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8075/8073 - Revision history
2026-06-10T19:46:11Z
Revision history for this page on the wiki
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https://en.xen.wiki/index.php?title=8075/8073&diff=178335&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 8075/8073 | Name = hagendorfisma | Color name = 23u19o17o3uyy1 <br> twethunosothuyoyo unison | Comma = yes }} '''8075/8073''', the '''hagendorfis..."
2025-01-26T16:56:03Z
<p>Created page with "{{Infobox Interval | Ratio = 8075/8073 | Name = hagendorfisma | Color name = 23u19o17o3uyy1 <br> twethunosothuyoyo unison | Comma = yes }} '''8075/8073''', the '''hagendorfis..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 8075/8073<br />
| Name = hagendorfisma<br />
| Color name = 23u19o17o3uyy1 <br> twethunosothuyoyo unison<br />
| Comma = yes<br />
}}<br />
<br />
'''8075/8073''', the '''hagendorfisma''', is a [[23-limit]] (also [[3.5.13.17.19.23 subgroup]]) [[unnoticeable comma]] of about 0.43 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following intervals:<br />
* [[897/896]] and [[8075/8064]]<br />
* [[1275/1274]] and [[1863/1862]]<br />
* [[2300/2299]] and [[42500/42471]]<br />
* [[3381/3380]] and [[79135/79092]]<br />
<br />
It can be factored into the following ratios:<br />
* [[4096/4095]] and [[282625/282624]]<br />
* [[4200/4199]] and [[104329/104328]]<br />
* [[4375/4374]] and [[52326/52325]]<br />
* [[4693/4692]] and [[28900/28899]]<br />
* [[6175/6174]] and [[11662/11661]]<br />
* [[14875/14872]] and [[21736/21735]]<br />
* [[19551/19550]] and [[361250/361179]]<br />
* [[44965/44954]] and [[328510/328509]]<br />
* [[104272/104247]] and [[126225/126224]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 23-limit leads to the rank-8 temperament '''hagendorfismic'''. Using the 3.5.13.17.19.23 subgroup leads to the rank-5 temperament '''hagendorfite'''.<br />
<br />
=== Hagendorfite ===<br />
<br />
[[Subgroup]]: 3.5.13.17.19.23<br />
<br />
[[Comma list]]: 8075/8073<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 2 || 2 || 1 || ],<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]]): ~3 = 1\1, ~5/3 = 884.308, ~13/9 = 636.683, ~17/9 = 1100.966, ~19/9 = 1293.517<br />
<br />
[[Optimal ET sequence]]: {{EDs| b6, b7, b9i, b11f, b13g, b15, b17, b24, b26, b28, b37i, b41, b52, b62, b69, b116, b131, b185, b299, b316, b385, b553, b684, b753, b869, b938, b1028, b1213, b1413, b1897, b1966, b2994, b3179, b4592, b4960h, b5145, b5276, b6489, b7242h, b8455gh |equave=t}}<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|Hagendorfite}}, the mineral.<br />
<br />
== See also ==<br />
* [[Unnoticeable comma]]<br />
<br />
[[Category:Commas named after minerals]]</div>
Francium