Aberschismic family: Difference between revisions

- kahoupokane (addressed in biyatismic clan)
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==== 11- and 13-limit extensions ====
==== 11- and 13-limit extensions ====
Strong extensions of hemifamity are [[#Pele|pele]], [[#Laka|laka]], [[#Akea|akea]], and [[#Lono|lono]]. The rest are weak extensions. Using the arrow to represent the syntonic~septimal comma, pele finds the [[11/8]] at the down diminished fifth (C–vGb); laka, up augmented third (C–^E#); akea, double-up fourth (C–^^F); lono, triple-down augmented fourth (C–v<sup>3</sup>F#). All these extensions follow the trend of tuning the fifth a little sharp. Thus a successful mapping of 13 can be found by fixing the [[13/11]] at the minor third (C–Eb), tempering out [[352/351]], [[847/845]], and [[2080/2079]].  
Strong extensions of hemifamity are [[#Pele|pele]], [[#Laka|laka]], [[#Akea|akea]], and [[#Lono|lono]]. The rest are weak extensions. Using the arrow to represent the syntonic~septimal comma, pele finds the [[11/8]] at the down diminished fifth (C–vGb); laka, up augmented third (C–^E#); akea, double-up fourth (C–^^F); lono, triple-down augmented fourth (C–v<sup>3</sup>F#). All these extensions follow the trend of tuning the fifth a little sharp. Thus a successful mapping of 13 can be found by fixing the [[13/11]] at the minor third (C–Eb), tempering out [[352/351]], [[847/845]], and [[2080/2079]].  
Temperaments discussed elsewhere include:
* ''[[Kahoupokane]]'' (+121/120) → [[Biyatismic clan #Kahoupokane|Biyatismic clan]]


==== Subgroup extensions ====
==== Subgroup extensions ====
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Badness (Sintel): 0.731
Badness (Sintel): 0.731
== Kahoupokane ==
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 121/120, 5120/5103
{{Mapping|legend=1| 1 0 1 11 2 | 0 1 1 -5 1 | 0 0 -2 -2 -1 }}
: mapping generators: ~2, ~3, ~11/10
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1911{{c}}, ~3/2 = 703.1412{{c}}, ~11/10 = 158.1068{{c}}
: [[error map]]: {{val| +0.191 +1.377 +0.996 +0.401 -5.710 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.0417{{c}}, ~11/10 = 157.9917{{c}}
: error map: {{val| 0.000 +1.087 +0.744 -0.018 -6.268 }}
{{Optimal ET sequence|legend=1| 7, 17c, 24d, 29, 46, 53, 82e, 99 }}
[[Badness]] (Sintel): 2.73
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 352/351
Mapping: {{mapping| 1 0 1 11 2 7 | 0 1 1 -5 1 -2 | 0 0 -2 -2 -1 -1 }}
Optimal tunings:
* WE: ~2 = 1200.4435{{c}}, ~3/2 = 703.1443{{c}}, ~11/10 = 158.4176{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9013{{c}}, ~11/10 = 158.1657{{c}}
{{Optimal ET sequence|legend=0| 7, 17c, 24d, 29, 46, 53, 82e, 99, 181eef }}
Badness (Sintel): 1.27


== References ==
== References ==