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5440/5439 - Revision history
2026-06-12T16:01:12Z
Revision history for this page on the wiki
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https://en.xen.wiki/index.php?title=5440/5439&diff=179445&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 5440/5439 | Name = teraosma | Color name = 37u17orry-2 <br> thisusoruruyo negative 2nd | Comma = yes }} '''5440/5439''', the '''teraosma''', is a..."
2025-02-04T11:55:53Z
<p>Created page with "{{Infobox Interval | Ratio = 5440/5439 | Name = teraosma | Color name = 37u17orry-2 <br> thisusoruruyo negative 2nd | Comma = yes }} '''5440/5439''', the '''teraosma''', is a..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 5440/5439<br />
| Name = teraosma<br />
| Color name = 37u17orry-2 <br> thisusoruruyo negative 2nd<br />
| Comma = yes<br />
}}<br />
<br />
'''5440/5439''', the '''teraosma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 0.32 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[260/259]] and [[273/272]]<br />
* [[442/441]] and [[481/480]]<br />
* [[1000/999]] and [[1225/1224]]<br />
* [[1275/1274]] and [[1665/1664]]<br />
* [[1296/1295]] and [[1701/1700]]<br />
* [[1666/1665]] and [[2401/2400]]<br />
* [[2080/2079]] and [[3367/3366]]<br />
* [[2500/2499]] and [[4625/4624]]<br />
<br />
It can be factored into the following superparticular intervals:<br />
* [[5776/5775]] and [[93500/93499]]<br />
* [[5797/5796]] and [[88320/88319]]<br />
* [[5832/5831]] and [[80920/80919]]<br />
* [[5888/5887]] and [[71485/71484]]<br />
* [[5916/5915]] and [[67600/67599]]<br />
* [[6175/6174]] and [[45696/45695]]<br />
* [[7106/7105]] and [[23200/23199]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''teraosmic'''. Using the 2.3.5.7.17.37 subgroup leads to the rank-5 temperament '''teraoic'''.<br />
<br />
=== Teraioc ===<br />
<br />
[[Subgroup]]: 2.3.5.7.17.37<br />
<br />
[[Comma list]]: 5440/5439<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 2 || 4 || 7 || ],<br />
|-<br />
| ⟨ || 0 || 1 || 0 || 0 || 0 || -1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 1 || 0 || -2 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]<br />
|}<br />
<br />
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.965, ~5/4 = 386.293, ~7/4 = 968.886, ~17/16 = 104.892<br />
<br />
{{Optimal ET sequence|legend=1| 5, 5gl, 7, 9g, 10, 12l, 15, 17cg, 19g, 22l, 26, 27g, 31l, 41gl, 46, 53, 68, 72, 99, 171, 311, 354, 400, 472, 482, 525, 571, 665, 764, 836, 935, 1236, 1407, 1646, 1718, 1817, 2000, 2072, 2171, 3889, 4824l, 6060l, 6995dl }}<br />
<br />
[[Badness]] (Sintel): 0.076<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|5440 Terao}}, the asteroid, which in turn was named after Hisashi Terao, the first Japanese professor of astronomy at the {{W|University of Tokyo}}.<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