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4301/4300 - Revision history
2026-06-12T01:17:47Z
Revision history for this page on the wiki
MediaWiki 1.43.6
https://en.xen.wiki/index.php?title=4301/4300&diff=182882&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 4301/4300 | Name = boydenisma | Color name = 43u23o17o1ogg2 <br> fothutwethosologugu 2nd | Comma = yes }} '''4301/4300''', the '''boydenisma''',..."
2025-02-24T06:15:19Z
<p>Created page with "{{Infobox Interval | Ratio = 4301/4300 | Name = boydenisma | Color name = 43u23o17o1ogg2 <br> fothutwethosologugu 2nd | Comma = yes }} '''4301/4300''', the '''boydenisma''',..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 4301/4300<br />
| Name = boydenisma<br />
| Color name = 43u23o17o1ogg2 <br> fothutwethosologugu 2nd<br />
| Comma = yes<br />
}}<br />
<br />
'''4301/4300''', the '''boydenisma''', is a [[43-limit]] [[superparticular interval|superparticular comma]] of about 0.40 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[345/344]] and [[375/374]]<br />
* [[391/390]] and [[430/429]]<br />
* [[646/645]] and [[760/759]]<br />
* [[1377/1376]] and [[2025/2024]]<br />
* [[1936/1935]] and [[3520/3519]]<br />
<br />
It can be factored into the following superparticular intervals:<br />
* [[4641/4640]] and [[58696/58695]]<br />
* [[4761/4760]] and [[44506/44505]]<br />
* [[5083/5082]] and [[27951/27950]]<br />
* [[5376/5375]] and [[21505/21504]]<br />
* [[7225/7224]] and [[10626/10625]]<br />
* [[7956/7955]] and [[9361/9360]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 43-limit leads to the rank-13 temperament '''boydenismic'''. Using the 2.5.11.17.23.43 subgroup leads to the rank-5 temperament '''boydenic'''.<br />
<br />
=== Boydenic ===<br />
<br />
[[Subgroup]]: 2.5.11.17.23.43<br />
<br />
[[Comma list]]: 4301/4300<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 2 || 3 || 4 || 4 || 5 || ],<br />
|-<br />
| ⟨ || 0 || 1 || 0 || 0 || 0 || -2 || ],<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, ~5/4 = 386.357, ~11/8 = 551.270, ~17/16 = 104.888, ~23/16 = 628.192<br />
<br />
{{Optimal ET sequence|legend=1| 4, 5egn, 6gn, 6, 8in, 9, 15, 16n, 21, 22i, 29g, 30, 31, 34n, 43n, 50, 59, 115, 124, 298, 422, 516, 640, 699, 814, 938, 1637, 2575, 3355i, 3479, 3777, 4417i, 5116i, 5414gi }}<br />
<br />
[[Badness]] (Sintel): 0.019<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|4301 Boyden}}, the asteroid, which in turn was named after {{W|Uriah A. Boyden}}, an American mechanical engineer.<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