BudjarnLambeth at 03:22, 11 April 2025

2025-04-11T03:22:59Z

← Older revision		Revision as of 03:22, 11 April 2025
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	[[Category:Commas named after asteroids]]		[[Category:Commas named after asteroids]]
	[[Category:Commas named after ~~myth~~ or ~~folk characters~~]]		[[Category:Commas named after mythology or literature]]

Francium: Created page with "{{Infobox Interval | Ratio = 5797/5796 | Name = bivojisma | Color name = 31o23u17o1or-2
thiwotwethusoloru negative 2nd | Comma = yes }} '''5797/5796''', the '''bivojism..."

2025-04-02T18:24:52Z

Created page with "{{Infobox Interval | Ratio = 5797/5796 | Name = bivojisma | Color name = 31o23u17o1or-2 <br> thiwotwethusoloru negative 2nd | Comma = yes }} '''5797/5796''', the '''bivojism..."

New page

{{Infobox Interval
| Ratio = 5797/5796
| Name = bivojisma
| Color name = 31o23u17o1or-2 <br> thiwotwethusoloru negative 2nd
| Comma = yes
}}

'''5797/5796''', the '''bivojisma''', is a [[31-limit]] [[superparticular interval|superparticular comma]] of about 0.30 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[323/322]] and [[342/341]]
* [[484/483]] and [[528/527]]
* [[561/560]] and [[621/620]]
* [[806/805]] and [[936/935]]
* [[1054/1053]] and [[1288/1287]]
* [[1105/1104]] and [[1365/1364]]
* [[1496/1495]] and [[2016/2015]]
* [[1519/1518]] and [[2058/2057]]
* [[2431/2430]] and [[4186/4185]]

It can be factored into the following superparticular ratios:
* [[5916/5915]] and [[288145/288144]]
* [[5929/5928]] and [[260338/260337]]
* [[6076/6075]] and [[126225/126224]]
* [[6138/6137]] and [[104329/104328]]
* [[7106/7105]] and [[31465/31464]]
* [[7905/7904]] and [[21736/21735]]
* [[7936/7935]] and [[21505/21504]]
* [[11271/11270]] and [[11935/11934]]

== Temperaments ==
Tempering out this comma in the full 31-limit leads to the rank-10 temperament '''bivojismic'''. Using the 2.3.7.11.17.23.31 subgroup leads to the rank-6 temperament '''bivojic'''.

=== Bivojic ===

[[Subgroup]]: 2.3.7.11.17.23.31

[[Comma list]]: 5797/5796

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 3 || 4 || 4 || 3 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 2 || ],
|-
| ⟨ || 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 = 701.971, ~7/4 = 968.852, ~11/8 = 551.279, ~17/16 = 104.901, ~23/16 = 628.341

{{Optimal ET sequence|legend=1| 5i, 5g, 7dgik, 7, 9gik, 10i, 12ik, 14, 22i, 24ik, 24, 26, 27egi, 31k, 32, 41g, 41i, 46, 75ei, 77, 82, 89, 121ik, 130, 135, 207k, 265, 311, 328, 342, 436, 518, 607, 653, 701, 764, 1029, 1043, 1371, 1417, 1807, 2118, 2460, 4532, 4578, 5949k, 7756k }}

[[Badness]] (Sintel): 0.058

== Etymology ==
This comma was named by [[Francium]] in 2025. It refers to {{W|5797 Bivoj}}, the asteroid, which in turn was named after a {{W|Bivoj}}, a mythological Bohemian hero.

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

[[Category:Commas named after asteroids]]
[[Category:Commas named after myth or folk characters]]

5797/5796 - Revision history

BudjarnLambeth at 03:22, 11 April 2025

Francium: Created page with "{{Infobox Interval | Ratio = 5797/5796 | Name = bivojisma | Color name = 31o23u17o1or-2 thiwotwethusoloru negative 2nd | Comma = yes }} '''5797/5796''', the '''bivojism..."

Francium: Created page with "{{Infobox Interval | Ratio = 5797/5796 | Name = bivojisma | Color name = 31o23u17o1or-2
thiwotwethusoloru negative 2nd | Comma = yes }} '''5797/5796''', the '''bivojism..."