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741/740 - Revision history
2026-06-05T06:20:56Z
Revision history for this page on the wiki
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https://en.xen.wiki/index.php?title=741/740&diff=178526&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 741/740 | Name = botolphisma | Color name = 37u19o3og1 <br> thisunothogu unison | Comma = yes }} '''741/740''', the '''botolphisma''', is a 37-..."
2025-01-29T17:08:07Z
<p>Created page with "{{Infobox Interval | Ratio = 741/740 | Name = botolphisma | Color name = 37u19o3og1 <br> thisunothogu unison | Comma = yes }} '''741/740''', the '''botolphisma''', is a 37-..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 741/740<br />
| Name = botolphisma<br />
| Color name = 37u19o3og1 <br> thisunothogu unison<br />
| Comma = yes<br />
}}<br />
<br />
'''741/740''', the '''botolphisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 2.3 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[171/170]] and [[222/221]]<br />
* [[260/259]] and [[400/399]]<br />
* [[297/296]] and [[495/494]]<br />
<br />
It can be factored into the following superparticular intervals:<br />
* [[760/759]] and [[29601/29600]]<br />
* [[806/805]] and [[9177/9176]]<br />
* [[897/896]] and [[4256/4255]]<br />
* [[931/930]] and [[3627/3626]]<br />
* [[936/935]] and [[3553/3552]]<br />
* [[969/968]] and [[3146/3145]]<br />
* [[1001/1000]] and [[2850/2849]]<br />
* [[1296/1295]] and [[1729/1728]]<br />
* [[1444/1443]] and [[1521/1520]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''botolphismic'''. Using the 2.3.5.13.19.37 subgroup leads to the rank-5 temperament '''botolphic'''.<br />
<br />
=== Botolphic ===<br />
<br />
[[Subgroup]]: 2.3.5.13.19.37<br />
<br />
[[Comma list]]: 741/740<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 3 || 4 || 4 || ],<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 = 701.867, ~5/4 = 386.502, ~13/8 = 840.048, ~19/16 = 296.881<br />
<br />
{{Optimal ET sequence|legend=1| 5, 5hl, 7h, 9l, 10, 12l, 15l, 19hl, 19, 24, 27, 34, 38fl, 41, 43, 46h, 50, 53, 164l, 183, 217l, 270, 323, 373, 426h, 537l, 590, 643 }}<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|741 Botolphia}}, the asteroid, which in turn was named after {{W|Saint Botolph}}.<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