Francium: /* See also */

2025-04-01T18:35:07Z

Francium: Created page with "{{Infobox Interval | Ratio = 4774/4773 | Name = hobetsisma | Color name = 43u37u31o1oz-2
fothuthisuthiwolozo negative 2nd | Comma = yes }} '''4774/4773''', the '''hobet..."

2025-04-01T18:34:48Z

Created page with "{{Infobox Interval | Ratio = 4774/4773 | Name = hobetsisma | Color name = 43u37u31o1oz-2 <br> fothuthisuthiwolozo negative 2nd | Comma = yes }} '''4774/4773''', the '''hobet..."

New page

{{Infobox Interval
| Ratio = 4774/4773
| Name = hobetsisma
| Color name = 43u37u31o1oz-2 <br> fothuthisuthiwolozo negative 2nd
| Comma = yes
}}

'''4774/4773''', the '''hobetsisma''', is a [[43-limit]] [[superparticular interval|superparticular comma]] of about 0.36 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[775/774]] and [[925/924]]
* [[1333/1332]] and [[1849/1848]]
* [[1463/1462]] and [[2109/2108]]
* [[1936/1935]] and [[3256/3255]]
* [[2108/2107]] and [[3774/3773]]

It can be factored into the following superparticular ratios:
* [[4785/4784]] and [[2076256/2076255]]
* [[4960/4959]] and [[127281/127280]]
* [[5292/5291]] and [[48763/48762]]
* [[5720/5719]] and [[28861/28860]]
* [[5797/5796]] and [[27048/27047]]
* [[6076/6075]] and [[22275/22274]]
* [[7956/7955]] and [[11935/11934]]

== Temperaments ==
Tempering out this comma in the full 43-limit leads to the rank-13 temperament '''hobetsismic'''. Using the 2.3.7.11.31.37.43 subgroup leads to the rank-6 temperament '''hobetsic'''.

=== Hobetsic ===

[[Subgroup]]: 2.3.7.11.31.37.43

[[Comma list]]: 4774/4773

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 3 || 4 || 5 || 4 || ],
|-
| ⟨ || 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 = 701.964, ~7/4 = 968.798, ~11/8 = 551.276, ~31/16 = 1144.950, ~37/32 = 251.439

{{Optimal ET sequence|legend=1| 5, 8dn, 9kn, 10k, 10n, 12kn, 14l, 17, 17kn, 22, 24, 27e, 31k, 41, 48n, 55l, 63, 72, 82, 87, 89, 121kl, 135, 152, 176, 301, 383, 400, 477, 612, 701, 877, 940, 1084, 1241, 1417, 1641, 2118, 3202, 3814, 3966, 4142, 4843ln, 6872ln }}

[[Badness]] (Sintel): 0.060

== Etymology ==
This comma was named by [[Francium]] in 2025. It refers to {{W|4774 Hobetsu}}, the asteroid, which in turn was named after a town in Japan.

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

[[Category:Commas named after asteroids]]
[[Category:Commas named after place names]]

← Older revision		Revision as of 18:35, 1 April 2025
Line 61:		Line 61:
	== See also ==		== See also ==
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]
	* [[List of superparticular ~~commas~~]]		* [[List of superparticular intervals]]

	[[Category:Commas named after asteroids]]		[[Category:Commas named after asteroids]]
	[[Category:Commas named after place names]]		[[Category:Commas named after place names]]

4774/4773 - Revision history

Francium: /* See also */

Francium: Created page with "{{Infobox Interval | Ratio = 4774/4773 | Name = hobetsisma | Color name = 43u37u31o1oz-2 fothuthisuthiwolozo negative 2nd | Comma = yes }} '''4774/4773''', the '''hobet..."

Francium: Created page with "{{Infobox Interval | Ratio = 4774/4773 | Name = hobetsisma | Color name = 43u37u31o1oz-2
fothuthisuthiwolozo negative 2nd | Comma = yes }} '''4774/4773''', the '''hobet..."