8edt - Revision history

Xenllium at 09:46, 26 February 2026

2026-02-26T09:46:38Z

← Older revision		Revision as of 09:46, 26 February 2026
Line 15:		Line 15:

	== See also ==		== See also ==
	* [~~https://en.xen.wiki/w/Equal-step_tuning#~~Alpha-beta~~-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions~~]		* [[Alpha, beta, and gamma family of equal divisions]]

	[[Category:Macrotonal]]		[[Category:Macrotonal]]

Contribution: /* See also */

2025-10-28T01:45:21Z

Contribution at 01:43, 28 October 2025

2025-10-28T01:43:51Z

← Older revision		Revision as of 01:43, 28 October 2025
Line 13:		Line 13:
	== Interval table ==		== Interval table ==
	{{Interval table}}		{{Interval table}}

			=== See also ===
			* [https://en.xen.wiki/w/Equal-step_tuning#Alpha-beta-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions]

	[[Category:Macrotonal]]		[[Category:Macrotonal]]

Lériendil at 18:42, 8 March 2025

2025-03-08T18:42:41Z

← Older revision		Revision as of 18:42, 8 March 2025
Line 5:		Line 5:
	As the double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactoring\|enfactored]] in the 3.5.7 subgroup.		As the double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactoring\|enfactored]] in the 3.5.7 subgroup.

	What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.		What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents, which has the side effect of bringing the step size slightly closer to [[8/7]].

	=== Harmonics ===		=== Harmonics ===

Akselai at 09:16, 20 May 2024

2024-05-20T09:16:28Z

← Older revision		Revision as of 09:16, 20 May 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	As a double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactoring\|enfactored]] in the 3.5.7 subgroup.		As the double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactoring\|enfactored]] in the 3.5.7 subgroup.

	What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.		What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.

FloraC: Section title; fix a link

2024-05-20T07:58:43Z

Section title; fix a link

← Older revision		Revision as of 07:58, 20 May 2024
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	As a double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactored]] in the 3.5.7 subgroup.		== Theory ==
			As a double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactoring\|enfactored]] in the 3.5.7 subgroup.

	What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.		What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.

	== Harmonics ==		=== Harmonics ===
	{{Harmonics in equal\|8\|3\|1\|}}		{{Harmonics in equal\|8\|3\|1\|}}
	{{Harmonics in equal\|8\|3\|1\|intervals=prime}}		{{Harmonics in equal\|8\|3\|1\|intervals=prime}}

FloraC: 8edt : 4edt :: 10edo : 5edo. -redundant categories

2024-05-20T07:58:04Z

8edt : 4edt :: 10edo : 5edo. -redundant categories

← Older revision		Revision as of 07:58, 20 May 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	~~{{todo\|clarify\|comment = why is 8edt the analog of 10edo? 8edt does not support 4L 5s (3/1-equivalent).\|inline=1}}~~		As a double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactored]] in the 3.5.7 subgroup.

	As a double of [[~~4edt\|~~4edt]], it is the analog of [[10edo]] ~~for~~ [[~~4L 5s (3/1-equivalent)\|Lambda~~]]~~-based systems~~. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactored]] in the 3.5.7 subgroup.

	What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.		What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.
Line 15:		Line 13:
	{{Interval table}}		{{Interval table}}

	[[Category:~~edt]]~~		[[Category:Macrotonal]]
	~~[[Category:tritave]]~~
	~~[[category:macrotonal~~]]

Akselai: clean up...?

2024-05-20T00:43:15Z

clean up...?

← Older revision		Revision as of 00:43, 20 May 2024
Line 2:		Line 2:
	{{EDO intro}}		{{EDO intro}}

	{{todo\|clarify\|comment = why is 8edt the analog of 10edo? 8edt does not support 4L 5s (3/1-equivalent).}}		{{todo\|clarify\|comment = why is 8edt the analog of 10edo? 8edt does not support 4L 5s (3/1-equivalent).\|inline=1}}

	As a double of [[4edt\|4edt]], it is the analog of [[10edo]] for [[4L 5s (3/1-equivalent)\|Lambda]]-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactored]] in the 3.5.7 subgroup.		As a double of [[4edt\|4edt]], it is the analog of [[10edo]] for [[4L 5s (3/1-equivalent)\|Lambda]]-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactored]] in the 3.5.7 subgroup.

Akselai: clean up...?

2024-05-20T00:42:05Z

clean up...?

← Older revision		Revision as of 00:42, 20 May 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
			{{EDO intro}}

	'''8 equal divisions of the tritave''' ('''8edt''') is the [[nonoctave]] [[tuning system]] derived by dividing the [[tritave]] (3/1) into 13 equal steps of 237.744 [[cent]]s each, or the eighth root of 3. As the double of [[4edt\|~~4edt]], harmonically, it~~ is the analog of [[10edo~~]] for [[~~4L 5s (3/1-equivalent)~~\|Lambda]]-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in 5edo~~.		{{todo\|clarify\|comment = why is 8edt the analog of 10edo? 8edt does not support 4L 5s (3/1-equivalent).}}

	What it does introduce are flat ~~pseudooctaves~~ and sharp 3:2's, making it related to 5edo melodically.		As a double of [[4edt\|4edt]], it is the analog of [[10edo]] for [[4L 5s (3/1-equivalent)\|Lambda]]-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactored]] in the 3.5.7 subgroup.

			What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.

			== Harmonics ==
			{{Harmonics in equal\|8\|3\|1\|}}
			{{Harmonics in equal\|8\|3\|1\|intervals=prime}}

	== Interval table ==		== Interval table ==
	{{Interval table}}		{{Interval table}}

	~~== Prime harmonics ==~~
	~~{{Harmonics in equal\|8\|3\|1\|intervals=prime}}~~

	[[Category:edt]]		[[Category:edt]]
	[[Category:tritave]]		[[Category:tritave]]
	[[category:macrotonal]]		[[category:macrotonal]]

CompactStar: No it is not lol

2024-02-27T17:35:21Z

No it is not lol

← Older revision		Revision as of 17:35, 27 February 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}

	'''8 equal divisions of the tritave''' ('''8edt''') is the [[nonoctave]] [[tuning system]] derived by dividing the [[tritave]] (3/1) into 13 equal steps of 237.744 [[cent]]s each, or the eighth root of 3~~. It is best known as the equal-tempered version of the [[Bohlen-Pierce]] scale~~. As the double of [[4edt\|4edt]], harmonically, it is the analog of [[10edo]] for [[4L 5s (3/1-equivalent)\|Lambda]]-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in 5edo.		'''8 equal divisions of the tritave''' ('''8edt''') is the [[nonoctave]] [[tuning system]] derived by dividing the [[tritave]] (3/1) into 13 equal steps of 237.744 [[cent]]s each, or the eighth root of 3. As the double of [[4edt\|4edt]], harmonically, it is the analog of [[10edo]] for [[4L 5s (3/1-equivalent)\|Lambda]]-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in 5edo.

	What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically.		What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically.

← Older revision		Revision as of 01:45, 28 October 2025
Line 14:		Line 14:
	{{Interval table}}		{{Interval table}}

	=== See also ===		== See also ==
	* [https://en.xen.wiki/w/Equal-step_tuning#Alpha-beta-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions]		* [https://en.xen.wiki/w/Equal-step_tuning#Alpha-beta-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions]

	[[Category:Macrotonal]]		[[Category:Macrotonal]]