Francium: /* Temperaments */ typo

2025-01-22T20:03:43Z

Temperaments: typo

← Older revision		Revision as of 20:03, 22 January 2025
Line 44:		Line 44:
	[[Optimal tuning]] ([[CTE]]): ~3 = 1\1, ~5/3 = 884.356, ~7/3 = 1466.867, ~11/9 = 347.413, ~13/9 = 636.611, ~253/243 = 69.841		[[Optimal tuning]] ([[CTE]]): ~3 = 1\1, ~5/3 = 884.356, ~7/3 = 1466.867, ~11/9 = 347.413, ~13/9 = 636.611, ~253/243 = 69.841

	[[Optimal ET sequence]]: {{EDs\| b7h, b10f, b13, b20efh, b21, b23, b26, b33, b34, b39, b46, b54, b56, b60, b71, b75, b110, b131, b241, b275, b301, b316, b376, b437, b447, b460, b591, b712, b822, b953, b1198, b1329, b1473, b2151, b2282, b2295, b2426, b3624, b3755, b6050, b6181, b8682, b9805 \|~~equal~~=t}}		[[Optimal ET sequence]]: {{EDs\| b7h, b10f, b13, b20efh, b21, b23, b26, b33, b34, b39, b46, b54, b56, b60, b71, b75, b110, b131, b241, b275, b301, b316, b376, b437, b447, b460, b591, b712, b822, b953, b1198, b1329, b1473, b2151, b2282, b2295, b2426, b3624, b3755, b6050, b6181, b8682, b9805 \|equave=t}}

	== Etymology ==		== Etymology ==

Francium: Created page with "{{Infobox Interval | Ratio = 110565/110561 | Name = jeffbenisma | Color name = L23uu19u3o1uzy-2
labitwethu-anutholuzoyo negative 2nd | Comma = yes }} '''110565/110561'''..."

2025-01-22T20:02:23Z

Created page with "{{Infobox Interval | Ratio = 110565/110561 | Name = jeffbenisma | Color name = L23uu19u3o1uzy-2 <br> labitwethu-anutholuzoyo negative 2nd | Comma = yes }} '''110565/110561'''..."

New page

{{Infobox Interval
| Ratio = 110565/110561
| Name = jeffbenisma
| Color name = L23uu19u3o1uzy-2 <br> labitwethu-anutholuzoyo negative 2nd
| Comma = yes
}}

'''110565/110561''', the '''jeffbenisma''', is a [[23-limit]] (also [[3.5.7.11.13.19.23 subgroup]]) [[unnoticeable comma]] of about 0.063 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following intervals:
* [[2025/2024]] and [[2185/2184]]
* [[12168/12167]] and [[21736/21735]]
* [[12636/12635]] and [[23276/23275]]
* [[13377/13376]] and [[25921/25920]]

It can be factored into the ratios [[43264/43263]] and [[76545/76544]].

== Temperaments ==
Tempering out this comma in the full 23-limit leads to the rank-8 temperament '''jeffbenismic'''. Using the 3.5.7.11.13.19.23 subgroup leads to the rank-6 temperament '''jeffbenite'''.

=== Jeffbenite ===

[[Subgroup]]: 3.5.7.11.13.19.23

[[Comma list]]: 110565/110561

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

[[Optimal tuning]] ([[CTE]]): ~3 = 1\1, ~5/3 = 884.356, ~7/3 = 1466.867, ~11/9 = 347.413, ~13/9 = 636.611, ~253/243 = 69.841

[[Optimal ET sequence]]: {{EDs| b7h, b10f, b13, b20efh, b21, b23, b26, b33, b34, b39, b46, b54, b56, b60, b71, b75, b110, b131, b241, b275, b301, b316, b376, b437, b447, b460, b591, b712, b822, b953, b1198, b1329, b1473, b2151, b2282, b2295, b2426, b3624, b3755, b6050, b6181, b8682, b9805 |equal=t}}

== Etymology ==
This comma was named by [[Francium]] in 2025. It refers to Jeffbenite, the mineral.

== See also ==
* [[Unnoticeable comma]]

[[Category:Commas named after minerals]]

110565/110561 - Revision history

Francium: /* Temperaments */ typo

Francium: Created page with "{{Infobox Interval | Ratio = 110565/110561 | Name = jeffbenisma | Color name = L23uu19u3o1uzy-2 labitwethu-anutholuzoyo negative 2nd | Comma = yes }} '''110565/110561'''..."

Francium: Created page with "{{Infobox Interval | Ratio = 110565/110561 | Name = jeffbenisma | Color name = L23uu19u3o1uzy-2
labitwethu-anutholuzoyo negative 2nd | Comma = yes }} '''110565/110561'''..."