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List of superparticular intervals/53-limit - Revision history
2026-07-01T04:47:44Z
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https://en.xen.wiki/index.php?title=List_of_superparticular_intervals/53-limit&diff=224078&oldid=prev
FloraC: Created page with "{{Breadcrumb}} == 53-limit (incomplete) == {| class="wikitable center-6" style="width:100%" ! width="10%" | Ratio ! width="10%" | Cents ! width="15%" | Factorization ! width="15%" | Monzo ! width="45%" | Name(s) ! width="5%" | Meta<ref name="ssp">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See square superparticular for details.</ref> |- | 53/52 | 32.977 | 53/(2<sup>2</sup>×13) | 2.13.53 {{monzo| -2..."
2026-02-15T13:40:44Z
<p>Created page with "{{Breadcrumb}} == 53-limit (incomplete) == {| class="wikitable center-6" style="width:100%" ! width="10%" | <a href="/w/Ratio" class="mw-redirect" title="Ratio">Ratio</a> ! width="10%" | <a href="/w/Cent" title="Cent">Cents</a> ! width="15%" | Factorization ! width="15%" | <a href="/w/Monzo" title="Monzo">Monzo</a> ! width="45%" | Name(s) ! width="5%" | Meta<ref name="ssp">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See <a href="/w/Square_superparticular" class="mw-redirect" title="Square superparticular">square superparticular</a> for details.</ref> |- | <a href="/index.php?title=53/52&action=edit&redlink=1" class="new" title="53/52 (page does not exist)">53/52</a> | 32.977 | 53/(2<sup>2</sup>×13) | 2.13.53 {{monzo| -2..."</p>
<p><b>New page</b></p><div>{{Breadcrumb}}<br />
<br />
== 53-limit (incomplete) ==<br />
{| class="wikitable center-6" style="width:100%"<br />
! width="10%" | [[Ratio]]<br />
! width="10%" | [[Cent]]s<br />
! width="15%" | Factorization<br />
! width="15%" | [[Monzo]]<br />
! width="45%" | Name(s)<br />
! width="5%" | Meta<ref name="ssp">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See [[square superparticular]] for details.</ref><br />
|-<br />
| [[53/52]]<br />
| 32.977<br />
| 53/(2<sup>2</sup>×13)<br />
| 2.13.53 {{monzo| -2 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[54/53]]<br />
| 32.360<br />
| (2×3<sup>3</sup>)/53<br />
| 2.3.53 {{monzo| 1 3 -1 }}<br />
| <br />
| <br />
|-<br />
| [[106/105]]<br />
| 16.410<br />
| (2×53)/(3×5×7)<br />
| 2.3.5.7.53 {{monzo| 1 -1 -1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[160/159]]<br />
| 10.854<br />
| (2<sup>5</sup>×5)/(3×53)<br />
| 2.3.5.53 {{monzo| 5 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[265/264]]<br />
| 6.5453<br />
| (5×53)/(2<sup>3</sup>×3×11)<br />
| 2.3.5.11.53 {{monzo| -3 -1 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[266/265]]<br />
| 6.5207<br />
| (2×7×19)/(5×53)<br />
| 2.5.7.19.53 {{monzo| 1 -1 1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[319/318]]<br />
| 5.4356<br />
| (11×29)/(2×3×53)<br />
| 2.3.11.29.53 {{monzo| -1 -1 1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[371/370]]<br />
| 4.6727<br />
| (7×53)/(2×5×37)<br />
| 2.5.7.37.53 {{monzo| -1 -1 1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[372/371]]<br />
| 4.6601<br />
| (2<sup>2</sup>×3×31)/(7×53)<br />
| 2.3.7.31.53 {{monzo| 2 1 -1 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[424/423]]<br />
| 4.0879<br />
| (2<sup>3</sup>×53)/(3<sup>2</sup>×47)<br />
| 2.3.47.53 {{monzo| 3 -2 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[425/424]]<br />
| 4.0783<br />
| (5<sup>2</sup>×17)/(2<sup>3</sup>×53)<br />
| 2.5.17.53 {{monzo| -3 2 1 -1 }}<br />
| <br />
| <br />
|-<br />
| [[477/476]]<br />
| 3.6332<br />
| (3<sup>2</sup>×53)/(2<sup>2</sup>×7×17)<br />
| 2.3.7.17.53 {{monzo| -2 2 -1 -1 1 }}<br />
| <br />
| <br />
|-<br />
| [[2809/2808]]<br />
| 0.61643<br />
| 53<sup>2</sup>/(2<sup>3</sup>×3<sup>3</sup>×13)<br />
| 2.3.13.53 {{monzo| -3 -3 -1 2 }}<br />
| <br />
| S53<br />
|-<br />
| [[4081/4080]]<br />
| 0.42427<br />
| (7×11×53)/(2<sup>4</sup>×3×5×17)<br />
| 2.3.5.7.11.17.53 {{monzo| -4 -1 -1 1 1 -1 1 }}<br />
| <br />
| <br />
|}<br />
<br />
== Notes ==<br />
<references/><br />
<br />
[[Category:Lists of intervals]]<br />
[[Category:Superparticular ratios|*]]</div>
FloraC