Blackwood family - Revision history

FloraC: /* Quindecic */ switch to Sintel's badness, WE & CWE tunings

2026-06-28T12:16:10Z

Quindecic: switch to Sintel's badness, WE & CWE tunings

← Older revision		Revision as of 12:16, 28 June 2026
Line 132:		Line 132:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~22/21 = 80.~~000~~, ~13/8 = ~~840~~.~~528~~ (~40/39 = 39.~~472~~)		* [[WE]]: ~22/21 = 79.770{{c}}, ~13/8 = 850.476{{c}} (~40/39 = 26.999{{c}})
	* [[~~POTE~~]]: ~22/21 = 80.000, ~13/8 = ~~852~~.~~924~~ (~40/39 = 27.~~076~~)		* [[CWE]]: ~22/21 = 80.000{{c}}, ~13/8 = 850.793{{c}} (~40/39 = 29.207{{c}})

	{{Optimal ET sequence\|legend=1\| 15, 30 }}		{{Optimal ET sequence\|legend=1\| 15, 30 }}

	[[Badness]]: 0.~~028944~~		[[Badness]] (Sintel): 1.20

	[[Category:Blackwood family\| ]] <!-- main article -->		[[Category:Blackwood family\| ]] <!-- main article -->
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: - interwiki (the German article corresponds to Blackwood article)

2026-06-28T11:20:03Z

- interwiki (the German article corresponds to Blackwood article)

← Older revision		Revision as of 11:20, 28 June 2026
Line 1:		Line 1:
	~~{{Interwiki~~
	~~\| en = Blackwood family~~
	~~\| de = Blackwood-Limmisch~~
	~~\| es =~~
	~~\| ja =~~
	}}
	{{Technical data page}}		{{Technical data page}}
	The '''blackwood family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] 256/243, the [[Pythagorean limma]]. As a consequence, [[3/2]] is always represented by 3\5, 720 [[cent]]s assuming pure octaves. While quite sharp, this is close enough to a just fifth to serve as a fifth, and some people are fond of it. All temperaments shown here are pentaploid acot.		The '''blackwood family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] 256/243, the [[Pythagorean limma]]. As a consequence, [[3/2]] is always represented by 3\5, 720 [[cent]]s assuming pure octaves. While quite sharp, this is close enough to a just fifth to serve as a fifth, and some people are fond of it. All temperaments shown here are pentaploid acot.

FloraC: Fix heading levels. + links

2026-06-28T10:52:31Z

Fix heading levels. + links

← Older revision		Revision as of 10:52, 28 June 2026
Line 34:		Line 34:

	== Septimal blackwood ==		== Septimal blackwood ==
			{{Main\| Blackwood }}

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Line 50:		Line 52:
	[[Badness]] (Sintel): 0.649		[[Badness]] (Sintel): 0.649

	==== Undecimal blackwood ====		=== Undecimal blackwood ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

Line 65:		Line 67:
	Badness (Sintel): 0.815		Badness (Sintel): 0.815

	===== 13-limit =====		==== 13-limit ====
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Line 80:		Line 82:
	Badness (Sintel): 0.847		Badness (Sintel): 0.847

	==== Farrier ====		=== Farrier ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

Line 95:		Line 97:
	Badness (Sintel): 0.965		Badness (Sintel): 0.965

	===== 13-limit =====		==== 13-limit ====
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Line 110:		Line 112:
	Badness (Sintel): 0.922		Badness (Sintel): 0.922

	==== Ferrum ====		=== Ferrum ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

FloraC: Quindecic belongs here for the same reasons catler belongs to compton family

2026-06-28T10:50:34Z

Quindecic belongs here for the same reasons catler belongs to compton family

@@ Line 124: / Line 124: @@
 Badness (Sintel): 1.02
 [[Category:Blackwood family| ]] <!-- main article -->
 [[Category:Temperament families]]
 [[Category:Rank 2]]

FloraC: - blackweed (moved to subgroup temps)

2026-06-28T10:48:04Z

- blackweed (moved to subgroup temps)

@@ Line 124: / Line 124: @@
 Badness (Sintel): 1.02
 [[Category:Blackwood family| ]] <!-- main article -->
-[[Category:Temperaments families]]
+[[Category:Temperament families]]
 [[Category:Rank 2]]

FloraC: FloraC moved page Limmic temperaments to Blackwood family

2026-06-28T10:44:17Z

FloraC moved page Limmic temperaments to Blackwood family

← Older revision	Revision as of 10:44, 28 June 2026
(No difference)

FloraC: Prepare for a move to blackwood family since there is another family member to be moved here

2026-06-28T10:44:01Z

Prepare for a move to blackwood family since there is another family member to be moved here

← Older revision		Revision as of 10:44, 28 June 2026
Line 1:		Line 1:
	{{~~interwiki~~		{{Interwiki
	\| en = ~~Limmic temperaments~~		\| en = Blackwood family
	\| de = Blackwood-Limmisch		\| de = Blackwood-Limmisch
	\| es =		\| es =
Line 6:		Line 6:
	}}		}}
	{{Technical data page}}		{{Technical data page}}
	'''~~Limmic temperaments~~''' ~~are~~ [[temperament]]~~s that~~ [[~~temper~~ out]] the Pythagorean limma~~, [[256/243~~]]. As a consequence, [[3/2]] is always represented by 3\5, 720 [[cent]]s assuming pure octaves. While quite sharp, this is close enough to a just fifth to serve as a fifth, and some people are fond of it. All temperaments shown here are pentaploid acot.		The '''blackwood family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] 256/243, the [[Pythagorean limma]]. As a consequence, [[3/2]] is always represented by 3\5, 720 [[cent]]s assuming pure octaves. While quite sharp, this is close enough to a just fifth to serve as a fifth, and some people are fond of it. All temperaments shown here are pentaploid acot.

	== Blackwood ==		== Blackwood ==
Line 15:		Line 15:
	The only extension to the 7-limit that makes any sense is to map the [[7/4\|harmonic seventh]] to 4\5, tempering out [[28/27]], [[49/48]], and [[64/63]]. This is known as ''blacksmith'' in earlier materials, including [[Graham Breed]]'s temperament finder.		The only extension to the 7-limit that makes any sense is to map the [[7/4\|harmonic seventh]] to 4\5, tempering out [[28/27]], [[49/48]], and [[64/63]]. This is known as ''blacksmith'' in earlier materials, including [[Graham Breed]]'s temperament finder.

	~~=== 5-limit ===~~
	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

Line 34:		Line 33:
	[[Badness]] (Sintel): 1.50		[[Badness]] (Sintel): 1.50

	==~~= 7-limit =~~==		== Septimal blackwood ==
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Line 134:		Line 133:

	{{Mapping\|legend=2\| 5 8 0 \| 0 0 1 }}		{{Mapping\|legend=2\| 5 8 0 \| 0 0 1 }}
			: mapping generators: ~9/8, ~11/7
	: ~~sval~~ mapping generators: ~9/8, ~11/7

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
Line 145:		Line 143:
	{{Optimal ET sequence\|legend=1\| 15, 20, 35b, 55b }}		{{Optimal ET sequence\|legend=1\| 15, 20, 35b, 55b }}

	[[Category:~~Temperament collections]]~~		[[Category:Blackwood family\| ]] <!-- main article -->
	~~[[Category:Limmic temperaments~~]] <!-- main article -->		[[Category:Temperaments families]]
	[[Category:Rank 2]]		[[Category:Rank 2]]
	~~[[Category:Blackwood]]~~

FloraC: Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

2025-11-27T12:30:24Z

Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

← Older revision		Revision as of 12:30, 27 November 2025
Line 146:		Line 146:

	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Limmic temperaments]] <!-- main article -->		[[Category:Limmic temperaments]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]
	[[Category:Blackwood]]		[[Category:Blackwood]]

FloraC: /* Blackweed */ this is a restriction of undecimal blackwood

2025-07-20T10:42:36Z

Blackweed: this is a restriction of undecimal blackwood

← Older revision		Revision as of 10:42, 20 July 2025
Line 127:		Line 127:

	== Blackweed ==		== Blackweed ==
	Blackweed is a ~~variant~~ of blackwood as it tempers out 256/243 alike but in the 2.3.11/7 [[subgroup]]. 20edo is close to the optimum, which has 4\20 as the period and 420{{c}} as the generator.		Blackweed is a [[restriction]] of undecimal blackwood as it tempers out 256/243 alike but in the 2.3.11/7 [[subgroup]]. 20edo is close to the optimum, which has 4\20 as the period and 420{{c}} as the generator.

	[[Subgroup]]: 2.3.11/7		[[Subgroup]]: 2.3.11/7

FloraC: - CTE & POTE tunings

2025-07-20T10:40:10Z

- CTE & POTE tunings

← Older revision		Revision as of 10:40, 20 July 2025
Line 29:		Line 29:
	* [[CWE]]: ~8/7 = 240.000{{c}}, ~5/4 = 395.126{{c}}		* [[CWE]]: ~8/7 = 240.000{{c}}, ~5/4 = 395.126{{c}}
	: error map: {{val\| 0.000 +18.045 +8.812 }}		: error map: {{val\| 0.000 +18.045 +8.812 }}
	~~<!-- * [[CTE]]: ~9/8 = 240.000{{c}}, ~5/4 = 386.314{{c}}~~
	~~: [[error map]]: {{val\| 0.000 +18.045 0.000 }}~~
	* [[POTE]]: ~9/8 = 240.000{{c}}, ~5/4 = 399.594{{c}}
	~~: error map: {{val\| 0.000 +18.045 +13.280 }} -->~~

	{{Optimal ET sequence\|legend=1\| 5, 10, 15 }}		{{Optimal ET sequence\|legend=1\| 5, 10, 15 }}
Line 50:		Line 46:
	* [[CWE]]: ~8/7 = 240.000{{c}}, ~5/4 = 391.098{{c}}		* [[CWE]]: ~8/7 = 240.000{{c}}, ~5/4 = 391.098{{c}}
	: error map: {{val\| 0.000 +18.045 +4.784 -8.826 }}		: error map: {{val\| 0.000 +18.045 +4.784 -8.826 }}
	~~<!-- * [[CTE]]: ~8/7 = 240.000{{c}}, ~5/4 = 386.313{{c}}~~
	~~: [[error map]]: {{val\| 0.000 +18.045 0.000 -8.826 }}~~
	* [[POTE]]: ~8/7 = 240.000{{c}}, ~5/4 = 392.767{{c}}
	~~: error map: {{val\| 0.000 +18.045 +6.454 -8.826 }} -->~~

	{{Optimal ET sequence\|legend=1\| 5, 10, 15, 40b }}		{{Optimal ET sequence\|legend=1\| 5, 10, 15, 40b }}
Line 69:		Line 61:
	* WE: ~8/7 = 239.341{{c}}, ~5/4 = 393.864{{c}}		* WE: ~8/7 = 239.341{{c}}, ~5/4 = 393.864{{c}}
	* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 394.655{{c}}		* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 394.655{{c}}
	~~<!-- * POTE: ~8/7 = 240.000{{c}}, ~5/4 = 394.948{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 5, 10, 15, 40be }}		{{Optimal ET sequence\|legend=0\| 5, 10, 15, 40be }}
Line 85:		Line 76:
	* WE: ~8/7 = 239.187{{c}}, ~5/4 = 389.713{{c}}		* WE: ~8/7 = 239.187{{c}}, ~5/4 = 389.713{{c}}
	* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 390.282{{c}}		* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 390.282{{c}}
	~~<!-- * POTE: ~8/7 = 240.000{{c}}, ~5/4 = 391.037{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 5, 10, 15, 25e }}		{{Optimal ET sequence\|legend=0\| 5, 10, 15, 25e }}
Line 101:		Line 91:
	* WE: ~8/7 = 239.389{{c}}, ~5/4 = 397.056{{c}}		* WE: ~8/7 = 239.389{{c}}, ~5/4 = 397.056{{c}}
	* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 396.599{{c}}		* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 396.599{{c}}
	~~<!-- * POTE: ~8/7 = 240.000{{c}}, ~5/4 = 398.070{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 5e, 10e, 15 }}		{{Optimal ET sequence\|legend=0\| 5e, 10e, 15 }}
Line 117:		Line 106:
	* WE: ~8/7 = 239.196{{c}}, ~5/4 = 395.483{{c}}		* WE: ~8/7 = 239.196{{c}}, ~5/4 = 395.483{{c}}
	* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 394.759{{c}}		* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 394.759{{c}}
	~~<!-- * POTE: ~8/7 = 240.000{{c}}, ~5/4 = 396.812{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 5e, 10e, 15 }}		{{Optimal ET sequence\|legend=0\| 5e, 10e, 15 }}
Line 133:		Line 121:
	* WE: ~8/7 = 239.058{{c}}, ~5/4 = 373.292{{c}}		* WE: ~8/7 = 239.058{{c}}, ~5/4 = 373.292{{c}}
	* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 371.659{{c}}		* CWE: ~8/7 = 240.000{{c}}, ~5/4 = 371.659{{c}}
	~~<!-- * POTE: ~8/7 = 240.000{{c}}, ~5/4 = 374.763{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 5e, 10 }}		{{Optimal ET sequence\|legend=0\| 5e, 10 }}
Line 155:		Line 142:
	* [[Tp tuning\|subgroup]] [[CWE]]: ~8/7 = 240.000{{c}}, ~11/7 = 784.967{{c}}		* [[Tp tuning\|subgroup]] [[CWE]]: ~8/7 = 240.000{{c}}, ~11/7 = 784.967{{c}}
	: error map: {{val\| 0.000 +18.045 +2.475 }}		: error map: {{val\| 0.000 +18.045 +2.475 }}
	~~<!-- * ([[Tp tuning\|subgroup POTE]]): ~9/8 = 240.0000{{c}}, ~11/7 = 786.2215{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 15, 20, 35b, 55b }}		{{Optimal ET sequence\|legend=1\| 15, 20, 35b, 55b }}