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4000/3999 - Revision history
2026-07-08T05:42:58Z
Revision history for this page on the wiki
MediaWiki 1.43.6
https://en.xen.wiki/index.php?title=4000/3999&diff=181421&oldid=prev
Francium: Created page with "{{Infobox Interval | Ratio = 4000/3999 | Name = hipparchusisma | Color name = 43u31uy<sup>3</sup>1 <br> fothuthiwutriyo unison | Comma = yes }} '''4000/3999''', the '''hippar..."
2025-02-19T14:45:00Z
<p>Created page with "{{Infobox Interval | Ratio = 4000/3999 | Name = hipparchusisma | Color name = 43u31uy<sup>3</sup>1 <br> fothuthiwutriyo unison | Comma = yes }} '''4000/3999''', the '''hippar..."</p>
<p><b>New page</b></p><div>{{Infobox Interval<br />
| Ratio = 4000/3999<br />
| Name = hipparchusisma<br />
| Color name = 43u31uy<sup>3</sup>1 <br> fothuthiwutriyo unison<br />
| Comma = yes<br />
}}<br />
<br />
'''4000/3999''', the '''hipparchusisma''', is a [[43-limit]] [[superparticular interval|superparticular comma]] of about 0.43 [[cent]]s.<br />
<br />
== Commatic relationships ==<br />
This comma is the difference between the following superparticular pairs:<br />
* [[125/124]] and [[129/128]]<br />
* [[280/279]] and [[301/300]]<br />
* [[560/559]] and [[651/650]]<br />
* [[775/774]] and [[961/960]]<br />
* [[1936/1935]] and [[3751/3750]]<br />
<br />
It can be factored into the following superparticular intervals:<br />
* [[4096/4095]] and [[170625/170624]]<br />
* [[4186/4185]] and [[90000/89999]]<br />
* [[4200/4199]] and [[83980/83979]]<br />
* [[4375/4374]] and [[46656/46655]]<br />
* [[4992/4991]] and [[20125/20124]]<br />
* [[5376/5375]] and [[15625/15624]]<br />
* [[6325/6324]] and [[10880/10879]]<br />
* [[6480/6479]] and [[10450/10449]]<br />
<br />
== Temperaments ==<br />
Tempering out this comma in the full 43-limit leads to the rank-13 temperament '''hipparchusismic'''. Using the 2.3.5.31.43 subgroup leads to the rank-4 temperament '''hipparchusic'''.<br />
<br />
=== Hipparchusic ===<br />
<br />
[[Subgroup]]: 2.3.5.31.43<br />
<br />
[[Comma list]]: 4000/3999<br />
<br />
[[Mapping]]: <br><br />
{| class="right-all"<br />
|-<br />
| [⟨ || 1 || 1 || 2 || 4 || 6 || ],<br />
|-<br />
| ⟨ || 0 || 1 || 0 || 0 || -1 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 1 || 0 || 3 || ],<br />
|-<br />
| ⟨ || 0 || 0 || 0 || 1 || -1 || ]]<br />
|}<br />
<br />
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.965, ~5/4 = 386.247, ~31/16 = 1145.137<br />
<br />
{{Optimal ET sequence|legend=1| 5n, 7k, 10k, 12k, 19, 41, 46, 65, 87, 106, 152, 171, 277, 323, 335, 441, 612, 1053, 1665, 3942kn, 5101kn, 5607kn, 5694kn, 5713kn, 6306kn, 6918knn, 7971kknn, 8583kknn }}<br />
<br />
[[Badness]] (Sintel): 0.028<br />
<br />
== Etymology ==<br />
This comma was named by [[Francium]] in 2025. It refers to {{W|4000 Hipparchus}}, the asteroid, which in turn was named after {{W|Hipparchus}}, an Ancient Greek scientist.<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