Trienstonic clan: Difference between revisions

Xenllium (talk | contribs)
No edit summary
-opossum (addressed in porcupine family)
Line 1: Line 1:
The '''trienstonic clan''' of temperaments tempers out [[28/27]], the septimal third-tone or trienstonic comma.  
The '''trienstonic clan''' of temperaments tempers out [[28/27]], the septimal third-tone or trienstonic comma.  


Adding 16/15 to 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are [[Dicot family #Sharp|sharp]], [[Archytas clan #Blacksmith|blacksmith]], and [[Meantone family #Sharptone|sharptone]].
Adding 16/15 to 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are:
* ''[[Sharp (temperament)|Sharp]]'' → [[Dicot family #Sharp|Dicot family]]
* ''[[Blacksmith]]'' → [[Archytas clan #Blacksmith|Archytas clan]]
* ''[[Sharptone]]'' → [[Meantone family #Sharptone|Meantone family]]
* ''[[Opossum]]'' → [[Porcupine family #Opossum|Porcupine family]]


== No-fives trienstonic ==
== No-fives trienstonic ==
Line 120: Line 124:


Badness: 0.030235
Badness: 0.030235
== Opossum ==
{{See also|Porcupine family}}
Subgroup: 2.3.5.7
[[Comma list]]: 28/27, 126/125
[[Mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -3 -5 -9 }}]
{{Multival|legend=1| 3 5 9 1 6 7 }}
[[POTE generator]]: ~10/9 = 159.691
[[Minimax tuning]]:
* [[7-odd-limit]] eigenmonzo subgroup: 2.7
* [[9-odd-limit]] eigenmonzo subgroup: 2.7
{{Val list|legend=1| 7d, 8d, 15 }}
[[Badness]]: 0.040650
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 28/27, 55/54, 77/75
Mapping: [{{val| 1 2 3 4 4 }}, {{val| 0 -3 -5 -9 -4 }}]
POTE generator: ~10/9 = 159.807
Minimax tuning:
* 11-odd-limit eigenmonzo subgroup: 2.7
Optimal GPV sequence: {{Val list| 7d, 8d, 15 }}
Badness: 0.022325
=== 13-limit  ===
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 55/54, 66/65
Mapping: [{{val| 1 2 3 4 4 4 }}, {{val| 0 -3 -5 -9 -4 -2 }}]
POTE generator: ~10/9 = 159.805
Minimax tuning:
* 13-odd-limit eigenmonzo subgroup: 2.7
* 15-odd-limit eigenmonzo subgroup: 2.7
Optimal GPV sequence: {{Val list| 7d, 8d, 15, 38bcef }}
Badness: 0.019389


== Kangaroo ==
== Kangaroo ==