Breed family: Difference between revisions

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The '''breed family''' of [[rank-3 ~~temperament|rank-3]] [[regular temperament|~~temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].

The '''breed family''' of [[rank-3 temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].

== Breed ==

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Badness (Sintel): 0.701

=== Semijove ===

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 441/440, 676/675

Mapping: {{mapping| 2 0 1 3 -1 -1 | 0 2 1 1 5 4 | 0 0 2 1 0 2 }}

: mapping generators: ~55/39, ~26/15, ~10/7

Optimal tunings:

* WE: ~55/39 = 599.9886{{c}}, ~26/15 = 950.6645{{c}}, ~10/7 = 618.1458{{c}}

* CWE: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6755{{c}}, ~10/7 = 618.1489{{c}}

Badness (Sintel): 0.948

== Agni ==

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== Lif ==

Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the ~~undevicesimal schisma of~~ [[513/512]] is also equated with the schisma.

Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the [[513/512|undevicesimal schisma]] is also equated with the schisma.

This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma, lifthrasirsma, after the human survivors of Ragnarök.

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[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = ~~350~~.0586{{c}}, ~10/7 = 617.7065{{c}}

* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 351.0586{{c}}, ~10/7 = 617.7065{{c}}

: [[error map]]: {{val| -0.061 +0.101 +0.096 -0.184 +0.075 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.0806{{c}}, ~10/7 = 617.7228{{c}}

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Badness (Sintel): 0.488

== Freyr ==

Freyr tempers out the [[symbiotic comma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[5120/5103|aberschisma]]. Freyr easily extends to the [[13-limit]], equating the [[352/351|major minthma]] with the aberschisma, and the no-17 [[19-limit]], equating the [[513/512|undevicesimal schisma]] with it too.

This temperament was named by [[Flora Canou]] in 2026, under the impression that it functions a counterpart of [[#Freya|freya]].

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 2401/2400, 19712/19683

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9474{{c}}, ~49/40 = 351.1064{{c}}, ~10/7 = 617.6483{{c}}

: [[error map]]: {{val| -0.053 +0.205 +0.037 -0.176 -0.104 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1156{{c}}, ~10/7 = 617.6499{{c}}

: error map: {{val| 0.000 +0.276 +0.102 -0.060 -0.003 }}

{{Optimal ET sequence|legend=1| 41, 58, 99e, 171e, 212, 270, 581, 851, 1121, 1972, 2881bc }}

[[Badness]] (Sintel): 1.23

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2401/2400, 10648/10647

Mapping: {{mapping| 1 1 1 2 -1 -2 | 0 2 1 1 17 23 | 0 0 2 1 -1 -2 }}

Optimal tunings:

* WE: ~2 = 1199.9432{{c}}, ~49/40 = 351.1128{{c}}, ~10/7 = 617.6419{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1232{{c}}, ~10/7 = 617.6431{{c}}

{{Optimal ET sequence|legend=0| 41, 58, 99ef, 154cef, 171ef, 212, 270, 581, 851, 1490, 1760, 2071be, 2341b }}

Badness (Sintel): 0.760

=== 2.3.5.7.11.13.19 subgroup ===

Subgroup: 2.3.5.7.11.13.19

Comma list: 1216/1215, 1540/1539, 2080/2079, 2401/2400

Mapping: {{mapping| 1 1 1 2 -1 -2 0 | 0 2 1 1 17 23 11 | 0 0 2 1 -1 -2 2 }}

Optimal tunings:

* WE: ~2 = 1199.9435{{c}}, ~49/40 = 351.1127{{c}}, ~10/7 = 617.6404{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1236{{c}}, ~10/7 = 617.6459{{c}}

{{Optimal ET sequence|legend=0| 41, 58h, 99ef, 171ef, 212h, 270, 581, 851, 1490h, 1760h, 2071beh, 2341bh }}

Badness (Sintel): 0.523

== Baldur ==

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== Freya ==

Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes ~~breed's~~ [[225/224]][[~]][[1029/1024]] [[kleisma (interval region)|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma #As an interval region|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.

[[Subgroup]]: 2.3.5.7.11

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[[Badness]] (Sintel): 0.204

[[Projection pair]]s: ~3 ~~= ~~~2401/800, ~5 ~~= ~~~22880495169/4575312500, ~7 ~~= ~~~1058841/151250, ~11 ~~= ~~~33275/3024 to 2.49/5.77/3

[[Projection pair]]s: <code>3 2401/800, 5 22880495169/4575312500, 7 1058841/151250, 11 33275/3024</code> to 2.49/5.77/3

=== 13-limit ===

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Subgroup: 2.3.5.7.11.13.17

Comma list: 715/714, 936/935, 1001/1000, 1225/1224~~, 1716/1715~~

Comma list: 715/714, 936/935, 1001/1000, 1225/1224

Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}

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* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}

{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} ~~<nowiki>~~*~~</nowiki>~~

{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} *

<nowiki>*~~</nowiki> [[~~optimal patent val]]: [[1241edo|1241]]

<nowiki/>* optimal patent val: [[1241edo|1241]]

Badness (Sintel): 0.873

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Badness (Sintel): 0.706

[[Category:Breed family| ]]

[[Category:Temperament families]]

[[Category:~~Breed family| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-3 temperaments]]

~~[[Category:Rank~~ 3]]

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 {{Technical data page}}
-The '''breed family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].
+The '''breed family''' of [[rank-3 temperament]]s are [[microtemperament]]s which [[tempering out|temper out]] [[2401/2400]].
 == Breed ==
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 Badness (Sintel): 0.701
+=== Semijove ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 441/440, 676/675
+Mapping: {{mapping| 2 0 1 3 -1 -1 | 0 2 1 1 5 4 | 0 0 2 1 0 2 }}
+: mapping generators: ~55/39, ~26/15, ~10/7
+Optimal tunings:
+* WE: ~55/39 = 599.9886{{c}}, ~26/15 = 950.6645{{c}}, ~10/7 = 618.1458{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6755{{c}}, ~10/7 = 618.1489{{c}}
+{{Optimal ET sequence|legend=0| 48c, 58, 72, 130 }}
+Badness (Sintel): 0.948
 == Agni ==
@@ Line 238: / Line 254: @@
 == Lif ==
-Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the undevicesimal schisma of [[513/512]] is also equated with the schisma.
+Lif tempers out the [[olympia]] and the [[lifthrasirsma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[32805/32768|schisma]]. Lif readily extends to the [[13-limit]] and the no-17 [[19-limit]], where the [[513/512|undevicesimal schisma]] is also equated with the schisma.
 This temperament was named by [[Flora Canou]] in 2023 along with the [[weak restriction]], [[lifthrasir]], and the corresponding comma, lifthrasirsma, after the human survivors of Ragnarök.
@@ Line 249: / Line 265: @@
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 350.0586{{c}}, ~10/7 = 617.7065{{c}}
+* [[WE]]: ~2 = 1199.9386{{c}}, ~49/40 = 351.0586{{c}}, ~10/7 = 617.7065{{c}}
 : [[error map]]: {{val| -0.061 +0.101 +0.096 -0.184 +0.075 }}
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.0806{{c}}, ~10/7 = 617.7228{{c}}
@@ Line 287: / Line 303: @@
 Badness (Sintel): 0.488
+== Freyr ==
+Freyr tempers out the [[symbiotic comma]], so that the [[rastma]] is split in halves with each part standing in not only for [[441/440]][[~]][[540/539]], but the [[5120/5103|aberschisma]]. Freyr easily extends to the [[13-limit]], equating the [[352/351|major minthma]] with the aberschisma, and the no-17 [[19-limit]], equating the [[513/512|undevicesimal schisma]] with it too.
+This temperament was named by [[Flora Canou]] in 2026, under the impression that it functions a counterpart of [[#Freya|freya]].
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 2401/2400, 19712/19683
+{{Mapping|legend=1| 1 1 1 2 -1 | 0 2 1 1 17 | 0 0 2 1 -1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9474{{c}}, ~49/40 = 351.1064{{c}}, ~10/7 = 617.6483{{c}}
+: [[error map]]: {{val| -0.053 +0.205 +0.037 -0.176 -0.104 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1156{{c}}, ~10/7 = 617.6499{{c}}
+: error map: {{val| 0.000 +0.276 +0.102 -0.060 -0.003 }}
+{{Optimal ET sequence|legend=1| 41, 58, 99e, 171e, 212, 270, 581, 851, 1121, 1972, 2881bc }}
+[[Badness]] (Sintel): 1.23
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 2401/2400, 10648/10647
+Mapping: {{mapping| 1 1 1 2 -1 -2 | 0 2 1 1 17 23 | 0 0 2 1 -1 -2 }}
+Optimal tunings:
+* WE: ~2 = 1199.9432{{c}}, ~49/40 = 351.1128{{c}}, ~10/7 = 617.6419{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1232{{c}}, ~10/7 = 617.6431{{c}}
+{{Optimal ET sequence|legend=0| 41, 58, 99ef, 154cef, 171ef, 212, 270, 581, 851, 1490, 1760, 2071be, 2341b }}
+Badness (Sintel): 0.760
+=== 2.3.5.7.11.13.19 subgroup ===
+Subgroup: 2.3.5.7.11.13.19
+Comma list: 1216/1215, 1540/1539, 2080/2079, 2401/2400
+Mapping: {{mapping| 1 1 1 2 -1 -2 0 | 0 2 1 1 17 23 11 | 0 0 2 1 -1 -2 2 }}
+Optimal tunings:
+* WE: ~2 = 1199.9435{{c}}, ~49/40 = 351.1127{{c}}, ~10/7 = 617.6404{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1236{{c}}, ~10/7 = 617.6459{{c}}
+{{Optimal ET sequence|legend=0| 41, 58h, 99ef, 171ef, 212h, 270, 581, 851, 1490h, 1760h, 2071beh, 2341bh }}
+Badness (Sintel): 0.523
 == Baldur ==
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 == Freya ==
-Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes breed's [[225/224]][[~]][[1029/1024]] [[kleisma (interval region)|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.
+Freya tempers out [[3025/3024]] and [[41503/41472]], so it splits breed's [[28/27]] into two [[55/54]]~[[56/55]]'s and [[8/7]] into two [[77/72]]'s. It also takes the [[225/224]][[~]][[1029/1024]] [[kleisma #As an interval region|kleisma]] to represent [[243/242]], and splits it in half to get [[385/384]], [[441/440]], and [[540/539]]. Since these are the commas tempered out by [[miracle]], the simple relations between them make freya an elegant miracle detemperament.
 [[Subgroup]]: 2.3.5.7.11
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 [[Badness]] (Sintel): 0.204
-[[Projection pair]]s: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3
+[[Projection pair]]s: <code>3 2401/800, 5 22880495169/4575312500, 7 1058841/151250, 11 33275/3024</code> to 2.49/5.77/3
 === 13-limit ===
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 Subgroup: 2.3.5.7.11.13.17
-Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715
+Comma list: 715/714, 936/935, 1001/1000, 1225/1224
 Mapping: {{mapping| 1 1 -1 1 5 -6 -5 | 0 2 3 2 1 6 6 | 0 0 4 2 -3 13 12 }}
@@ Line 532: / Line 599: @@
 * CWE: ~2 = 1200.0000{{c}}, ~49/40 = 350.9526{{c}}, ~70/39 = 1013.3747{{c}}
-{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>
+{{Optimal ET sequence|legend=0| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} *
-<nowiki>*</nowiki> [[optimal patent val]]: [[1241edo|1241]]
+<nowiki/>* optimal patent val: [[1241edo|1241]]
 Badness (Sintel): 0.873
@@ Line 572: / Line 640: @@
 Badness (Sintel): 0.706
+[[Category:Breed family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Breed family| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]