Francium: Created page with "{{Infobox Interval | Ratio = 18241/18240 | Name = Genzelisma | Color name = 37o29o19u17og2
thisotwenonusogu 2nd | Comma = yes }} '''18241/18240''', the '''genzelisma''',..."

2024-11-21T16:22:20Z

Created page with "{{Infobox Interval | Ratio = 18241/18240 | Name = Genzelisma | Color name = 37o29o19u17og2 <br> thisotwenonusogu 2nd | Comma = yes }} '''18241/18240''', the '''genzelisma''',..."

New page

{{Infobox Interval
| Ratio = 18241/18240
| Name = Genzelisma
| Color name = 37o29o19u17og2 <br> thisotwenonusogu 2nd
| Comma = yes
}}

'''18241/18240''', the '''genzelisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 0.095 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[481/480]] and [[494/493]]
* [[2146/2145]] and [[2432/2431]]
* [[6993/6992]] and [[11340/11339]]
* [[7696/7695]] and [[13312/13311]]

It can be factored into following superparticular intervals:
* [[21505/21504]] and [[120176/120175]]
* [[23409/23408]] and [[82621/82620]]
* [[23751/23750]] and [[78625/78624]]

== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''genzelismic'''. Using the 2.3.5.17.19.29.37 subgroup leads to the rank-6 temperament '''genzelic'''.

=== Genzelismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37

[[Comma list]]: 18241/18240

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 4 || 4 || 5 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ],
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.958, ~5/4 = 386.319, ~7/4 = 968.826, ~11/8 = 551.318, ~13/8 = 840.528, ~17/16 = 104.938, ~19/16 = 297.531, ~23/16 = 628.274, ~29/16 = 1029.553, ~31/16 = 1145.036

=== Genzelic ===

[[Subgroup]]: 2.3.5.17.19.29.37

[[Comma list]]: 18241/18240

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 4 || 4 || 4 || 5 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || -1 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.958, ~5/4 = 386.319, ~17/16 = 104.938, ~19/16 = 297.531, ~29/16 = 1029.553

{{Optimal ET sequence|legend=1| 5g, 5ghj, 7gh, 10j, 10h, 12, 19gh, 19, 22h, 24, 26, 34, 38j, 43, 46hj, 53, 56, 65l, 72, 77, 80, 99, 106, 149, 183, 205, 388, 472, 513, 559, 593, 631, 677, 730, 836, 1041, 1190, 1395, 1718, 1795, 2000, 2836, 3190, 4026, 6026, 8257, 8934, 10052 }}

== Etymology ==
This comma was named by [[Francium]] in 2024. It refers to {{W|18241 Genzel}}, the asteroid, which in turn was named after the German astronomer {{W|Reinhard Genzel}}.

== See also ==
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]

[[Category:Commas named after asteroids]]
[[Category:Commas named after individuals]]

Genzelisma - Revision history

Francium: Created page with "{{Infobox Interval | Ratio = 18241/18240 | Name = Genzelisma | Color name = 37o29o19u17og2 thisotwenonusogu 2nd | Comma = yes }} '''18241/18240''', the '''genzelisma''',..."

Francium: Created page with "{{Infobox Interval | Ratio = 18241/18240 | Name = Genzelisma | Color name = 37o29o19u17og2
thisotwenonusogu 2nd | Comma = yes }} '''18241/18240''', the '''genzelisma''',..."