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5577/5576 - Revision history
2026-06-12T20:45:59Z
Revision history for this page on the wiki
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https://en.xen.wiki/index.php?title=5577/5576&diff=186120&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 5577/5576 | Name = priestlisma | Color name = 41u17u3oo1o1 <br> fowusuthotholo unison | Comma = yes }} '''5577/5576''', the '''priestlisma''', is..."
2025-03-14T17:28:24Z
<p>Created page with "{{Infobox Interval | Ratio = 5577/5576 | Name = priestlisma | Color name = 41u17u3oo1o1 <br> fowusuthotholo unison | Comma = yes }} '''5577/5576''', the '''priestlisma''', is..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 5577/5576<br />
| Name = priestlisma<br />
| Color name = 41u17u3oo1o1 <br> fowusuthotholo unison<br />
| Comma = yes<br />
}}<br />
<br />
'''5577/5576''', the '''priestlisma''', is a [[41-limit]] [[superparticular interval|superparticular comma]] of about 0.31 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[165/164]] and [[170/169]]<br />
* [[273/272]] and [[287/286]]<br />
<br />
It can be factored into the following superparticular ratios:<br />
* [[5643/5642]] and [[476749/476748]]<br />
* [[5985/5984]] and [[81796/81795]]<br />
* [[6138/6137]] and [[61009/61008]]<br />
* [[6325/6324]] and [[47151/47150]]<br />
* [[6561/6560]] and [[37180/37179]]<br />
* [[6930/6929]] and [[28561/28560]]<br />
* [[7176/7175]] and [[25025/25024]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 41-limit leads to the rank-12 temperament '''priestlismic'''. Using the 2.3.11.13.17.41 subgroup leads to the rank-5 temperament '''priestlic'''.<br />
<br />
=== Priestlic ===<br />
<br />
[[Subgroup]]: 2.3.11.13.17.41<br />
<br />
[[Comma list]]: 5577/5576<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 3 || 3 || 4 || 3 || ],<br />
|-<br />
| ⟨ || 0 || 1 || 0 || 0 || 0 || 1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 1 || 0 || 2 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 0 || 1 || -1 || ]]<br />
|}<br />
<br />
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.948, ~11/8 = 551.286, ~13/8 = 840.454, ~17/16 = 105.001<br />
<br />
{{Optimal ET sequence|legend=1| 5fm, 7m, 8mm, 9g, 10, 15gm, 17g, 24, 41, 70, 111, 137, 166g, 183, 207, 390, 460, 470, 511, 581, 607, 677, 718, 788, 971, 1178, 1395, 1648, 1689, 1855, 1966, 2366, 3154, 3361, 4332, 5727, 6698f }}<br />
<br />
[[Badness]] (Sintel): 0.040<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|5577 Priestley}}, the asteroid, which in turn was named after {{W|Joseph Priestley}}, an English clergyman.<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