1749edo - Revision history

Eliora at 00:04, 12 September 2026

2026-09-12T00:04:46Z

← Older revision		Revision as of 00:04, 12 September 2026
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1749}}		{{Harmonics in equal\|1749}}

			=== Subsets and supersets ===
			Since 1749 factors as {{Factorization\|1749}}, 1749edo has subset edos {{EDOs\|1, 3, 11, 33, 53, 159, 583}}.

			[[3498edo]], which divides the step in two, improves on the harmonic 11 and is consistent in the [[25-odd-limit]].

FloraC: Fix misinformation; improve links; - redundant category

2026-09-11T08:31:58Z

Fix misinformation; improve links; - redundant category

← Older revision		Revision as of 08:31, 11 September 2026
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	== Theory ==		== Theory ==
	1749edo is [[consistent]] in the 7-odd-limit with strong approximations, however the approximation to the 11th harmonic is poor. The most straightforward extension is the 2.3.5.7.13.17.31 subgroup.		1749edo is [[consistent]] in the [[9-odd-limit]] with strong approximations; however the approximation to the [[11/1\|11th harmonic]] is poor. The most straightforward extension is the 2.3.5.7.13.17.31 subgroup.

	It ~~provides~~ the optimal ~~patent val~~ for the [[aemilic]] temperament in the [[7-limit]], as a multiple of [[159edo]].		It is part of the [[optimal ET sequence]] for the [[aemilic]] temperament in the [[7-limit]], as a multiple of [[159edo]].

	1749e val is the most straightforward extension into the 11-limit, as it is better tuned than the patent val and strongly supports 11-limit [[aemilic]] extension.		1749e val is the most straightforward extension into the 11-limit, as it is better tuned than the patent val and strongly supports 11-limit [[aemilic]] extension.

			=== Prime harmonics ===
	{{Harmonics in equal\|1749}}		{{Harmonics in equal\|1749}}

	~~[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->~~

Eliora: /* Theory */

2026-09-10T19:25:18Z

Theory

← Older revision		Revision as of 19:25, 10 September 2026
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	== Theory ==		== Theory ==
	~~This EDO has a consistency level of only 9~~, ~~nevertheless, a reasonable representation in~~ the 2.3.5.7.13.17 subgroup ~~exists through the patent val~~.		1749edo is [[consistent]] in the 7-odd-limit with strong approximations, however the approximation to the 11th harmonic is poor. The most straightforward extension is the 2.3.5.7.13.17.31 subgroup.

	It provides the optimal patent val for the [[aemilic]] temperament in the [[7-limit]], as a multiple of [[159edo]].		It provides the optimal patent val for the [[aemilic]] temperament in the [[7-limit]], as a multiple of [[159edo]].

			1749e val is the most straightforward extension into the 11-limit, as it is better tuned than the patent val and strongly supports 11-limit [[aemilic]] extension.

	{{Harmonics in equal\|1749}}		{{Harmonics in equal\|1749}}

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

Eliora at 18:54, 10 September 2026

2026-09-10T18:54:25Z

← Older revision		Revision as of 18:54, 10 September 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	This EDO has a consistency level of only 9, nevertheless, ~~it's well-behaved~~ in the 2.3.5.7.13.17 subgroup.		This EDO has a consistency level of only 9, nevertheless, a reasonable representation in the 2.3.5.7.13.17 subgroup exists through the patent val.

			It provides the optimal patent val for the [[aemilic]] temperament in the [[7-limit]], as a multiple of [[159edo]].

	{{Harmonics in equal\|1749}}		{{Harmonics in equal\|1749}}

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

Francium: changed EDO intro to ED intro

2025-02-19T18:28:32Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:28, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1749~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Aura: Created page with "{{Infobox ET}} {{EDO intro|1749}} == Theory == This EDO has a consistency level of only 9, nevertheless, it's well-behaved in the 2.3.5.7.13.17 subgroup. {{Harmonics in equa..."

2022-12-22T10:15:30Z

Created page with "{{Infobox ET}} {{EDO intro|1749}} == Theory == This EDO has a consistency level of only 9, nevertheless, it's well-behaved in the 2.3.5.7.13.17 subgroup. {{Harmonics in equa..."

New page

{{Infobox ET}}
{{EDO intro|1749}}

== Theory ==
This EDO has a consistency level of only 9, nevertheless, it's well-behaved in the 2.3.5.7.13.17 subgroup.

{{Harmonics in equal|1749}}

[[Category:Equal divisions of the octave|####]]