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Semicomma family: Difference between revisions

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m Units & misc. cleanup
Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~75/64 = 271.670{{c}}
* [[WE]]: ~2 = 1200.2902{{c}}, ~75/64 = 271.6929{{c}}
: [[error map]]: {{val| +0.290 -0.104 -0.522 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~75/64 = 271.6394{{c}}
: error map: {{val| 0.000 -0.479 -1.232 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~75/64 = 271.670{{c}}
: [[error map]]: {{val| 0.000 -0.264 -1.324 }}
: [[error map]]: {{val| 0.000 -0.264 -1.324 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~75/64 = 271.627{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~75/64 = 271.627{{c}}
: error map: {{val| 0.000 -0.564 -1.195 }}
: error map: {{val| 0.000 -0.564 -1.195 }} -->


[[Tuning ranges]]:
[[Tuning ranges]]:
Line 22: Line 26:
* 5-odd-limit [[diamond tradeoff]]: ~75/64 = [271.229, 271.708] (1/3-comma to 2/7-comma)
* 5-odd-limit [[diamond tradeoff]]: ~75/64 = [271.229, 271.708] (1/3-comma to 2/7-comma)


{{Optimal ET sequence|legend=1| 22, 31, 53, 190, 243, 296, 645c }}
{{Optimal ET sequence|legend=1| 22, 31, 53, 190, 243, 296, 645c, 1586bccc }}


[[Badness]] (Smith): 0.040807
[[Badness]] (Sintel): 0.957


=== Overview to extensions ===
=== Overview to extensions ===
Line 48: Line 52:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 271.513{{c}}
* [[WE]]: ~2 = 1200.0192{{c}}, ~7/6 = 271.5130{{c}}
: [[error map]]: {{val| +0.019 -1.364 -0.795 +3.297 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/6 = 271.5097{{c}}
: error map: {{val| 0.000 -1.387 -0.843 +3.252 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 271.513{{c}}
: [[error map]]: {{val| 0.000 -1.364 -0.853 +3.278 }}
: [[error map]]: {{val| 0.000 -1.364 -0.853 +3.278 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 271.509{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 271.509{{c}}
: error map: {{val| 0.000 -1.394 -0.840 +3.243 }}
: error map: {{val| 0.000 -1.394 -0.840 +3.243 }} -->


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 69: Line 77:
[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.
[[Algebraic generator]]: Sabra3, the real root of 12''x<sup>3</sup> - 7''x'' - 48.


{{Optimal ET sequence|legend=1| 9, 22, 31, 53, 84, 137, 221d, 358d }}
{{Optimal ET sequence|legend=1| 9, 22, 31, 53, 84, 137, 221d }}


[[Badness]] (Smith): 0.020735
[[Badness]] (Sintel): 0.525


=== 11-limit ===
=== 11-limit ===
Line 81: Line 89:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.560{{c}}
* WE: ~2 = 1200.5989{{c}}, ~7/6 = 271.5616{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.426{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 271.4552{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.560{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.426{{c}} -->


Minimax tuning:
Minimax tuning:
Line 95: Line 105:
{{Optimal ET sequence|legend=0| 9, 22, 31, 53, 84e }}
{{Optimal ET sequence|legend=0| 9, 22, 31, 53, 84e }}


Badness (Smith): 0.015231
Badness (Sintel): 0.504


==== 13-limit ====
==== 13-limit ====
Line 105: Line 115:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.556{{c}}
* WE: ~2 = 1200.3621{{c}}, ~7/6 = 271.6283{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.546{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 271.5477{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.556{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.546{{c}} -->


Tuning ranges:
Tuning ranges:
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{{Optimal ET sequence|legend=0| 22, 31, 53, 84e }}
{{Optimal ET sequence|legend=0| 22, 31, 53, 84e }}


Badness (Smith): 0.019718
Badness (Sintel): 0.815


==== Blair ====
==== Blair ====
Line 124: Line 136:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.747{{c}}
* WE: ~2 = 1201.8031{{c}}, ~7/6 = 271.7083{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.301{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 271.3846{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.747{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.301{{c}} -->


{{Optimal ET sequence|legend=0| 9, 22, 31f }}
{{Optimal ET sequence|legend=0| 9, 22, 31f }}


Badness (Smith): 0.023086
Badness (Sintel): 0.954


==== Winston ====
==== Winston ====
Line 139: Line 153:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.163{{c}}
* WE: ~2 = 1200.2846{{c}}, ~7/6 = 271.1524{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.088{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 271.1032{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.163{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.088{{c}} -->


Tuning ranges:
Tuning ranges:
Line 148: Line 164:
{{Optimal ET sequence|legend=0| 9, 22f, 31 }}
{{Optimal ET sequence|legend=0| 9, 22f, 31 }}


Badness (Smith): 0.019931
Badness (Sintel): 0.824


==== Doublethink ====
==== Doublethink ====
Line 160: Line 176:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 135.811{{c}}
* WE: ~2 = 1200.6876{{c}}, ~13/12 = 135.8006{{c}}
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 135.723{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 135.7410{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~13/12 = 135.811{{c}}
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 135.723{{c}} -->


Tuning ranges:
Tuning ranges:
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* 13- and 15-odd-limit diamond tradeoff: ~13/12 = [128.298, 138.573]
* 13- and 15-odd-limit diamond tradeoff: ~13/12 = [128.298, 138.573]


{{Optimal ET sequence|legend=0| 9, 35bd, 44, 53, 62, 115ef }}
{{Optimal ET sequence|legend=0| 9, 35bd, 44, 53, 115ef }}


Badness (Smith): 0.027120
Badness (Sintel): 1.12


=== Newspeak ===
=== Newspeak ===
Line 181: Line 199:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.316{{c}}
* WE: ~2 = 1200.2072{{c}}, ~7/6 = 271.3353{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.288{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 271.2952{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/6 = 271.316{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 271.288{{c}} -->


Tuning ranges:
Tuning ranges:
Line 190: Line 210:
{{Optimal ET sequence|legend=0| 22e, 31, 84, 115 }}
{{Optimal ET sequence|legend=0| 22e, 31, 84, 115 }}


Badness (Smith): 0.031438
Badness (Sintel): 1.04


=== Borwell ===
=== Borwell ===
Line 197: Line 217:
Comma list: 225/224, 243/242, 1728/1715
Comma list: 225/224, 243/242, 1728/1715


Mapping: {{mapping| 1 7 0 9 17 | 0 -14 6 -16 -35 }}
Mapping: {{mapping| 1 -7 6 -7 -18 | 0 14 -6 16 35 }}
: mapping generators: ~2, ~72/55
: mapping generators: ~2, ~72/55


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~55/36 = 735.754{{c}}
* WE: ~2 = 1200.0194{{c}}, ~55/36 = 735.7641{{c}}
* POTE: ~2 = 1200.000{{c}}, ~55/36 = 735.752{{c}}
* CWE: ~2 = 1200.000{{c}}, ~55/36 = 735.7527{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~55/36 = 735.754{{c}}
* POTE: ~2 = 1200.000{{c}}, ~55/36 = 735.752{{c}} -->


{{Optimal ET sequence|legend=0| 31, 75e, 106, 137 }}
{{Optimal ET sequence|legend=0| 31, 75e, 106, 137 }}


Badness (Smith): 0.038377
Badness (Sintel): 1.27


== Sabric ==
== Sabric ==
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