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9177/9176 - Revision history
2026-06-30T20:40:18Z
Revision history for this page on the wiki
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https://en.xen.wiki/index.php?title=9177/9176&diff=178847&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 9177/9176 | Name = donsaarisma | Color name = 37u31u23o19oz2 <br> thisuthiwutwethonozo 2nd | Comma = yes }} '''9177/9176''', the '''donsaarisma''..."
2025-01-31T09:12:33Z
<p>Created page with "{{Infobox Interval | Ratio = 9177/9176 | Name = donsaarisma | Color name = 37u31u23o19oz2 <br> thisuthiwutwethonozo 2nd | Comma = yes }} '''9177/9176''', the '''donsaarisma''..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 9177/9176<br />
| Name = donsaarisma<br />
| Color name = 37u31u23o19oz2 <br> thisuthiwutwethonozo 2nd<br />
| Comma = yes<br />
}}<br />
<br />
'''9177/9176''', the '''donsaarisma''', is a [[37-limit]] [[superparticular interval|superparticular ratio]] of about 0.19 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[741/740]] and [[806/805]]<br />
* [[2295/2294]] and [[3060/3059]]<br />
* [[3220/3219]] and [[4960/4959]]<br />
* [[3553/3552]] and [[5797/5796]]<br />
* [[4186/4185]] and [[7696/7695]]<br />
* [[4256/4255]] and [[7936/7935]]<br />
<br />
It can be factored into the following superparticular intervals:<br />
* [[9361/9360]] and [[466830/466829]]<br />
* [[10241/10240]] and [[88320/88319]]<br />
* [[12673/12672]] and [[33264/33263]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''donsaarismic'''. Using the 2.3.7.19.23.31.37 subgroup leads to the rank-6 temperament '''donsaaric'''.<br />
<br />
=== Donsaaric ===<br />
<br />
[[Subgroup]]: 2.3.7.19.23.31.37<br />
<br />
[[Comma list]]: 9177/9176<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 4 || 4 || 4 || 4 || ],<br />
|-<br />
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || -1 || ]]<br />
|}<br />
<br />
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.950, ~7/4 = 968.811, ~19/16 = 297.479, ~23/16 = 628.236, ~31/16 = 1145.082<br />
<br />
{{Optimal ET sequence|legend=1| 5ik, 5, 7l, 9ikl, 10k, 10h, 12, 12ik, 14l, 17, 19, 22hkk, 26ik, 27, 31hk, 32, 36, 41l, 48, 53, 68l, 72, 77, 99k, 116l, 125, 130, 207k, 229, 265, 306, 395, 436, 653, 701, 783, 1012, 1089, 1219, 1614, 1920, 2118, 2347k, 2424, 2554, 3337, 3566, 3643, 4038, 4474, 5257, 6592, 7209, 7604, 8823, 10464i }}<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|9177 Donsaari}}, the asteroid, which in turn was named after {{W|Donald G. Saari}}, an American mathematician.<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