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616/615 - Revision history
2026-07-02T02:41:29Z
Revision history for this page on the wiki
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https://en.xen.wiki/index.php?title=616/615&diff=175671&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 616/615 | Name = ellisma | Color name = 41u1ozg2 <br> fowulozogu 2nd | Comma = yes }} '''616/615''', the '''ellisma''', is a 41-limit super..."
2025-01-11T19:09:46Z
<p>Created page with "{{Infobox Interval | Ratio = 616/615 | Name = ellisma | Color name = 41u1ozg2 <br> fowulozogu 2nd | Comma = yes }} '''616/615''', the '''ellisma''', is a <a href="/w/41-limit" title="41-limit">41-limit</a> super..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 616/615<br />
| Name = ellisma<br />
| Color name = 41u1ozg2 <br> fowulozogu 2nd<br />
| Comma = yes<br />
}}<br />
<br />
'''616/615''', the '''ellisma''', is a [[41-limit]] [[superparticular interval|superparticular comma]] of about 2.8 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[42/41]] and [[45/44]]<br />
* [[154/153]] and [[205/204]]<br />
* [[165/164]] and [[225/224]]<br />
* [[176/175]] and [[246/245]]<br />
* [[196/195]] and [[287/286]]<br />
* [[231/230]] and [[369/368]]<br />
* [[288/287]] and [[540/539]]<br />
<br />
It can be factored into the following superparticular intervals:<br />
* [[621/620]] and [[76384/76383]]<br />
* [[638/637]] and [[17836/17835]]<br />
* [[651/650]] and [[11440/11439]]<br />
* [[676/675]] and [[6930/6929]]<br />
* [[704/703]] and [[4921/4920]]<br />
* [[726/725]] and [[4060/4059]]<br />
* [[736/735]] and [[3773/3772]]<br />
* [[780/779]] and [[2926/2925]]<br />
* [[784/783]] and [[2871/2870]]<br />
* [[1001/1000]] and [[1600/1599]]<br />
* [[1026/1025]] and [[1540/1539]]<br />
* [[1190/1189]] and [[1276/1275]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 41-limit leads to the rank-12 temperament '''ellismic'''. Using the 2.3.5.7.11.41 subgroup leads to the rank-5 temperament '''ellic'''.<br />
<br />
=== Ellic ===<br />
<br />
[[Subgroup]]: 2.3.5.7.11.41<br />
<br />
[[Comma list]]: 616/615<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 || 1 || 1 || ]]<br />
|}<br />
<br />
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.080, ~5/4 = 386.582, ~7/4 = 968.433, ~11/8 = 550.722<br />
<br />
{{Optimal ET sequence|legend=1| 5e, 7dm, 8d, 9, 10, 12e, 12m, 15, 19em, 19, 22, 27e, 31, 53, 58, 72, 80, 87, 99em, 111, 118, 152m, 198, 239m, 270 }}<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|616 Elly}}, the asteroid, which in turn was named after Elly Boehm, wife of German mathematician Karl Boehm.<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