Trienstonic clan: Difference between revisions
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The '''trienstonic clan''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] [[28/27]], the septimal third-tone or trienstonic comma. This equates very different intervals with each other | The '''trienstonic clan''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] [[28/27]], the septimal third-tone or trienstonic comma. This equates very different intervals with each other; in particular, [[9/8]] is equated with [[7/6]], [[8/7]] with [[32/27]], and [[4/3]] with [[9/7]]. Trienstonian is inaccurate enough that it is close to the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]]. | ||
Adding 16/15 to 28/27 leads to father, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 35/32 gives wallaby. Other members of the clan discussed elsewhere are: | Adding 16/15 to 28/27 leads to father, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 35/32 gives wallaby. Other members of the clan discussed elsewhere are: | ||
* ''[[Sharptone]]'' (+21/20) | * ''[[Sharptone]]'' (+21/20) → [[Meantone family #Sharptone|Meantone family]] | ||
* ''[[Sharp (temperament)|Sharp]]'' (+25/24) | * ''[[Sharp (temperament)|Sharp]]'' (+25/24) → [[Dicot family #Sharp|Dicot family]] | ||
* ''[[Inflated]]'' (+128/125) | * ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]] | ||
* ''[[Opossum]]'' (+126/125) | * ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]] | ||
* ''[[Blacksmith]]'' (+49/48) | * ''[[Blacksmith]]'' (+49/48) → [[Limmic temperaments #Blacksmith|Limmic temperaments]] | ||
== Trienstonian == | == Trienstonian == | ||
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{{Mapping|legend=2| 1 0 -2 | 0 1 3 }} | {{Mapping|legend=2| 1 0 -2 | 0 1 3 }} | ||
: | : Mapping generators: ~2, ~3 | ||
{{Mapping|legend=3| 1 0 0 -2 | 0 1 0 3 }} | {{Mapping|legend=3| 1 0 0 -2 | 0 1 0 3 }} | ||
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{{Mapping|legend=1| 2 0 -5 | 0 1 3 }} | {{Mapping|legend=1| 2 0 -5 | 0 1 3 }} | ||
: | : Mapping generators: ~27/20, ~3 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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{{Mapping|legend=1| 1 0 -3 -2 | 0 3 10 9 }} | {{Mapping|legend=1| 1 0 -3 -2 | 0 3 10 9 }} | ||
: | : Mapping generators: ~2, ~10/7 | ||
{{Multival|legend=1| 3 10 9 9 6 -7 }} | {{Multival|legend=1| 3 10 9 9 6 -7 }} | ||
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Mapping: {{mapping| 15 24 35 42 52 0 | 0 0 0 0 0 1 }} | Mapping: {{mapping| 15 24 35 42 52 0 | 0 0 0 0 0 1 }} | ||
: | : Mapping generators: ~22/21, ~13 | ||
Optimal tunings: | Optimal tunings: | ||
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[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Trienstonic clan| ]] <!-- | [[Category:Trienstonic clan| ]] <!-- Main article --> | ||
[[Category:Trienstonic| ]] <!-- | [[Category:Trienstonic| ]] <!-- Key article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||