Subgroup temperaments: Difference between revisions

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2.….11/7.… subgroups: move blackweed here
 
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== 2.….11/7.… subgroups ==
== 2.….11/7.… subgroups ==
=== Blackweed ===
Blackweed is a [[restriction]] of undecimal [[blackwood]] as it tempers out 256/243 alike but in the 2.3.11/7 subgroup. 20edo is close to the optimum, which has 4\20 as the period and 420{{c}} as the generator.
[[Subgroup]]: 2.3.11/7
[[Comma list]]: {{monzo| 8 -5 }} (256/243)
{{Mapping|legend=2| 5 8 0 | 0 0 1 }}
: mapping generators: ~9/8, ~11/7
[[Optimal tuning]]s:
* [[Tp tuning|subgroup]] [[WE]]: ~8/7 = 238.851{{c}}, ~11/7 = 782.457{{c}}
: [[error map]]: {{val| -5.746 +8.852 -0.035 }}
* [[Tp tuning|subgroup]] [[CWE]]: ~8/7 = 240.000{{c}}, ~11/7 = 784.967{{c}}
: error map: {{val| 0.000 +18.045 +2.475 }}
{{Optimal ET sequence|legend=1| 15, 20, 35b, 55b }}
=== Pepperoni ===
=== Pepperoni ===
{{Main| Parapyth }}
{{Main| Parapyth }}
Line 1,656: Line 1,674:
{{Mapping|legend=2| 1 1 1 | 0 17 11 }}
{{Mapping|legend=2| 1 1 1 | 0 17 11 }}
: mapping generators: ~2, ~2250/2197
: mapping generators: ~2, ~2250/2197
{{Todo|inline=1| comment=Optimal tunings and error maps showed below is not yet precise enough.}}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.000{{c}}, ~2250/2197 = 41.291{{c}}
* WE: ~2 = 1200.000{{c}}, ~2250/2197 = 41.291{{c}}
: error map: {{val| 0.000 0.001 -0.007}}
: error map: {{val| +0.000 +0.001 -0.007}}
* CWE: ~2 = 1200.000{{c}}, ~2250/2197 = 41.292{{c}}
* CWE: ~2 = 1200.000{{c}}, ~2250/2197 = 41.292{{c}}
: error map: {{val| 0.000 0.001 -0.007}}
: error map: {{val| +0.000 +0.001 -0.007}}


edos: 29, 465, 494, 436, 523, 407, 378, 349, 30[-3], 28[+3], 320, 291, 59[-3], 262
edos: 29, 465, 494, 436, 523, 407, 378, 349, 30[-3], 28[+3], 320, 291, 59[-3], 262
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{{Mapping|legend=2| 1 1 1 1 | 0 17 4 11 }}
{{Mapping|legend=2| 1 1 1 1 | 0 17 4 11 }}
: mapping generators: ~2, ~2250/2197
: mapping generators: ~2, ~169/165


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.993{{c}}, ~169/165 = 41.292{{c}}
* WE: ~2 = 1199.993{{c}}, ~169/165 = 41.292{{c}}
: error map: {{val| -0.007 -0.000 0.157 -0.010}}
: error map: {{val| -0.007 -0.000 +0.157 -0.010}}
* CWE: ~2 = 1200.000{{c}}, ~169/165 = 41.292{{c}}
* CWE: ~2 = 1200.000{{c}}, ~169/165 = 41.292{{c}}
: error map: {{val| 0.000 0.005 0.163 -0.005}}
: error map: {{val| +0.000 +0.005 +0.163 -0.005}}


edos: 29, 465, 494, 436, 523, 407, 378, 349, 320, 291, 30[-3], 262, 28[+3], 233
edos: 29, 465, 494, 436, 523, 407, 378, 349, 320, 291, 30[-3], 262, 28[+3], 233