375/374: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Godtone (talk | contribs)
autopatrolled, emailconfirmed
2,289 edits
no explanation of the name ursulisma was included so im adding this alternative name
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,312 edits
mNo edit summary
 
(8 intermediate revisions by 4 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Name = septendecimal wholetones comma, ursulisma
| 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]].
The '''septendecimal wholetones comma''', or '''ursulisma''', 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 ==
== Commatic relations ==
Line 27: Line 26:


== Temperaments ==
== Temperaments ==
Tempering out this comma in the 17-limit leads to the rank-6 '''ursulismic temperament'''.
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]]

Latest revision as of 01:17, 4 November 2024

Interval information
Ratio 375/374
Factorization 2-1 × 3 × 53 × 11-1 × 17-1
Monzo [-1 1 3 0 -1 0 -1⟩
Size in cents 4.622791¢
Names ursulisma,
ursulic comma
Color name 17u1uy3-2, sulutriyo negative 2nd
FJS name [math]\displaystyle{ \text{dd}{-2}^{5,5,5}_{11,17} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 17.0976
Weil height (log2 max(n, d)) 17.1015
Wilson height (sopfr(nd)) 48
Comma size small
Open this interval in xen-calc

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:

It factors into the following superparticular pairs:

Not to mention some nonsuperparticular but useful relations:

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:

[⟨ 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: 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

Subgroup-val mapping: [⟨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: 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 VIxen in 2023. It refers to 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 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.

Retrieved from "https://en.xen.wiki/index.php?title=375/374&oldid=163976"