1152edo - Revision history

Overthink: You can't represent a "prime limit" consistently

2026-03-27T04:19:02Z

You can't represent a "prime limit" consistently

← Older revision		Revision as of 04:19, 27 March 2026
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	1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo\|1 -27 18}}, as well as {{monzo\|99 2 -44}}, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as {{Monzo\|94 -33 -24 5}} in the 7-limit. It supports the [[hemiennealimmal]] temperament and [[germanium]] temperament in the 11-limit despite not being consistent.		1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo\|1 -27 18}}, as well as {{monzo\|99 2 -44}}, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as {{Monzo\|94 -33 -24 5}} in the 7-limit. It supports the [[hemiennealimmal]] temperament and [[germanium]] temperament in the 11-limit despite not being consistent.

	It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd~~-limit]] and not just [[23-limit\|23-prime~~-limit]]. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating [[70/69]] to 1 step of [[48edo]].		It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the remaining intervals of the [[25-odd-limit]]. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating [[70/69]] to 1 step of [[48edo]].

	The 1152deef val provides a tuning close to the POTE tuning of the [[stockhausenic]] temperament.		The 1152deef val provides a tuning close to the POTE tuning of the [[stockhausenic]] temperament.

Squib: add redlink for abundancy index

2026-03-27T03:07:02Z

add redlink for abundancy index

← Older revision		Revision as of 03:07, 27 March 2026
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	Since 1152 factors as {{Factorization\|1152}}, 1152edo has subset edos {{EDOs\|1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576}}.		Since 1152 factors as {{Factorization\|1152}}, 1152edo has subset edos {{EDOs\|1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576}}.

	1152edo is a [[highly factorable edo]]. Its abundancy index is around 1.87.		1152edo is a [[highly factorable edo]]. Its [[abundancy index]] is around 1.87.
	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]

Francium: changed EDO intro to ED intro

2025-02-21T05:48:19Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:48, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1152~~}}		{{ED intro}}

	1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo\|1 -27 18}}, as well as {{monzo\|99 2 -44}}, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as {{Monzo\|94 -33 -24 5}} in the 7-limit. It supports the [[hemiennealimmal]] temperament and [[germanium]] temperament in the 11-limit despite not being consistent.		1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo\|1 -27 18}}, as well as {{monzo\|99 2 -44}}, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as {{Monzo\|94 -33 -24 5}} in the 7-limit. It supports the [[hemiennealimmal]] temperament and [[germanium]] temperament in the 11-limit despite not being consistent.

Eliora at 00:11, 11 March 2024

2024-03-11T00:11:29Z

← Older revision		Revision as of 00:11, 11 March 2024
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	{{EDO intro\|1152}}		{{EDO intro\|1152}}

	1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo\|1 -27 18}}, as well as {{monzo\|99 2 -44}}, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as {{Monzo\|94 -33 -24 5}} in the 7-limit. It supports the [[hemiennealimmal]] temperament in the 11-limit despite not being consistent.		1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo\|1 -27 18}}, as well as {{monzo\|99 2 -44}}, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as {{Monzo\|94 -33 -24 5}} in the 7-limit. It supports the [[hemiennealimmal]] temperament and [[germanium]] temperament in the 11-limit despite not being consistent.

	It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd-limit]] and not just [[23-limit\|23-prime-limit]]. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating [[70/69]] to 1 step of [[48edo]].		It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd-limit]] and not just [[23-limit\|23-prime-limit]]. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating [[70/69]] to 1 step of [[48edo]].

			The 1152deef val provides a tuning close to the POTE tuning of the [[stockhausenic]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
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	1152edo is a [[highly factorable edo]]. Its abundancy index is around 1.87.		1152edo is a [[highly factorable edo]]. Its abundancy index is around 1.87.
			[[Category:Ennealimmal]]

Eliora at 16:11, 10 March 2024

2024-03-10T16:11:57Z

← Older revision		Revision as of 16:11, 10 March 2024
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	{{EDO intro\|1152}}		{{EDO intro\|1152}}

	1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo\|1 -27 18}}, as well as (99 2 -44), in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as [94 -33 -24 5⟩ in the 7-limit. It supports the [[hemiennealimmal]] temperament in the 11-limit despite not being consistent.		1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo\|1 -27 18}}, as well as {{monzo\|99 2 -44}}, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as {{Monzo\|94 -33 -24 5}} in the 7-limit. It supports the [[hemiennealimmal]] temperament in the 11-limit despite not being consistent.

	It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd-limit]] and not just [[23-limit\|23-prime-limit]]. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating [[70/69]] to 1 step of [[48edo]].		It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd-limit]] and not just [[23-limit\|23-prime-limit]]. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating [[70/69]] to 1 step of [[48edo]].
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	=== Subsets and supersets ===		=== Subsets and supersets ===
			Since 1152 factors as {{Factorization\|1152}}, 1152edo has subset edos {{EDOs\|1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576}}.

	1152edo is a [[highly factorable edo]].		1152edo is a [[highly factorable edo]]. Its abundancy index is around 1.87.

Eliora at 16:09, 10 March 2024

2024-03-10T16:09:42Z

← Older revision		Revision as of 16:09, 10 March 2024
Line 2:		Line 2:
	{{EDO intro\|1152}}		{{EDO intro\|1152}}

	1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5.		1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo\|1 -27 18}}, as well as (99 2 -44), in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as [94 -33 -24 5⟩ in the 7-limit. It supports the [[hemiennealimmal]] temperament in the 11-limit despite not being consistent.

	It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd-limit]] and not just [[23-limit\|23-prime-limit]].		It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd-limit]] and not just [[23-limit\|23-prime-limit]]. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating [[70/69]] to 1 step of [[48edo]].

			=== Prime harmonics ===
	{{harmonics in equal\|1152}}		{{harmonics in equal\|1152}}

Eliora: Created page with "{{Infobox ET}} {{EDO intro|1152}} 1152edo is consistent in the 9-odd-limit, where it corrects the 576edo's mapping for 5. It is a strong 2.3.5.7.13.17.23 subgro..."

2024-03-10T15:58:45Z

Created page with "{{Infobox ET}} {{EDO intro|1152}} 1152edo is consistent in the 9-odd-limit, where it corrects the 576edo's mapping for 5. It is a strong 2.3.5.7.13.17.23 subgro..."

New page

{{Infobox ET}}
{{EDO intro|1152}}

1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5.

It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd-limit]] and not just [[23-limit|23-prime-limit]].

{{harmonics in equal|1152}}

=== Subsets and supersets ===

1152edo is a [[highly factorable edo]].