Trienstonic clan: Difference between revisions
-quindecic (moved to 15th-octave temps) |
Unify to 3 decimal places. Misc cleanup |
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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 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1\1, ~3/2 = 717. | * [[CTE]]: ~2 = 1\1, ~3/2 = 717.517 | ||
* [[POTE]]: ~2 = 1\1, ~3/2 = 721. | * [[POTE]]: ~2 = 1\1, ~3/2 = 721.559 | ||
{{Optimal ET sequence|legend=1| 2d, 3d, 5 }} | {{Optimal ET sequence|legend=1| 2d, 3d, 5 }} | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1\1, ~3/2 = 731. | * [[CTE]]: ~2 = 1\1, ~3/2 = 731.394 | ||
* [[POTE]]: ~2 = 1\1, ~3/2 = 731.177 | * [[POTE]]: ~2 = 1\1, ~3/2 = 731.177 | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1\1, ~3/2 = 691. | * [[CTE]]: ~2 = 1\1, ~3/2 = 691.757 | ||
* [[POTE]]: ~2 = 1\1, ~3/2 = 691.351 | * [[POTE]]: ~2 = 1\1, ~3/2 = 691.351 | ||
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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: | ||
* [[CTE]]: ~27/20 = 1\2, ~3/2 = 726. | * [[CTE]]: ~27/20 = 1\2, ~3/2 = 726.548 | ||
* [[POTE]]: ~27/20 = 1\2, ~3/2 = 729.097 | * [[POTE]]: ~27/20 = 1\2, ~3/2 = 729.097 | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~7/5 = 1\2, ~3/2 = 723. | * [[CTE]]: ~7/5 = 1\2, ~3/2 = 723.371 | ||
* [[POTE]]: ~7/5 = 1\2, ~3/2 = 728.874 | * [[POTE]]: ~7/5 = 1\2, ~3/2 = 728.874 | ||
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Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 1\2, ~3/2 = 723. | * CTE: ~7/5 = 1\2, ~3/2 = 723.371 | ||
* POTE: ~7/5 = 1\2, ~3/2 = 732.330 | * POTE: ~7/5 = 1\2, ~3/2 = 732.330 | ||
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== Parakangaroo == | == Parakangaroo == | ||
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Kangaroo]].'' | : ''For the 5-limit version of this temperament, see [[High badness temperaments #Kangaroo]].'' | ||
This temperament used to be known as '''kangaroo'''. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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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 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1\1, ~10/7 = 638. | * [[CTE]]: ~2 = 1\1, ~10/7 = 638.863 | ||
* [[POTE]]: ~2 = 1\1, ~10/7 = 639.672 | * [[POTE]]: ~2 = 1\1, ~10/7 = 639.672 | ||
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Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1\1, ~10/7 = 639. | * CTE: ~2 = 1\1, ~10/7 = 639.036 | ||
* POTE: ~2 = 1\1, ~10/7 = 639.845 | * POTE: ~2 = 1\1, ~10/7 = 639.845 | ||
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Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1\1, ~10/7 = 638. | * CTE: ~2 = 1\1, ~10/7 = 638.717 | ||
* POTE: ~2 = 1\1, ~10/7 = 640.230 | * POTE: ~2 = 1\1, ~10/7 = 640.230 | ||