FloraC: FloraC moved page Viljevisma to 2553/2552 over redirect: 8-digit ratios are okay as page titles

2025-01-07T14:23:50Z

FloraC moved page Viljevisma to 2553/2552 over redirect: 8-digit ratios are okay as page titles

← Older revision	Revision as of 14:23, 7 January 2025
(No difference)

Francium: Created page with "{{Infobox Interval | Ratio = 2553/2552 | Name = viljevisma | Color name = 37o29u23o1u2
thisotwenutwetholu 2nd | Comma = yes }} '''2553/2552''', the '''viljevisma''', is..."

2024-12-23T15:29:38Z

Created page with "{{Infobox Interval | Ratio = 2553/2552 | Name = viljevisma | Color name = 37o29u23o1u2 <br> thisotwenutwetholu 2nd | Comma = yes }} '''2553/2552''', the '''viljevisma''', is..."

New page

{{Infobox Interval
| Ratio = 2553/2552
| Name = viljevisma
| Color name = 37o29u23o1u2 <br> thisotwenutwetholu 2nd
| Comma = yes
}}

'''2553/2552''', the '''viljevisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 0.68 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[111/110]] and [[116/115]]
* [[407/406]] and [[484/483]]
* [[552/551]] and [[704/703]]
* [[851/850]] and [[1276/1275]]
* [[925/924]] and [[1450/1449]]

It can be factored into the following superparticular ratios:
* [[2640/2639]] and [[77441/77440]]
* [[2737/2736]] and [[37962/37961]]
* [[3249/3248]] and [[11914/11913]]
* [[3367/3366]] and [[10557/10556]]
* [[3510/3509]] and [[9361/9360]]
* [[3565/3564]] and [[8991/8990]]
* [[3626/3625]] and [[8625/8624]]
* [[3774/3773]] and [[7889/7888]]

== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''viljevismic'''. Using the 2.3.11.23.29.37 subgroup leads to the rank-5 temperament '''viljevic'''.

=== Viljevismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37

[[Comma list]]: 2553/2552

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 4 || 4 || 5 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.935, ~5/4 = 386.314, ~7/4 = 968.826, ~11/8 = 551.413, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.112, ~29/16 = 1029.764, ~31/16 = 1145.036

=== Viljevic ===

[[Subgroup]]: 2.3.11.23.29.37

[[Comma list]]: 2553/2552

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 3 || 4 || 4 || 5 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.935, ~11/8 = 551.413, ~23/16 = 628.112, ~29/16 = 1029.764

{{Optimal ET sequence|legend=1| 5i, 7ijj, 7, 10i, 12el, 14, 15, 17, 29, 31j, 46j, 48, 111, 128, 159, 176, 224, 248, 311, 359, 735, 783, 812, 860, 1171, 1219, 2614il, 2973il }}

== Etymology ==
This comma was named by [[Francium]] in 2024. It refers to {{W|2553 Viljev}}, which in turn was named after Mikhail Anatolyevich Vilyev, a Russian astronomer.

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

[[Category:Commas named after asteroids]]
[[Category:Commas named after individuals]]

2553/2552 - Revision history

FloraC: FloraC moved page Viljevisma to 2553/2552 over redirect: 8-digit ratios are okay as page titles

Francium: Created page with "{{Infobox Interval | Ratio = 2553/2552 | Name = viljevisma | Color name = 37o29u23o1u2 thisotwenutwetholu 2nd | Comma = yes }} '''2553/2552''', the '''viljevisma''', is..."

Francium: Created page with "{{Infobox Interval | Ratio = 2553/2552 | Name = viljevisma | Color name = 37o29u23o1u2
thisotwenutwetholu 2nd | Comma = yes }} '''2553/2552''', the '''viljevisma''', is..."