FloraC: FloraC moved page Alphonsinisma to 925/924 over redirect: 6-digit ratios are okay as page titles

2025-01-07T14:18:53Z

FloraC moved page Alphonsinisma to 925/924 over redirect: 6-digit ratios are okay as page titles

← Older revision	Revision as of 14:18, 7 January 2025
(No difference)

Francium: /* Temperaments */ typo

2025-01-06T15:03:23Z

Temperaments: typo

← Older revision		Revision as of 15:03, 6 January 2025
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''alphonsinismic'''. Using the 2.3.5.7.11.37 subgroup leads to the rank-5 temperament '''~~alphonsic~~'''.		Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''alphonsinismic'''. Using the 2.3.5.7.11.37 subgroup leads to the rank-5 temperament '''alphonsinic'''.

	=== ~~Alphonsismic~~ ===		=== Alphonsinismic ===

	[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37		[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37
Line 71:		Line 71:
	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

	=== ~~Alphonsic~~ ===		=== Alphonsinic ===

	[[Subgroup]]: 2.3.5.7.11.37		[[Subgroup]]: 2.3.5.7.11.37

Francium: Created page with "{{Infobox Interval | Ratio = 925/924 | Name = alphonsinisma | Color name = 37o1uryy1
thisoluruyoyo unison | Comma = yes }} '''925/924''', the '''alphonsinisma''', is a [..."

2025-01-05T20:10:05Z

Created page with "{{Infobox Interval | Ratio = 925/924 | Name = alphonsinisma | Color name = 37o1uryy1 <br> thisoluruyoyo unison | Comma = yes }} '''925/924''', the '''alphonsinisma''', is a [..."

New page

{{Infobox Interval
| Ratio = 925/924
| Name = alphonsinisma
| Color name = 37o1uryy1 <br> thisoluruyoyo unison
| Comma = yes
}}

'''925/924''', the '''alphonsinisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 1.9 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[100/99]] and [[112/111]]
* [[111/110]] and [[126/125]]
* [[148/147]] and [[176/175]]
* [[155/154]] and [[186/185]]
* [[225/224]] and [[297/296]]
* [[400/399]] and [[704/703]]

It can be factored into the following superparticular intervals:
* [[931/930]] and [[143375/143374]]
* [[936/935]] and [[78625/78624]]
* [[969/968]] and [[20350/20349]]
* [[1036/1035]] and [[8625/8624]]
* [[1156/1155]] and [[4625/4624]]
* [[1184/1183]] and [[4225/4224]]
* [[1225/1224]] and [[3774/3773]]
* [[1275/1274]] and [[3367/3366]]
* [[1332/1331]] and [[3025/3024]]
* [[1369/1368]] and [[2850/2849]]
* [[1450/1449]] and [[2553/2552]]
* [[1480/1479]] and [[2465/2464]]
* [[1625/1624]] and [[2146/2145]]
* [[1665/1664]] and [[2080/2079]]
* [[1702/1701]] and [[2025/2024]]

== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''alphonsinismic'''. Using the 2.3.5.7.11.37 subgroup leads to the rank-5 temperament '''alphonsic'''.

=== Alphonsismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37

[[Comma list]]: 925/924

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

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

=== Alphonsic ===

[[Subgroup]]: 2.3.5.7.11.37

[[Comma list]]: 925/924

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

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633

{{Optimal ET sequence|legend=1| 7d, 8d, 9l, 10e, 12el, 12, 15, 19el, 19, 22, 27e, 31, 41, 50, 53, 60el, 72, 130, 152, 224, 311, 342l, 463, 494, 566l, 805l, 877l }}

== Etymology ==
This comma was named by [[Francium]] in 2025. It refers to {{W|925 Alphonsina}}, the asteroid, which in turn was named after two Spanish kings.

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

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

925/924 - Revision history

FloraC: FloraC moved page Alphonsinisma to 925/924 over redirect: 6-digit ratios are okay as page titles

Francium: /* Temperaments */ typo

Francium: Created page with "{{Infobox Interval | Ratio = 925/924 | Name = alphonsinisma | Color name = 37o1uryy1 thisoluruyoyo unison | Comma = yes }} '''925/924''', the '''alphonsinisma''', is a [..."

Francium: Created page with "{{Infobox Interval | Ratio = 925/924 | Name = alphonsinisma | Color name = 37o1uryy1
thisoluruyoyo unison | Comma = yes }} '''925/924''', the '''alphonsinisma''', is a [..."