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Gamelismic clan: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (3/)
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== Gorgo ==
== Gorgo ==
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Laconic]].''
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Laconic]].''
 
{{See also| Llywelynsmic clan }}
{{See also| Shoe }}


Gorgo tempers the generator of ~8/7 together with ~10/9. It can be described as the {{nowrap| 16 & 21 }} temperament.  
Gorgo tempers the generator of ~8/7 together with ~10/9. It can be described as the {{nowrap| 16 & 21 }} temperament.  
Line 690: Line 689:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 228.724{{c}}
* [[WE]]: ~2 = 1200.9847{{c}}, ~8/7 = 228.5210{{c}}
: [[error map]]: {{val| +0.985 -15.407 +14.318 +5.607 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 228.4371{{c}}
: error map: {{val| 0.000 -16.644 +12.746 +2.737 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 228.724{{c}}
: [[error map]]: {{val| 0.000 -15.782 +14.756 +2.450 }}
: [[error map]]: {{val| 0.000 -15.782 +14.756 +2.450 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 228.334{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 228.334{{c}}
: error map: {{val| 0.000 -16.954 +12.022 +2.840 }}
: error map: {{val| 0.000 -16.954 +12.022 +2.840 }} -->


{{Optimal ET sequence|legend=1| 5, 11c, 16, 21 }}
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21 }}


[[Badness]] (Smith): 0.060663
[[Badness]] (Sintel): 1.54


=== 11-limit ===
=== 11-limit ===
Line 707: Line 710:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 227.833{{c}}
* WE: ~2 = 1201.3609{{c}}, ~8/7 = 227.6312{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 227.373{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.4955{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 227.833{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 227.373{{c}} -->


{{Optimal ET sequence|legend=0| 5e, 16, 21, 37b }}
{{Optimal ET sequence|legend=0| 5e, 16, 21, 37b }}


Badness (Smith): 0.049500
Badness (Sintel): 1.64


==== 13-limit ====
==== 13-limit ====
Line 722: Line 727:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 227.633{{c}}
* WE: ~2 = 1201.0996{{c}}, ~8/7 = 227.4378{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 227.230{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.3327{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 227.633{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 227.230{{c}} -->


{{Optimal ET sequence|legend=0| 5e, 16, 21, 37b }}
{{Optimal ET sequence|legend=0| 5e, 16, 21, 37b }}


Badness (Smith): 0.032664
Badness (Sintel): 1.35


=== Spartan ===
=== Spartan ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 229.420{{c}}
* WE: ~2 = 1198.9344{{c}}, ~8/7 = 229.3316{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 229.535{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 229.5124{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 229.420{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 229.535{{c}} -->


{{Optimal ET sequence|legend=0| 5, 16e, 21 }}
{{Optimal ET sequence|legend=0| 5, 16e, 21 }}


Badness (Smith): 0.062683
Badness (Sintel): 2.07


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 228.758{{c}}
* WE: ~2 = 1198.3002{{c}}, ~8/7 = 228.7341{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 229.059{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 229.0044{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 228.758{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 229.059{{c}} -->


{{Optimal ET sequence|legend=0| 5, 16e, 21 }}
{{Optimal ET sequence|legend=0| 5, 16e, 21 }}


Badness (Smith): 0.047071
Badness (Sintel): 1.95


; Music
; Music
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 227.100{{c}}
* [[WE]]: ~2 = 1192.4932{{c}}, ~8/7 = 229.3187{{c}}
: [[error map]]: {{val| -7.507 -21.506 +57.310 -20.665 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 229.6649{{c}}
: error map: {{val| 0.000 -12.960 +73.016 +1.509 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 227.100{{c}}
: [[error map]]: {{val| 0.000 -20.655 +67.886 +4.074 }}
: [[error map]]: {{val| 0.000 -20.655 +67.886 +4.074 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 230.762{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 230.762{{c}}
: error map: {{val| 0.000 -9.668 +75.211 +0.412 }}
: error map: {{val| 0.000 -9.668 +75.211 +0.412 }} -->


{{Optimal ET sequence|legend=1| 1b, 5 }}
{{Optimal ET sequence|legend=1| 1b, 5 }}


[[Badness]] (Smith): 0.062262
[[Badness]] (Sintel): 1.58


== Oncle ==
== Oncle ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Oncle]].''
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Oncle]].''


Oncle can be described as the {{nowrap|31 & 36c}} temperament.  
Oncle can be described as the {{nowrap| 31 & 36c }} temperament.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 232.383{{c}}
* [[WE]]: ~2 = 1201.2246{{c}}, ~8/7 = 232.7354{{c}}
: [[error map]]: {{val| +1.225 -2.524 -0.939 +2.112 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 232.4718{{c}}
: error map: {{val| 0.000 -4.539 -3.279 -1.298 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 232.383{{c}}
: [[error map]]: {{val| 0.000 -4.807 -1.585 -1.209 }}
: [[error map]]: {{val| 0.000 -4.807 -1.585 -1.209 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 232.498{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 232.498{{c}}
: error map: {{val| 0.000 -4.461 -3.778 -1.324 }}
: error map: {{val| 0.000 -4.461 -3.778 -1.324 }} -->


{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc }}
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc }}


[[Badness]] (Smith): 0.088384
[[Badness]] (Sintel): 2.24


== Archaeotherium ==
== Archaeotherium ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Archaeotherium]].''
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Archaeotherium]].''


Archaeotherium can be described as the {{nowrap|21 & 26}} temperament.  
Archaeotherium can be described as the {{nowrap| 21 & 26 }} temperament.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 229.951{{c}}
* [[WE]]: ~2 = 1202.7179{{c}}, ~8/7 = 230.7800{{c}}
: [[error map]]: {{val| +2.718 -6.897 -3.644 +8.548 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 230.1909{{c}}
: error map: {{val| 0.000 -11.382 -8.986 +0.983 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 229.951{{c}}
: [[error map]]: {{val| 0.000 -12.102 -5.626 +1.223 }}
: [[error map]]: {{val| 0.000 -12.102 -5.626 +1.223 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 230.258{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 230.258{{c}}
: error map: {{val| 0.000 -11.180 -9.933 +0.916 }}
: error map: {{val| 0.000 -11.180 -9.933 +0.916 }} -->


{{Optimal ET sequence|legend=1| 21, 26, 47, 73bc, 99bc }}
{{Optimal ET sequence|legend=1| 21, 26, 47, 73bc }}


[[Badness]] (Smith): 0.146306
[[Badness]] (Sintel): 3.70


== Clyndro ==
== Clyndro ==
{{See also| Mavila family }}
{{See also| Mavila family }}


Clyndro tempers out [[135/128]] and finds the interval class of 5 at a stack of -3 fifths as does any temperament in the [[mavila family]]. It can be described as the {{nowrap|11 &amp; 16}} temperament.  
Clyndro tempers out [[135/128]] and finds the interval class of 5 at a stack of -3 fifths as does any temperament in the [[mavila family]]. It can be described as the {{nowrap| 11 & 16 }} temperament.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 837: Line 860:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 225.752{{c}}
* [[WE]]: ~2 = 1205.6135{{c}}, ~8/7 = 227.5283{{c}}
: [[error map]]: {{val| +5.613 -13.757 -11.614 +20.486 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.3207{{c}}
: error map: {{val| 0.000 -22.993 -23.200 +4.853 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 225.752{{c}}
: [[error map]]: {{val| 0.000 -24.699 -18.081 +5.422 }}
: [[error map]]: {{val| 0.000 -24.699 -18.081 +5.422 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 226.469{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 226.469{{c}}
: error map: {{val| 0.000 -22.548 -24.534 +4.705 }}
: error map: {{val| 0.000 -22.548 -24.534 +4.705 }} -->


{{Optimal ET sequence|legend=1| 5c, 11, 16 }}
{{Optimal ET sequence|legend=1| 5c, 11, 16 }}


[[Badness]] (Smith): 0.159179
[[Badness]] (Sintel): 4.03


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 225.384{{c}}
* WE: ~2 = 1206.2134{{c}}, ~8/7 = 227.6004{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 226.428{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.2421{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 225.384{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 226.428{{c}} -->


{{Optimal ET sequence|legend=0| 5c, 11, 16 }}
{{Optimal ET sequence|legend=0| 5c, 11, 16 }}


Badness (Smith): 0.069703
Badness (Sintel): 2.30


== Miracle ==
== Miracle ==
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