Trienstonic clan: Difference between revisions

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[[Comma list]]: 28/27

: mapping generators: ~2, ~3

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* ''[[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~~]]

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

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

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

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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

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Comma list: 28/27, 50/49, 55/54

~~Mapping:~~ {{~~mapping~~| 2 0 -5 -4 7 | 0 1 3 3 0 }}

Optimal tunings:

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Comma list: 28/27, 77/75, 245/242

~~Mapping:~~ {{~~mapping~~| 1 0 -3 -2 -4 | 0 3 10 9 14 }}

Optimal tunings:

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Comma list: 28/27, 40/39, 66/65, 147/143

~~Mapping:~~ {{~~mapping~~| 1 0 -3 -2 -4 0 | 0 3 10 9 14 7 }}

Optimal tunings:

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Badness (Sintel): 1.35

[[Category:Trienstonic clan| ]]

[[Category:Temperament clans]]

[[Category:~~Trienstonic clan| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-2 temperaments]]

~~[[Category:Rank~~ 2]]

@@ Line 9: / Line 9: @@
 [[Comma list]]: 28/27
-{{Mapping|legend=2| 1 0 -2 | 0 1 3 }}
+{{Mapping|legend=3| 1 0 -2 | 0 1 3 }}
-{{Mapping|legend=3| 1 0 0 -2 | 0 1 0 3 }}
+{{Mapping|legend=5| 1 0 0 -2 | 0 1 0 3 }}
 : mapping generators: ~2, ~3
@@ Line 37: / Line 37: @@
 * ''[[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]]
+* [[Blackwood]] (+49/48) → [[Blackwood family #Blackwood|Blackwood family]]
 * ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]]
 * ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]]
@@ Line 70: / Line 70: @@
 == 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 95: / Line 96: @@
 Comma list: 28/27, 50/49, 55/54
-Mapping: {{mapping| 2 0 -5 -4 7 | 0 1 3 3 0 }}
+{{Mapping|legend=0| 2 0 -5 -4 7 | 0 1 3 3 0 }}
 Optimal tunings:
@@ Line 133: / Line 134: @@
 Comma list: 28/27, 77/75, 245/242
-Mapping: {{mapping| 1 0 -3 -2 -4 | 0 3 10 9 14 }}
+{{Mapping|legend=0| 1 0 -3 -2 -4 | 0 3 10 9 14 }}
 Optimal tunings:
@@ Line 148: / Line 149: @@
 Comma list: 28/27, 40/39, 66/65, 147/143
-Mapping: {{mapping| 1 0 -3 -2 -4 0 | 0 3 10 9 14 7 }}
+{{Mapping|legend=0| 1 0 -3 -2 -4 0 | 0 3 10 9 14 7 }}
 Optimal tunings:
@@ Line 158: / Line 159: @@
 Badness (Sintel): 1.35
+[[Category:Trienstonic clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Trienstonic clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]