375/374: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = ursulisma, ursulic comma | ||
| Color name = | | Color name = 17u1uy<sup>3</sup>-2, sulutriyo negative 2nd | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The '''ursulisma''', or '''ursulic comma''', is a [[17-limit]] (also 2.3.5.11.17 [[subgroup]]) [[superparticular]] [[comma]] with a [[ratio]] of '''375/374'''. It is the interval that separates [[17/15]] from [[25/22]], as well as separating [[25/17]] from [[22/15]]. | |||
== Commatic relations == | |||
This comma identifies itself as the difference between the following superparticular pairs: | |||
* [[100/99]] and [[136/135]] | |||
* [[120/119]] and [[176/175]] | |||
* [[225/224]] and [[561/560]] | |||
* [[273/272]] and [[1001/1000]] | |||
* [[325/324]] and [[2431/2430]] | |||
* [[364/363]] and [[12376/12375]] | |||
It factors into the following superparticular pairs: | |||
* [[625/624]] and [[936/935]] | |||
* [[540/539]] and [[1225/1224]] | |||
* [[441/440]] and [[2500/2499]] | |||
* [[385/384]] and [[14400/14399]] | |||
Not to mention some nonsuperparticular but useful relations: | |||
* [[595/594]] and [[2025/2023]] | |||
== Temperaments == | |||
Tempering out this comma in the 17-limit leads to the rank-6 '''ursulismic temperament'''. Tempering it out in the 2.3.5.11.17 subgroup leads to the rank-4 '''ursulic temperament''', enabling [[ursulismic chords]]. You may find a list of good equal temperaments that support these temperaments below. | |||
=== Ursulismic === | |||
[[Subgroup]]: 2.3.5.7.11.13.17 | |||
[[Mapping]]: <br> | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -1 || ], | |||
|- | |||
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 3 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || -1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | |||
|} | |||
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.8093, ~5/4 = 385.3757, ~7/4, ~11/8 = 552.0120, ~13/8 | |||
{{Optimal ET sequence|legend=1| 12f, 15g, 16, 19g, 22, 27eg, 29g, 31, 38df, 41g, 43, 49fg, 50, 53, 60e, 65d, 72, 103, 121, 152fg, 159, 171, 193, 224, 296, 395e, 467, 554g, 691eg }} | |||
=== Ursulic === | |||
[[Subgroup]]: 2.3.5.11.17 | |||
{{Mapping|legend=2| 1 0 0 0 -1 | 0 1 0 0 1 | 0 0 1 0 3 | 0 0 0 1 -1 }} | |||
: sval mapping generators: ~2, ~3, ~5, ~11 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.8093, ~5/4 = 385.3757, ~11/8 = 552.0120 | |||
{{Optimal ET sequence|legend=1| 12, 15g, 19g, 22, 31, 34, 50, 53, 56, 60e, 65, 72, 137, 159, 296, 455, 489 }} | |||
== Etymology == | |||
The ursulisma was named by [[Aura]] and [[User:VIxen|VIxen]] in 2023. It refers to [[Wikipedia: 375 Ursula|375 Ursula]], the asteroid. After some naming attempts in the XA Discord Server that turned out dissatisfactory to the participants, VIxen came up with the idea to look up the [[Wikipedia: List of minor planets|list of minor planets]] in case everything else failed, and Aura was the first to put together the word ''ursulisma''. | |||
The origin for the asteroid’s own name is unknown. | |||
[[Category:Ursulismic]] | |||
[[Category:Commas named after asteroids]] | |||