User:Moremajorthanmajor/4wtn - Revision history

FloraC: Text replacement - "{{todo|clarify|unify precision|inline=1}}" to ""

2025-09-01T09:31:27Z

Text replacement - "{{todo|clarify|unify precision|inline=1}}" to ""

← Older revision		Revision as of 09:31, 1 September 2025
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	[[Category:Well tempered nonet]]		[[Category:Well tempered nonet]]

	~~{{todo\|clarify\|unify precision\|inline=1}}~~

Sintel: Sintel moved page 4wtn to User:Moremajorthanmajor/4wtn: move all wtn subpages

2025-03-31T17:15:30Z

Sintel moved page 4wtn to User:Moremajorthanmajor/4wtn: move all wtn subpages

← Older revision	Revision as of 17:15, 31 March 2025
(No difference)

Xenwolf: cat+todo

2021-06-02T06:56:05Z

cat+todo

← Older revision		Revision as of 06:56, 2 June 2021
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	\|''1501.955''		\|''1501.955''
	\|}		\|}

			[[Category:Well tempered nonet]]

			{{todo\|clarify\|unify precision\|inline=1}}

Moremajorthanmajor at 23:48, 1 June 2021

2021-06-01T23:48:27Z

← Older revision		Revision as of 23:48, 1 June 2021
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	'''4WTN''', if the attempt is made to use it as an actual scale, would alternate dividing the [[just perfect fifth]] into two equal parts, each of size 350.9775 cents, which is to say sqrt(3/2) as a frequency ratio, alternating these with two equal steps of another interval between 300 and 400 cents. This will create an interval exactly halfway between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.		'''4WTN''', if the attempt is made to use it as an actual scale, would optimally alternate dividing the [[just perfect fifth]] into two equal parts, each of size 350.9775 cents, which is to say sqrt(3/2) as a frequency ratio, alternating these with two equal steps of another interval between 300 and 400 cents. This will create an interval exactly halfway between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.

	==Factoids about 4WTN==		==Factoids about 4WTN==

Moremajorthanmajor at 18:30, 29 May 2021

2021-05-29T18:30:49Z

← Older revision		Revision as of 18:30, 29 May 2021
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	'''4WTN''', if the attempt is made to use it as an actual scale, would alternate dividing the [[just perfect fifth]] into two equal parts, each of size 350.9775 cents, which is to say sqrt(3/2) as a frequency ratio, ~~and~~ two equal steps of another interval between 300 and 400 cents. This will create an interval exactly halfway between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.		'''4WTN''', if the attempt is made to use it as an actual scale, would alternate dividing the [[just perfect fifth]] into two equal parts, each of size 350.9775 cents, which is to say sqrt(3/2) as a frequency ratio, alternating these with two equal steps of another interval between 300 and 400 cents. This will create an interval exactly halfway between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.

	==Factoids about 4WTN==		==Factoids about 4WTN==

Moremajorthanmajor at 02:57, 29 May 2021

2021-05-29T02:57:38Z

← Older revision		Revision as of 02:57, 29 May 2021
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	!''“fifth” 2 = 800¢''		!''“fifth” 2 = 800¢''
	\|-		\|-
	\|1		!1
	\| colspan="5" \|350.9775		! colspan="5" \|350.9775
	\|-		\|-
	\|2		!2
	\| colspan="5" \|701.955		! colspan="5" \|701.955
	\|-		\|-
	\|3		\|3

Moremajorthanmajor at 00:55, 29 May 2021

2021-05-29T00:55:29Z

← Older revision		Revision as of 00:55, 29 May 2021
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	'''4WTN''', if the attempt is made to use it as an actual scale, would alternate dividing the [[just perfect fifth]] into two equal parts, each of size 350.9775 cents, which is to say sqrt(3/2) as a frequency ratio, and two equal steps of another interval between 300 and 400 cents. This will create ~~three equally-spaced intervals~~ between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.		'''4WTN''', if the attempt is made to use it as an actual scale, would alternate dividing the [[just perfect fifth]] into two equal parts, each of size 350.9775 cents, which is to say sqrt(3/2) as a frequency ratio, and two equal steps of another interval between 300 and 400 cents. This will create an interval exactly halfway between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.

	==Factoids about 4WTN==		==Factoids about 4WTN==

Moremajorthanmajor: Created page with "'''4WTN''', if the attempt is made to use it as an actual scale, would alternate dividing the just perfect fifth into two equal parts, each of size 350.9775 cents, which i..."

2021-05-28T01:05:20Z

Created page with "'''4WTN''', if the attempt is made to use it as an actual scale, would alternate dividing the just perfect fifth into two equal parts, each of size 350.9775 cents, which i..."

New page

'''4WTN''', if the attempt is made to use it as an actual scale, would alternate dividing the [[just perfect fifth]] into two equal parts, each of size 350.9775 cents, which is to say sqrt(3/2) as a frequency ratio, and two equal steps of another interval between 300 and 400 cents. This will create three equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. If we want to consider it to be a temperament, it tempers out [[6/5]], [[9/7]], [[32/27]], and [[81/80]] in the patent val.

==Factoids about 4WTN==
60/49 and 49/40 are [[Nearest just interval|good rational representations]] of the square root of 3/2.

The best tunings of 4WTN are closely related to the [[Breedsmic temperaments|hemififths temperament]], which tempers out 2401/2400 and 5120/5103 in the 7-limit.

== Intervals ==
{| class="wikitable"
|+
!
!''“fifth” 2 = 600¢''
!“nonet” = 1351.429¢
!step 2 = 11/9
!“nonet” = 1460¢
!''“fifth” 2 = 800¢''
|-
|1
| colspan="5" |350.9775
|-
|2
| colspan="5" |701.955
|-
|3
|''1001.955''
|1026.692
|1049.363
|1080.9775
|''1101.955''
|-
|4
|''1301.955''
|1351.429
|1396.771
|1460
|''1501.955''
|}