https://en.xen.wiki/index.php?action=history&feed=atom&title=646%2F645
646/645 - Revision history
2026-06-29T01:41:12Z
Revision history for this page on the wiki
MediaWiki 1.43.6
https://en.xen.wiki/index.php?title=646/645&diff=190863&oldid=prev
BudjarnLambeth at 03:23, 11 April 2025
2025-04-11T03:23:28Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 03:23, 11 April 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l63">Line 63:</td>
<td colspan="2" class="diff-lineno">Line 63:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Commas named after asteroids]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Commas named after asteroids]]</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Commas named after <del style="font-weight: bold; text-decoration: none;">myth </del>or <del style="font-weight: bold; text-decoration: none;">folk characters</del>]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Commas named after <ins style="font-weight: bold; text-decoration: none;">mythology </ins>or <ins style="font-weight: bold; text-decoration: none;">literature</ins>]]</div></td></tr>
</table>
BudjarnLambeth
https://en.xen.wiki/index.php?title=646/645&diff=183392&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 646/645 | Name = kastalisma | Color name = 43u19o17og2 <br> fothunosogu 2nd | Comma = yes }} '''646/645''', the '''kastalisma''', is a 43-limit..."
2025-02-27T10:21:19Z
<p>Created page with "{{Infobox Interval | Ratio = 646/645 | Name = kastalisma | Color name = 43u19o17og2 <br> fothunosogu 2nd | Comma = yes }} '''646/645''', the '''kastalisma''', is a 43-limit..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 646/645<br />
| Name = kastalisma<br />
| Color name = 43u19o17og2 <br> fothunosogu 2nd<br />
| Comma = yes<br />
}}<br />
<br />
'''646/645''', the '''kastalisma''', is a [[43-limit]] [[superparticular interval|superparticular comma]] of about 2.7 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[76/75]] and [[86/85]]<br />
* [[136/135]] and [[172/171]]<br />
* [[216/215]] and [[324/323]]<br />
<br />
It can be factored into the following superparticular ratios:<br />
* [[651/650]] and [[83980/83979]]<br />
* [[676/675]] and [[14535/14534]]<br />
* [[703/702]] and [[7956/7955]]<br />
* [[741/740]] and [[5032/5031]]<br />
* [[760/759]] and [[4301/4300]]<br />
* [[775/774]] and [[3876/3875]]<br />
* [[931/930]] and [[2108/2107]]<br />
* [[969/968]] and [[1936/1935]]<br />
* [[1156/1155]] and [[1463/1462]]<br />
* [[1216/1215]] and [[1377/1376]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 43-limit leads to the rank-13 temperament '''kastalismic'''. Using the 2.3.5.17.19.43 subgroup leads to the rank-5 temperament '''kastalic'''.<br />
<br />
=== Kastalic ===<br />
<br />
[[Subgroup]]: 2.3.5.17.19.43<br />
<br />
[[Comma list]]: 646/645<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 4 || 4 || 6 || ],<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 = 702.048, ~5/4 = 386.514, ~17/16 = 104.334, ~19/16 = 296.842<br />
<br />
{{Optimal ET sequence|legend=1| 5g, 5ghn, 7ghn, 9, 10, 12, 27g, 34, 34hn, 38, 46h, 50, 53, 65, 77, 94, 106, 171, 183, 205n, 217n, 323, 506, 723n }}<br />
<br />
[[Badness]] (Sintel): 0.120<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|646 Kastalia}}, the asteroid, which in turn was named after {{W|Castalia}}, a Greek nymph.<br />
<br />
== See also ==<br />
* [[Unnoticeable comma]]<br />
* [[List of superparticular intervals]]<br />
<br />
[[Category:Commas named after asteroids]]<br />
[[Category:Commas named after myth or folk characters]]</div>
Francium