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12321/12320 - Revision history
2026-07-03T19:08:32Z
Revision history for this page on the wiki
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https://en.xen.wiki/index.php?title=12321/12320&diff=180822&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 12321/12320 | Name = zurakowskisma | Color name = 37oo1urg2 <br> bithiso-alurugu 2nd | Comma = yes }} '''12321/12320''', the '''zurakowskisma''',..."
2025-02-15T19:50:05Z
<p>Created page with "{{Infobox Interval | Ratio = 12321/12320 | Name = zurakowskisma | Color name = 37oo1urg2 <br> bithiso-alurugu 2nd | Comma = yes }} '''12321/12320''', the '''zurakowskisma''',..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 12321/12320<br />
| Name = zurakowskisma<br />
| Color name = 37oo1urg2 <br> bithiso-alurugu 2nd<br />
| Comma = yes<br />
}}<br />
<br />
'''12321/12320''', the '''zurakowskisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 0.14 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[111/110]] and [[112/111]]<br />
* [[666/665]] and [[704/703]]<br />
* [[925/924]] and [[1000/999]]<br />
* [[1665/1664]] and [[1925/1924]]<br />
* [[3774/3773]] and [[5440/5439]]<br />
<br />
It can be factored into the following superparticular intervals:<br />
* [[12376/12375]] and [[2772225/2772224]]<br />
* [[12636/12635]] and [[494209/494208]]<br />
* [[12673/12672]] and [[443556/443555]]<br />
* [[13311/13310]] and [[165649/165648]]<br />
* [[13377/13376]] and [[156066/156065]]<br />
* [[13690/13689]] and [[123201/123200]]<br />
* [[14652/14651]] and [[77441/77440]]<br />
* [[18241/18240]] and [[37962/37961]]<br />
* [[19251/19250]] and [[34225/34224]]<br />
* [[23409/23408]] and [[26011/26010]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''zurakowskismic'''. Using the 2.3.5.7.11.37 subgroup leads to the rank-5 temperament '''zurakowskic'''.<br />
<br />
=== Zurakowskic ===<br />
<br />
[[Subgroup]]: 2.3.5.7.11.37<br />
<br />
[[Comma list]]: 12321/12320<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 2 || 3 || 5 || ],<br />
|-<br />
| ⟨ || 0 || 1 || 0 || 0 || 0 || -1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 1 || 0 || 1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 0 || -2 || -1 || ]]<br />
|}<br />
<br />
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.950, ~5/4 = 386.319, ~7/4 = 968.834, ~140/111 = 401.911<br />
<br />
{{Optimal ET sequence|legend=1| 5, 7d, 8d, 9, 10, 12, 15, 19, 24, 27e, 45e, 53, 60el, 72, 140, 152, 224, 301, 311, 400, 472, 525, 540, 612, 836, 1084, 1236, 1848, 2684, 3920, 4079, 4231, 4532, 5315, 5927, 6079, 7163, 7927, 7999, 8611l, 9847 }}<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|12321 Zurakowski}}, the asteroid, which in turn was named after Paul R. Zurakowski, a volunteer director of the Chabot Observatory Telescope Maker’s Workshop for more than 30 years.<br />
<br />
== See also ==<br />
* [[Unnoticeable comma]]<br />
* [[List of superparticular intervals]]<br />
<br />
[[Category:Commas named after asteroids]]<br />
[[Category:Commas named after individuals]]</div>
Francium