Breed family: Difference between revisions

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== Lif ==

Lif tempers out the [[olympia]] and readily extends to the [[13-limit]] and the no-17 [[19-limit]] ~~such that~~ the undevicesimal schisma of [[513/512]] is equated with ~~[[441/440]][[~]][[540/539]]~~.

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.

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.

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.

[[Subgroup]]: 2.3.5.7.11

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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 the [[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.

[[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 ===

Freya's canonical 13-limit extension maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.

Subgroup: 2.3.5.7.11.13

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=== Eir ===

[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the ibnsinma that evokes associations with medicine.

[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the [[ibnsinma]] that evokes associations with medicine. It maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament.

Subgroup: 2.3.5.7.11.13

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=== Heimlaug ===

VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament.

VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament. It maps [[351/350]] and [[625/624]] to the half-kleisma.

Subgroup: 2.3.5.7.11.13

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==== 17-limit ====

~~Equave 10/7 and 16-note scales with that period are of interest.~~

Subgroup: 2.3.5.7.11.13.17

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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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: error map: {{val| 0.000 +0.021 -0.016 -0.183 -0.040 }}

{{Optimal ET sequence|legend=1| 72~~, …~~, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}

{{Optimal ET sequence|legend=1| 72, 171(e), 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}

[[Badness]] (Sintel): 0.330

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* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}

{{Optimal ET sequence|legend=0| 72~~, …~~, 171, 198, 270, 639, 711, 981, 1692e }}

{{Optimal ET sequence|legend=0| 72, 171(ef), 198, 270, 639, 711, 981, 1692e }}

Badness (Sintel): 0.706

@@ Line 238: / Line 238: @@
 == Lif ==
-Lif tempers out the [[olympia]] and readily extends to the [[13-limit]] and the no-17 [[19-limit]] such that the undevicesimal schisma of [[513/512]] is equated with [[441/440]][[~]][[540/539]].
+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.
-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.
+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.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 348: / Line 348: @@
 == 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 the [[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.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 368: / Line 370: @@
 [[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 ===
+Freya's canonical 13-limit extension maps [[352/351]] to the half-kleisma. It has [[miraculous]] as a sub-temperament.
 Subgroup: 2.3.5.7.11.13
@@ Line 388: / Line 392: @@
 === Eir ===
-[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the ibnsinma that evokes associations with medicine.
+[[User:VIxen|VIxen]] named this extension after a healer goddess or valkyrie from the Norse mythology, as it is an extension of freya with the [[ibnsinma]] that evokes associations with medicine. It maps [[325/324]], [[364/363]], and [[729/728]] to the half-kleisma and has [[manna]] as a sub-temperament.
 Subgroup: 2.3.5.7.11.13
@@ Line 435: / Line 439: @@
 === Heimlaug ===
-VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament.
+VIxen named this extension after a völva (seeress) from the Gull-Þóris saga of Icelanders. It is an extension of freya with the [[1001/1000|fairytale comma]] and the [[936/935|ainisma]], both adding to the mystical theme. The one of prophecy is bolstered by that this extension has [[benediction]] as a subtemperament. It maps [[351/350]] and [[625/624]] to the half-kleisma.
 Subgroup: 2.3.5.7.11.13
@@ Line 452: / Line 456: @@
 ==== 17-limit ====
-Equave 10/7 and 16-note scales with that period are of interest.
 Subgroup: 2.3.5.7.11.13.17
@@ Line 530: / Line 532: @@
 * 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 551: / Line 554: @@
 : error map: {{val| 0.000 +0.021 -0.016 -0.183 -0.040 }}
-{{Optimal ET sequence|legend=1| 72, …, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}
+{{Optimal ET sequence|legend=1| 72, 171(e), 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd, 6903dd }}
 [[Badness]] (Sintel): 0.330
@@ Line 566: / Line 569: @@
 * CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3905{{c}}, ~11/8 = 551.7085{{c}}
-{{Optimal ET sequence|legend=0| 72, …, 171, 198, 270, 639, 711, 981, 1692e }}
+{{Optimal ET sequence|legend=0| 72, 171(ef), 198, 270, 639, 711, 981, 1692e }}
 Badness (Sintel): 0.706