Francium: /* Commatic relationships */ typo

2025-03-21T15:39:35Z

Commatic relationships: typo

← Older revision		Revision as of 15:39, 21 March 2025
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	* [[841/840]] and [[3220/3219]]		* [[841/840]] and [[3220/3219]]
	* [[1000/999]] and [[2001/2000]]		* [[1000/999]] and [[2001/2000]]


	== Temperaments ==		== Temperaments ==

Francium: Created page with "{{Infobox Interval | Ratio = 667/666 | Name = denisisma | Color name = 37u29o23o1
thisutwenotwetho unison | Comma = yes }} '''667/666''', the '''denisisma''', is a 37-..."

2025-03-21T15:39:11Z

Created page with "{{Infobox Interval | Ratio = 667/666 | Name = denisisma | Color name = 37u29o23o1 <br> thisutwenotwetho unison | Comma = yes }} '''667/666''', the '''denisisma''', is a 37-..."

New page

{{Infobox Interval
| Ratio = 667/666
| Name = denisisma
| Color name = 37u29o23o1 <br> thisutwenotwetho unison
| Comma = yes
}}

'''667/666''', the '''denisisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 2.6 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[145/144]] and [[185/184]]
* [[253/252]] and [[407/406]]

It can be factored into the following superparticular ratios:
* [[676/675]] and [[50025/50024]]
* [[704/703]] and [[12673/12672]]
* [[736/735]] and [[7105/7104]]
* [[741/740]] and [[6670/6669]]
* [[841/840]] and [[3220/3219]]
* [[1000/999]] and [[2001/2000]]

== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''denisismic'''. Using the 2.3.23.29.37 subgroup leads to the rank-4 temperament '''denisic'''.

=== Denisic ===

[[Subgroup]]: 2.3.23.29.37

[[Comma list]]: 667/666

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

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.116, ~23/16 = 627.620, ~29/16 = 1028.823

{{Optimal ET sequence|legend=1| 3, 5, 7i, 9ijl, 10, 12l, 17, 19, 22, 29, 48, 77, 99, 147, 176, 224, 323, 547, 706ij }}

[[Badness]] (Sintel): 0.036

== Etymology ==
This comma was named by [[Francium]] in 2025. It refers to {{W|667 Denise}}, the asteroid. The origin of the asteroid's name is unknown, it could be inspired by its provisional designation, containing the letters "DN".

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

[[Category:Commas named after asteroids]]
[[Category:Commas with unknown etymology]]

667/666 - Revision history

Francium: /* Commatic relationships */ typo

Francium: Created page with "{{Infobox Interval | Ratio = 667/666 | Name = denisisma | Color name = 37u29o23o1 thisutwenotwetho unison | Comma = yes }} '''667/666''', the '''denisisma''', is a 37-..."

Francium: Created page with "{{Infobox Interval | Ratio = 667/666 | Name = denisisma | Color name = 37u29o23o1
thisutwenotwetho unison | Comma = yes }} '''667/666''', the '''denisisma''', is a 37-..."