6480/6479 - Revision history

FloraC: FloraC moved page Scarlattisma to 6480/6479 over redirect: 8-digit ratios are okay as page titles

2025-01-07T14:22:40Z

FloraC moved page Scarlattisma to 6480/6479 over redirect: 8-digit ratios are okay as page titles

← Older revision	Revision as of 14:22, 7 January 2025
(No difference)

BudjarnLambeth at 02:40, 4 November 2024

2024-11-04T02:40:39Z

← Older revision		Revision as of 02:40, 4 November 2024
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	[[Category:Commas named after asteroids]]		[[Category:Commas named after asteroids]]
	[[Category:Commas named after ~~individuals~~]]		[[Category:Commas named after composers]]

BudjarnLambeth at 01:50, 4 November 2024

2024-11-04T01:50:10Z

← Older revision		Revision as of 01:50, 4 November 2024
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	== Etymology ==		== Etymology ==
	The scarlattisma was named by [[Francium]] in 2024. It refers to {{W\|6480 Scarlatti}}, the asteroid. Which in turn~~, fittingly enough,~~ was named after ~~the~~ Italian composer ~~Scarlatti~~.		The scarlattisma was named by [[Francium]] in 2024. It refers to {{W\|6480 Scarlatti}}, the asteroid. Which in turn was named after an Italian composer.

	== See also ==		== See also ==

BudjarnLambeth at 01:48, 4 November 2024

2024-11-04T01:48:35Z

← Older revision		Revision as of 01:48, 4 November 2024
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	== Etymology ==		== Etymology ==
	The scarlattisma was named by [[Francium]] in 2024. It refers to {{W\|6480 Scarlatti}}, the asteroid.		The scarlattisma was named by [[Francium]] in 2024. It refers to {{W\|6480 Scarlatti}}, the asteroid. Which in turn, fittingly enough, was named after the Italian composer Scarlatti.

	== See also ==		== See also ==
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	[[Category:Commas named after asteroids]]		[[Category:Commas named after asteroids]]
			[[Category:Commas named after individuals]]

BudjarnLambeth at 08:36, 3 November 2024

2024-11-03T08:36:19Z

← Older revision		Revision as of 08:36, 3 November 2024
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	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

			[[Category:Commas named after asteroids]]

Francium: Created page with "{{Infobox Interval | Ratio = 6480/6479 | Name = scarlattisma | Color name = 31u19u1uy1
thiwunuluyo unison | Comma = yes }} '''6480/6479''', the '''scarlattisma''', is a..."

2024-10-30T11:22:57Z

Created page with "{{Infobox Interval | Ratio = 6480/6479 | Name = scarlattisma | Color name = 31u19u1uy1 <br> thiwunuluyo unison | Comma = yes }} '''6480/6479''', the '''scarlattisma''', is a..."

New page

{{Infobox Interval
| Ratio = 6480/6479
| Name = scarlattisma
| Color name = 31u19u1uy1 <br> thiwunuluyo unison
| Comma = yes
}}

'''6480/6479''', the '''scarlattisma''', is a [[31-limit]] [[superparticular ratio|superparticular comma]] of about 0.27 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[210/209]] and [[217/216]]
* [[324/323]] and [[341/340]]
* [[540/539]] and [[589/588]]
* [[837/836]] and [[961/960]]
* [[2025/2024]] and [[2945/2944]]
* [[2300/2299]] and [[3565/3564]]
* [[2376/2375]] and [[3751/3750]]
* [[3060/3059]] and [[5797/5796]]
* [[3136/3135]] and [[6076/6075]]

It can be factored into the following superparticular commas:
* [[6656/6655]] and [[245025/245024]]
* [[6670/6669]] and [[227448/227447]]
* [[6728/6727]] and [[175770/175769]]
* [[6860/6859]] and [[116964/116963]]
* [[8526/8525]] and [[27000/26999]]
* [[8960/8959]] and [[23409/23408]]
* [[9425/9424]] and [[20736/20735]]
* [[11781/11780]] and [[14400/14399]]
* [[12636/12635]] and [[13300/13299]]

== Temperaments ==
Tempering out this comma in the full 31-limit leads to the rank-10 temperament '''scarlattismic'''. Using the 2.3.5.11.19.31 subgroup leads to the rank-5 temperament '''scarlattic'''.

=== Scarlattismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31

[[Comma list]]: 6480/6479

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

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.928, ~5/4 = 386.299, ~7/4 = 968.826, ~11/8 = 551.350, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.561, ~23/16 = 628.274, ~29/16 = 1029.577

=== Scarlattic ===

[[Subgroup]]: 2.3.5.11.19.31

[[Comma list]]: 6480/6479

[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 2 || 3 || 4 || 3 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 4 || ],
|-
| ⟨ || 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 = 701.928, ~5/4 = 386.299, ~11/8 = 551.350, ~19/16 = 297.561

{{Optimal ET sequence|legend=1| 7k, 9k, 12, 14c, 15k, 22h, 24, 38, 41, 65, 152, 190, 217, 255, 270, 335, 407, 422, 487, 525, 612, 677, 988, 1243, 1395, 1665, 1730, 2407, 3395k, 3650, 4072k, 5315, 7045k, 7722hk, 9452hk }}

== Etymology ==
The scarlattisma was named by [[Francium]] in 2024. It refers to {{W|6480 Scarlatti}}, the asteroid.

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