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4186/4185 - Revision history
2026-06-13T05:47:37Z
Revision history for this page on the wiki
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https://en.xen.wiki/index.php?title=4186/4185&diff=178434&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 4186/4185 | Name = tamashimisma | Color name = 31u23o3ozg3 <br> thiwutwethothozogu 3rd | Comma = yes }} '''4186/4185''', the '''tamashimisma''',..."
2025-01-28T10:38:47Z
<p>Created page with "{{Infobox Interval | Ratio = 4186/4185 | Name = tamashimisma | Color name = 31u23o3ozg3 <br> thiwutwethothozogu 3rd | Comma = yes }} '''4186/4185''', the '''tamashimisma''',..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 4186/4185<br />
| Name = tamashimisma<br />
| Color name = 31u23o3ozg3 <br> thiwutwethothozogu 3rd<br />
| Comma = yes<br />
}}<br />
<br />
'''4186/4185''', the '''tamashimisma''', is a [[31-limit]] [[superparticular interval|superparticular comma]] of about 0.41 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[91/90]] and [[93/92]]<br />
* [[156/155]] and [[162/161]]<br />
* [[280/279]] and [[300/299]]<br />
* [[621/620]] and [[729/728]]<br />
* [[676/675]] and [[806/805]]<br />
* [[931/930]] and [[1197/1196]]<br />
* [[1288/1287]] and [[1860/1859]]<br />
* [[1365/1364]] and [[2025/2024]]<br />
* [[1729/1728]] and [[2945/2944]]<br />
* [[1768/1767]] and [[3060/3059]]<br />
* [[2016/2015]] and [[3888/3887]]<br />
<br />
It can be factored into the following superparticular ratios:<br />
* [[4200/4199]] and [[1255501/1255500]]<br />
* [[4225/4224]] and [[453376/453375]]<br />
* [[4375/4374]] and [[96876/96875]]<br />
* [[4641/4640]] and [[42688/42687]]<br />
* [[4992/4991]] and [[25921/25920]]<br />
* [[5083/5082]] and [[23716/23715]]<br />
* [[6076/6075]] and [[13455/13454]]<br />
* [[6325/6324]] and [[12376/12375]]<br />
* [[8092/8091]] and [[8671/8670]]<br />
* [[8281/8280]] and [[8464/8463]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 31-limit leads to the rank-10 temperament '''tamashimismic'''. Using the 2.3.5.7.13.23.31 subgroup leads to the rank-6 temperament '''tamashimic'''.<br />
<br />
=== Tamashimic ===<br />
<br />
[[Subgroup]]: 2.3.5.7.13.23.31<br />
<br />
[[Comma list]]: 4186/4185<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 2 || 3 || 4 || 5 || ],<br />
|-<br />
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -3 || ],<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 = 701.988, ~5/4 = 386.337, ~7/4 = 968.791, ~13/8 = 840.468, ~23/16 = 628.185<br />
<br />
{{Optimal ET sequence|legend=1| 5, 7dik, 8di, 9ik, 10k, 12, 12fk, 14cf, 15, 17c, 19ikk, 19, 29k, 31fk, 31, 34dk, 39dfik, 41, 53, 68, 87, 94, 99fk, 111, 121ik, 130, 198, 224, 243, 251i, 311, 373, 383i, 422, 441, 954, 1205, 1646, 2159, 2600, 3171, 4376, 4817k, 5771, 6976k, 7417k }}<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|4186 Tamashima}}, the asteroid, which in turn was named after a town in Japan.<br />
<br />
== See also ==<br />
* [[Unnoticeable comma]]<br />
* [[List of superparticular intervals]]<br />
<br />
[[Category:Commas named after asteroids]]<br />
[[Category:Commas named after place names]]</div>
Francium