Trienstonic clan: Difference between revisions

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Members of the clan discussed elsewhere are:

* ''[[~~Wallaby~~]]'' (+35/32) → [[Very low accuracy temperaments #~~Wallaby~~|Very low accuracy temperaments]]

* [[Antonian]] (+10/9 or +15/14) → [[Very low accuracy temperaments #Septimal antonian|Very low accuracy temperaments]]

* [[Father]] (+16/15) → [[Father family #Septimal father|Father family]]

* ''[[Sharptone]]'' (+21/20) → [[Meantone family #Sharptone|Meantone family]]

* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie|Dicot family]]

* ''[[Mite]]'' (+27/25) → [[Bug family #Mite|Bug family]]

* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]]

* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood|Limmic temperaments]]

* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]]

* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]]

* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]]

* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood|Limmic temperaments]]

~~Considered below are father, sharptone, uncle, octokaidecal, and parakangaroo.~~

~~== Father ==~~

~~{{Main| Father }}~~

~~Father tempers out [[16/15]] and uses the generator for [[~]][[8/5]]. See [[Father family #Septimal father]].~~

~~== Sharptone ==~~

Considered below are uncle, octokaidecal, and parakangaroo.

~~Sharptone tempers out [[21/20]]~~ and ~~maps the interval class of 5 to four generator steps as in [[meantone]]. See [[Meantone family #Sharptone]]~~.

== Uncle ==

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== Octokaidecal ==

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Supersharp]].''

Octokaidecal extends trienstonian by tempering out [[50/49]], thus splitting the octave in half. It generates the [[8L 2s]] (taric) mos scale, with tunings on the other side of [[10edo]] as [[2L 8s]] (jaric). Compared to [[pajara]], decatonic thirds ([[8/7]] and [[7/6]]) and fourths ([[6/5]] and [[5/4]]) have their mappings reversed, meaning octokaidecal can be considered what is to pajara as [[mavila]] is to [[meantone]].

[[Subgroup]]: 2.3.5.7

@@ Line 30: / Line 30: @@
 Members of the clan discussed elsewhere are:
-* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]]
+* [[Antonian]] (+10/9 or +15/14) → [[Very low accuracy temperaments #Septimal antonian|Very low accuracy temperaments]]
+* [[Father]] (+16/15) → [[Father family #Septimal father|Father family]]
+* ''[[Sharptone]]'' (+21/20) → [[Meantone family #Sharptone|Meantone family]]
 * ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie|Dicot family]]
 * ''[[Mite]]'' (+27/25) → [[Bug family #Mite|Bug family]]
+* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]]
+* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
+* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]]
 * ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]]
-* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]]
-* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
-Considered below are father, sharptone, uncle, octokaidecal, and parakangaroo.
-== Father ==
-{{Main| Father }}
-Father tempers out [[16/15]] and uses the generator for [[~]][[8/5]]. See [[Father family #Septimal father]].
-== Sharptone ==
+Considered below are uncle, octokaidecal, and parakangaroo.
-Sharptone tempers out [[21/20]] and maps the interval class of 5 to four generator steps as in [[meantone]]. See [[Meantone family #Sharptone]].
 == Uncle ==
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 == Octokaidecal ==
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Supersharp]].''
+Octokaidecal extends trienstonian by tempering out [[50/49]], thus splitting the octave in half. It generates the [[8L 2s]] (taric) mos scale, with tunings on the other side of [[10edo]] as [[2L 8s]] (jaric). Compared to [[pajara]], decatonic thirds ([[8/7]] and [[7/6]]) and fourths ([[6/5]] and [[5/4]]) have their mappings reversed, meaning octokaidecal can be considered what is to pajara as [[mavila]] is to [[meantone]].
 [[Subgroup]]: 2.3.5.7