Alphatricot family - Revision history

Hkm: /* Alphatrillium */

2026-06-08T18:04:43Z

Alphatrillium

← Older revision		Revision as of 18:04, 8 June 2026
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	Subgroup: 2.3.5.13		Subgroup: 2.3.5.13

	Comma list: ~~140628~~/140625~~, 256000~~/~~255879~~		Comma list: 256000/255879, 140625/140608

	Mapping: {{mapping\| 1 0 -13 -28 \| 0 3 29 60 }}		Mapping: {{mapping\| 1 0 -13 -28 \| 0 3 29 60 }}

Overthink: /* Alphatrillium */ use more accurate language; expand sentence

2026-02-25T05:10:05Z

Alphatrillium: use more accurate language; expand sentence

← Older revision		Revision as of 05:10, 25 February 2026
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	== Alphatrillium ==		== Alphatrillium ==
	Alphatrillium, named by [[Xenllium]] in 2021 as ''trillium'' but renamed following the specifications of ploidacot, can be described as the {{nowrap\| 53 & 441 }} temperament, tempering out the [[ragisma]] aside from the alphatricot comma. [[441edo]] is a good tuning for this temperament, with generator 233\441. The harmonic 7 is found at -95 generator steps, so that the smallest [[mos scale]] is the 123-~~tone~~ one. For much simpler mappings of 7 at the cost of higher errors, you could try [[#Alphatrident\|alphatrident]] and [[#Alphatrimot\|alphatrimot]].		Alphatrillium, named by [[Xenllium]] in 2021 as ''trillium'' but renamed following the specifications of ploidacot, can be described as the {{nowrap\| 53 & 441 }} temperament, tempering out the [[ragisma]] aside from the alphatricot comma. [[441edo]] is a good tuning for this temperament, with generator 233\441. The harmonic 7 is found at -95 generator steps, so that the smallest [[mos scale]] that contains it is the 123-note one, though otonal and utonal tetrads don't occur until the 176-note mos due to 7/5 being mapped to -124 generators. For much simpler mappings of 7 at the cost of higher errors, you could try [[#Alphatrident\|alphatrident]] and [[#Alphatrimot\|alphatrimot]].

	It can be extended to the 11-limit by tempering out [[131072/130977]], and to the 13-limit by tempering out [[2080/2079]], [[4096/4095]] and [[4225/4224]]. The optimal tunings in the 11- and 13-limit lean towards [[494edo]]; [[935edo]] and especially [[1429edo]] are recommendable tunings.		It can be extended to the 11-limit by tempering out [[131072/130977]], and to the 13-limit by tempering out [[2080/2079]], [[4096/4095]] and [[4225/4224]]. The optimal tunings in the 11- and 13-limit lean towards [[494edo]]; [[935edo]] and especially [[1429edo]] are recommendable tunings.

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:30:32Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:30, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Alphatricot family\| ]] <!-- main article -->		[[Category:Alphatricot family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Superlong ratios

2025-10-28T16:17:03Z

Superlong ratios

← Older revision		Revision as of 16:17, 28 October 2025
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	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: 4375/4374, ~~1099511627776/1098337086315~~		[[Comma list]]: 4375/4374, {{monzo\| 40 -22 -1 -1 }}

	{{Mapping\|legend=1\| 1 0 -13 53 \| 0 3 29 -95 }}		{{Mapping\|legend=1\| 1 0 -13 53 \| 0 3 29 -95 }}
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	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: 250047/250000, ~~11785390260224/11767897353375~~		[[Comma list]]: 250047/250000, {{monzo\| 35 -23 -3 3 }}

	{{Mapping\|legend=1\| 3 0 -39 -74 \| 0 3 29 52 }}		{{Mapping\|legend=1\| 3 0 -39 -74 \| 0 3 29 52 }}

FloraC: - redundant category

2025-10-28T16:15:23Z

- redundant category

← Older revision		Revision as of 16:15, 28 October 2025
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	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:Alphatricot family\| ]] <!-- main article -->		[[Category:Alphatricot family\| ]] <!-- main article -->
	~~[[Category:Alphatricot\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: - CTE & POTE tunings

2025-10-28T16:14:32Z

- CTE & POTE tunings

Show changes

FloraC: /* Alphatrimot (2.3.5.13 subgroup) */ accidentally left this out

2025-10-28T16:12:30Z

Alphatrimot (2.3.5.13 subgroup): accidentally left this out

← Older revision		Revision as of 16:12, 28 October 2025
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	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.0000{{c}}, ~13/9 = 634.0179{{c}}		* WE: ~2 = 1200.2092{{c}}, ~13/9 = 634.1076{{c}}
	* POTE: ~2 = 1200.0000{{c}}, ~13/9 = 633.9970{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~13/9 = 634.0032{{c}}
			<!-- * CTE: ~2 = 1200.0000{{c}}, ~13/9 = 634.0179{{c}}
			* POTE: ~2 = 1200.0000{{c}}, ~13/9 = 633.9970{{c}} -->

	{{Optimal ET sequence\|legend=0\| 17c, 36c, 53 }}		{{Optimal ET sequence\|legend=0\| 17c, 36c, 53, 335f, 388f, …, 653ff }}

	Badness (Sintel): 1.~~262~~		Badness (Sintel): 1.26

	=== Alphatrillium (2.3.5.13 subgroup) ===		=== Alphatrillium (2.3.5.13 subgroup) ===

FloraC: Switch to Sintel's badness, WE & CWE tunings, per community consensus

2025-10-28T16:09:45Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus

Show changes

FloraC: Units & misc. cleanup

2025-10-28T11:17:23Z

Units & misc. cleanup

Show changes

FloraC: See talk

2025-09-09T08:49:16Z

See talk

← Older revision		Revision as of 08:49, 9 September 2025
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	* [[Alphatricot19]] – improper [[17L 2s]]		* [[Alphatricot19]] – improper [[17L 2s]]

	=== 2.3.5.13 subgroup ===		=== Alphatrimot (2.3.5.13 subgroup) ===
	{{See also\| No-fives subgroup temperaments #Threedic }}		{{See also\| No-fives subgroup temperaments #Threedic }}