Biyatismic clan: Difference between revisions

(6 intermediate revisions by the same user not shown)

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* ''[[Bisector]]'' (+245/243) → [[Sensamagic family #Bisector|Sensamagic family]]

Considered below are zeus, artemis, oxpecker, big brother, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].

Considered below are zeus, artemis, oxpecker, kahoupokane, big brother, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].

== Protomere ==

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* [[WE]]: ~2 = 1200.6628{{c}}, ~3/2 = 701.8452{{c}}, ~11/10 = 157.8337{{c}}

: [[error map]]: {{val| +0.663 +0.553 +1.190 -5.318 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~11~~/10~~ = 157.6099{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~12/11 = 157.6099{{c}}

: error map: {{val| 0.000 +0.030 +0.451 -6.943 }}

~~~~

{{Optimal ET sequence|legend=1| 7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee }}

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[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.1693{{c}}, ~3/2 = 702.2521{{c}}, ~11~~/10~~ = 157.1102{{c}}

* [[WE]]: ~2 = 1200.1693{{c}}, ~3/2 = 702.2521{{c}}, ~12/11 = 157.1102{{c}}

: [[error map]]: {{val| +0.169 +0.466 +2.057 +0.761 -5.668 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2478{{c}}, ~11~~/10~~ = 157.1265{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2478{{c}}, ~12/11 = 157.1265{{c}}

: error map: {{val| 0.000 +0.293 +1.681 +0.306 -6.197 }}

~~~~

[[Minimax tuning]]:

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Optimal tunings:

* WE: ~2 = 1200.2411{{c}}, ~3/2 = 702.0090{{c}}, ~11~~/10~~ = 156.9897{{c}}

* WE: ~2 = 1200.2411{{c}}, ~3/2 = 702.0090{{c}}, ~12/11 = 156.9897{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8818{{c}}, ~11~~/10~~ = 156.9568{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8818{{c}}, ~12/11 = 156.9568{{c}}

~~~~

Minimax tuning:

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Optimal tunings:

* WE: ~2 = 1199.9251{{c}}, ~3/2 = 699.2984{{c}}, ~11~~/10~~ = 155.3569{{c}}

* WE: ~2 = 1199.9251{{c}}, ~3/2 = 699.2984{{c}}, ~12/11 = 155.3569{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2982{{c}}, ~11~~/10~~ = 155.3484{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2982{{c}}, ~12/11 = 155.3484{{c}}

~~~~

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* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.2777{{c}}, ~11/10 = 158.3100{{c}}

: error map: {{val| 0.000 -1.677 -2.656 -0.955 -9.350 }}

~~~~

{{Optimal ET sequence|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 60e, 84e, 91e, 113e, 144ee }}

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* WE: ~2 = 1201.7896{{c}}, ~3/2 = 699.7509{{c}}, ~11/10 = 158.9484{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.1687{{c}}, ~11/10 = 158.7345{{c}}

~~~~

{{Optimal ET sequence|legend=0| 9, 20, 22f, 29, 31, 60e, 129cddee }}

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* WE: ~2 = 1200.9110{{c}}, ~3/2 = 701.5110{{c}}, ~11/10 = 159.1256{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.9717{{c}}, ~11/10 = 158.7903{{c}}

~~~~

{{Optimal ET sequence|legend=0| 22, 29, 31, 53, 82e, 84e, 113e }}

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[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.4124{{c}}, ~3/2 = 701.1291{{c}}, ~11~~/10~~ = 155.8292{{c}}

* [[WE]]: ~2 = 1200.4124{{c}}, ~3/2 = 701.1291{{c}}, ~12/11 = 155.8292{{c}}

: [[error map]]: {{val| +0.412 -0.414 +3.982 -1.435 -4.781 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2359{{c}}, ~11~~/10~~ = 155.7399{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2359{{c}}, ~12/11 = 155.7399{{c}}

: error map: {{val| 0.000 -0.719 +3.442 -2.029 -5.822 }}

~~~~

{{Optimal ET sequence|legend=1| 7d, 8d, 15, 23de, 24d, 31, 46, 77 }}

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Optimal tunings:

* WE: ~2 = 1198.9113{{c}}, ~3/2 = 700.9581{{c}}, ~11~~/10~~ = 154.7247{{c}}

* WE: ~2 = 1198.9113{{c}}, ~3/2 = 700.9581{{c}}, ~12/11 = 154.7247{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.6409{{c}}, ~11~~/10~~ = 154.9115{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.6409{{c}}, ~12/11 = 154.9115{{c}}

~~~~

Badness (Sintel): 1.02

== Kahoupokane ==

Named by [[Tristan Bay]] in 2025, Kahoupokane tempers out [[5120/5103]] and may be described as the {{nowrap| 29 & 46 & 53 }} temperament.

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 121/120, 5120/5103

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.1911{{c}}, ~3/2 = 703.1412{{c}}, ~11/10 = 158.1068{{c}}

: [[error map]]: {{val| +0.191 +1.377 +0.996 +0.401 -5.710 }}

* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.0417{{c}}, ~11/10 = 157.9917{{c}}

: error map: {{val| 0.000 +1.087 +0.744 -0.018 -6.268 }}

{{Optimal ET sequence|legend=1| 7, 17c, 24d, 29, 46, 53, 82e, 99 }}

[[Badness]] (Sintel): 2.73

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 169/168, 352/351

Mapping: {{mapping| 1 0 1 11 2 7 | 0 1 1 -5 1 -2 | 0 0 -2 -2 -1 -1 }}

Optimal tunings:

* WE: ~2 = 1200.4435{{c}}, ~3/2 = 703.1443{{c}}, ~11/10 = 158.4176{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9013{{c}}, ~11/10 = 158.1657{{c}}

{{Optimal ET sequence|legend=0| 7, 17c, 24d, 29, 46, 53, 82e, 99, 181eef }}

Badness (Sintel): 1.27

== Big brother ==

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* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.8990{{c}}, ~22/21 = 78.4412{{c}}

: error map: {{val| 0.000 -1.056 +0.820 -4.150 -7.301 }}

~~~~

{{Optimal ET sequence|legend=1| 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee }}

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[[Badness]] (Sintel): 0.701

===~~= 13-limit =~~===

=== Eros ===

~~Subgroup: 2.3.5.7.11.13~~

Eros fairs impressively into the 23-limit as a rank-3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but has the pleasing property that all the harmonics are on the negative side of the last generator. Specifically, -3 to 2 fifths and -5 to 0 [[~]][[23/22]]'s will provide odd harmonics 1–23 up to octave equivalence; you can think of this as a 6×6 grid, which is a recommendable place to start looking at its structure.

~~Comma list: 121/120, 351/350, 441/440~~

~~Mapping: {{mapping| 1 0 1 3 2 6 | 0 1 1 0 1~~ -~~1 | 0 0 -4~~ -3 -~~2 -11 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1201.0656{{c}}, ~~~3/2 = 700~~.~~7374{{c}}~~, ~~~22/21 = 78.5908{{c}}~~

* CWE: ~2 = 1200.0000{{c}}, ~3/2 ~~= 700.7005{{c}}, ~22/21 = 78.3253{{c}}~~

<!-~~- * POTE:~~ ~~~2 = 1200.0000{{c}}, ~3~~/~~2 = 700.1158{{c}}~~, ~~~21/20 = 78~~.~~5211{{c}} -->~~

~~{{Optimal ET sequence|legend=0| 14cf, 29ff, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}~~

~~Badness~~ (~~Sintel~~): 1.36

Tempering out the less accurate comma 121/120 can be seen as an implication of tempering out [[441/440]] ({{S|21}}), [[484/483]] ({{S|22}}), and [[529/528]] ({{S|23}}). Therefore, characteristic of any good tuning is the prime [[11/1|11]] being the flattest prime, with other primes having strictly less than 5{{cent}} of error.

~~==== Eros ====~~

This temperament was discovered by [[Scott Dakota]]. Note that the 17-limit extension requires the 29g val for 29edo, which has the sizes of 17/16 and 18/17 swapped.

~~Eros fairs impressively into~~ the 23-limit ~~as a rank 3 temperament; not only is it fairly simple (considering this is a subgroup as complex as~~ the ~~full 23-limit~~, ~~with many challenges) but all the generators are positive (or only 1 into the negatives in the case of the fifth) meaning it's even simpler than it might appear and~~ has the ~~pleasing property~~ of ~~all harmonics and subharmonics being "on the same side"; specifically: -3 to 1 fifths ([[2L 3s]]) and -5 to 0 ~[[23~~/~~22]]'s will get you every prime, up to octave equivalence; you can think of this as a 5 by 6 grid if you like~~ and ~~is a recommendable place to start looking at its structure. Tempering the less accurate comma [[121/120|S11]] can be seen as a consequence of tempering {[[441/440|S21]], [[484/483|S22]], [[529~~/528|S23]]} so is very natural and given its properties certainly excusable. Therefore characteristic of any good tuning is the ~11 being the most flat prime, with other primes having strictly less than 5{{cent}} of error. This temperament was first logged on x31eq by [[Scott Dakota]].

Subgroup: 2.3.5.7.11.13

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* WE: ~2 = 1200.6419{{c}}, ~3/2 = 701.8766{{c}}, ~22/21 = 78.6564{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5612{{c}}, ~22/21 = 78.4778{{c}}

~~~~

{{Optimal ET sequence|legend=0| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }}

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Badness (Sintel): 1.08

===== 17-limit =====

==== 17-limit ====

~~Note that this extension requires the 29g val for 29edo, which has the sizes of 17/16 and 18/17 swapped.~~

Subgroup: 2.3.5.7.11.13.17

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* WE: ~2 = 1200.6172{{c}}, ~3/2 = 702.1026{{c}}, ~22/21 = 78.7963{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7925{{c}}, ~22/21 = 78.6203{{c}}

~~~~

{{Optimal ET sequence|legend=0| 17cg, 29g, 31, 46, 60e, 77, 106de }}

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Badness (Sintel): 0.931

===== 19-limit =====

==== 19-limit ====

Subgroup: 2.3.5.7.11.13.17.19

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* WE: ~2 = 1200.6224{{c}}, ~3/2 = 702.0959{{c}}, ~22/21 = 78.8004{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.6963{{c}}, ~22/21 = 78.6479{{c}}

~~~~

{{Optimal ET sequence|legend=0| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}

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Badness (Sintel): 1.16

===== 23-limit =====

==== 23-limit ====

Subgroup: 2.3.5.7.11.13.17.19.23

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* WE: ~2 = 1200.7268{{c}}, ~3/2 = 702.2463{{c}}, ~22/21 = 78.8824{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8010{{c}}, ~23/22 = 78.7188{{c}}

~~~~

{{Optimal ET sequence|legend=0| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}

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Badness (Sintel): 1.08

==== Inanna ====

=== Astarte ===

This extension is catalogued as tridecimal aphrodite in [[Graham Breed]]'s temperament finder.

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 351/350, 441/440

Mapping: {{mapping| 1 0 1 3 2 6 | 0 1 1 0 1 -1 | 0 0 -4 -3 -2 -11 }}

Optimal tunings:

* WE: ~2 = 1201.0656{{c}}, ~3/2 = 700.7374{{c}}, ~22/21 = 78.5908{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.7005{{c}}, ~22/21 = 78.3253{{c}}

{{Optimal ET sequence|legend=0| 14cf, 29ff, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}

Badness (Sintel): 1.36

=== Inanna ===

Subgroup: 2.3.5.7.11.13

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* WE: ~2 = 1201.7881{{c}}, ~3/2 = 699.8166{{c}}, ~22/21 = 79.7282{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.5926{{c}}, ~22/21 = 79.3822{{c}}

~~~~

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Badness (Sintel): 1.01

==== Ishtar ====

=== Ishtar ===

Subgroup: 2.3.5.7.11.13

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* WE: ~2 = 1200.7875{{c}}, ~3/2 = 703.8568{{c}}, ~22/21 = 79.0096{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7640{{c}}, ~22/21 = 78.8025{{c}}

~~~~

{{Optimal ET sequence|legend=0| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }}

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[[Category:Temperament clans]]

[[Category:Biyatismic clan| ]]

~~[[Category:Biyatismic| ]] ~~

[[Category:Rank 3]]

@@ Line 7: / Line 7: @@
 * ''[[Bisector]]'' (+245/243) → [[Sensamagic family #Bisector|Sensamagic family]]
-Considered below are zeus, artemis, oxpecker, big brother, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].
+Considered below are zeus, artemis, oxpecker, kahoupokane, big brother, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].
 == Protomere ==
@@ Line 20: / Line 20: @@
 * [[WE]]: ~2 = 1200.6628{{c}}, ~3/2 = 701.8452{{c}}, ~11/10 = 157.8337{{c}}
 : [[error map]]: {{val| +0.663 +0.553 +1.190 -5.318 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~11/10 = 157.6099{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~12/11 = 157.6099{{c}}
 : error map: {{val| 0.000 +0.030 +0.451 -6.943 }}
-<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4578{{c}}, ~11/10 = 157.7466{{c}} -->
 {{Optimal ET sequence|legend=1| 7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee }}
@@ Line 45: / Line 44: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.1693{{c}}, ~3/2 = 702.2521{{c}}, ~11/10 = 157.1102{{c}}
+* [[WE]]: ~2 = 1200.1693{{c}}, ~3/2 = 702.2521{{c}}, ~12/11 = 157.1102{{c}}
 : [[error map]]: {{val| +0.169 +0.466 +2.057 +0.761 -5.668 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2478{{c}}, ~11/10 = 157.1265{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2478{{c}}, ~12/11 = 157.1265{{c}}
 : error map: {{val| 0.000 +0.293 +1.681 +0.306 -6.197 }}
-<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1530{{c}}, ~11/10 = 157.0881{{c}} -->
 [[Minimax tuning]]:
@@ Line 86: / Line 84: @@
 Optimal tunings:
-* WE: ~2 = 1200.2411{{c}}, ~3/2 = 702.0090{{c}}, ~11/10 = 156.9897{{c}}
+* WE: ~2 = 1200.2411{{c}}, ~3/2 = 702.0090{{c}}, ~12/11 = 156.9897{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8818{{c}}, ~11/10 = 156.9568{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8818{{c}}, ~12/11 = 156.9568{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8679{{c}}, ~11/10 = 156.9582{{c}} -->
 Minimax tuning:
@@ Line 115: / Line 112: @@
 Optimal tunings:
-* WE: ~2 = 1199.9251{{c}}, ~3/2 = 699.2984{{c}}, ~11/10 = 155.3569{{c}}
+* WE: ~2 = 1199.9251{{c}}, ~3/2 = 699.2984{{c}}, ~12/11 = 155.3569{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2982{{c}}, ~11/10 = 155.3484{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2982{{c}}, ~12/11 = 155.3484{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 699.3420{{c}}, ~11/10 = 155.3666{{c}} -->
 {{Optimal ET sequence|legend=0| 7, 9, 15, 22f, 24, 31 }}
@@ Line 137: / Line 133: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.2777{{c}}, ~11/10 = 158.3100{{c}}
 : error map: {{val| 0.000 -1.677 -2.656 -0.955 -9.350 }}
-<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 699.8719{{c}}, ~11/10 = 158.3232{{c}} -->
 {{Optimal ET sequence|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 60e, 84e, 91e, 113e, 144ee }}
@@ Line 153: / Line 148: @@
 * WE: ~2 = 1201.7896{{c}}, ~3/2 = 699.7509{{c}}, ~11/10 = 158.9484{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.1687{{c}}, ~11/10 = 158.7345{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 698.7090{{c}}, ~11/10 = 158.7117{{c}} -->
 {{Optimal ET sequence|legend=0| 9, 20, 22f, 29, 31, 60e, 129cddee }}
@@ Line 169: / Line 163: @@
 * WE: ~2 = 1200.9110{{c}}, ~3/2 = 701.5110{{c}}, ~11/10 = 159.1256{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.9717{{c}}, ~11/10 = 158.7903{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 700.9789{{c}}, ~11/10 = 159.0048{{c}} -->
 {{Optimal ET sequence|legend=0| 22, 29, 31, 53, 82e, 84e, 113e }}
@@ Line 183: / Line 176: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.4124{{c}}, ~3/2 = 701.1291{{c}}, ~11/10 = 155.8292{{c}}
+* [[WE]]: ~2 = 1200.4124{{c}}, ~3/2 = 701.1291{{c}}, ~12/11 = 155.8292{{c}}
 : [[error map]]: {{val| +0.412 -0.414 +3.982 -1.435 -4.781 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2359{{c}}, ~11/10 = 155.7399{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2359{{c}}, ~12/11 = 155.7399{{c}}
 : error map: {{val| 0.000 -0.719 +3.442 -2.029 -5.822 }}
-<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.8882{{c}}, ~11/10 = 155.7756{{c}} -->
 {{Optimal ET sequence|legend=1| 7d, 8d, 15, 23de, 24d, 31, 46, 77 }}
@@ Line 201: / Line 193: @@
 Optimal tunings:
-* WE: ~2 = 1198.9113{{c}}, ~3/2 = 700.9581{{c}}, ~11/10 = 154.7247{{c}}
+* WE: ~2 = 1198.9113{{c}}, ~3/2 = 700.9581{{c}}, ~12/11 = 154.7247{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.6409{{c}}, ~11/10 = 154.9115{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.6409{{c}}, ~12/11 = 154.9115{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5946{{c}}, ~11/10 = 154.8652{{c}} -->
 {{Optimal ET sequence|legend=0| 7d, 8d, 15, 23de, 24d, 31 }}
 Badness (Sintel): 1.02
+== Kahoupokane ==
+Named by [[Tristan Bay]] in 2025, Kahoupokane tempers out [[5120/5103]] and may be described as the {{nowrap| 29 & 46 & 53 }} temperament.
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 121/120, 5120/5103
+{{Mapping|legend=1| 1 0 1 11 2 | 0 1 1 -5 1 | 0 0 -2 -2 -1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1911{{c}}, ~3/2 = 703.1412{{c}}, ~11/10 = 158.1068{{c}}
+: [[error map]]: {{val| +0.191 +1.377 +0.996 +0.401 -5.710 }}
+* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.0417{{c}}, ~11/10 = 157.9917{{c}}
+: error map: {{val| 0.000 +1.087 +0.744 -0.018 -6.268 }}
+{{Optimal ET sequence|legend=1| 7, 17c, 24d, 29, 46, 53, 82e, 99 }}
+[[Badness]] (Sintel): 2.73
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 121/120, 169/168, 352/351
+Mapping: {{mapping| 1 0 1 11 2 7 | 0 1 1 -5 1 -2 | 0 0 -2 -2 -1 -1 }}
+Optimal tunings:
+* WE: ~2 = 1200.4435{{c}}, ~3/2 = 703.1443{{c}}, ~11/10 = 158.4176{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9013{{c}}, ~11/10 = 158.1657{{c}}
+{{Optimal ET sequence|legend=0| 7, 17c, 24d, 29, 46, 53, 82e, 99, 181eef }}
+Badness (Sintel): 1.27
 == Big brother ==
@@ Line 261: / Line 286: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.8990{{c}}, ~22/21 = 78.4412{{c}}
 : error map: {{val| 0.000 -1.056 +0.820 -4.150 -7.301 }}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 700.3200{{c}}, ~22/21 = 78.6421{{c}} -->
 {{Optimal ET sequence|legend=1| 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee }}
@@ Line 267: / Line 291: @@
 [[Badness]] (Sintel): 0.701
-==== 13-limit ====
+=== Eros ===
-Subgroup: 2.3.5.7.11.13
+Eros fairs impressively into the 23-limit as a rank-3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but has the pleasing property that all the harmonics are on the negative side of the last generator. Specifically, -3 to 2 fifths and -5 to 0 [[~]][[23/22]]'s will provide odd harmonics 1–23 up to octave equivalence; you can think of this as a 6×6 grid, which is a recommendable place to start looking at its structure.
-Comma list: 121/120, 351/350, 441/440
-Mapping: {{mapping| 1 0 1 3 2 6 | 0 1 1 0 1 -1 | 0 0 -4 -3 -2 -11 }}
-Optimal tunings:
-* WE: ~2 = 1201.0656{{c}}, ~3/2 = 700.7374{{c}}, ~22/21 = 78.5908{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.7005{{c}}, ~22/21 = 78.3253{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 700.1158{{c}}, ~21/20 = 78.5211{{c}} -->
-{{Optimal ET sequence|legend=0| 14cf, 29ff, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}
-Badness (Sintel): 1.36
+Tempering out the less accurate comma 121/120 can be seen as an implication of tempering out [[441/440]] ({{S|21}}), [[484/483]] ({{S|22}}), and [[529/528]] ({{S|23}}). Therefore, characteristic of any good tuning is the prime [[11/1|11]] being the flattest prime, with other primes having strictly less than 5{{cent}} of error.
-==== Eros ====
+This temperament was discovered by [[Scott Dakota]]. Note that the 17-limit extension requires the 29g val for 29edo, which has the sizes of 17/16 and 18/17 swapped.
-Eros fairs impressively into the 23-limit as a rank 3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but all the generators are positive (or only 1 into the negatives in the case of the fifth) meaning it's even simpler than it might appear and has the pleasing property of all harmonics and subharmonics being "on the same side"; specifically: -3 to 1 fifths ([[2L 3s]]) and -5 to 0 ~[[23/22]]'s will get you every prime, up to octave equivalence; you can think of this as a 5 by 6 grid if you like and is a recommendable place to start looking at its structure. Tempering the less accurate comma [[121/120|S11]] can be seen as a consequence of tempering {[[441/440|S21]], [[484/483|S22]], [[529/528|S23]]} so is very natural and given its properties certainly excusable. Therefore characteristic of any good tuning is the ~11 being the most flat prime, with other primes having strictly less than 5{{cent}} of error. This temperament was first logged on x31eq by [[Scott Dakota]].
 Subgroup: 2.3.5.7.11.13
@@ Line 295: / Line 307: @@
 * WE: ~2 = 1200.6419{{c}}, ~3/2 = 701.8766{{c}}, ~22/21 = 78.6564{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5612{{c}}, ~22/21 = 78.4778{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5014{{c}}, ~21/20 = 78.6143{{c}} -->
 {{Optimal ET sequence|legend=0| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }}
@@ Line 301: / Line 312: @@
 Badness (Sintel): 1.08
-===== 17-limit =====
+==== 17-limit ====
-Note that this extension requires the 29g val for 29edo, which has the sizes of 17/16 and 18/17 swapped.
 Subgroup: 2.3.5.7.11.13.17
@@ Line 313: / Line 322: @@
 * WE: ~2 = 1200.6172{{c}}, ~3/2 = 702.1026{{c}}, ~22/21 = 78.7963{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7925{{c}}, ~22/21 = 78.6203{{c}}
-<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9299{{c}}, ~22/21 = 78.2539{{c}} -->
 {{Optimal ET sequence|legend=0| 17cg, 29g, 31, 46, 60e, 77, 106de }}
@@ Line 319: / Line 327: @@
 Badness (Sintel): 0.931
-===== 19-limit =====
+==== 19-limit ====
 Subgroup: 2.3.5.7.11.13.17.19
@@ Line 329: / Line 337: @@
 * WE: ~2 = 1200.6224{{c}}, ~3/2 = 702.0959{{c}}, ~22/21 = 78.8004{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.6963{{c}}, ~22/21 = 78.6479{{c}}
-<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5642{{c}}, ~22/21 = 78.2353{{c}} -->
 {{Optimal ET sequence|legend=0| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}
@@ Line 335: / Line 342: @@
 Badness (Sintel): 1.16
-===== 23-limit =====
+==== 23-limit ====
 Subgroup: 2.3.5.7.11.13.17.19.23
@@ Line 345: / Line 352: @@
 * WE: ~2 = 1200.7268{{c}}, ~3/2 = 702.2463{{c}}, ~22/21 = 78.8824{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8010{{c}}, ~23/22 = 78.7188{{c}}
-<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7115{{c}}, ~23/22 = 78.2054{{c}} -->
 {{Optimal ET sequence|legend=0| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}
@@ Line 351: / Line 357: @@
 Badness (Sintel): 1.08
-==== Inanna ====
+=== Astarte ===
+This extension is catalogued as tridecimal aphrodite in [[Graham Breed]]'s temperament finder.
+Subgroup: 2.3.5.7.11.13
+Comma list: 121/120, 351/350, 441/440
+Mapping: {{mapping| 1 0 1 3 2 6 | 0 1 1 0 1 -1 | 0 0 -4 -3 -2 -11 }}
+Optimal tunings:
+* WE: ~2 = 1201.0656{{c}}, ~3/2 = 700.7374{{c}}, ~22/21 = 78.5908{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.7005{{c}}, ~22/21 = 78.3253{{c}}
+{{Optimal ET sequence|legend=0| 14cf, 29ff, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}
+Badness (Sintel): 1.36
+=== Inanna ===
 Subgroup: 2.3.5.7.11.13
@@ Line 361: / Line 384: @@
 * WE: ~2 = 1201.7881{{c}}, ~3/2 = 699.8166{{c}}, ~22/21 = 79.7282{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.5926{{c}}, ~22/21 = 79.3822{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 698.7754{{c}}, ~21/20 = 79.6096{{c}} -->
 {{Optimal ET sequence|legend=0| 14cf, 15, 29, 31, 45ef, 60e }}
@@ Line 367: / Line 389: @@
 Badness (Sintel): 1.01
-==== Ishtar ====
+=== Ishtar ===
 Subgroup: 2.3.5.7.11.13
@@ Line 377: / Line 399: @@
 * WE: ~2 = 1200.7875{{c}}, ~3/2 = 703.8568{{c}}, ~22/21 = 79.0096{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7640{{c}}, ~22/21 = 78.8025{{c}}
-<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.3952{{c}}, ~21/20 = 78.9578{{c}} -->
 {{Optimal ET sequence|legend=0| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }}
@@ Line 387: / Line 408: @@
 [[Category:Temperament clans]]
 [[Category:Biyatismic clan| ]] <!-- main article -->
-[[Category:Biyatismic| ]] <!-- key article -->
 [[Category:Rank 3]]