Francium: changed category, since Kálmán was a composer

2025-01-08T13:21:45Z

changed category, since Kálmán was a composer

← Older revision		Revision as of 13:21, 8 January 2025
Line 99:		Line 99:

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

FloraC: FloraC moved page Kalmanisma to 4992/4991 over redirect: 8-digit ratios are okay as page titles

2025-01-07T14:20:18Z

FloraC moved page Kalmanisma to 4992/4991 over redirect: 8-digit ratios are okay as page titles

← Older revision	Revision as of 14:20, 7 January 2025
(No difference)

Francium: Created page with "{{Infobox Interval | Ratio = 4992/4991 | Name = kalmanisma | Color name = 31u23u3or1
thiwutwethuthoru unison | Comma = yes }} '''4992/4991''', the '''kalmanisma''', is a..."

2024-12-15T14:54:25Z

Created page with "{{Infobox Interval | Ratio = 4992/4991 | Name = kalmanisma | Color name = 31u23u3or1 <br> thiwutwethuthoru unison | Comma = yes }} '''4992/4991''', the '''kalmanisma''', is a..."

New page

{{Infobox Interval
| Ratio = 4992/4991
| Name = kalmanisma
| Color name = 31u23u3or1 <br> thiwutwethuthoru unison
| Comma = yes
}}

'''4992/4991''', the '''kalmanisma''', is a [[31-limit]] [[superparticular interval|superparticular comma]] of about 0.35 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[156/155]] and [[161/160]]
* [[208/207]] and [[217/216]]
* [[576/575]] and [[651/650]]
* [[806/805]] and [[961/960]]
* [[1024/1023]] and [[1288/1287]]
* [[1520/1519]] and [[2185/2184]]
* [[1768/1767]] and [[2737/2736]]
* [[2016/2015]] and [[3381/3380]]
* [[2080/2079]] and [[3565/3564]]

It can be factored into the following superparticular ratios:
* [[5083/5082]] and [[278784/278783]]
* [[5104/5103]] and [[227448/227447]]
* [[5643/5642]] and [[43264/43263]]
* [[5888/5887]] and [[32799/32798]]
* [[6480/6479]] and [[21736/21735]]
* [[6656/6655]] and [[19965/19964]]
* [[6728/6727]] and [[19344/19343]]
* [[7936/7935]] and [[13455/13454]]
* [[8464/8463]] and [[12168/12167]]
* [[8960/8959]] and [[11271/11270]]

== Temperaments ==
Tempering out this comma in the full 31-limit leads to the rank-10 temperament '''kalmanismic'''. Using the 2.3.7.13.23.31 subgroup leads to the rank-5 temperament '''kalmanic'''.

=== Kalmanismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31

[[Comma list]]: 4992/4991

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

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.942, ~5/4 = 386.314, ~7/4 = 968.865, ~11/8 = 551.318, ~13/8 = 840.459, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.377, ~29/16 = 1029.577

=== Kalmanic ===

[[Subgroup]]: 2.3.7.13.23.31

[[Comma list]]: 4992/4991

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 3 || 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 = 701.942, ~7/4 = 968.865, ~13/8 = 840.459, ~23/16 = 628.377

{{Optimal ET sequence|legend=1| 5fi, 5, 9k, 10, 14f, 17, 27, 36, 46, 63, 82, 84, 94, 113, 130, 311, 436, 441, 571, 1335, 1470, 1600, 1776, 1906, 2347k, 2477, 2954, 3525, 3853i, 3983i, 4554ik, 6330ik, 6460ik, 6901ikk, 7031ikk }}

== Etymology ==
This comma was named by [[Francium]] in 2024. It refers to {{W|4992 Kálmán}}, the asteroid, which in turn was named after {{W|Emmerich Kálmán}}, a Hungarian composer of operettas.

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

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

4992/4991 - Revision history

Francium: changed category, since Kálmán was a composer

FloraC: FloraC moved page Kalmanisma to 4992/4991 over redirect: 8-digit ratios are okay as page titles

Francium: Created page with "{{Infobox Interval | Ratio = 4992/4991 | Name = kalmanisma | Color name = 31u23u3or1 thiwutwethuthoru unison | Comma = yes }} '''4992/4991''', the '''kalmanisma''', is a..."

Francium: Created page with "{{Infobox Interval | Ratio = 4992/4991 | Name = kalmanisma | Color name = 31u23u3or1
thiwutwethuthoru unison | Comma = yes }} '''4992/4991''', the '''kalmanisma''', is a..."