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3220/3219 - Revision history
2026-06-09T19:37:14Z
Revision history for this page on the wiki
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https://en.xen.wiki/index.php?title=3220/3219&diff=189710&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 3220/3219 | Name = murayamisma | Color name = 37u29u23ozy1 <br> thisutwenutwethozoyo unison | Comma = yes }} '''3220/3219''', the '''murayamism..."
2025-04-03T12:44:46Z
<p>Created page with "{{Infobox Interval | Ratio = 3220/3219 | Name = murayamisma | Color name = 37u29u23ozy1 <br> thisutwenutwethozoyo unison | Comma = yes }} '''3220/3219''', the '''murayamism..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 3220/3219<br />
| Name = murayamisma<br />
| Color name = 37u29u23ozy1 <br> thisutwenutwethozoyo unison <br />
| Comma = yes<br />
}}<br />
<br />
'''3220/3219''', the '''murayamisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 0.54 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[112/111]] and [[116/115]]<br />
* [[175/174]] and [[185/184]]<br />
* [[552/551]] and [[666/665]]<br />
* [[630/629]] and [[783/782]]<br />
* [[667/666]] and [[841/840]]<br />
* [[784/783]] and [[1036/1035]]<br />
* [[1000/999]] and [[1450/1449]]<br />
* [[1288/1287]] and [[2146/2145]]<br />
* [[1480/1479]] and [[2738/2737]]<br />
<br />
It can be factored into the following superparticular ratios:<br />
* [[3249/3248]] and [[360640/360639]]<br />
* [[3250/3249]] and [[348726/348725]]<br />
* [[3381/3380]] and [[67600/67599]]<br />
* [[3510/3509]] and [[38962/38961]]<br />
* [[3565/3564]] and [[33264/33263]]<br />
* [[3626/3625]] and [[28750/28749]]<br />
* [[4186/4185]] and [[13950/13949]]<br />
* [[4256/4255]] and [[13225/13224]]<br />
* [[4960/4959]] and [[9177/9176]]<br />
* [[5440/5439]] and [[7889/7888]]<br />
* [[5888/5887]] and [[7105/7104]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''murayamismic'''. Using the 2.3.5.7.23.29.37 subgroup leads to the rank-6 temperament '''murayamic'''.<br />
<br />
=== Murayamic ===<br />
<br />
[[Subgroup]]: 2.3.5.7.23.29.37<br />
<br />
[[Comma list]]: 3220/3219<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 2 || 4 || 4 || 5 || ],<br />
|-<br />
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ],<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 = 701.971, ~5/4 = 386.280, ~7/4 = 968.777, ~23/16 = 628.148, ~29/16 = 1029.723<br />
<br />
{{Optimal ET sequence|legend=1| 5j, 7dijj, 8dijj, 9ij, 9, 10j, 12, 12ij, 15, 19il, 19, 22, 31, 39dijl, 41l, 53j, 60l, 72, 77, 80, 84, 99, 224, 289l, 311, 373, 410, 472, 571, 612, 711, 783, 882, 1007, 1106, 1889, 1988l, 2501, 2600, 4489jl }}<br />
<br />
[[Badness]] (Sintel): 0.108<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|3220 Murayama}}, the asteroid, which in turn was named after Sadao Murayama, a Japanese astronomer.<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