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Syntonic–kleismic equivalence continuum: Difference between revisions

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| [[Mowgli]] || 15/2 = 7.5 || {{monzo| 0 22 -15 }}
| [[Mowgli]] || 15/2 = 7.5 || {{monzo| 0 22 -15 }}
|}
|}
== Parakleismic (5-limit) ==
{{Main| Parakleismic }}
: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]].''
The 5-limit version of parakleismic tempers out the [[parakleisma]]. It corresponds to {{nowrap| ''n'' {{=}} 13/2 }}, and 13 generator steps give the interval class of [[3/1|3]].
[[Subgroup]]: 2.3.5
[[Comma list]]: 1224440064/1220703125
{{Mapping|legend=1| 1 -8 -8 | 0 13 14 }}
: mapping generators: ~2, ~5/3
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.971{{c}}, ~5/3 = 884.7383{{c}}
: [[error map]]: {{val| -0.029 -0.127 +0.253 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 884.8576{{c}}
: error map: {{val| 0.000 -0.106 +0.293 }}
{{Optimal ET sequence|legend=1| 19, 61, 80, 99, 118, 453, 571, 689, 1496 }}
[[Badness]] (Sintel): 1.02


== Negri ==
== Negri ==
Line 148: Line 125:
[[Badness]] (Sintel): 2.04
[[Badness]] (Sintel): 2.04


== Counterhanson ==
== Lalasepyo (8c & 11) ==
: ''For extensions, see [[Ragismic microtemperaments #Counterkleismic]].''
 
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{monzo| -20 -24 25 }}
[[Comma list]]: 4613203125/4294967296


{{Mapping|legend=1| 1 -5 -4 | 0 25 24 }}
{{Mapping|legend=1| 1 -1 6 | 0 7 -10 }}
: mapping generators: ~2, ~6/5
: mapping generators: ~2, ~675/512


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.0419{{c}}, ~6/5 = 316.0916{{c}}
* [[WE]]: ~2 = 1202.5641{{c}}, ~675/512 = 443.2124{{c}}
: [[error map]]: {{val| +0.042 +0.126 -0.282 }}
: [[error map]]: {{val| +2.564 -2.033 -3.053 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.0021{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~675/512 = 442.2692{{c}}
: error map: {{val| 0.000 +0.097 -0.344 }}
: error map: {{val| 0.000 -6.071 -9.006 }}
 
{{Optimal ET sequence|legend=1| 8c, 11, 19 }}
 
[[Badness]] (Sintel): 24.9
 
[http://x31eq.com/cgi-bin/rt.cgi?ets=19_8c&limit=5 The temperament finder - 5-limit 19 & 8c]


{{Optimal ET sequence|legend=1| 19, …, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}
== Parakleismic (5-limit) ==
{{Main| Parakleismic }}
: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]].''


[[Badness]] (Sintel): 7.45
The 5-limit version of parakleismic tempers out the [[parakleisma]]. It corresponds to {{nowrap| ''n'' {{=}} 13/2 }}, and 13 generator steps give the interval class of [[3/1|3]].  


== Countermeantone ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{monzo| 10 23 -20 }}
[[Comma list]]: 1224440064/1220703125


{{Mapping|legend=1| 1 -10 -11 | 0 20 23 }}
{{Mapping|legend=1| 1 -8 -8 | 0 13 14 }}
: mapping generators: ~2, ~78125/52488
: mapping generators: ~2, ~5/3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.9478{{c}}, ~78125/52488 = 695.0566{{c}}
* [[WE]]: ~2 = 1199.971{{c}}, ~5/3 = 884.7383{{c}}
: [[error map]]: {{val| -0.052 -0.301 +0.562 }}
: [[error map]]: {{val| -0.029 -0.127 +0.253 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~78125/52488 = 695.0846{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 884.8576{{c}}
: error map: {{val| 0.000 -0.264 +0.631 }}
: error map: {{val| 0.000 -0.106 +0.293 }}


{{Optimal ET sequence|legend=1| 19, …, 126, 145, 164, 183, 713, 896c, 1079c, 1262c, 1445c }}
{{Optimal ET sequence|legend=1| 19, 61, 80, 99, 118, 453, 571, 689, 1496 }}


[[Badness]] (Sintel): 8.76
[[Badness]] (Sintel): 1.02


== Mowgli ==
== Mowgli ==
Line 208: Line 190:
[[Badness]] (Sintel): 15.3
[[Badness]] (Sintel): 15.3


== Lalasepyo (8c & 11) ==
== Countermeantone ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 4613203125/4294967296
[[Comma list]]: {{monzo| 10 23 -20 }}


{{Mapping|legend=1| 1 -1 6 | 0 7 -10 }}
{{Mapping|legend=1| 1 -10 -11 | 0 20 23 }}
: mapping generators: ~2, ~675/512
: mapping generators: ~2, ~78125/52488


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1202.5641{{c}}, ~675/512 = 443.2124{{c}}
* [[WE]]: ~2 = 1199.9478{{c}}, ~78125/52488 = 695.0566{{c}}
: [[error map]]: {{val| +2.564 -2.033 -3.053 }}
: [[error map]]: {{val| -0.052 -0.301 +0.562 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~675/512 = 442.2692{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~78125/52488 = 695.0846{{c}}
: error map: {{val| 0.000 -6.071 -9.006 }}
: error map: {{val| 0.000 -0.264 +0.631 }}
 
{{Optimal ET sequence|legend=1| 19, …, 126, 145, 164, 183, 713, 896c, 1079c, 1262c, 1445c }}
 
[[Badness]] (Sintel): 8.76
 
== Counterhanson ==
: ''For extensions, see [[Ragismic microtemperaments #Counterkleismic]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -20 -24 25 }}
 
{{Mapping|legend=1| 1 -5 -4 | 0 25 24 }}
: mapping generators: ~2, ~6/5


{{Optimal ET sequence|legend=1| 8c, 11, 19 }}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0419{{c}}, ~6/5 = 316.0916{{c}}
: [[error map]]: {{val| +0.042 +0.126 -0.282 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.0021{{c}}
: error map: {{val| 0.000 +0.097 -0.344 }}


[[Badness]] (Sintel): 24.9
{{Optimal ET sequence|legend=1| 19, …, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}


[http://x31eq.com/cgi-bin/rt.cgi?ets=19_8c&limit=5 The temperament finder - 5-limit 19 & 8c]
[[Badness]] (Sintel): 7.45


== Oviminor ==
== Oviminor ==
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