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1666/1665 - Revision history
2026-06-07T02:10:10Z
Revision history for this page on the wiki
MediaWiki 1.43.6
https://en.xen.wiki/index.php?title=1666/1665&diff=178508&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 1666/1665 | Name = gentisma | Color name = 37u17ozzg2 <br> thisusozozogu 2nd | Comma = yes }} '''1666/1665''', the '''gentisma''', is a 37-limi..."
2025-01-29T11:56:11Z
<p>Created page with "{{Infobox Interval | Ratio = 1666/1665 | Name = gentisma | Color name = 37u17ozzg2 <br> thisusozozogu 2nd | Comma = yes }} '''1666/1665''', the '''gentisma''', is a 37-limi..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 1666/1665<br />
| Name = gentisma<br />
| Color name = 37u17ozzg2 <br> thisusozozogu 2nd<br />
| Comma = yes<br />
}}<br />
<br />
'''1666/1665''', the '''gentisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 1.04 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[112/111]] and [[120/119]]<br />
* [[136/135]] and [[148/147]]<br />
* [[196/195]] and [[222/221]]<br />
* [[408/407]] and [[540/539]]<br />
* [[595/594]] and [[925/924]]<br />
* [[784/783]] and [[1480/1479]]<br />
* [[833/832]] and [[1665/1664]]<br />
<br />
It can be factored into the following superparticular intervals:<br />
* [[1683/1682]] and [[164836/164835]]<br />
* [[1701/1700]] and [[80920/80919]]<br />
* [[1729/1728]] and [[45696/45695]]<br />
* [[1768/1767]] and [[28861/28860]]<br />
* [[1925/1924]] and [[12376/12375]]<br />
* [[2176/2175]] and [[7105/7104]]<br />
* [[2295/2294]] and [[6076/6075]]<br />
* [[2401/2400]] and [[5440/5439]]<br />
* [[2431/2430]] and [[5292/5291]]<br />
* [[2737/2736]] and [[4256/4255]]<br />
* [[3136/3135]] and [[3553/3552]]<br />
* [[3220/3219]] and [[3451/3450]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''gentismic'''. Using the 2.3.5.7.17.37 subgroup leads to the rank-5 temperament '''gentic'''.<br />
<br />
=== Gentic ===<br />
<br />
[[Subgroup]]: 2.3.5.7.17.37<br />
<br />
[[Comma list]]: 1666/1665<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 2 || 4 || 5 || ],<br />
|-<br />
| ⟨ || 0 || 1 || 0 || 0 || 0 || -2 || ],<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 = 702.013, ~5/4 = 386.375, ~7/4 = 968.645, ~17/16 = 104.764<br />
<br />
{{Optimal ET sequence|legend=1| 5g, 7dgll, 8d, 9, 10, 12, 19gl, 19, 22, 27g, 31l, 39dgl, 41gl, 49gl, 50, 58, 60l, 68, 72, 99, 171, 311, 400, 472, 482, 571, 711, 882 }}<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|1666 van Gent}}, the asteroid, which in turn was named after {{W|Hendrik van Gent}}, a Dutch astronomer.<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