Porwell family - Revision history

FloraC: + intro to hera and semiporwell

2026-04-22T11:17:35Z

+ intro to hera and semiporwell

← Older revision		Revision as of 11:17, 22 April 2026
Line 52:		Line 52:

	== Hera ==		== Hera ==
			Hera tempers out 8019/8000, the [[trimitone comma]]. It was named by [[Flora Canou]] in 2021 as a more complex counterpart of [[zeus]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Line 84:		Line 86:

	== Semiporwell ==		== Semiporwell ==
			Named by [[Flora Canou]] in 2021, semiporwell tempers out 9801/9800, the [[kalisma]], as well as 16384/16335, the [[semiporwellisma]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-04-22T11:02:57Z

Switch to Sintel's badness, WE & CWE tunings

← Older revision		Revision as of 11:02, 22 April 2026
Line 12:		Line 12:
	: mapping generators: ~2, ~3, ~35/32		: mapping generators: ~2, ~3, ~35/32

	[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.~~3482~~{{c}}, ~35/32 = 157.~~4677~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.7101{{c}}, ~3/2 = 702.1785{{c}}, ~35/32 = 157.4296{{c}}
			: [[error map]]: {{val\| -0.290 -0.066 +0.426 +0.415 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1875{{c}}, ~35/32 = 157.3944{{c}}
			: error map: {{val\| 0.000 +0.233 +1.085 +1.170 }}

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 21:		Line 25:
	{{Optimal ET sequence\|legend=1\| 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381 }}		{{Optimal ET sequence\|legend=1\| 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381 }}

	[[Badness]] (~~Smith~~): 0.~~142 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.628

	[[Projection pair]]s: <code>3 6125/2048</code> to 2.5.7		[[Projection pair]]s: <code>3 6125/2048</code> to 2.5.7
Line 36:		Line 40:

	{{Mapping\|legend=1\| 1 0 1 4 -5 \| 0 1 1 -1 6 \| 0 0 -2 3 -8 }}		{{Mapping\|legend=1\| 1 0 1 4 -5 \| 0 1 1 -1 6 \| 0 0 -2 3 -8 }}

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.7232{{c}}, ~3/2 = 701.9496{{c}}, ~35/32 = 157.4667{{c}}
			: [[error map]]: {{val\| -0.277 -0.282 +0.149 +0.794 +0.369 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9677{{c}}, ~35/32 = 157.4315{{c}}
			: error map: {{val\| 0.000 +0.013 +0.791 +1.501 +1.037 }}

	{{Optimal ET sequence\|legend=1\| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }}		{{Optimal ET sequence\|legend=1\| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }}

	[[Badness]] (~~Smith~~): 0.~~562 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.676

	== Hera ==		== Hera ==
Line 48:		Line 58:
	{{Mapping\|legend=1\| 1 0 1 4 9 \| 0 1 1 -1 -3 \| 0 0 -2 3 -6 }}		{{Mapping\|legend=1\| 1 0 1 4 9 \| 0 1 1 -1 -3 \| 0 0 -2 3 -6 }}

	[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.8035{{c}}, ~35/32 = 157.~~1649~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.8410{{c}}, ~3/2 = 701.7105{{c}}, ~35/32 = 157.1441{{c}}
			: [[error map]]: {{val\| -0.159 -0.403 +0.791 +0.419 -0.268 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8035{{c}}, ~35/32 = 157.1741{{c}}
			: error map: {{val\| 0.000 -0.153 +1.140 +0.894 +0.232 }}

	{{Optimal ET sequence\|legend=1\| 46, 53, 84, 99, 130, 183, 313, 359, 542c, 672c }}		{{Optimal ET sequence\|legend=1\| 46, 53, 84, 99, 130, 183, 313, 359, 542c, 672c }}

	[[Badness]] (~~Smith~~): 2.~~23 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 2.68

	=== 13-limit ===		=== 13-limit ===
Line 61:		Line 75:
	Mapping: {{mapping\| 1 0 1 4 9 7 \| 0 1 1 -1 -3 -2 \| 0 0 -2 3 -6 -1 }}		Mapping: {{mapping\| 1 0 1 4 9 7 \| 0 1 1 -1 -3 -2 \| 0 0 -2 3 -6 -1 }}

	Optimal ~~tuning (POTE)~~: ~2 = 1200.0000{{c}}, ~3/2 = 701.~~6641~~{{c}}, ~35/32 = 157.~~1899~~{{c}}		Optimal tunings:
			* WE: ~2 = 1199.9170{{c}}, ~3/2 = 701.6155{{c}}, ~35/32 = 157.1791{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.6672{{c}}, ~35/32 = 157.1942{{c}}

	{{Optimal ET sequence\|legend=0\| 46, 53, 84, 99, 130, 183, 313 }}		{{Optimal ET sequence\|legend=0\| 46, 53, 84, 99, 130, 183, 313 }}

	Badness (~~Smith~~): 1.~~30 × 10<sup>-3</sup>~~		Badness (Sintel): 1.21

	== Semiporwell ==		== Semiporwell ==
Line 75:		Line 91:
	: mapping generators: ~99/70, ~3, ~128/99		: mapping generators: ~99/70, ~3, ~128/99

	[[Optimal tuning]] ([[~~POTE~~]]): ~99/70 = 600.0000{{c}}, ~3/2 = 702.~~4613~~{{c}}, ~128/99 = 442.~~4903~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~99/70 = 599.8385{{c}}, ~3/2 = 702.2722{{c}}, ~128/99 = 442.3712{{c}}
			: [[error map]]: {{val\| -0.323 -0.006 +0.378 +0.335 +0.152 }}
			* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.4280{{c}}, ~128/99 = 442.5202{{c}}
			: error map: {{val\| 0.000 +0.473 +1.155 +1.185 +1.306 }}

	{{Optimal ET sequence\|legend=1\| 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee }}		{{Optimal ET sequence\|legend=1\| 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee }}

	[[Badness]] (~~Smith~~): 1.~~25 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 1.51

	=== 13-limit ===		=== 13-limit ===
Line 88:		Line 108:
	Mapping: {{mapping\| 2 0 0 11 14 15 \| 0 1 1 -1 -2 -1 \| 0 0 2 -3 -1 -6 }}		Mapping: {{mapping\| 2 0 0 11 14 15 \| 0 1 1 -1 -2 -1 \| 0 0 2 -3 -1 -6 }}

	Optimal ~~tuning (POTE)~~: ~99/70 = 600.0000{{c}}, ~3/2 = 702.~~3964~~{{c}}, ~84/65 = 442.~~5902~~{{c}}		Optimal tunings:
			* WE: ~99/70 = 599.8357{{c}}, ~3/2 = 702.2041{{c}}, ~84/65 = 442.4690{{c}}
			* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.3576{{c}}, ~84/65 = 442.6282{{c}}

	{{Optimal ET sequence\|legend=0\| 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff }}		{{Optimal ET sequence\|legend=0\| 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff }}

	Badness (~~Smith~~): 1.~~22 × 10<sup>-3</sup>~~		Badness (Sintel): 1.14

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Porwell family\| ]] <!-- main article -->		[[Category:Porwell family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Withdraw hewuermity

2026-04-22T10:43:09Z

Withdraw *hewuermity*

← Older revision		Revision as of 10:43, 22 April 2026
Line 2:		Line 2:
	The '''porwell family''' of [[rank-3 temperament\|rank-3]] [[regular temperament]]s [[tempering out\|tempers out]] the [[porwell comma]] ({{monzo\|legend=1\| 11 1 -3 -2 }}, [[ratio]]: 6144/6125).		The '''porwell family''' of [[rank-3 temperament\|rank-3]] [[regular temperament]]s [[tempering out\|tempers out]] the [[porwell comma]] ({{monzo\|legend=1\| 11 1 -3 -2 }}, [[ratio]]: 6144/6125).

	== Porwell ~~a.k.a. hewuermity~~ ==		== Porwell ==
			Porwell is catalogued as ''hewuermity'' in [[Graham Breed]]'s temperament finder.

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

FloraC: Units & misc. cleanup

2026-04-22T10:38:18Z

Units & misc. cleanup

← Older revision		Revision as of 10:38, 22 April 2026
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	The '''porwell family''' of [[rank-3 temperament]]s tempers out the porwell comma, {{monzo\| 11 1 -3 -2 }} = [[6144/6125]].		The '''porwell family''' of [[rank-3 temperament\|rank-3]] [[regular temperament]]s [[tempering out\|tempers out]] the [[porwell comma]] ({{monzo\|legend=1\| 11 1 -3 -2 }}, [[ratio]]: 6144/6125).

	== Porwell a.k.a. hewuermity ==		== Porwell a.k.a. hewuermity ==
Line 8:		Line 8:

	{{Mapping\|legend=1\| 1 0 1 4 \| 0 1 1 -1 \| 0 0 -2 3 }}		{{Mapping\|legend=1\| 1 0 1 4 \| 0 1 1 -1 \| 0 0 -2 3 }}

	: mapping generators: ~2, ~3, ~35/32		: mapping generators: ~2, ~3, ~35/32

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 702.3482, ~35/32 = 157.4677		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.3482{{c}}, ~35/32 = 157.4677{{c}}

	[[Minimax tuning]]:		[[Minimax tuning]]:
	* 7- and [[9-odd-limit]]		* [[7-odd-limit\|7-]] and [[9-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 11/5 1/5 2/5 -2/5 \| 11/5 1/5 -3/5 3/5 }}		: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 11/5 1/5 2/5 -2/5 \| 11/5 1/5 -3/5 3/5 }}
	: [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5		: [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

	{{Optimal ET sequence\|legend=1\| 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381 }}		{{Optimal ET sequence\|legend=1\| 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381 }}

	[[Badness]]: 0.142 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.142 × 10<sup>-3</sup>

	[[Projection pair]]s: 3 6125/2048 to 2.5.7		[[Projection pair]]s: <code>3 6125/2048</code> to 2.5.7

	== Zeus ==		== Zeus ==
Line 38:		Line 37:
	{{Optimal ET sequence\|legend=1\| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }}		{{Optimal ET sequence\|legend=1\| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }}

	[[Badness]]: 0.562 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.562 × 10<sup>-3</sup>

	== Hera ==		== Hera ==
Line 47:		Line 46:
	{{Mapping\|legend=1\| 1 0 1 4 9 \| 0 1 1 -1 -3 \| 0 0 -2 3 -6 }}		{{Mapping\|legend=1\| 1 0 1 4 9 \| 0 1 1 -1 -3 \| 0 0 -2 3 -6 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 701.8035, ~35/32 = 157.1649		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.8035{{c}}, ~35/32 = 157.1649{{c}}

	{{Optimal ET sequence\|legend=1\| 46, 53, 84, 99, 130, 183, 313, 359, 542c, 672c }}		{{Optimal ET sequence\|legend=1\| 46, 53, 84, 99, 130, 183, 313, 359, 542c, 672c }}

	[[Badness]]: 2.23 × 10<sup>-3</sup>		[[Badness]] (Smith): 2.23 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
Line 60:		Line 59:
	Mapping: {{mapping\| 1 0 1 4 9 7 \| 0 1 1 -1 -3 -2 \| 0 0 -2 3 -6 -1 }}		Mapping: {{mapping\| 1 0 1 4 9 7 \| 0 1 1 -1 -3 -2 \| 0 0 -2 3 -6 -1 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~3/2 = 701.6641, ~35/32 = 157.1899		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.6641{{c}}, ~35/32 = 157.1899{{c}}

	{{Optimal ET sequence\|legend=1\| 46, 53, 84, 99, 130, 183, 313 }}		{{Optimal ET sequence\|legend=0\| 46, 53, 84, 99, 130, 183, 313 }}

	Badness: 1.30 × 10<sup>-3</sup>		Badness (Smith): 1.30 × 10<sup>-3</sup>

	== Semiporwell ==		== Semiporwell ==
Line 72:		Line 71:

	{{Mapping\|legend=1\| 2 0 0 11 14 \| 0 1 1 -1 -2 \| 0 0 2 -3 -1 }}		{{Mapping\|legend=1\| 2 0 0 11 14 \| 0 1 1 -1 -2 \| 0 0 2 -3 -1 }}

	: mapping generators: ~99/70, ~3, ~128/99		: mapping generators: ~99/70, ~3, ~128/99

	[[Optimal tuning]] ([[POTE]]): ~99/70 = ~~1\2~~, ~3/2 = 702.4613, ~128/99 = 442.4903		[[Optimal tuning]] ([[POTE]]): ~99/70 = 600.0000{{c}}, ~3/2 = 702.4613{{c}}, ~128/99 = 442.4903{{c}}

	{{Optimal ET sequence\|legend=1\| 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee }}		{{Optimal ET sequence\|legend=1\| 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee }}

	[[Badness]]: 1.25 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.25 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
Line 88:		Line 86:
	Mapping: {{mapping\| 2 0 0 11 14 15 \| 0 1 1 -1 -2 -1 \| 0 0 2 -3 -1 -6 }}		Mapping: {{mapping\| 2 0 0 11 14 15 \| 0 1 1 -1 -2 -1 \| 0 0 2 -3 -1 -6 }}

	Optimal tuning (POTE): ~99/70 = ~~1\2~~, ~3/2 = 702.3964, ~84/65 = 442.5902		Optimal tuning (POTE): ~99/70 = 600.0000{{c}}, ~3/2 = 702.3964{{c}}, ~84/65 = 442.5902{{c}}

	{{Optimal ET sequence\|legend=1\| 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff }}		{{Optimal ET sequence\|legend=0\| 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff }}

	Badness: 1.22 × 10<sup>-3</sup>		Badness (Smith): 1.22 × 10<sup>-3</sup>

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Porwell family\| ]] <!-- main article -->		[[Category:Porwell family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-11-27T12:17:55Z

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

← Older revision		Revision as of 12:17, 27 November 2025
Line 95:		Line 95:

	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Porwell family\| ]] <!-- main article -->		[[Category:Porwell family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: - category

2025-10-23T08:51:57Z

- category

← Older revision		Revision as of 08:51, 23 October 2025
Line 97:		Line 97:
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:Porwell family\| ]] <!-- main article -->		[[Category:Porwell family\| ]] <!-- main article -->
	~~[[Category:Porwell\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

2025-06-24T00:38:56Z

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

← Older revision		Revision as of 00:38, 24 June 2025
Line 95:		Line 95:

	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Porwell family\| ]] <!-- main article -->		[[Category:Porwell family\| ]] <!-- main article -->
	[[Category:Porwell\| ]] <!-- key article -->		[[Category:Porwell\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

Lériendil: Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) "

2025-06-21T06:57:41Z

Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) "

← Older revision		Revision as of 06:57, 21 June 2025
Line 16:		Line 16:
	* 7- and [[9-odd-limit]]		* 7- and [[9-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 11/5 1/5 2/5 -2/5 \| 11/5 1/5 -3/5 3/5 }}		: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 11/5 1/5 2/5 -2/5 \| 11/5 1/5 -3/5 3/5 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.3.7/5		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

	{{Optimal ET sequence\|legend=1\| 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381 }}		{{Optimal ET sequence\|legend=1\| 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381 }}

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:44:37Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:44, 13 April 2025
Line 1:		Line 1:
	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''porwell family''' of [[rank-3 temperament]]s tempers out the porwell comma, {{monzo\| 11 1 -3 -2 }} = [[6144/6125]].		The '''porwell family''' of [[rank-3 temperament]]s tempers out the porwell comma, {{monzo\| 11 1 -3 -2 }} = [[6144/6125]].

BudjarnLambeth: {{Technical data page}}

+ add link

2025-04-13T11:03:02Z

{{Technical data page}}<br><br> + add link

← Older revision		Revision as of 11:03, 13 April 2025
Line 1:		Line 1:
	The '''porwell family''' of rank-3 ~~temperaments~~ tempers out the porwell comma, {{monzo\| 11 1 -3 -2 }} = [[6144/6125]].		{{Technical data page}}<br><br>
			The '''porwell family''' of [[rank-3 temperament]]s tempers out the porwell comma, {{monzo\| 11 1 -3 -2 }} = [[6144/6125]].

	== Porwell a.k.a. hewuermity ==		== Porwell a.k.a. hewuermity ==