Porwell family: Difference between revisions

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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 ==

Porwell is catalogued as ''hewuermity'' in [[Graham Breed]]'s temperament finder.

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

[[Subgroup]]: 2.3.5.7

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

[[Optimal tuning]] ([[~~POTE~~]]): ~2 = ~~1\1~~, ~3/2 = 702.~~3482~~, ~35/32 = 157.~~4677~~

[[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]]:

* 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 }}

: [[~~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 }}

[[Badness]]: 0.~~142 × 10-3~~

[[Badness]] (Sintel): 0.628

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

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

== Zeus ==

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[[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 }}

[[Badness]]: 0.~~562 × 10-3~~

[[Badness]] (Sintel): 0.676

== 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

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[[Optimal tuning]] ([[~~POTE~~]]): ~2 = ~~1\1~~, ~3/2 = 701.8035, ~35/32 = 157.~~1649~~

[[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 }}

[[Badness]]: 2.~~23 × 10-3~~

[[Badness]] (Sintel): 2.68

=== 13-limit ===

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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 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}}

Badness: 1.~~30 × 10-3~~

Badness (Sintel): 1.21

== 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

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

[[Optimal tuning]] ([[~~POTE~~]]): ~99/70 = 1\2, ~3/2 = 702.~~4613~~, ~128/99 = 442.~~4903~~

[[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 }}

[[Badness]]: 1.~~25 × 10-3~~

[[Badness]] (Sintel): 1.51

=== 13-limit ===

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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 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=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 × 10-3~~

Badness (Sintel): 1.14

[[Category:Temperament families]]

[[Category:Porwell family| ]]

~~[[Category:Porwell| ]] ~~

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
 {{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 ==
+Porwell is catalogued as ''hewuermity'' in [[Graham Breed]]'s temperament finder.
-== Porwell a.k.a. hewuermity ==
 [[Subgroup]]: 2.3.5.7
@@ Line 8: / Line 10: @@
 {{Mapping|legend=1| 1 0 1 4 | 0 1 1 -1 | 0 0 -2 3 }}
 : mapping generators: ~2, ~3, ~35/32
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.3482, ~35/32 = 157.4677
+[[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]]:
-* 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 }}
-: [[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 }}
-[[Badness]]: 0.142 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.628
-[[Projection pair]]s: 3 6125/2048 to 2.5.7
+[[Projection pair]]s: <code>3 6125/2048</code> to 2.5.7
 == Zeus ==
@@ Line 35: / Line 40: @@
 {{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 }}
-[[Badness]]: 0.562 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.676
 == 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
@@ Line 47: / Line 60: @@
 {{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]]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 }}
-[[Badness]]: 2.23 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 2.68
 === 13-limit ===
@@ Line 60: / Line 77: @@
 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 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=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 (Sintel): 1.21
 == 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
@@ Line 72: / Line 93: @@
 {{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
-[[Optimal tuning]] ([[POTE]]): ~99/70 = 1\2, ~3/2 = 702.4613, ~128/99 = 442.4903
+[[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 }}
-[[Badness]]: 1.25 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.51
 === 13-limit ===
@@ Line 88: / Line 112: @@
 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 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=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 (Sintel): 1.14
 [[Category:Temperament families]]
 [[Category:Porwell family| ]] <!-- main article -->
-[[Category:Porwell| ]] <!-- key article -->
 [[Category:Rank 3]]