 -1 0 2⟩ Buzurgisma, dhanvantarisma S13
196/195 8.8554 (2×7)2/(3×5×13) [2 -1 -1 2 0 -1⟩ Mynucuma S14
325/324 5.3351 (5/(2×32))2×13 [-2 -4 2 0 0 1⟩ Marveltwin comma
351/350 4.9393 (33×13)/(2×52×7) [-1 3 -2 -1 0 1⟩ Ratwolfsma
352/351 4.9253 (25×11)/(33×13) [5 -3 0 0 1 -1⟩ Major minthma, major gentle comma
364/363 4.7627 (2/11)2×((7×13)/3) [2 -1 0 1 -2 1⟩ Minor minthma, minor gentle comma
625/624 2.7722 (5/2)4/(3×13) [-4 -1 4 0 0 -1⟩ Tunbarsma S25
676/675 2.5629 ((2×13)/5)2/33 [2 -3 -2 0 0 2⟩ Island comma S26
729/728 2.3764 (32/2)3/(7×13) [-3 6 0 -1 0 -1⟩ Squbema S27
1001/1000 1.7304 (7×11×13)/(2×5)3 [-3 0 -3 1 1 1⟩ Sinbadma
1716/1715 1.0092 (22×3×11×13)/(5×73) [2 1 -1 -3 1 1⟩ Lummic comma
2080/2079 0.83252 (25×5×13)/(33×7×11) [5 -3 1 -1 -1 1⟩ Ibnsinma, sinaisma
4096/4095 0.42272 (26/3)2/(5×7×13) [12 -2 -1 -1 0 -1⟩ Minisma S64
4225/4224 0.40981 (5×13)2/(27×3×11) [-7 -1 2 0 -1 2⟩ Leprechaun comma S65
6656/6655 0.26012 (23/11)3×(13/5) [9 0 -1 0 -3 1⟩ Jacobin comma
10648/10647 0.16260 (2×11)3/((3×13)2×7) [3 -2 0 -1 3 -2⟩ Harmonisma
123201/123200 0.014052 (3/2)6×(13/5)2/(7×11) [-6 6 -2 -1 -1 2⟩ Chalmersia S351

17-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
17/16 104.955 17/24 [-4 0 0 0 0 0 1⟩ Large septendecimal semitone,
octave-reduced 17th harmonic
18/17 98.955 (2×32)/17 [1 2 0 0 0 0 -1⟩ Small septendecimal semitone,
Arabic lute index finger
34/33 51.682 (2×17)/(3×11) [1 -1 0 0 -1 0 1⟩ Large septendecimal 1/4-tone
35/34 50.184 (5×7)/(2×17) [-1 0 1 1 0 0 -1⟩ Small septendecimal 1/4-tone
51/50 34.283 (3×17)/(2×52) [-1 1 -2 0 0 0 1⟩ Large septendecimal 1/6-tone
52/51 33.617 (22×13)/(3×17) [2 -1 0 0 0 1 -1⟩ Small septendecimal 1/6-tone
85/84 20.488 (5×17)/(22×3×7) [-2 -1 1 -1 0 0 1⟩ Monk comma
120/119 14.487 (23×3×5)/(7×17) [3 1 1 -1 0 0 -1⟩ Lynchisma
136/135 12.777 (2/3)3×(17/5) [3 -3 -1 0 0 0 1⟩ Diatisma, septendecimal major second comma
154/153 11.278 (2×7×11)/(32×17) [1 -2 0 1 1 0 -1⟩ Augustma
170/169 10.214 (2×5×17)/132 [1 0 1 0 0 -2 1⟩ Major naiadma
221/220 7.8514 (13×17)/(22×5×11) [-2 0 -1 0 -1 1 1⟩ Minor naiadma
256/255 6.7759 28/(3×5×17) [8 -1 -1 0 0 0 -1⟩ Charisma, charic comma,
septendecimal kleisma 		S16
273/272 6.3532 (3×7×13)/(24×17) [-4 1 0 1 0 1 -1⟩ Tannisma, prototannisma
289/288 6.0008 (17/3)2/25 [-5 -2 0 0 0 0 2⟩ Semitonisma S17
375/374 4.6228 (3×53)/(2×11×17) [-1 1 3 0 -1 0 -1⟩ Ursulisma
442/441 3.9213 (2×13×17)/(3×7)2 [1 -2 0 -2 0 1 1⟩ Seminaiadma
561/560 3.0887 (3×11×17)/(24×5×7) [-4 1 -1 -1 1 0 1⟩ Monardisma, tsaharuk comma
595/594 2.9121 (5×7×17)/(2×33×11) [-1 -3 1 1 -1 0 1⟩ Dakotisma
715/714 2.4230 (5×11×13)/(2×3×7×17) [-1 -1 1 -1 1 1 -1⟩ September comma, septembrisma
833/832 2.0796 (72×17)/(26×13) [-6 0 0 2 0 -1 1⟩ Horizma, horizon comma
936/935 1.8506 (23×32×13)/(5×11×17) [3 2 -1 0 -1 1 -1⟩ Ainisma, ainic comma
1089/1088 1.5905 (3×11)2/(26×17) [-6 2 0 0 2 0 -1⟩ Twosquare comma S33
1156/1155 1.4983 (2×17)2/(3×5×7×11) [2 -1 -1 -1 -1 0 2⟩ Quadrantonisma S34
1225/1224 1.4138 (5×7)2/(23×32×17) [-3 -2 2 2 0 0 -1⟩ Noellisma S35
1275/1274 1.3584 (3×52×17)/(2×72×13) [-1 1 2 -2 0 -1 1⟩ Cimbrisma
1701/1700 1.0181 (35×7)/((2×5)2×17) [-2 5 -2 1 0 0 -1⟩ Palingenetic comma, palingenesis
2058/2057 0.84143 (2×3×73)/(112×17) [1 1 0 3 -2 0 -1⟩ Xenisma
2431/2430 0.71230 (11×13×17)/(2×35×5) [-1 -5 -1 0 1 1 1⟩ Heptacircle comma
2500/2499 0.69263 (2×52)2/(3×72×17) [2 -1 4 -2 0 0 -1⟩ Sperasma S50
2601/2600 0.66573 (3×17)2/(23×52×13) [-3 2 -2 0 0 -1 2⟩ Sextantonisma S51
4914/4913 0.35234 (2×33×7×13)/173 [1 3 0 1 0 1 -3⟩ Baladisma
5832/5831 0.29688 (2×32)3/(73×17) [3 6 0 -3 0 0 -1⟩ Chlorisma
12376/12375 0.13989 (23×7×13×17)/(32×53×11) [3 -2 -3 1 -1 1 1⟩ Flashma
14400/14399 0.12023 (23×3×5)2/(7×112×17) [6 2 2 -1 -2 0 -1⟩ Sparkisma S120
28561/28560 0.060616 (13/2)4/(3×5×7×17) [-4 -1 -1 -1 0 4 -1⟩ Pisanoisma S169
31213/31212 0.055466 (74×13)/(22×33×172) [-2 -3 0 4 0 1 -2⟩ E-shaped comma
37180/37179 0.046564 (22×5×11×132)/(37×17) [2 -7 1 0 1 2 -1⟩ Lateral comma
194481/194480 0.0089018 (3×7)4/(24×5×11×13×17) [-4 4 -1 4 -1 -1 -1⟩ Scintillisma S441
336141/336140 0.0051503 (32×133×17)/(22×5×75) [-2 2 -1 -5 0 3 1⟩ Aksial comma

19-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
19/18 93.603 19/(2×32) [-1 -2 0 0 0 0 0 1⟩ Large undevicesimal semitone
20/19 88.801 (22×5)/19 [2 0 1 0 0 0 0 -1⟩ Small undevicesimal semitone
39/38 44.970 (3×13)/(2×19) [-1 1 0 0 0 1 0 -1⟩ Undevicesimal diesis,
undevicesimal 2/9-tone
57/56 30.642 (3×19)/(23×7) [-3 1 0 -1 0 0 0 1⟩ Hendrix comma
76/75 22.931 (22×19)/(3×52) [2 -1 -2 0 0 0 0 1⟩ Large undevicesimal 1/9-tone
77/76 22.631 (7×11)/(22×19) [-2 0 0 1 1 0 0 -1⟩ Small undevicesimal 1/9-tone
96/95 18.128 (25×3)/(5×19) [5 1 -1 0 0 0 0 -1⟩ 19th-partial chroma
133/132 13.066 (7×19)/(22×3×11) [-2 -1 0 1 -1 0 0 1⟩ Minithirdma
153/152 11.352 (32×17)/(23×19) [-3 2 0 0 0 0 1 -1⟩ Ganassisma, Ganassi's comma
171/170 10.154 (32×19)/(2×5×17) [-1 2 -1 0 0 0 -1 1⟩ Malcolmisma
190/189 9.1358 (2×5×19)/(33×7) [1 -3 1 -1 0 0 0 1⟩ Cotylisma
209/208 8.3033 (11×19)/(24×13) [-4 0 0 0 1 -1 0 1⟩ Yama comma
210/209 8.2637 (2×3×5×7)/(11×19) [1 1 1 1 -1 0 0 -1⟩ Spleen comma
286/285 6.0639 (2×11×13)/(3×5×19) [1 -1 -1 0 1 1 0 -1⟩ Chthonisma
324/323 5.3516 (2×32)2/(17×19) [2 4 0 0 0 0 -1 -1⟩ Photisma S18
343/342 5.0547 73/(2×32×19) [-1 -2 0 3 0 0 0 -1⟩ Nutrisma
361/360 4.8023 192/(23×32×5) [-3 -2 -1 0 0 0 0 2⟩ Go comma, Dudon comma S19
400/399 4.3335 (22×5)2/(3×7×19) [4 -1 2 -1 0 0 0 -1⟩ Devichroma S20
456/455 3.8007 (23×3×19)/(5×7×13) [3 1 -1 -1 0 -1 0 1⟩ Abnobisma
476/475 3.6409 (22×7×17)/(52×19) [2 0 -2 1 0 0 1 -1⟩ Hedwigma
495/494 3.5010 (32×5×11)/(2×13×19) [-1 2 1 0 1 -1 0 -1⟩ Eulalisma
513/512 3.3780 (33×19)/29 [-9 3 0 0 0 0 0 1⟩ Undevicesimal comma, undevicesimal schisma,
Boethius' comma, 513th harmonic
969/968 1.7875 (3×17×19)/(23×112) [-3 1 0 0 -2 0 1 1⟩ Kingfisher comma
1216/1215 1.4243 (26×19)/(35×5) [6 -5 -1 0 0 0 0 1⟩ Password comma, Eratosthenes' comma
1331/1330 1.3012 113/(2×5×7×19) [-1 0 -1 -1 3 0 0 -1⟩ Solvejgsma
1445/1444 1.1985 5×(17/(2×19))2 [-2 0 1 0 0 0 2 -2⟩ Aureusma
1521/1520 1.1386 (3×13)2/(24×5×19) [-4 2 -1 0 0 2 0 -1⟩ Pinkanberry S39
1540/1539 1.1245 (22×5×7×11)/(34×19) [2 -4 1 1 1 0 0 -1⟩ Kevolisma
1729/1728 1.0016 (7×13×19)/(22×3)3 [-6 -3 0 1 0 1 0 1⟩ Ramanujanisma
2376/2375 0.72879 ((2×3)/5)3×(11/19) [3 3 -3 0 1 0 0 -1⟩ Trichthonisma
2432/2431 0.71200 (27×19)/(11×13×17) [7 0 0 0 -1 -1 -1 1⟩ Blumeyer comma
2926/2925 0.59177 (2×7×11×19)/((3×5)2×13) [1 -2 -2 1 1 -1 0 1⟩ Neovulture comma, neovulturisma
3136/3135 0.55214 (23×7)2/(3×5×11×19) [6 -1 -1 2 -1 0 0 -1⟩ Neomirkwai comma, neomirkwaisma S56
3250/3249 0.53277 (2×53×13)/(3×19)2 [1 -2 3 0 0 1 0 -2⟩ Martebisma
4200/4199 0.41225 (23×3×52×7)/(13×17×19) [3 1 2 1 0 -1 -1 -1⟩ Neosatanisma
5776/5775 0.29975 (22×19)2/(3×52×7×11) [4 -1 -2 -1 -1 0 0 2⟩ Neovish comma, neovishma S76
5929/5928 0.29202 (7×11)2/(23×3×13×19) [-3 -1 0 2 2 -1 0 -1⟩ Manzanisma S77
5985/5984 0.28929 (32×5×7×19)/(25×11×17) [-5 2 1 1 -1 0 -1 1⟩ Neogrendel comma, neogrendelisma
6175/6174 0.28038 (52×13×19)/(2×32×73) [-1 -2 2 -3 0 1 0 1⟩ Neonewtisma
6860/6859 0.25238 (22×5×73)/193 [2 0 1 3 0 0 0 -3⟩ Devicubisma
10241/10240 0.16906 (72×11×19)/(211×5) [-11 0 -1 2 1 0 0 1⟩
10830/10829 0.15986 (2×3×5×192)/(72×13×17) [1 1 1 -2 0 -1 -1 2⟩
12636/12635 0.13701 (22×35×13)/(5×7×192) [2 5 -1 -1 0 1 0 -2⟩ Padriellisma
13377/13376 0.12942 (3×73×13)/(26×11×19) [-6 1 0 3 -1 1 0 -1⟩
14080/14079 0.12296 (28×5×11)/(3×13×192) [8 -1 1 0 1 -1 0 -2⟩
14365/14364 0.12052 (5×132×17)/(22×33×7×19) [-2 -3 1 -1 0 2 1 -1⟩
23409/23408 0.073957 ((3/2)2×17)2/(7×11×19) [-4 4 0 -1 -1 0 2 -1⟩ S153
27456/27455 0.063056 (26×3×11×13)/(5×172×19) [6 1 -1 0 1 1 -2 -1⟩
28900/28899 0.059905 ((2×5×17)/(3×13))2/19 [2 -2 2 0 0 -2 2 -1⟩ S170
43681/43680 0.039634 (11×19)2/(25×3×5×7×13) [-5 -1 -1 -1 2 -1 0 2⟩ S209
89376/89375 0.019370 (25×3×72×19)/(54×11×13) [5 1 -4 2 -1 -1 0 1⟩
104976/104975 0.016492 (2×32)4/(52×13×17×19) [4 8 -2 0 0 -1 -1 -1⟩ S324
165376/165375 0.010469 (29×17×19)/((3×5)3×72) [9 -3 -3 -2 0 0 1 1⟩ Decimillisma
228096/228095 0.0075900 ((22×3)/7)4×(11/(5×19)) [8 4 -1 -4 1 0 0 -1⟩
601426/601425 0.0028786 (2×72×17×192)/(37×52×11) [1 -7 -2 2 -1 0 1 2⟩
633556/633555 0.0027326 (22×7×113×17)/(33×5×13×192) [2 -3 -1 1 3 -1 1 -2⟩ Devicisma
709632/709631 0.0024396 (210×32×7×11)/(133×17×19) [10 2 0 1 1 -3 -1 -1⟩
5909761/5909760 0.00029294 (11×13×17)2/(28×35×5×19) [-8 -5 -1 0 2 2 2 -1⟩ S2431
11859211/11859210 0.00014598 (19/(3×11))4×((7×13)/(2×5)) [-1 -4 -1 1 -4 1 0 4⟩ Tredekisma

23-limit

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

Higher-limit

See:

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Denoted by S-expressions, where sk is defined as (k/(k - 1))/((k + 1)/k). See square superparticular for details.

External links

Retrieved from "https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&oldid=227006"