Breedsmic–syntonic equivalence continuum - Revision history

Xenllium at 12:39, 9 January 2026

2026-01-09T12:39:54Z

← Older revision		Revision as of 12:39, 9 January 2026
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	Comma list: {{monzo\| 146 34 59 -120 }}		Comma list: {{monzo\| 146 34 59 -120 }}

	POTE generators: 1901.9549, -775.6679		POTE generators: ~3 = 1901.9549, 775.6679

	Mapping: [{{val\| 1 0 26 14 }}, {{val\| 0 1 34 17 }}, {{val\| 0 0 120 59 }}]		Mapping: [{{val\| 1 0 26 14 }}, {{val\| 0 1 34 17 }}, {{val\| 0 0 -120 -59 }}]

	{{Optimal ET sequence\|legend=1\| 1677, 5014, 6691, 41854, 43531, 46868, 48545, 50222, 55236, 97090 }}		{{Optimal ET sequence\|legend=1\| 1677, 5014, 6691, 41854, 43531, 46868, 48545, 50222, 55236, 97090 }}

	~~[http~~:~~//x31eq~~.~~com/cgi-bin/rt.cgi?ets=1677_6691_41854&limit=7 The temperament finder -~~ 7~~-limit 1677 & 6691 & 41854]~~		Badness (Sintel): 475.7

	== ~~34p~~ & 31 & 14c ==		== 34 & 31 & 14c ==
	Comma list: {{monzo\| -13 7 -4 4 }} = 5250987/5120000		Comma list: {{monzo\| -13 7 -4 4 }} = 5250987/5120000

	POTE generators: -425.3382, ~5 = 2785.5671		POTE generators: ~80/63 = 425.3382, ~5 = 2785.5671

	Mapping: [{{val\| 1 3 0 -2 }}, {{val\| 0 4 0 -7 }}, {{val\| 0 0 1 1 }}]		Mapping: [{{val\| 1 3 0 -2 }}, {{val\| 0 -4 0 7 }}, {{val\| 0 0 1 1 }}]

	{{Optimal ET sequence\|legend=1\| 3, 14c, 17c, 17d, 20c, 31, 34, 45, 62, 65 }}		{{Optimal ET sequence\|legend=1\| 3, 14c, 17c, 17d, 20c, 31, 34, 45, 62, 65 }}

	~~[http~~:~~//x31eq~~.~~com/cgi-bin/rt.cgi?ets=34p_31_14c&limit=7 The temperament finder - 7-limit 34p & 31 & 14c]~~		Badness (Sintel): 19.984

	[[Category:Squares]]		[[Category:Squares]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

FloraC: Cleanup. Mark as mathematical interest

2025-08-27T13:11:14Z

Cleanup. Mark as mathematical interest

← Older revision		Revision as of 13:11, 27 August 2025
Line 1:		Line 1:
			{{Mathematical interest}}

	The '''breedsmic–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit temperament families which equate a number of [[2401/2400\|breedsmas (2401/2400)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Meantone family#Squares\|squares]] temperament. In addition, 81/80 and 2401/2400 are the smallest 5-limit and 7-limit [[superparticular]] intervals to be tempered out by [[31edo]].		The '''breedsmic–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit temperament families which equate a number of [[2401/2400\|breedsmas (2401/2400)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Meantone family#Squares\|squares]] temperament. In addition, 81/80 and 2401/2400 are the smallest 5-limit and 7-limit [[superparticular]] intervals to be tempered out by [[31edo]].

Line 14:		Line 16:
	\|-		\|-
	\| −4		\| −4
	\| 217 &~~amp;~~ 31 &~~amp;~~ 14c		\| 217 & 31 & 14c
	\|		\|
	\| {{~~monzo~~\|-24 0 -9 16}}		\| {{Monzo\| -24 0 -9 16 }}
	\|-		\|-
	\| −3		\| −3
	\| 159 &~~amp;~~ 31 &~~amp;~~ 14c		\| 159 & 31 & 14c
	\|		\|
	\| {{~~monzo~~\|-19 1 -7 12}}		\| {{Monzo\| -19 1 -7 12 }}
	\|-		\|-
	\| −2		\| −2
	\| 87 &~~amp;~~ 31 &~~amp;~~ 14c		\| 87 & 31 & 14c
	\| 51883209/51200000		\| 51883209/51200000
	\| {{~~monzo~~\|-14 2 -5 8}}		\| {{Monzo\| -14 2 -5 8 }}
	\|-		\|-
	\| −1		\| −1
	\| [[Squalentine]]		\| [[Squalentine]]
	\| [[64827/64000]]		\| [[64827/64000]]
	\| {{~~monzo~~\|-9 3 -3 4}}		\| {{Monzo\| -9 3 -3 4 }}
	\|-		\|-
	\| 0		\| 0
	\| [[~~Didymus rank three family\|~~Didymus]]		\| [[Didymus]]
	\| [[81/80]]		\| [[81/80]]
	\| {{~~monzo~~\|-4 4 -1}}		\| {{Monzo\| -4 4 -1 }}
	\|-		\|-
	\| 1		\| 1
	\| [[~~Nuwell family\|~~Nuwell]]		\| [[Nuwell]]
	\| [[2430/2401]]		\| [[2430/2401]]
	\| {{~~monzo~~\|1 5 1 -4}}		\| {{Monzo\| 1 5 1 -4 }}
	\|-		\|-
	\| 2		\| 2
	\| 14c &~~amp;~~ 31 &~~amp;~~ 80		\| 14c & 31 & 80
	\| 5832000/5764801		\| 5832000/5764801
	\| {{~~monzo~~\|6 6 3 -8}}		\| {{Monzo\| 6 6 3 -8 }}
	\|-		\|-
	\| 3		\| 3
	\| 14c &~~amp;~~ 31 &~~amp;~~ 152		\| 14c & 31 & 152
	\| 13996800000/13841287201		\| 13996800000/13841287201
	\| {{~~monzo~~\|11 7 5 -12}}		\| {{Monzo\| 11 7 5 -12 }}
	\|-		\|-
	\| 4		\| 4
	\| 14c &~~amp;~~ 31 &~~amp;~~ 224		\| 14c & 31 & 224
	\|		\|
	\| {{~~monzo~~\|16 8 7 -16}}		\| {{Monzo\| 16 8 7 -16 }}
	\|-		\|-
	\| 5		\| 5
	\| 265 &~~amp;~~ 31 &~~amp;~~ 282		\| 265 & 31 & 282
	\|		\|
	\| {{~~monzo~~\|21 9 9 -20}}		\| {{Monzo\| 21 9 9 -20 }}
	\|-		\|-
	\| 6		\| 6
	\| 14c &~~amp;~~ 31 &~~amp;~~ 323		\| 14c & 31 & 323
	\|		\|
	\| {{~~monzo~~\|26 10 11 -24}}		\| {{Monzo\| 26 10 11 -24 }}
	\|-		\|-
	\| 7		\| 7
	\| 17c &~~amp;~~ 395 &~~amp;~~ 364		\| 17c & 395 & 364
	\|		\|
	\| {{~~monzo~~\|31 11 13 -28}}		\| {{Monzo\| 31 11 13 -28 }}
	\|-		\|-
	\| 8		\| 8
	\| 14c &~~amp;~~ 31 &~~amp;~~ 422		\| 14c & 31 & 422
	\|		\|
	\| {{~~monzo~~\|36 12 15 -32}}		\| {{Monzo\| 36 12 15 -32 }}
	\|-		\|-
	\| …		\| …
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	\|-		\|-
	\| 30		\| 30
	\| 1677 &~~amp;~~ 6691 &~~amp;~~ 41854		\| 1677 & 6691 & 41854
	\|		\|
	\| {{~~monzo~~\|146 34 59 -120}}		\| {{Monzo\| 146 34 59 -120 }}
	\|-		\|-
	\| …		\| …
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	\| [[Breedsmic temperaments\|Breedsmic]]		\| [[Breedsmic temperaments\|Breedsmic]]
	\| [[2401/2400]]		\| [[2401/2400]]
	\| {{~~monzo~~\| -5 -1 -2 4}}		\| {{Monzo\| -5 -1 -2 4 }}
	\|}		\|}

	Examples of temperaments with fractional values of ''n'':		Examples of temperaments with fractional values of ''n'':
	* ~~34p~~ & 31 & 14c ({{nowrap\|''n'' {{=}} −{{frac\|1\|2}} {{=}} −0.5}})		* 34 & 31 & 14c ({{nowrap\|''n'' {{=}} −{{frac\|1\|2}} {{=}} −0.5}})
	* [[Subgroup temperaments#Skwares 3\|Skwares]] ({{nowrap\|''n'' {{=}} {{frac\|1\|2}} {{=}} 0.5}})		* [[Subgroup temperaments#Skwares 3\|Skwares]] ({{nowrap\|''n'' {{=}} {{frac\|1\|2}} {{=}} 0.5}})

ArrowHead294 at 22:33, 1 January 2025

2025-01-01T22:33:35Z

← Older revision		Revision as of 22:33, 1 January 2025
Line 1:		Line 1:
	The '''breedsmic–syntonic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of [[2401/2400\|breedsmas (2401/2400)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Meantone family#Squares\|squares]] temperament. In addition, 81/80 and 2401/2400 are the smallest 5-limit and 7-limit [[superparticular]] intervals to be tempered out by [[31edo]].		The '''breedsmic–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit temperament families which equate a number of [[2401/2400\|breedsmas (2401/2400)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Meantone family#Squares\|squares]] temperament. In addition, 81/80 and 2401/2400 are the smallest 5-limit and 7-limit [[superparticular]] intervals to be tempered out by [[31edo]].

	All temperaments in the continuum satisfy {{nowrap\|(2401/2400)<sup>''n''</sup> ~ 81/80}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[Breedsmic temperaments\|breedsmic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by squares (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 29.820259, and temperaments having ''n'' near this value tend to be the most accurate ones.		All temperaments in the continuum satisfy {{nowrap\|(2401/2400)<sup>''n''</sup> ~ 81/80}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[Breedsmic temperaments\|breedsmic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by squares (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 29.820259, and temperaments having ''n'' near this value tend to be the most accurate ones.

ArrowHead294 at 22:32, 1 January 2025

2025-01-01T22:32:47Z

← Older revision		Revision as of 22:32, 1 January 2025
Line 1:		Line 1:
	The '''~~breedsmic-syntonic~~ equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of [[2401/2400\|breedsmas (2401/2400)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Meantone family#Squares\|squares]] temperament. In addition, 81/80 and 2401/2400 are the smallest 5-limit and 7-limit [[superparticular]] intervals to be tempered out by [[31edo]].		The '''breedsmic–syntonic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of [[2401/2400\|breedsmas (2401/2400)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Meantone family#Squares\|squares]] temperament. In addition, 81/80 and 2401/2400 are the smallest 5-limit and 7-limit [[superparticular]] intervals to be tempered out by [[31edo]].

	All temperaments in the continuum satisfy (2401/2400)<sup>''n''</sup> ~ 81/80. Varying ''n'' results in different temperament families listed in the table below. It converges to [[Breedsmic temperaments\|breedsmic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by squares (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 29.~~82025...~~, and temperaments having ''n'' near this value tend to be the most accurate ones.		All temperaments in the continuum satisfy {{nowrap\|(2401/2400)<sup>''n''</sup> ~ 81/80}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[Breedsmic temperaments\|breedsmic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by squares (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 29.820259, and temperaments having ''n'' near this value tend to be the most accurate ones.

	{\| class="wikitable center-1 center-2"		{\| class="wikitable center-1 center-2"
	\|+ Temperament families in the continuum		\|+ style="font-size: 105%;" \| Temperament families in the continuum
	\|-		\|-
	! rowspan="2" \| ''n''		! rowspan="2" \| ''n''
Line 13:		Line 13:
	! Monzo		! Monzo
	\|-		\|-
	\| -4		\| −4
	\| 217 & 31 & 14c		\| 217 & 31 & 14c
	\|		\|
	\| {{monzo\|-24 0 -9 16}}		\| {{monzo\|-24 0 -9 16}}
	\|-		\|-
	\| -3		\| −3
	\| 159 & 31 & 14c		\| 159 & 31 & 14c
	\|		\|
	\| {{monzo\|-19 1 -7 12}}		\| {{monzo\|-19 1 -7 12}}
	\|-		\|-
	\| -2		\| −2
	\| 87 & 31 & 14c		\| 87 & 31 & 14c
	\| 51883209/51200000		\| 51883209/51200000
	\| {{monzo\|-14 2 -5 8}}		\| {{monzo\|-14 2 -5 8}}
	\|-		\|-
	\| -1		\| −1
	\| [[Squalentine]]		\| [[Squalentine]]
	\| [[64827/64000]]		\| [[64827/64000]]
Line 44:		Line 44:
	\|-		\|-
	\| 2		\| 2
	\| 14c & 31 & 80		\| 14c & 31 & 80
	\| 5832000/5764801		\| 5832000/5764801
	\| {{monzo\|6 6 3 -8}}		\| {{monzo\|6 6 3 -8}}
	\|-		\|-
	\| 3		\| 3
	\| 14c & 31 & 152		\| 14c & 31 & 152
	\| 13996800000/13841287201		\| 13996800000/13841287201
	\| {{monzo\|11 7 5 -12}}		\| {{monzo\|11 7 5 -12}}
	\|-		\|-
	\| 4		\| 4
	\| 14c & 31 & 224		\| 14c & 31 & 224
	\|		\|
	\| {{monzo\|16 8 7 -16}}		\| {{monzo\|16 8 7 -16}}
	\|-		\|-
	\| 5		\| 5
	\| 265 & 31 & 282		\| 265 & 31 & 282
	\|		\|
	\| {{monzo\|21 9 9 -20}}		\| {{monzo\|21 9 9 -20}}
	\|-		\|-
	\| 6		\| 6
	\| 14c & 31 & 323		\| 14c & 31 & 323
	\|		\|
	\| {{monzo\|26 10 11 -24}}		\| {{monzo\|26 10 11 -24}}
	\|-		\|-
	\| 7		\| 7
	\| 17c & 395 & 364		\| 17c & 395 & 364
	\|		\|
	\| {{monzo\|31 11 13 -28}}		\| {{monzo\|31 11 13 -28}}
	\|-		\|-
	\| 8		\| 8
	\| 14c & 31 & 422		\| 14c & 31 & 422
	\|		\|
	\| {{monzo\|36 12 15 -32}}		\| {{monzo\|36 12 15 -32}}
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	\|-		\|-
	\| 30		\| 30
	\| 1677 & 6691 & 41854		\| 1677 & 6691 & 41854
	\|		\|
	\| {{monzo\|146 34 59 -120}}		\| {{monzo\|146 34 59 -120}}
Line 100:		Line 100:

	Examples of temperaments with fractional values of ''n'':		Examples of temperaments with fractional values of ''n'':
	* 34p & 31 & 14c (''n'' = -1/2 = -0.5)		* 34p & 31 & 14c ({{nowrap\|''n'' {{=}} −{{frac\|1\|2}} {{=}} −0.5}})
	* [[Subgroup temperaments#Skwares 3\|Skwares]] (''n'' = 1/2 = 0.5)		* [[Subgroup temperaments#Skwares 3\|Skwares]] ({{nowrap\|''n'' {{=}} {{frac\|1\|2}} {{=}} 0.5}})

	== 1677 & 6691 & 41854 ==		== 1677 & 6691 & 41854 ==

	Comma list: {{monzo\| 146 34 59 -120 }}		Comma list: {{monzo\| 146 34 59 -120 }}

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	== 34p & 31 & 14c ==		== 34p & 31 & 14c ==

	Comma list: {{monzo\| -13 7 -4 4 }} = 5250987/5120000		Comma list: {{monzo\| -13 7 -4 4 }} = 5250987/5120000

ArrowHead294: ArrowHead294 moved page Breedsmic-syntonic equivalence continuum to Breedsmic–syntonic equivalence continuum

2025-01-01T22:29:56Z

ArrowHead294 moved page Breedsmic-syntonic equivalence continuum to Breedsmic–syntonic equivalence continuum

← Older revision	Revision as of 22:29, 1 January 2025
(No difference)

FloraC: Links

2024-05-29T08:28:14Z

Links

← Older revision		Revision as of 08:28, 29 May 2024
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	\|-		\|-
	\| -1		\| -1
	\| [[~~Squalentine temperament\|~~Squalentine]]		\| [[Squalentine]]
	\| [[64827/64000]]		\| [[64827/64000]]
	\| {{monzo\|-9 3 -3 4}}		\| {{monzo\|-9 3 -3 4}}
	\|-		\|-
	\| 0		\| 0
	\| [[~~Meantone~~ family\|~~Meantone~~]]		\| [[Didymus rank three family\|Didymus]]
	\| [[81/80]]		\| [[81/80]]
	\| {{monzo\|-4 4 -1}}		\| {{monzo\|-4 4 -1}}

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:45:11Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 18:45, 7 May 2023
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	Mapping: [{{val\| 1 0 26 14 }}, {{val\| 0 1 34 17 }}, {{val\| 0 0 120 59 }}]		Mapping: [{{val\| 1 0 26 14 }}, {{val\| 0 1 34 17 }}, {{val\| 0 0 120 59 }}]

	{{~~Val list~~\|legend=1\| 1677, 5014, 6691, 41854, 43531, 46868, 48545, 50222, 55236, 97090 }}		{{Optimal ET sequence\|legend=1\| 1677, 5014, 6691, 41854, 43531, 46868, 48545, 50222, 55236, 97090 }}

	[http://x31eq.com/cgi-bin/rt.cgi?ets=1677_6691_41854&limit=7 The temperament finder - 7-limit 1677 & 6691 & 41854]		[http://x31eq.com/cgi-bin/rt.cgi?ets=1677_6691_41854&limit=7 The temperament finder - 7-limit 1677 & 6691 & 41854]
Line 123:		Line 123:
	Mapping: [{{val\| 1 3 0 -2 }}, {{val\| 0 4 0 -7 }}, {{val\| 0 0 1 1 }}]		Mapping: [{{val\| 1 3 0 -2 }}, {{val\| 0 4 0 -7 }}, {{val\| 0 0 1 1 }}]

	{{~~Val list~~\|legend=1\| 3, 14c, 17c, 17d, 20c, 31, 34, 45, 62, 65 }}		{{Optimal ET sequence\|legend=1\| 3, 14c, 17c, 17d, 20c, 31, 34, 45, 62, 65 }}

	[http://x31eq.com/cgi-bin/rt.cgi?ets=34p_31_14c&limit=7 The temperament finder - 7-limit 34p & 31 & 14c]		[http://x31eq.com/cgi-bin/rt.cgi?ets=34p_31_14c&limit=7 The temperament finder - 7-limit 34p & 31 & 14c]

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

2022-02-28T20:06:45Z

Removing from Category:Temperament using Cat-a-lot

← Older revision		Revision as of 20:06, 28 February 2022
Line 128:		Line 128:

	[[Category:Squares]]		[[Category:Squares]]
	~~[[Category:Temperament]]~~
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

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

2022-02-28T20:05:57Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 20:05, 28 February 2022
Line 128:		Line 128:

	[[Category:Squares]]		[[Category:Squares]]
	~~[[Category:Theory]]~~
	[[Category:Temperament]]		[[Category:Temperament]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

Flirora: yay another one.

2021-03-15T09:31:56Z

yay another one.

New page

The '''breedsmic-syntonic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of [[2401/2400|breedsmas (2401/2400)]] with a [[81/80|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Meantone family#Squares|squares]] temperament. In addition, 81/80 and 2401/2400 are the smallest 5-limit and 7-limit [[superparticular]] intervals to be tempered out by [[31edo]].

All temperaments in the continuum satisfy (2401/2400)<sup>''n''</sup> ~ 81/80. Varying ''n'' results in different temperament families listed in the table below. It converges to [[Breedsmic temperaments|breedsmic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by squares (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 29.82025..., and temperaments having ''n'' near this value tend to be the most accurate ones.

{| class="wikitable center-1 center-2"
|+ Temperament families in the continuum
|-
! rowspan="2" | ''n''
! rowspan="2" | Temperament family
! colspan="2" | Comma
|-
! Ratio
! Monzo
|-
| -4
| 217 & 31 & 14c
|
| {{monzo|-24 0 -9 16}}
|-
| -3
| 159 & 31 & 14c
|
| {{monzo|-19 1 -7 12}}
|-
| -2
| 87 & 31 & 14c
| 51883209/51200000
| {{monzo|-14 2 -5 8}}
|-
| -1
| [[Squalentine temperament|Squalentine]]
| [[64827/64000]]
| {{monzo|-9 3 -3 4}}
|-
| 0
| [[Meantone family|Meantone]]
| [[81/80]]
| {{monzo|-4 4 -1}}
|-
| 1
| [[Nuwell family|Nuwell]]
| [[2430/2401]]
| {{monzo|1 5 1 -4}}
|-
| 2
| 14c & 31 & 80
| 5832000/5764801
| {{monzo|6 6 3 -8}}
|-
| 3
| 14c & 31 & 152
| 13996800000/13841287201
| {{monzo|11 7 5 -12}}
|-
| 4
| 14c & 31 & 224
|
| {{monzo|16 8 7 -16}}
|-
| 5
| 265 & 31 & 282
|
| {{monzo|21 9 9 -20}}
|-
| 6
| 14c & 31 & 323
|
| {{monzo|26 10 11 -24}}
|-
| 7
| 17c & 395 & 364
|
| {{monzo|31 11 13 -28}}
|-
| 8
| 14c & 31 & 422
|
| {{monzo|36 12 15 -32}}
|-
| …
| …
| …
| …
|-
| 30
| 1677 & 6691 & 41854
|
| {{monzo|146 34 59 -120}}
|-
| …
| …
| …
| …
|-
| ∞
| [[Breedsmic temperaments|Breedsmic]]
| [[2401/2400]]
| {{monzo| -5 -1 -2 4}}
|}

Examples of temperaments with fractional values of ''n'':
* 34p & 31 & 14c (''n'' = -1/2 = -0.5)
* [[Subgroup temperaments#Skwares 3|Skwares]] (''n'' = 1/2 = 0.5)

== 1677 & 6691 & 41854 ==

Comma list: {{monzo| 146 34 59 -120 }}

POTE generators: 1901.9549, -775.6679

Mapping: [{{val| 1 0 26 14 }}, {{val| 0 1 34 17 }}, {{val| 0 0 120 59 }}]

{{Val list|legend=1| 1677, 5014, 6691, 41854, 43531, 46868, 48545, 50222, 55236, 97090 }}

[http://x31eq.com/cgi-bin/rt.cgi?ets=1677_6691_41854&limit=7 The temperament finder - 7-limit 1677 & 6691 & 41854]

== 34p & 31 & 14c ==

Comma list: {{monzo| -13 7 -4 4 }} = 5250987/5120000

POTE generators: -425.3382, ~5 = 2785.5671

Mapping: [{{val| 1 3 0 -2 }}, {{val| 0 4 0 -7 }}, {{val| 0 0 1 1 }}]

{{Val list|legend=1| 3, 14c, 17c, 17d, 20c, 31, 34, 45, 62, 65 }}

[http://x31eq.com/cgi-bin/rt.cgi?ets=34p_31_14c&limit=7 The temperament finder - 7-limit 34p & 31 & 14c]

[[Category:Squares]]
[[Category:Theory]]
[[Category:Temperament]]
[[Category:Equivalence continua]]