Tetrameantone - Revision history

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:28:31Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:28, 29 April 2025
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	[[Category:Tetrameantone\| ]] <!-- main article -->		[[Category:Tetrameantone\| ]] <!-- main article -->
	[[Category:~~Rank~~-2 temperaments]]		[[Category:Non-octave temperaments]]
	~~[[Category:Subgroup temperaments]]~~
	~~[[Category:Nonoctave~~]]
	{{Todo\| review }}		{{Todo\| review }}

FloraC: - parent category

2025-04-28T14:47:02Z

- parent category

← Older revision		Revision as of 14:47, 28 April 2025
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	[[POTE generator]]: ~325/243 = 508.099		[[POTE generator]]: ~325/243 = 508.099

	[[Category:~~Temperaments~~]]		[[Category:Tetrameantone\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
			[[Category:Subgroup temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	~~[[Category:Rank-2 temperaments]]~~
	{{Todo\| review }}		{{Todo\| review }}

Lériendil at 00:06, 20 April 2025

2025-04-20T00:06:15Z

← Older revision		Revision as of 00:06, 20 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
			[[Category:Rank-2 temperaments]]
	{{Todo\| review }}		{{Todo\| review }}

Dummy index: /* b15 & b4p */ link to superflat

2025-01-27T12:42:45Z

b15 & b4p: link to superflat

← Older revision		Revision as of 12:42, 27 January 2025
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	\|}		\|}
	=== b15 & b4p ===		=== b15 & b4p ===
			: ''Temperament being restricted in different directions: [[No-fives subgroup temperaments #Superflat]]''

	Subgroup: 3.5.13		Subgroup: 3.5.13

BudjarnLambeth: For technical information see Subgroup temperaments#Tetrameantone.

2024-10-28T10:44:02Z

For technical information see Subgroup temperaments#Tetrameantone.

← Older revision		Revision as of 10:44, 28 October 2024
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	The '''tetrameantone''' temperament is a [[nonoctave]] [[regular temperament\|temperament]] [[tempering out]] [[81/80]] in the 4.3.5-[[subgroup]]. It is similar to [[meantone]] but repeats at the double octave [[4/1]]. It is generated by [[3/1]] and, like in normal meantone temperament, four of them make a [[5/1]] plus two double octaves.		The '''tetrameantone''' temperament is a [[nonoctave]] [[regular temperament\|temperament]] [[tempering out]] [[81/80]] in the 4.3.5-[[subgroup]]. It is similar to [[meantone]] but repeats at the double octave [[4/1]]. It is generated by [[3/1]] and, like in normal meantone temperament, four of them make a [[5/1]] plus two double octaves.

			For technical information see [[Subgroup temperaments#Tetrameantone]].

	== Interval chain ==		== Interval chain ==

FloraC: More to be reviewed

2024-09-21T19:28:10Z

More to be reviewed

← Older revision		Revision as of 19:28, 21 September 2024
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
			{{Todo\| review }}

FloraC: Rework intro and invert the interval chain since 3/1 and 5/1 (or 5/4) are more recognizable

2024-09-21T19:11:33Z

Rework intro and invert the interval chain since 3/1 and 5/1 (or 5/4) are more recognizable

← Older revision		Revision as of 19:11, 21 September 2024
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	The '''tetrameantone''' temperament is a [[nonoctave]] [[~~meantone~~]] ~~temperament,~~ tempering out ~~the~~ [[81/80]] in the 4.3.5 subgroup ~~and repeating~~ at the double octave [[4/1]]. It is generated by [[4/3]] and, like in normal meantone temperament, 4 of them make a [[8/5]] plus ~~an octave~~.		The '''tetrameantone''' temperament is a [[nonoctave]] [[regular temperament\|temperament]] [[tempering out]] [[81/80]] in the 4.3.5-[[subgroup]]. It is similar to [[meantone]] but repeats at the double octave [[4/1]]. It is generated by [[3/1]] and, like in normal meantone temperament, four of them make a [[5/1]] plus two double octaves.

	== Interval chain ==		== Interval chain ==
			In the following table, odd harmonics 1–5 are '''bolded'''.

	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	! ~~Generators~~		! #
	! Cents ~~(POTE)~~		! Cents*
	! Approximate ~~ratios~~		! Approximate Ratios
	\|-
	~~\| -7~~
	~~\| 1273.671~~
	~~\| 25/12~~
	\|-
	~~\| -6~~
	~~\| 1777.432~~
	~~\| 45/16~~
	\|-
	~~\| -5~~
	~~\| 2281.193~~
	~~\| 15/4~~
	\|-
	~~\| -4~~
	~~\| 384.955~~
	~~\| [[5/4]]~~
	\|-
	~~\| -3~~
	~~\| 888.716~~
	~~\| [[5/3]]~~
	\|-
	~~\| -2~~
	~~\| 1392.477~~
	~~\| 9/4, 20/9~~
	\|-
	~~\| -1~~
	~~\| 1896.239~~
	~~\| [[3/1]]~~
	\|-		\|-
	\| 0		\| 0
	\| 0.000		\| 0.000
	\| [[1/1]]		\| '''1/1'''
	\|-		\|-
	\| 1		\| 1
	\| ~~503~~.~~761~~		\| 1896.239
	\| ~~[[4~~/~~3]]~~		\| '''3/1'''
	\|-		\|-
	\| 2		\| 2
	\| ~~1007~~.~~523~~		\| 1392.477
	\| ~~[[16~~/~~9]]~~, [[9~~/5]]~~		\| 9/4, 20/9
	\|-		\|-
	\| 3		\| 3
	\| ~~1511~~.~~284~~		\| 888.716
	\| 12/5		\| 5/3
	\|-		\|-
	\| 4		\| 4
	\| ~~2015~~.~~045~~		\| 384.955
	\| 16/5		\| '''5/4'''
	\|-		\|-
	\| 5		\| 5
	\| ~~118~~.~~807~~		\| 2281.193
	\| ~~[[16~~/~~15]]~~		\| 15/4
	\|-		\|-
	\| 6		\| 6
	\| ~~622~~.~~568~~		\| 1777.432
	\| ~~[[64~~/~~45]]~~		\| 45/16
	\|-		\|-
	\| 7		\| 7
	\| ~~1126~~.~~329~~		\| 1273.671
	\| ~~[[48~~/~~25]]~~		\| 25/12
	\|}		\|}
			<nowiki>*</nowiki> in 4.3.5-subgroup POTE tuning

	== Tetrameantone on tritave ==		== Tetrameantone on tritave ==
	Tritave-repeating tetrameantone (3.4.5 subgroup) is made by cutting off the 4/3 interval range of the tetratave scale. extension will start at 3.4.5.14 subgroup. If we want strict no-twos subgroup, will be 3.5.13.		Tritave-repeating tetrameantone (3.4.5 subgroup) is made by cutting off the 4/3 interval range of the tetratave scale. extension will start at 3.4.5.14 subgroup. If we want strict no-twos subgroup, will be 3.5.13.

FloraC: Why did you document an interval in a temperament page??

2024-09-21T18:57:23Z

Why did you document an interval in a temperament page??

@@ Line 160: / Line 160: @@
 [[POTE generator]]: ~325/243 = 508.099
 [[Category:Temperaments]]
 [[Category:Nonoctave]]

Dummy index: /* 531441/528125 */

2024-09-21T14:06:40Z

531441/528125

← Older revision		Revision as of 14:06, 21 September 2024
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	Tempering out this comma means equating a stack of two 325/243 (tridecimal marvelous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. flattone.		Tempering out this comma means equating a stack of two 325/243 (tridecimal marvelous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. flattone.
	==== Etymology ====		==== Etymology ====
	The name "dinos" is proposed by Dummy index in 2024. It means: "miNOr Seventh is divided into 2 equal parts".		The name "dinos" is proposed by Dummy index in 2024. It means: "miNOr Seventh is divided into 2 equal parts". The same argument holds for 3136/3125 = (9/5)/(75/56)<sup>2</sup> (hemimean comma) and 589824/588245 = (9/5)/(343/256)^2 (hewuermera comma), but the comma is no-twos and requires only one additional prime base (3.5 for 9/5 and additional .13 for the comma).

	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

Dummy index: /* 531441/528125 */

2024-09-21T12:40:53Z

531441/528125

← Older revision		Revision as of 12:40, 21 September 2024
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	\| Ratio = 531441/528125		\| Ratio = 531441/528125
	\| Name = dinos comma		\| Name = dinos comma
			\| Color name = L3uug^51, lathuthuquingu 1sn
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''531441/528125''', the '''dinos comma''', is a small 13-limit comma. It can be expressed as (9/5)/(325/243)<sup>2</sup>.		'''531441/528125''', the '''dinos comma''', is a small 13-limit comma. It can be expressed as (9/5)/(325/243)<sup>2</sup>, (9/5)/(4/3)<sup>2</sup>/(325/324)<sup>2</sup> and (81/80)/(325/324)<sup>2</sup>, among other expressions.
	==== Temperaments ====		==== Temperaments ====
	Tempering out this comma means equating two 325/243 (tridecimal marvelous fourth) with 9/5. This comma is ~~included~~ in some 13-limit ~~temeraments~~, e.g. flattone.		Tempering out this comma means equating a stack of two 325/243 (tridecimal marvelous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. flattone.
	==== Etymology ====		==== Etymology ====
	The name "dinos" is proposed by Dummy index in 2024. It means: "miNOr Seventh is divided into 2 equal parts".		The name "dinos" is proposed by Dummy index in 2024. It means: "miNOr Seventh is divided into 2 equal parts".