FloraC: + a missing pair of ratios

2025-09-17T12:36:37Z

+ a missing pair of ratios

← Older revision		Revision as of 12:36, 17 September 2025
Line 10:		Line 10:
	== Commatic relationships ==		== Commatic relationships ==
	This comma is the difference between the following superparticular pairs:		This comma is the difference between the following superparticular pairs:
			* [[320/319]] and [[324/323]]
	* [[595/594]] and [[609/608]]		* [[595/594]] and [[609/608]]
	* [[760/759]] and [[783/782]]		* [[760/759]] and [[783/782]]

Francium: Created page with "{{Infobox Interval | Ratio = 25840/25839 | Name = vuillafansisma | Color name = 29u19o17o1uy2
twenunosoluyo 2nd | Comma = yes }} '''25840/25839''', the '''vuillafansisma..."

2024-11-13T06:30:15Z

Created page with "{{Infobox Interval | Ratio = 25840/25839 | Name = vuillafansisma | Color name = 29u19o17o1uy2 <br> twenunosoluyo 2nd | Comma = yes }} '''25840/25839''', the '''vuillafansisma..."

New page

{{Infobox Interval
| Ratio = 25840/25839
| Name = vuillafansisma
| Color name = 29u19o17o1uy2 <br> twenunosoluyo 2nd
| Comma = yes
}}

'''25840/25839''', the '''vuillafansisma''' is a [[29-limit]] [[superparticular interval|superparticular comma]] of about 0.067 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[595/594]] and [[609/608]]
* [[760/759]] and [[783/782]]
* [[1216/1215]] and [[1276/1275]]
* [[2080/2079]] and [[2262/2261]]
* [[12376/12375]] and [[23751/23750]]

It can be factored into following superparticular commas:
* [[27000/26999]] and [[601426/601425]]
* [[28900/28899]] and [[244036/244035]]
* [[30625/30624]] and [[165376/165375]]
* [[30856/30855]] and [[158950/158949]]

== Temperaments ==
Tempering out this comma in the full 29-limit leads to the rank-9 temperament '''vuillafansismic'''. Using the 2.3.5.11.17.19.29 subgroup leads to the rank-6 temperament '''vuillafansic'''.

=== Vuillafansismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29

[[Comma list]]: 25840/25839

[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 7 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || -4 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.961, ~5/4 = 386.311, ~7/4 = 968.826, ~11/8 = 551.325, ~13/8 = 840.528, ~17/16 = 104.946, ~19/16 = 297.503, ~23/16 = 628.274

=== Vuillafansic ===

[[Subgroup]]: 2.3.5.11.17.19.29

[[Comma list]]: 25840/25839

[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 2 || 3 || 4 || 4 || 7 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -4 || ],
|-
| ⟨ || 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 = 701.961, ~5/4 = 386.311, ~11/8 = 551.325, ~17/16 = 104.946, ~19/16 = 297.503

{{Optimal ET sequence|legend=1| 5eghj, 7ghjj, 7g, 10ej, 12eh, 12, 15g, 19egh, 22j, 22h, 24, 34h, 39gj, 41, 46hj, 50, 53g, 65, 87, 99e, 118, 183, 205, 270, 349gh, 354, 388, 422, 472, 487, 559, 653, 677, 836, 1323, 1395, 1513, 1783, 2000, 2836, 3395, 4231, 4619, 5178, 6014, 8014 }}

== Etymology ==
The vuillafansisma was named by [[Francium]] in 2024. It refers to the postal code of Vuillafans, France.

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

[[Category:Commas named after place names]]

Vuillafansisma - Revision history

FloraC: + a missing pair of ratios

Francium: Created page with "{{Infobox Interval | Ratio = 25840/25839 | Name = vuillafansisma | Color name = 29u19o17o1uy2 twenunosoluyo 2nd | Comma = yes }} '''25840/25839''', the '''vuillafansisma..."

Francium: Created page with "{{Infobox Interval | Ratio = 25840/25839 | Name = vuillafansisma | Color name = 29u19o17o1uy2
twenunosoluyo 2nd | Comma = yes }} '''25840/25839''', the '''vuillafansisma..."