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Kleismic family: Difference between revisions

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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* CTE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0308{{c}}
* [[WE]]: ~2 = 1200.1659{{c}}, ~6/5 = 317.0504{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.007{{c}}
: [[error map]]: {{val| +0.166 +0.347 -0.896 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.0308{{c}}
: error map: {{val| 0.000 +0.230 -1.160 }}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0586{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.007{{c}} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 28: Line 32:
* 5-odd-limit [[diamond tradeoff]]: ~6/5 = [315.641, 317.263] (untempered to 1/5-comma)
* 5-odd-limit [[diamond tradeoff]]: ~6/5 = [315.641, 317.263] (untempered to 1/5-comma)


{{Optimal ET sequence|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }}
{{Optimal ET sequence|legend=1| 15, 19, 34, 53, 458, 511c, …, 829c, 882c }}


[[Badness]] (Smith): 0.013234
[[Badness]] (Sintel): 0.310


=== Overview to extensions ===
=== Overview to extensions ===
Line 47: Line 51:
{{Mapping|legend=1| 1 0 1 -3 | 0 6 5 22 }}
{{Mapping|legend=1| 1 0 1 -3 | 0 6 5 22 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~6/5 = 316.732{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.5965{{c}}, ~6/5 = 316.8893{{c}}
: [[error map]]: {{val| +0.596 -0.619 -1.271 +0.948 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.7705{{c}}
: error map: {{val| 0.000 -1.332 -2.461 +0.126 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 316.732{{c}} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 55: Line 64:
{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197, 269c }}
{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197, 269c }}


[[Badness]] (Smith): 0.021501
[[Badness]] (Sintel): 0.544


==== 2.3.5.7.13 subgroup ====
==== 2.3.5.7.13 subgroup ====
Line 66: Line 75:
Subgroup-val mapping: {{mapping| 1 0 1 -3 0 | 0 6 5 22 14 }}
Subgroup-val mapping: {{mapping| 1 0 1 -3 0 | 0 6 5 22 14 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 316.8865{{c}}
Optimal tunings:
* WE: ~2 = 1200.7838{{c}}, ~6/5 = 316.9478{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 316.7939{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~6/5 = 316.8865{{c}} -->


{{Optimal ET sequence|legend=0| 19, 34d, 53, 72, 125f, 197f }}
{{Optimal ET sequence|legend=0| 19, 34d, 53, 72, 125f, 197f }}


Badness (Smith): 0.0118
Badness (Sintel): 0.410


=== 11-limit ===
=== 11-limit ===
Line 79: Line 91:
Mapping: {{mapping| 1 0 1 -3 9 | 0 6 5 22 -21 }}
Mapping: {{mapping| 1 0 1 -3 9 | 0 6 5 22 -21 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 316.719{{c}}
Optimal tunings:
* WE: ~2 = 1200.6524{{c}}, ~6/5 = 316.8911{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 316.7267{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 316.719{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 85: Line 100:
* 11-odd-limit diamond tradeoff range: ~6/5 = [315.641, 317.263]
* 11-odd-limit diamond tradeoff range: ~6/5 = [315.641, 317.263]


{{Optimal ET sequence|legend=0| 19, 34de, 53, 72, 197e, 269ce, 341ce, 610bccee }}
{{Optimal ET sequence|legend=0| 19, 53, 72, 197e, 269ce, 341ce }}


Badness (Smith): 0.021849
Badness (Sintel): 0.722


==== 13-limit ====
==== 13-limit ====
Line 96: Line 111:
Mapping: {{mapping| 1 0 1 -3 9 0 | 0 6 5 22 -21 14 }}
Mapping: {{mapping| 1 0 1 -3 9 0 | 0 6 5 22 -21 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 316.738{{c}}
Optimal tunings:
* WE: ~2 = 1200.7982{{c}}, ~6/5 = 316.9482{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 316.7491{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 316.738{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 102: Line 120:
* 13- and 15-odd-limit diamond tradeoff: ~6/5 = [315.641, 318.309]
* 13- and 15-odd-limit diamond tradeoff: ~6/5 = [315.641, 318.309]


{{Optimal ET sequence|legend=0| 19, 34de, 53, 72, 125f, 197ef, 269ceff }}
{{Optimal ET sequence|legend=0| 19, 53, 72, 125f, 197ef }}


Badness (Smith): 0.016883
Badness (Sintel): 0.698


=== Cataclysmic ===
=== Cataclysmic ===
Line 113: Line 131:
Mapping: {{mapping| 1 0 1 -3 -5 | 0 6 5 22 32 }}
Mapping: {{mapping| 1 0 1 -3 -5 | 0 6 5 22 32 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.042{{c}}
Optimal tunings:
* WE: ~2 = 1199.9590{{c}}, ~6/5 = 317.0315{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0403{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.042{{c}} -->


{{Optimal ET sequence|legend=0| 19e, 34d, 53 }}
{{Optimal ET sequence|legend=0| 19e, 34d, 53 }}


Badness (Smith): 0.039954
Badness (Sintel): 1.32


==== 13-limit ====
==== 13-limit ====
Line 126: Line 147:
Mapping: {{mapping| 1 0 1 -3 -5 0 | 0 6 5 22 32 14 }}
Mapping: {{mapping| 1 0 1 -3 -5 0 | 0 6 5 22 32 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.036{{c}}
Optimal tunings:
* WE: ~2 = 1200.0797{{c}}, ~6/5 = 317.0571{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0400{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.036{{c}} -->


{{Optimal ET sequence|legend=0| 19e, 34d, 53 }}
{{Optimal ET sequence|legend=0| 19e, 34d, 53 }}


Badness (Smith): 0.022555
Badness (Sintel): 0.932


=== Catalytic ===
=== Catalytic ===
Line 139: Line 163:
Mapping: {{mapping| 1 0 1 -3 -10 | 0 6 5 22 51 }}
Mapping: {{mapping| 1 0 1 -3 -10 | 0 6 5 22 51 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 316.653{{c}}
Optimal tunings:
* WE: ~2 = 1200.8102{{c}}, ~6/5 = 316.8669{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 316.6768{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 316.653{{c}} -->


{{Optimal ET sequence|legend=0| 19e, 53e, 72 }}
{{Optimal ET sequence|legend=0| 19e, 53e, 72 }}


Badness (Smith): 0.030422
Badness (Sintel): 1.01


==== 13-limit ====
==== 13-limit ====
Line 152: Line 179:
Mapping: {{mapping| 1 0 1 -3 -10 0 | 0 6 5 22 51 14 }}
Mapping: {{mapping| 1 0 1 -3 -10 0 | 0 6 5 22 51 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 316.639{{c}}
Optimal tunings:
* WE: ~2 = 1201.0807{{c}}, ~6/5 = 316.9246{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 316.6700{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 316.639{{c}} -->


{{Optimal ET sequence|legend=0| 19e, 53e, 72 }}
{{Optimal ET sequence|legend=0| 19e, 53e, 72, 307bcdeeffff }}


Badness (Smith): 0.022337
Badness (Sintel): 0.923


=== Cataleptic ===
=== Cataleptic ===
Line 165: Line 195:
Mapping: {{mapping| 1 0 1 -3 4 | 0 6 5 22 -2 }}
Mapping: {{mapping| 1 0 1 -3 4 | 0 6 5 22 -2 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.083{{c}}
Optimal tunings:
* WE: ~2 = 1198.6575{{c}}, ~6/5 = 316.7282{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0257{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.083{{c}} -->


{{Optimal ET sequence|legend=0| 19, 34d, 53e }}
{{Optimal ET sequence|legend=0| 19, 34d, 53e }}


Badness (Smith): 0.044335
Badness (Sintel): 1.47


==== 13-limit ====
==== 13-limit ====
Line 178: Line 211:
Mapping: {{mapping| 1 0 1 -3 4 0 | 0 6 5 22 -2 14 }}
Mapping: {{mapping| 1 0 1 -3 4 0 | 0 6 5 22 -2 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.118{{c}}
Optimal tunings:
* WE: ~2 = 1198.8403{{c}}, ~6/5 = 316.8111{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0652{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.118{{c}} -->


{{Optimal ET sequence|legend=0| 19, 34d, 53e, 87dee }}
{{Optimal ET sequence|legend=0| 19, 34d, 53e }}


Badness (Smith): 0.027343
Badness (Sintel): 1.13


=== Bikleismic ===
=== Bikleismic ===
Line 192: Line 228:
: mapping generators: ~99/70, ~6/5
: mapping generators: ~99/70, ~6/5


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~6/5 = 316.721{{c}}
Optimal tunings:
* WE: ~99/70 = 600.2674{{c}}, ~6/5 = 316.8624{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~6/5 = 316.7575{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~6/5 = 316.721{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 72, 322c, …, 610bcc }}
{{Optimal ET sequence|legend=0| 34d, 72, 322c, 394c }}


Badness (Smith): 0.029319
Badness (Sintel): 0.969


==== 13-limit ====
==== 13-limit ====
Line 205: Line 244:
Mapping: {{mapping| 2 0 2 -6 -1 0 | 0 6 5 22 15 14 }}
Mapping: {{mapping| 2 0 2 -6 -1 0 | 0 6 5 22 15 14 }}


Optimal tuning (POTE): ~55/39 = 600.000{{c}}, ~6/5 = 316.726{{c}}
Optimal tunings:
* WE: ~55/39 = 600.3582{{c}}, ~6/5 = 316.9152{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~6/5 = 316.7759{{c}}
<!-- * POTE: ~55/39 = 600.000{{c}}, ~6/5 = 316.726{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 72 }}
{{Optimal ET sequence|legend=0| 34d, 72 }}


Badness (Smith): 0.021814
Badness (Sintel): 0.901


==== 17-limit ====
==== 17-limit ====
Line 218: Line 260:
Mapping: {{mapping| 2 0 2 -6 -1 0 5 | 0 6 5 22 15 14 6 }}
Mapping: {{mapping| 2 0 2 -6 -1 0 5 | 0 6 5 22 15 14 6 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~6/5 = 316.726{{c}}
Optimal tunings:
* WE: ~17/12 = 600.4210{{c}}, ~6/5 = 316.9282{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~6/5 = 316.7578{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~6/5 = 316.726{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 38df, 72 }}
{{Optimal ET sequence|legend=0| 34d, 38df, 72 }}


Badness (Smith): 0.015656
Badness (Sintel): 0.798


==== 19-limit ====
==== 19-limit ====
Line 231: Line 276:
Mapping: {{mapping| 2 0 2 -6 -1 0 5 -1 | 0 6 5 22 15 14 6 18 }}
Mapping: {{mapping| 2 0 2 -6 -1 0 5 -1 | 0 6 5 22 15 14 6 18 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~6/5 = 316.726{{c}}
Optimal tunings:
* WE: ~17/12 = 600.3763{{c}}, ~6/5 = 316.8720{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~6/5 = 316.7205{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~6/5 = 316.726{{c}} -->


{{Optimal ET sequence|legend=0| 34dh, 38df, 72 }}
{{Optimal ET sequence|legend=0| 34dh, 38df, 72 }}


Badness (Smith): 0.015771
Badness (Sintel): 0.959


== Keemun ==
== Keemun ==
Line 246: Line 294:
{{Mapping|legend=1| 1 0 1 2 | 0 6 5 3 }}
{{Mapping|legend=1| 1 0 1 2 | 0 6 5 3 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~6/5 = 316.473{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1202.6235{{c}}, ~6/5 = 317.1646{{c}}
: [[error map]]: {{val| +2.624 +1.033 +2.133 -12.085 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.8293{{c}}
: error map: {{val| 0.000 -0.979 -2.167 -18.388 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 316.473{{c}} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 253: Line 306:
* 7- and 9-odd-limit [[diamond tradeoff]]: ~6/5 = [308.744, 322.942]
* 7- and 9-odd-limit [[diamond tradeoff]]: ~6/5 = [308.744, 322.942]


{{Optimal ET sequence|legend=1| 15, 19, 53d, 72dd, 91dd }}
{{Optimal ET sequence|legend=1| 15, 19, 53d, 72dd }}


[[Badness]] (Smith): 0.027408
[[Badness]] (Sintel): 0.694


=== 11-limit ===
=== 11-limit ===
Line 264: Line 317:
Mapping: {{mapping| 1 0 1 2 4 | 0 6 5 3 -2 }}
Mapping: {{mapping| 1 0 1 2 4 | 0 6 5 3 -2 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.576{{c}}
Optimal tunings:
* WE: ~2 = 1199.7353{{c}}, ~6/5 = 317.5055{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.5546{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.576{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 270: Line 326:
* 11-odd-limit diamond tradeoff: ~6/5 = [308.744, 324.341]
* 11-odd-limit diamond tradeoff: ~6/5 = [308.744, 324.341]


{{Optimal ET sequence|legend=0| 4, 15, 19, 34 }}
{{Optimal ET sequence|legend=0| 15, 19, 34 }}


Badness (Smith): 0.027410
Badness (Sintel): 0.906


==== 13-limit ====
==== 13-limit ====
Line 281: Line 337:
Mapping: {{mapping| 1 0 1 2 4 5 | 0 6 5 3 -2 -5 }}
Mapping: {{mapping| 1 0 1 2 4 5 | 0 6 5 3 -2 -5 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 316.611{{c}}
Optimal tunings:
* WE: ~2 = 1201.8360{{c}}, ~6/5 = 317.0958{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 316.6829{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 316.611{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 287: Line 346:
* 13- and 15-odd-limit diamond tradeoff: ~6/5 = [303.597, 324.341]
* 13- and 15-odd-limit diamond tradeoff: ~6/5 = [303.597, 324.341]


{{Optimal ET sequence|legend=0| 4, 15f, 19, 53def, 72def }}
{{Optimal ET sequence|legend=0| 4, 15f, 19 }}


Badness (Smith): 0.029749
Badness (Sintel): 1.23


==== Kema ====
==== Kema ====
Line 298: Line 357:
Mapping: {{mapping| 1 0 1 2 4 0 | 0 6 5 3 -2 14 }}
Mapping: {{mapping| 1 0 1 2 4 0 | 0 6 5 3 -2 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.423{{c}}
Optimal tunings:
* WE: ~2 = 1199.7816{{c}}, ~6/5 = 317.3653{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.4070{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.423{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 305: Line 367:
* 13- and 15-odd-limit diamond tradeoff: ~6/5 = [308.744, 324.341]
* 13- and 15-odd-limit diamond tradeoff: ~6/5 = [308.744, 324.341]


{{Optimal ET sequence|legend=0| 15, 19, 34, 87ddee }}
{{Optimal ET sequence|legend=0| 15, 19, 34 }}


Badness (Smith): 0.022749
Badness (Sintel): 0.940


==== Kumbaya ====
==== Kumbaya ====
Line 316: Line 378:
Mapping: {{mapping| 1 0 1 2 4 4 | 0 6 5 3 -2 -1 }}
Mapping: {{mapping| 1 0 1 2 4 4 | 0 6 5 3 -2 -1 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 318.595{{c}}
Optimal tunings:
* WE: ~2 = 1196.7615{{c}}, ~6/5 = 317.7353{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 319.4059{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 318.595{{c}} -->


{{Optimal ET sequence|legend=0| 4, 15, 19f, 34ff }}
{{Optimal ET sequence|legend=0| 4, 11b, 15 }}


Badness (Smith): 0.031633
Badness (Sintel): 1.31


=== Qeema ===
=== Qeema ===
Line 329: Line 394:
Mapping: {{mapping| 1 0 1 2 -1 | 0 6 5 3 17 }}
Mapping: {{mapping| 1 0 1 2 -1 | 0 6 5 3 17 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 314.730{{c}}
Optimal tunings:
* WE: ~2 = 1204.5534{{c}}, ~6/5 = 315.9247{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 315.1686{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 314.730{{c}} -->


{{Optimal ET sequence|legend=0| 4e, 19, 42bcd, 61bcdd }}
{{Optimal ET sequence|legend=0| 4e, 19, 42bcd }}


Badness (Smith): 0.040056
Badness (Sintel): 1.32


==== 13-limit ====
==== 13-limit ====
Line 342: Line 410:
Mapping: {{mapping| 1 0 1 2 -1 0 | 0 6 5 3 17 14 }}
Mapping: {{mapping| 1 0 1 2 -1 0 | 0 6 5 3 17 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 315.044{{c}}
Optimal tunings:
* WE: ~2 = 1204.4937{{c}}, ~6/5 = 316.2241{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 315.4748{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 315.044{{c}} -->


{{Optimal ET sequence|legend=0| 4ef, 19 }}
{{Optimal ET sequence|legend=0| 4ef, 19 }}


Badness (Smith): 0.029419
Badness (Sintel): 1.22


=== Darjeeling ===
=== Darjeeling ===
Line 355: Line 426:
Mapping: {{mapping| 1 0 1 2 0 | 0 6 5 3 13 }}
Mapping: {{mapping| 1 0 1 2 0 | 0 6 5 3 13 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.656{{c}}
Optimal tunings:
* WE: ~2 = 1201.6569{{c}}, ~6/5 = 318.0942{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.8547{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.656{{c}} -->


{{Optimal ET sequence|legend=0| 15, 19e, 34e }}
{{Optimal ET sequence|legend=0| 15, 19e, 34e }}


Badness (Smith): 0.027648
Badness (Sintel): 0.914


==== 13-limit ====
==== 13-limit ====
Line 368: Line 442:
Mapping: {{mapping| 1 0 1 2 0 0 | 0 6 5 3 13 14 }}
Mapping: {{mapping| 1 0 1 2 0 0 | 0 6 5 3 13 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.298{{c}}
Optimal tunings:
* WE: ~2 = 1201.9324{{c}}, ~6/5 = 317.8090{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.5170{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.298{{c}} -->


{{Optimal ET sequence|legend=0| 15, 19e, 34e, 53dee }}
{{Optimal ET sequence|legend=0| 15, 19e, 34e }}


Badness (Smith): 0.021445
Badness (Sintel): 0.886


== Catalan ==
== Catalan ==
Line 381: Line 458:
{{Mapping|legend=1| 1 0 1 6 | 0 6 5 -12 }}
{{Mapping|legend=1| 1 0 1 6 | 0 6 5 -12 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~6/5 = 318.267{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1197.1789{{c}}, ~6/5 = 317.5185{{c}}
: [[error map]]: {{val| -2.821 +3.156 -1.542 +4.025 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 318.2411{{c}}
: error map: {{val| 0.000 +7.492 +4.892 +12.281 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 318.267{{c}} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 389: Line 471:
{{Optimal ET sequence|legend=1| 15, 34d, 49, 132bcdd, 181bbcddd }}
{{Optimal ET sequence|legend=1| 15, 34d, 49, 132bcdd, 181bbcddd }}


[[Badness]] (Smith): 0.094872
[[Badness]] (Sintel): 2.40


=== 11-limit ===
=== 11-limit ===
Line 398: Line 480:
Mapping: {{mapping| 1 0 1 6 4 | 0 6 5 -12 -2 }}
Mapping: {{mapping| 1 0 1 6 4 | 0 6 5 -12 -2 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 318.282{{c}}
Optimal tunings:
* WE: ~2 = 1197.0368{{c}}, ~6/5 = 317.4956{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 318.2672{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 318.282{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 406: Line 491:
{{Optimal ET sequence|legend=0| 15, 34d, 49, 181bbcdddeee }}
{{Optimal ET sequence|legend=0| 15, 34d, 49, 181bbcdddeee }}


Badness (Smith): 0.036894
Badness (Sintel): 1.22


=== 13-limit ===
=== 13-limit ===
Line 415: Line 500:
Mapping: {{mapping| 1 0 1 6 4 0 | 0 6 5 -12 -2 14 }}
Mapping: {{mapping| 1 0 1 6 4 0 | 0 6 5 -12 -2 14 }}


Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 317.9159{{c}}
Optimal tunings:
* WE: ~2 = 1196.8961{{c}}, ~6/5 = 317.3837{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 318.1621{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~6/5 = 317.9159{{c}} -->


{{Optimal ET sequence|legend=0| 15, 34d, 49f, 83def, 132bcddeefff }}
{{Optimal ET sequence|legend=0| 15, 34d, 49f, 83def, 132bcddeefff }}


Badness (Smith): 0.0263
Badness (Sintel): 1.09


== Countercata ==
== Countercata ==
Line 428: Line 516:
{{Mapping|legend=1| 1 0 1 11 | 0 6 5 -31 }}
{{Mapping|legend=1| 1 0 1 11 | 0 6 5 -31 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~6/5 = 317.121{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9172{{c}}, ~6/5 = 317.0995{{c}}
: [[error map]]: {{val| -0.083 +0.642 -0.899 +0.178 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.1220{{c}}
: error map: {{val| 0.000 +0.777 -0.704 +0.391 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 317.121{{c}} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 434: Line 527:
* 7- and 9-odd-limit [[diamond tradeoff]]: ~6/5 = [315.641, 317.263]
* 7- and 9-odd-limit [[diamond tradeoff]]: ~6/5 = [315.641, 317.263]


{{Optimal ET sequence|legend=1| 19d, 34, 53, 87, 140, 333, 473, 806b }}
{{Optimal ET sequence|legend=1| 19d, 34, 53, 87, 140, 333, 473 }}


[[Badness]] (Smith): 0.052129
[[Badness]] (Sintel): 1.32


=== 11-limit ===
=== 11-limit ===
Line 445: Line 538:
Mapping: {{mapping| 1 0 1 11 -5 | 0 6 5 -31 32 }}
Mapping: {{mapping| 1 0 1 11 -5 | 0 6 5 -31 32 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.162{{c}}
Optimal tunings:
* WE: ~2 = 1200.0980{{c}}, ~6/5 = 317.1879{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.1623{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.162{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 451: Line 547:
* 11-odd-limit diamond tradeoff: ~6/5 = [315.641, 317.370]
* 11-odd-limit diamond tradeoff: ~6/5 = [315.641, 317.370]


{{Optimal ET sequence|legend=0| 34, 53, 87, 140, 227, 367e, 507e }}
{{Optimal ET sequence|legend=0| 34, 53, 87, 140, 227, 367e }}


Badness (Smith): 0.039770
Badness (Sintel): 1.31


=== 13-limit ===
=== 13-limit ===
Line 462: Line 558:
Mapping: {{mapping| 1 0 1 11 -5 0 | 0 6 5 -31 32 14 }}
Mapping: {{mapping| 1 0 1 11 -5 0 | 0 6 5 -31 32 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.162{{c}}
Optimal tunings:
* WE: ~2 = 1200.0936{{c}}, ~6/5 = 317.1864{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.1622{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.162{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 471: Line 570:
{{Optimal ET sequence|legend=0| 34, 53, 87, 140, 367e, 507e }}
{{Optimal ET sequence|legend=0| 34, 53, 87, 140, 367e, 507e }}


Badness (Smith): 0.020156
Badness (Sintel): 0.833


== Metakleismic ==
== Metakleismic ==
Line 480: Line 579:
{{Mapping|legend=1| 1 0 1 -12 | 0 6 5 56 }}
{{Mapping|legend=1| 1 0 1 -12 | 0 6 5 56 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~6/5 = 317.314{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5969{{c}}, ~6/5 = 317.2079{{c}}
: [[error map]]: {{val| -0.403 +1.292 -0.678 -0.349 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.3071{{c}}
: error map: {{val| 0.000 +1.887 +0.222 +0.370 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 317.314{{c}} -->


{{Optimal ET sequence|legend=1| 34d, 87, 121, 208 }}
{{Optimal ET sequence|legend=1| 34d, 87, 121, 208, 537b }}


[[Badness]] (Smith): 0.163519
[[Badness]] (Sintel): 4.14


=== 11-limit ===
=== 11-limit ===
Line 493: Line 597:
Mapping: {{mapping| 1 0 1 -12 -5 | 0 6 5 56 32 }}
Mapping: {{mapping| 1 0 1 -12 -5 | 0 6 5 56 32 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.311{{c}}
Optimal tunings:
* WE: ~2 = 1199.5425{{c}}, ~6/5 = 317.1901{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.3020{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.311{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 53d, 87, 121, 208 }}
{{Optimal ET sequence|legend=0| 34d, 53d, 87, 121, 208 }}


Badness (Smith): 0.048570
Badness (Sintel): 1.61


=== 13-limit ===
=== 13-limit ===
Line 506: Line 613:
Mapping: {{mapping| 1 0 1 -12 -5 0 | 0 6 5 56 32 14 }}
Mapping: {{mapping| 1 0 1 -12 -5 0 | 0 6 5 56 32 14 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 317.311{{c}}
Optimal tunings:
* WE: ~2 = 1199.5339{{c}}, ~6/5 = 317.1882{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.3028{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 317.311{{c}} -->


{{Optimal ET sequence|legend=0| 34d, 53d, 87, 121, 208 }}
{{Optimal ET sequence|legend=0| 34d, 53d, 87, 121, 208 }}


Badness (Smith): 0.024371
Badness (Sintel): 1.01


== Hemikleismic ==
== Hemikleismic ==
Retrieved from "https://en.xen.wiki/w/Kleismic_family"