2edt - Revision history

Squib: /* Harmonics */added more columns so that harmonic 13 is shown, since it is mentioned right above

2026-03-06T04:34:56Z

Harmonics: added more columns so that harmonic 13 is shown, since it is mentioned right above

← Older revision		Revision as of 04:34, 6 March 2026
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|2\|3\|1}}		{{Harmonics in equal\|2\|3\|1\|columns = 14}}

	== Relationship to octave temperaments ==		== Relationship to octave temperaments ==
	One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as [[monzismic]].		One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as [[monzismic]].

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:21:52Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:21, 1 August 2025
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	== Relationship to octave temperaments ==		== Relationship to octave temperaments ==
	One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as [[monzismic]].		One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as [[monzismic]].

	~~[[Category:Edonoi]]~~

Fredg999 category edits: Removing from Category:Edt using Cat-a-lot

2025-07-31T15:31:29Z

Removing from Category:Edt using Cat-a-lot

← Older revision		Revision as of 15:31, 31 July 2025
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	One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as [[monzismic]].		One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as [[monzismic]].

	~~[[Category:Edt]]~~
	[[Category:Edonoi]]		[[Category:Edonoi]]

ArrowHead294 at 19:10, 20 February 2025

2025-02-20T19:10:13Z

← Older revision		Revision as of 19:10, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Mitigate the silly trivial statements. Switch to integer harmonics for the table

2024-04-28T12:34:43Z

Mitigate the silly trivial statements. Switch to integer harmonics for the table

← Older revision		Revision as of 12:34, 28 April 2024
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	== Theory ==		== Theory ==

	As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5.		As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5.

	Since [[26/15]] is a [[convergent]] of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma.		Since [[26/15]] is a [[convergent]] of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma.

	~~One step of 2edt is close to the optimal TE generator of [[Very high accuracy temperaments\|monzismic temperament]], which tempers out~~ {{~~monzo~~\|~~54 -37~~ 2}}~~, the monzisma.~~		=== Harmonics ===
			{{Harmonics in equal\|2\|3\|1}}

	==~~=Odd harmonics=~~==		== Relationship to octave temperaments ==
	~~{{Harmonics in equal\|~~2~~\|3\|1\|intervals=odd}}~~		One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as [[monzismic]].

	[[Category:Edt]]		[[Category:Edt]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

Akselai at 12:01, 28 April 2024

2024-04-28T12:01:23Z

← Older revision		Revision as of 12:01, 28 April 2024
Line 2:		Line 2:
	{{EDO intro}}		{{EDO intro}}

	=== Theory ===		== Theory ==

	As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5.		As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5.

	Since [[26/15]] is a convergent of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma.		Since [[26/15]] is a [[convergent]] of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma.

	One step of 2edt is close to the optimal TE generator of [[Very high accuracy temperaments\|monzismic temperament]], which tempers out {{monzo\|54 -37 2}}, the monzisma.		One step of 2edt is close to the optimal TE generator of [[Very high accuracy temperaments\|monzismic temperament]], which tempers out {{monzo\|54 -37 2}}, the monzisma.

Akselai: clean up

2024-04-28T09:28:15Z

clean up

← Older revision		Revision as of 09:28, 28 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''2EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1\|tritave]] into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out [[27/25]], equating 5/3 with 9/5.		{{EDO intro}}

	==~~Factoids about 2EDT~~==		=== Theory ===
	~~[[26/15]] and 45/26 are [[Nearest just interval\|good rational representations]] of the square root of 3.~~

	~~2EDT~~ is ~~closely related~~ to the [[Very high accuracy temperaments\|monzismic temperament]], which tempers out \|54 -37 2~~>~~, the monzisma.		As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5.

			Since [[26/15]] is a convergent of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma.

			One step of 2edt is close to the optimal TE generator of [[Very high accuracy temperaments\|monzismic temperament]], which tempers out {{monzo\|54 -37 2}}, the monzisma.

			===Odd harmonics===
			{{Harmonics in equal\|2\|3\|1\|intervals=odd}}

	[[Category:Edt]]		[[Category:Edt]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

Plumtree: Infobox ET added

2022-10-05T19:41:26Z

Infobox ET added

← Older revision		Revision as of 19:41, 5 October 2022
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			{{Infobox ET}}
	'''2EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1\|tritave]] into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out [[27/25]], equating 5/3 with 9/5.		'''2EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1\|tritave]] into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out [[27/25]], equating 5/3 with 9/5.

Bootmii: the simplest no-twos comma is 27/25 and 2edt tempers it out

2022-03-07T00:49:19Z

the simplest no-twos comma is 27/25 and 2edt tempers it out

← Older revision		Revision as of 00:49, 7 March 2022
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	'''2EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1\|tritave]] into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out [[4/~~3]] as well as [[1edo~~]].		'''2EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1\|tritave]] into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out [[27/25]], equating 5/3 with 9/5.

	==Factoids about 2EDT==		==Factoids about 2EDT==

Xenllium: Created page with "'''2EDT''', if the attempt is made to use it as an actual scale, would divide the tritave into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as..."

2019-02-01T08:16:52Z

Created page with "'''2EDT''', if the attempt is made to use it as an actual scale, would divide the tritave into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as..."

New page

'''2EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1|tritave]] into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out [[4/3]] as well as [[1edo]].

==Factoids about 2EDT==
[[26/15]] and 45/26 are [[Nearest just interval|good rational representations]] of the square root of 3.

2EDT is closely related to the [[Very high accuracy temperaments|monzismic temperament]], which tempers out |54 -37 2>, the monzisma.

[[Category:Edt]]
[[Category:Edonoi]]