Subgroup temperaments: Difference between revisions
FilterNashi (talk | contribs) Tags: Mobile edit Mobile web edit Advanced mobile edit |
→2.….11/7.… subgroups: move blackweed here |
||
| (5 intermediate revisions by one other user not shown) | |||
| Line 1,551: | Line 1,551: | ||
== 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 | ||
| Line 1,674: | Line 1,694: | ||
{{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, ~ | : 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| | : 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 | ||