1612edo - Revision history

FloraC: - deleted name

2026-06-20T12:32:18Z

- deleted name

← Older revision		Revision as of 12:32, 20 June 2026
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	1612edo is a strong [[5-limit]] system, but it is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]]s [[7/1\|7]] and [[11/1\|11]] are about halfway between its steps. Nonetheless, the [[patent val]] is a strong 2.3.5.13.17.23.29.31 [[subgroup]] tuning.		1612edo is a strong [[5-limit]] system, but it is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]]s [[7/1\|7]] and [[11/1\|11]] are about halfway between its steps. Nonetheless, the [[patent val]] is a strong 2.3.5.13.17.23.29.31 [[subgroup]] tuning.

	It provides a tuning for [[quasithird]], [[aluminium]] ~~and [[counterorson]] temperaments~~ in the 5-limit.		It provides a tuning for [[quasithird]] and [[aluminium]] in the 5-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

Francium: changed EDO intro to ED intro

2025-02-21T05:36:26Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:36, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1612~~}}		{{ED intro}}

	1612edo is a strong [[5-limit]] system, but it is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]]s [[7/1\|7]] and [[11/1\|11]] are about halfway between its steps. Nonetheless, the [[patent val]] is a strong 2.3.5.13.17.23.29.31 [[subgroup]] tuning.		1612edo is a strong [[5-limit]] system, but it is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]]s [[7/1\|7]] and [[11/1\|11]] are about halfway between its steps. Nonetheless, the [[patent val]] is a strong 2.3.5.13.17.23.29.31 [[subgroup]] tuning.

FloraC: Rework theory; adopt template: Factorization

2023-10-30T13:57:20Z

Rework theory; adopt template: Factorization

← Older revision		Revision as of 13:57, 30 October 2023
Line 2:		Line 2:
	{{EDO intro\|1612}}		{{EDO intro\|1612}}

	1612edo is a strong [[5-limit]] system, ~~providing~~ the tuning for [[quasithird]], [[aluminium]] and [[counterorson]] temperaments.		1612edo is a strong [[5-limit]] system, but it is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]]s [[7/1\|7]] and [[11/1\|11]] are about halfway between its steps. Nonetheless, the [[patent val]] is a strong 2.3.5.13.17.23.29.31 [[subgroup]] tuning.

			It provides a tuning for [[quasithird]], [[aluminium]] and [[counterorson]] temperaments in the 5-limit.

	~~While it is only consistent up to 5-limit, there are higher-limit mappings to be considered. The patent val is a strong 2.3.5.13.17.23.29.31 subgroup tuning.~~
	=== Prime harmonics ===		=== Prime harmonics ===
	{{~~harmonics~~ in equal\|1612}}		{{Harmonics in equal\|1612}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	[[3224edo]], which doubles 1612edo, corrects mapping for 7 and 11.		Since 1612 factors into {{factorization\|1612}}, 1612edo has subset edos {{EDOs\| 2, 4, 13, 26, 31, 52, 62, 124, 403, and 806 }}. [[3224edo]], which doubles 1612edo, corrects the mapping for 7 and 11.

Eliora: I have no idea why I made this mistake or why x31eq put out 1612df as tuning for silicon when it's not even divisible by 14

2023-10-21T14:06:51Z

I have no idea why I made this mistake or why x31eq put out 1612df as tuning for silicon when it's not even divisible by 14

← Older revision		Revision as of 14:06, 21 October 2023
Line 4:		Line 4:
	1612edo is a strong [[5-limit]] system, providing the tuning for [[quasithird]], [[aluminium]] and [[counterorson]] temperaments.		1612edo is a strong [[5-limit]] system, providing the tuning for [[quasithird]], [[aluminium]] and [[counterorson]] temperaments.

	While it is only consistent up to 5-limit, there are higher-limit mappings to be considered~~. 1612df val is the unique system supporting both the [[silicon]] and [[iron]] temperaments~~. The patent val is a strong 2.3.5.13.17.23.29.31 subgroup tuning.		While it is only consistent up to 5-limit, there are higher-limit mappings to be considered. The patent val is a strong 2.3.5.13.17.23.29.31 subgroup tuning.
	=== Prime harmonics ===		=== Prime harmonics ===
	{{harmonics in equal\|1612}}		{{harmonics in equal\|1612}}

Eliora at 14:20, 17 October 2023

2023-10-17T14:20:48Z

← Older revision		Revision as of 14:20, 17 October 2023
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{harmonics in equal\|1612}}		{{harmonics in equal\|1612}}

			=== Subsets and supersets ===
			[[3224edo]], which doubles 1612edo, corrects mapping for 7 and 11.

Eliora: Created page with "{{Infobox ET}} {{EDO intro|1612}} 1612edo is a strong 5-limit system, providing the tuning for quasithird, aluminium and counterorson temperaments. While it..."

2023-10-15T15:14:09Z

Created page with "{{Infobox ET}} {{EDO intro|1612}} 1612edo is a strong 5-limit system, providing the tuning for quasithird, aluminium and counterorson temperaments. While it..."

New page

{{Infobox ET}}
{{EDO intro|1612}}

1612edo is a strong [[5-limit]] system, providing the tuning for [[quasithird]], [[aluminium]] and [[counterorson]] temperaments.

While it is only consistent up to 5-limit, there are higher-limit mappings to be considered. 1612df val is the unique system supporting both the [[silicon]] and [[iron]] temperaments. The patent val is a strong 2.3.5.13.17.23.29.31 subgroup tuning.
=== Prime harmonics ===
{{harmonics in equal|1612}}