Tarot equivalence continuum - Revision history

FloraC: Mark as mathematical interest. Todo

2025-08-13T14:38:14Z

Mark as mathematical interest. Todo

← Older revision		Revision as of 14:38, 13 August 2025
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			{{Mathematical interest}}

	The Tarot equivalence continuum is a continuum of 2.3.5 subgroup temperaments which all equate a number of [[22nd-octave temperaments#Major Arcana\|Major Arcana]] commas with the [[barium]] comma, which due to it being period-56 can also be called Minor Arcana comma. Since there's 22 cards in the Major Arcana, and 56 in the Minor Arcana, the natural name that arises is Tarot equivalence continuum.		The Tarot equivalence continuum is a continuum of 2.3.5 subgroup temperaments which all equate a number of [[22nd-octave temperaments#Major Arcana\|Major Arcana]] commas with the [[barium]] comma, which due to it being period-56 can also be called Minor Arcana comma. Since there's 22 cards in the Major Arcana, and 56 in the Minor Arcana, the natural name that arises is Tarot equivalence continuum.

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	[[Category:1848edo]]		[[Category:1848edo]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]
			{{Todo\| cleanup \| discuss title }}

Godtone: link

2025-03-04T18:03:21Z

link

← Older revision		Revision as of 18:03, 4 March 2025
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	\|-		\|-
	\| 3		\| 3
	\| 1848 & 53		\| [[#Empress\|Empress]] (1848 & 53)
	\| {{Monzo\|-177 119 -5}}		\| {{Monzo\|-177 119 -5}}
	\|-		\|-

ArrowHead294: /* Empress */

2024-12-03T18:54:37Z

Empress

← Older revision		Revision as of 18:54, 3 December 2024
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	== Empress ==		== Empress ==
	Empress tempers out ~~the~~ {{Monzo\|-177 119 -5}} ~~comma~~, and since it's number 3 in the equivalence continuum, it is named after the 3rd Major Arcana card.		Empress tempers out {{Monzo\|-177 119 -5}}, and since it's number 3 in the equivalence continuum, it is named after the 3rd Major Arcana card.

	Subgroup: 2.3.5		Subgroup: 2.3.5

ArrowHead294 at 18:54, 3 December 2024

2024-12-03T18:54:22Z

← Older revision		Revision as of 18:54, 3 December 2024
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	The Tarot equivalence continuum is a continuum of 2.3.5 subgroup temperaments which all equate a number of [[22nd-octave temperaments#Major Arcana\|Major Arcana]] commas with the [[barium]] comma, which due to it being period-56 can also be called Minor Arcana comma. Since there's 22 cards in the Major Arcana, and 56 in the Minor Arcana, the natural name that arises is Tarot equivalence continuum.		The Tarot equivalence continuum is a continuum of 2.3.5 subgroup temperaments which all equate a number of [[22nd-octave temperaments#Major Arcana\|Major Arcana]] commas with the [[barium]] comma, which due to it being period-56 can also be called Minor Arcana comma. Since there's 22 cards in the Major Arcana, and 56 in the Minor Arcana, the natural name that arises is Tarot equivalence continuum.

	All temperaments in this continuum satisfy (2<sup>-193</sup>3<sup>154</sup>･5<sup>-22</sup>)<sup>''n''</sup> ~ (2<sup>-225</sup>･3<sup>224</sup>･5<sup>-56</sup>). If we allow non-integer and infinite ''n'', the continuum describes the set of all 5-limit temperaments supported by [[1848edo]], due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of n is approximately 2.0070839..., and temperaments having ''n'' near this value tend to be the most accurate ones.		All temperaments in this continuum satisfy {{nowrap\|(2<sup>−193</sup> 3<sup>154</sup> 5<sup>−22</sup>)<sup>''n''</sup> ~ (2<sup>−225</sup> 3<sup>224</sup> 5<sup>−56</sup>)}}. If we allow non-integer and infinite ''n'', the continuum describes the set of all 5-limit temperaments supported by [[1848edo]], due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of n is approximately 2.0070839..., and temperaments having ''n'' near this value tend to be the most accurate ones.

	The continuum contains two notable 5-limit temperaments supported by 1848edo, minortone and atomic.		The continuum contains two notable 5-limit temperaments supported by 1848edo, minortone and atomic.
	{\| class="wikitable center-1 center-2 center-4 center-5"		{\| class="wikitable center-1 center-2 center-4 center-5"
	\|-		\|-
	!''n''		! ''n''
	!Temperament		! Temperament
	!Comma (monzo)		! Comma (monzo)
	\|-		\|-
	\|0		\| 0
	\|[[22nd-octave temperaments#Major Arcana\|Major Arcana]]		\| [[22nd-octave temperaments#Major Arcana\|Major Arcana]]
	\|{{Monzo\|-193 154 -22}}		\| {{Monzo\|-193 154 -22}}
	\|-		\|-
	\|1		\| 1
	\|[[Minortone]]		\| [[Minortone]]
	\|{{Monzo\|-16 35 -17}}		\| {{Monzo\|-16 35 -17}}
	\|-		\|-
	\|2		\| 2
	\|[[Atomic]]		\| [[Atomic]]
	\|[[Kirnberger's atom\|[161 -84 -12⟩]]		\| [[Kirnberger's atom\|[161 -84 -12⟩]]
	\|-		\|-
	\|3		\| 3
	\|1848 & 53		\| 1848 & 53
	\|{{Monzo\|-177 119 -5}}		\| {{Monzo\|-177 119 -5}}
	\|-		\|-
	\|4		\| 4
	\|1848 & 3296		\| 1848 & 3296
	\|{{Monzo\|-547 392 -32}}		\| {{Monzo\|-547 392 -32}}
	\|-		\|-
	\|5		\| 5
	\|1848 & 3243		\| 1848 & 3243
	\|{{Monzo\|-370 273 -27}}		\| {{Monzo\|-370 273 -27}}
	\|-		\|-
	\|…		\| …
	\|…		\| …
	\|…		\| …
	\|-		\|-
	\|∞		\| ∞
	\|[[Barium]]		\| [[Barium]]
	\|		\|
	\|}		\|}

Godtone: correct minortone

2024-07-18T02:16:26Z

correct minortone

← Older revision		Revision as of 02:16, 18 July 2024
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	\|1		\|1
	\|[[Minortone]]		\|[[Minortone]]
	\|{{Monzo\|16 35 -17}}		\|{{Monzo\|-16 35 -17}}
	\|-		\|-
	\|2		\|2

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T20:08:34Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 20:08, 7 May 2023
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	Optimal tuning (CTE): ~343597383680/282429536481 = 339.611		Optimal tuning (CTE): ~343597383680/282429536481 = 339.611

	~~Vals:~~ {{~~EDOs~~\|53, 1530, 1583, 1636, 1689, 1742, 1795, 1848, 1901, 1954}}, ...		{{Optimal ET sequence\|legend=1\|53, 1530, 1583, 1636, 1689, 1742, 1795, 1848, 1901, 1954}}, ...

	[[Category:1848edo]]		[[Category:1848edo]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

Eliora at 11:42, 9 April 2023

2023-04-09T11:42:29Z

@@ Line 43: / Line 43: @@
 |}
 [[Category:1848edo]]
 [[Category:Equivalence continua]]

Eliora at 23:28, 17 January 2023

2023-01-17T23:28:53Z

← Older revision		Revision as of 23:28, 17 January 2023
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	\|		\|
	\|}		\|}


			[[Category:1848edo]]
			[[Category:Equivalence continua]]

Eliora at 23:28, 17 January 2023

2023-01-17T23:28:24Z

← Older revision		Revision as of 23:28, 17 January 2023
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	\|0		\|0
	\|[[22nd-octave temperaments#Major Arcana\|Major Arcana]]		\|[[22nd-octave temperaments#Major Arcana\|Major Arcana]]
	\|[-193 154 -~~22⟩~~		\|{{Monzo\|-193 154 -22}}
	\|-		\|-
	\|1		\|1
	\|[[Minortone]]		\|[[Minortone]]
	\|[-16 35 -~~17⟩~~		\|{{Monzo\|16 35 -17}}
	\|-		\|-
	\|2		\|2
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	\|3		\|3
	\|1848 & 53		\|1848 & 53
	\|[-177 119 -5⟩		\|{{Monzo\|-177 119 -5}}
	\|-		\|-
	\|4		\|4
	\|1848 & 3296		\|1848 & 3296
	\|[-547,392,-32>		\|{{Monzo\|-547 392 -32}}
	\|-		\|-
	\|5		\|5
	\|1848 & 3243		\|1848 & 3243
	\| -370,273,-27>		\|{{Monzo\|-370 273 -27}}
	\|-		\|-
	\|…		\|…

Eliora at 23:26, 17 January 2023

2023-01-17T23:26:40Z

← Older revision		Revision as of 23:26, 17 January 2023
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	The Tarot equivalence continuum is a continuum of 2.3.5 subgroup temperaments which all equate a number of [[22nd-octave temperaments#Major Arcana\|Major Arcana]] commas with the [[barium]] comma, which due to it being period-56 can also be called Minor Arcana comma. Since there's 22 cards in the Major Arcana, and 56 in the Minor Arcana, the natural name that arises is Tarot equivalence continuum.		The Tarot equivalence continuum is a continuum of 2.3.5 subgroup temperaments which all equate a number of [[22nd-octave temperaments#Major Arcana\|Major Arcana]] commas with the [[barium]] comma, which due to it being period-56 can also be called Minor Arcana comma. Since there's 22 cards in the Major Arcana, and 56 in the Minor Arcana, the natural name that arises is Tarot equivalence continuum.

	All temperaments in this continuum satisfy (2<sup>-193</sup>3<sup>154</sup>･5<sup>-22</sup>)<sup>''n''</sup> ~ (2<sup>-225</sup>･3<sup>224</sup>･5<sup>-56</sup>). If we allow non-integer and infinite ''n'', the continuum describes the set of all 5-limit temperaments supported by [[1848edo]] due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of n is approximately 2.0070839..., and temperaments having ''n'' near this value tend to be the most accurate ones.		All temperaments in this continuum satisfy (2<sup>-193</sup>3<sup>154</sup>･5<sup>-22</sup>)<sup>''n''</sup> ~ (2<sup>-225</sup>･3<sup>224</sup>･5<sup>-56</sup>). If we allow non-integer and infinite ''n'', the continuum describes the set of all 5-limit temperaments supported by [[1848edo]], due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of n is approximately 2.0070839..., and temperaments having ''n'' near this value tend to be the most accurate ones.

			The continuum contains two notable 5-limit temperaments supported by 1848edo, minortone and atomic.
	{\| class="wikitable center-1 center-2 center-4 center-5"		{\| class="wikitable center-1 center-2 center-4 center-5"
	\|-		\|-
	! ~~rowspan="2" \|~~''n''		!''n''
	! ~~rowspan="2" \|~~Temperament		!Temperament
	! ~~colspan="2" \|Comma~~		!Comma (monzo)
	~~! rowspan="2" \|1 / ''n''~~
	~~! rowspan="2" \|Temperament~~
	~~! colspan="2" \|~~Comma
	\|-		\|-
	~~!Ratio~~
	~~!Monzo~~
	~~!Ratio~~
	~~!Monzo~~
	\|-
	\|0
	\|
	\|
	\|
	\|0		\|0
	\|		\|[[22nd-octave temperaments#Major Arcana\|Major Arcana]]
	\|		\|[-193 154 -22⟩
	\|
	\|-		\|-
	\|1		\|1
	\|		\|[[Minortone]]
	\|		\|[-16 35 -17⟩
	\|
	\|1
	\|
	\|
	\|
	\|-		\|-
	\|2		\|2
	\|		\|[[Atomic]]
	\|		\|[[Kirnberger's atom\|[161 -84 -12⟩]]
	\|
	\|2
	\|
	\|
	\|
	\|-		\|-
	\|3		\|3
	\|		\|1848 & 53
	\|		\|[-177 119 -5⟩
	\|		\|-
	\|3		\|4
	\|		\|1848 & 3296
	\|		\|[-547,392,-32>
	\|		\|-
			\|5
			\|1848 & 3243
			\| -370,273,-27>
	\|-		\|-
	\|…
	\|…
	\|…
	\|…
	\|…
	\|…		\|…
	\|…		\|…
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	\|-		\|-
	\|∞		\|∞
	\|		\|[[Barium]]
	\|
	\|
	\|∞
	\|
	\|
	\|		\|
	\|}		\|}