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Diaschismic family: Difference between revisions

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: mapping generators: ~45/32, ~3
: mapping generators: ~45/32, ~3


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~3/2 = 704.898{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 599.4107{{c}}, ~3/2 = 704.2059{{c}}
: [[error map]]: {{val| -1.179 +1.072 +1.150 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.9585{{c}}
: error map: {{val| 0.000 +3.003 +3.769 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~3/2 = 704.898{{c}} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 23: Line 28:
{{Optimal ET sequence|legend=1| 10, 12, 22, 34, 46, 80, 206c, 286bc }}
{{Optimal ET sequence|legend=1| 10, 12, 22, 34, 46, 80, 206c, 286bc }}


[[Badness]] (Smith): 0.019915
[[Badness]] (Sintel): 0.467


=== Overview to extensions ===
=== Overview to extensions ===
Line 53: Line 58:
: mapping generators: ~17/12, ~3
: mapping generators: ~17/12, ~3


Optimal tuning (CTE): ~17/12 = 600.0000{{c}}, ~3/2 = 705.1272{{c}}
Optimal tunings:
* WE: ~45/32 = 599.5585{{c}}, ~3/2 = 704.6188{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 705.1356{{c}}
<!-- * CTE: ~17/12 = 600.0000{{c}}, ~3/2 = 705.1272{{c}} -->


{{Optimal ET sequence|legend=0| 10, 12, 22, 34, 80, 114, 194bc }}
{{Optimal ET sequence|legend=0| 10, 12, 22, 34, 80, 114, 194bc }}


Badness (Smith): 0.00575
Badness (Sintel): 0.212


== Septimal diaschismic ==
== Septimal diaschismic ==
Line 73: Line 81:
{{Mapping|legend=1| 2 0 11 31 | 0 1 -2 -8 }}
{{Mapping|legend=1| 2 0 11 31 | 0 1 -2 -8 }}


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~3/2 = 703.681{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 599.4449{{c}}, ~3/2 = 703.0299{{c}}
: [[error map]]: {{val| -1.110 -0.035 +3.740 -1.391 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 703.7739{{c}}
: error map: {{val| 0.000 +1.819 +6.138 +0.983 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~3/2 = 703.681{{c}} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 79: Line 92:
* 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.955, 706.843]
* 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.955, 706.843]


{{Optimal ET sequence|legend=1| 12, 46, 58, 104c, 162c }}
{{Optimal ET sequence|legend=1| 12, 34, 46, 58, 104c, 162c }}


[[Badness]] (Smith): 0.037914
[[Badness]] (Sintel): 0.959


=== 11-limit ===
=== 11-limit ===
Line 90: Line 103:
Mapping: {{mapping| 2 0 11 31 45 | 0 1 -2 -8 -12 }}
Mapping: {{mapping| 2 0 11 31 45 | 0 1 -2 -8 -12 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~3/2 = 703.714{{c}}
Optimal tunings:
* WE: ~45/32 = 599.4471{{c}}, ~3/2 = 703.0657{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 703.7996{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~3/2 = 703.714{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 96: Line 112:
* 11-odd-limit diamond tradeoff: ~3/2 = [701.955, 706.843]
* 11-odd-limit diamond tradeoff: ~3/2 = [701.955, 706.843]


{{Optimal ET sequence|legend=0| 12, 46, 58, 104c, 162ce }}
{{Optimal ET sequence|legend=0| 12, 34e, 46, 58, 104c, 162ce }}


Badness (Smith): 0.025034
Badness (Sintel): 0.828


=== 13-limit ===
=== 13-limit ===
Line 107: Line 123:
Mapping: {{mapping| 2 0 11 31 45 55 | 0 1 -2 -8 -12 -15 }}
Mapping: {{mapping| 2 0 11 31 45 55 | 0 1 -2 -8 -12 -15 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~3/2 = 703.704{{c}}
Optimal tunings:
* WE: ~45/32 = 599.4451{{c}}, ~3/2 = 703.0528{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 703.7813{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~3/2 = 703.704{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 114: Line 133:
* 15-odd-limit diamond tradeoff: ~3/2 = [701.955, 711.731]
* 15-odd-limit diamond tradeoff: ~3/2 = [701.955, 711.731]


{{Optimal ET sequence|legend=0| 46, 58, 104c, 162cef }}
{{Optimal ET sequence|legend=0| 12f, 34ef, 46, 58, 104c, 162cef }}


Badness (Smith): 0.018926
Badness (Sintel): 0.782


=== 17-limit ===
=== 17-limit ===
Line 125: Line 144:
Mapping: {{mapping| 2 0 11 31 45 55 5 | 0 1 -2 -8 -12 -15 1 }}
Mapping: {{mapping| 2 0 11 31 45 55 5 | 0 1 -2 -8 -12 -15 1 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~3/2 = 703.812{{c}}
Optimal tunings:
* WE: ~17/12 = 599.6253{{c}}, ~3/2 = 703.3726{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 703.8520{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 703.812{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 131: Line 153:
* 17-odd-limit diamond tradeoff: ~3/2 = [698.955, 711.731]
* 17-odd-limit diamond tradeoff: ~3/2 = [698.955, 711.731]


{{Optimal ET sequence|legend=0| 46, 58, 104c }}
{{Optimal ET sequence|legend=0| 12f, 34ef, 46, 58, 104c }}


Badness (Smith): 0.016425
Badness (Sintel): 0.837


=== 2.3.5.7.11.13.17.23 subgroup (Na"Naa') ===
=== 2.3.5.7.11.13.17.23 subgroup (Na"Naa') ===
Line 142: Line 164:
Comma list: 126/125, 136/135, 176/175, 196/195, 231/230, 256/255
Comma list: 126/125, 136/135, 176/175, 196/195, 231/230, 256/255


Sval mapping: {{mapping| 2 0 11 31 45 55 5 63 | 0 1 -2 -8 -12 -15 1 -17 }}
Subgroup-val mapping: {{mapping| 2 0 11 31 45 55 5 63 | 0 1 -2 -8 -12 -15 1 -17 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~3/2 = 703.870{{c}}
Optimal tunings:
* WE: ~17/12 = 599.6272{{c}}, ~3/2 = 703.4326{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 703.9093{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 703.870{{c}} -->


{{Optimal ET sequence|legend=0| 46, 58i, 104ci }}
{{Optimal ET sequence|legend=0| 12i, 34efi, 46, 58i, 104ci }}
 
Badness (Sintel): 0.882


== Pajara ==
== Pajara ==
Line 161: Line 188:
{{Mapping|legend=1| 2 0 11 12 | 0 1 -2 -2 }}
{{Mapping|legend=1| 2 0 11 12 | 0 1 -2 -2 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 600.000{{c}}, ~3/2 = 707.048{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~7/5 = 598.8483{{c}}, ~3/2 = 705.6906{{c}}
: [[error map]]: {{val| -2.303 +1.432 -5.756 +10.580 }}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 707.3438{{c}}
: error map: {{val| 0.000 +5.389 -1.001 +16.487 }}
<!-- [[POTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 707.048{{c}} -->


[[Tuning ranges]]:
[[Tuning ranges]]:
Line 169: Line 201:
{{Optimal ET sequence|legend=1| 10, 12, 22, 34d, 56d }}
{{Optimal ET sequence|legend=1| 10, 12, 22, 34d, 56d }}


[[Badness]] (Smith): 0.020033
[[Badness]] (Sintel): 0.507


=== 11-limit ===
=== 11-limit ===
Line 178: Line 210:
Mapping: {{mapping| 2 0 11 12 26 | 0 1 -2 -2 -6 }}
Mapping: {{mapping| 2 0 11 12 26 | 0 1 -2 -2 -6 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 706.885{{c}}
Optimal tunings:
* WE: ~7/5 = 598.8485{{c}}, ~3/2 = 705.5285{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 707.1826{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 706.885{{c}} -->


Tuning ranges:
Tuning ranges:
Line 186: Line 221:
{{Optimal ET sequence|legend=0| 10e, 12, 22, 34d, 56d }}
{{Optimal ET sequence|legend=0| 10e, 12, 22, 34d, 56d }}


Badness (Smith): 0.020343
Badness (Sintel): 0.673


==== 13-limit ====
==== 13-limit ====
Line 195: Line 230:
Mapping: {{mapping| 2 0 11 12 26 1 | 0 1 -2 -2 -6 2 }}
Mapping: {{mapping| 2 0 11 12 26 1 | 0 1 -2 -2 -6 2 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 708.919{{c}}
Optimal tunings:
* WE: ~7/5 = 599.9732{{c}}, ~3/2 = 708.8873{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.9227{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 708.919{{c}} -->


{{Optimal ET sequence|legend=0| 10e, 12, 22 }}
{{Optimal ET sequence|legend=0| 10e, 12, 22 }}


Badness (Smith): 0.027642
Badness (Sintel): 1.14


===== 17-limit =====
===== 17-limit =====
Line 208: Line 246:
Mapping: {{mapping| 2 0 11 12 26 1 5 | 0 1 -2 -2 -6 2 1 }}
Mapping: {{mapping| 2 0 11 12 26 1 5 | 0 1 -2 -2 -6 2 1 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 708.806{{c}}
Optimal tunings:
* WE: ~7/5 = 599.8871{{c}}, ~3/2 = 708.6725{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.8176{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 708.806{{c}} -->


{{Optimal ET sequence|legend=0| 10e, 12, 22 }}
{{Optimal ET sequence|legend=0| 10e, 12, 22 }}


Badness (Smith): 0.020899
Badness (Sintel): 1.06


==== Pajarina ====
==== Pajarina ====
Line 221: Line 262:
Mapping: {{mapping| 2 0 11 12 26 36 | 0 1 -2 -2 -6 -9 }}
Mapping: {{mapping| 2 0 11 12 26 36 | 0 1 -2 -2 -6 -9 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 706.133{{c}}
Optimal tunings:
* WE: ~7/5 = 598.7732{{c}}, ~3/2 = 704.6889{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 706.3950{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 706.133{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 22, 34d }}
{{Optimal ET sequence|legend=0| 12f, 22, 34d }}


Badness (Smith): 0.022327
Badness (Sintel): 0.923


===== 17-limit =====
===== 17-limit =====
Line 234: Line 278:
Mapping: {{mapping| 2 0 11 12 26 36 5 | 0 1 -2 -2 -6 -9 1 }}
Mapping: {{mapping| 2 0 11 12 26 36 5 | 0 1 -2 -2 -6 -9 1 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 706.410{{c}}
Optimal tunings:
* WE: ~7/5 = 599.0204{{c}}, ~3/2 = 705.2572{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 706.5660{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 706.410{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 22, 34d }}
{{Optimal ET sequence|legend=0| 12f, 22, 34d }}


Badness (Smith): 0.018375
Badness (Sintel): 0.936


==== Pajarita ====
==== Pajarita ====
Line 247: Line 294:
Mapping: {{mapping| 2 0 11 12 26 17 | 0 1 -2 -2 -6 -3 }}
Mapping: {{mapping| 2 0 11 12 26 17 | 0 1 -2 -2 -6 -3 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 707.450{{c}}
Optimal tunings:
* WE: ~7/5 = 598.3048{{c}}, ~3/2 = 705.4512{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 707.9238{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 707.450{{c}} -->


{{Optimal ET sequence|legend=0| 10e, 12f, 22f }}
{{Optimal ET sequence|legend=0| 10e, 12f, 22f, 34dff }}


Badness (Smith): 0.022677
Badness (Sintel): 0.937


===== 17-limit =====
===== 17-limit =====
Line 260: Line 310:
Mapping: {{mapping| 2 0 11 12 26 17 5 | 0 1 -2 -2 -6 -3 1 }}
Mapping: {{mapping| 2 0 11 12 26 17 5 | 0 1 -2 -2 -6 -3 1 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 707.947{{c}}
Optimal tunings:
* WE: ~7/5 = 598.6103{{c}}, ~3/2 = 706.3076{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.2256{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 707.947{{c}} -->


{{Optimal ET sequence|legend=0| 10e, 12f, 22f }}
{{Optimal ET sequence|legend=0| 10e, 12f, 22f }}


Badness (Smith): 0.019007
Badness (Sintel): 0.968


=== Pajarous ===
=== Pajarous ===
Line 273: Line 326:
Mapping: {{mapping| 2 0 11 12 -9 | 0 1 -2 -2 5 }}
Mapping: {{mapping| 2 0 11 12 -9 | 0 1 -2 -2 5 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 709.578{{c}}
Optimal tunings:
* WE: ~7/5 = 599.4055{{c}}, ~3/2 = 708.8747{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 709.5508{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 709.578{{c}} -->


Tuning ranges:
Tuning ranges:
Line 281: Line 337:
{{Optimal ET sequence|legend=0| 10, 12e, 22, 120bce, 142bce }}
{{Optimal ET sequence|legend=0| 10, 12e, 22, 120bce, 142bce }}


Badness (Smith): 0.028349
Badness (Sintel): 0.937


==== 13-limit ====
==== 13-limit ====
Line 290: Line 346:
Mapping: {{mapping| 2 0 11 12 -9 1 | 0 1 -2 -2 5 2 }}
Mapping: {{mapping| 2 0 11 12 -9 1 | 0 1 -2 -2 5 2 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 710.240{{c}}
Optimal tunings:
* WE: ~7/5 = 599.9064{{c}}, ~3/2 = 710.1289{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 710.2325{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 710.240{{c}} -->


{{Optimal ET sequence|legend=0| 10, 22, 54f, 76bdff }}
{{Optimal ET sequence|legend=0| 10, 22 }}


Badness (Smith): 0.025176
Badness (Sintel): 1.04


===== 17-limit =====
===== 17-limit =====
Line 303: Line 362:
Mapping: {{mapping| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}
Mapping: {{mapping| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 710.221{{c}}
Optimal tunings:
* WE: ~7/5 = 599.8239{{c}}, ~3/2 = 710.0128{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 710.2067{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 710.221{{c}} -->


{{Optimal ET sequence|legend=0| 10, 22, 54f, 76bdff }}
{{Optimal ET sequence|legend=0| 10, 22, 54f, 76bdff }}


Badness (Smith): 0.018249
Badness (Sintel): 0.930


==== Pajaro ====
==== Pajaro ====
Line 316: Line 378:
Mapping: {{mapping| 2 0 11 12 -9 17 | 0 1 -2 -2 5 -3 }}
Mapping: {{mapping| 2 0 11 12 -9 17 | 0 1 -2 -2 5 -3 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 710.818{{c}}
Optimal tunings:
* WE: ~7/5 = 598.8257{{c}}, ~3/2 = 709.4266{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 710.8414{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 710.818{{c}} -->


{{Optimal ET sequence|legend=0| 10, 22f, 32f, 54ff }}
{{Optimal ET sequence|legend=0| 10, 22f, 32f }}


Badness (Smith): 0.027355
Badness (Sintel): 1.13


===== 17-limit =====
===== 17-limit =====
Line 329: Line 394:
Mapping: {{mapping| 2 0 11 12 -9 17 5 | 0 1 -2 -2 5 -3 1 }}
Mapping: {{mapping| 2 0 11 12 -9 17 5 | 0 1 -2 -2 5 -3 1 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 710.866{{c}}
Optimal tunings:
* WE: ~7/5 = 598.8865{{c}}, ~3/2 = 709.5472{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 710.8704{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 710.866{{c}} -->


{{Optimal ET sequence|legend=0| 10, 22f, 32f, 54ff }}
{{Optimal ET sequence|legend=0| 10, 22f, 32f }}


Badness (Smith): 0.019844
Badness (Sintel): 1.01


=== Pajaric ===
=== Pajaric ===
Line 342: Line 410:
Mapping: {{mapping| 2 0 11 12 7 | 0 1 -2 -2 0 }}
Mapping: {{mapping| 2 0 11 12 7 | 0 1 -2 -2 0 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 705.524{{c}}
Optimal tunings:
* WE: ~7/5 = 597.4807{{c}}, ~3/2 = 702.5616{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 706.0542{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 705.524{{c}} -->


{{Optimal ET sequence|legend=0| 10, 12, 22e, 34dee }}
{{Optimal ET sequence|legend=0| 10, 12, 22e }}


Badness (Smith): 0.023798
Badness (Sintel): 0.787


==== 13-limit ====
==== 13-limit ====
Line 355: Line 426:
Mapping: {{mapping| 2 0 11 12 7 17 | 0 1 -2 -2 0 -3 }}
Mapping: {{mapping| 2 0 11 12 7 17 | 0 1 -2 -2 0 -3 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 707.442{{c}}
Optimal tunings:
* WE: ~7/5 = 597.1952{{c}}, ~3/2 = 704.1350{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.1989{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 707.442{{c}} -->


{{Optimal ET sequence|legend=0| 10, 12f, 22ef }}
{{Optimal ET sequence|legend=0| 10, 12f, 22ef }}


Badness (Smith): 0.020461
Badness (Sintel): 0.845


==== 17-limit ====
==== 17-limit ====
Line 368: Line 442:
Mapping: {{mapping| 2 0 11 12 7 17 5 | 0 1 -2 -2 0 -3 1 }}
Mapping: {{mapping| 2 0 11 12 7 17 5 | 0 1 -2 -2 0 -3 1 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~3/2 = 708.544{{c}}
Optimal tunings:
* WE: ~7/5 = 597.6509{{c}}, ~3/2 = 705.7702{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.9719{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 708.544{{c}} -->


{{Optimal ET sequence|legend=0| 10, 12f, 22ef }}
{{Optimal ET sequence|legend=0| 10, 12f, 22ef }}


Badness (Smith): 0.017592
Badness (Sintel): 0.896


=== Hemipaj ===
=== Hemipaj ===
Line 381: Line 458:
Mapping: {{mapping| 2 1 9 10 8 | 0 2 -4 -4 -1 }}
Mapping: {{mapping| 2 1 9 10 8 | 0 2 -4 -4 -1 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~11/8 = 546.383{{c}}
: mapping generators: ~2, ~16/11
 
Optimal tunings:
* WE: ~7/5 = 597.6509{{c}}, ~16/11 = 652.7788{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 653.7119{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~16/11 = 653.617{{c}} -->


{{Optimal ET sequence|legend=0| 20, 22, 68d, 90d }}
{{Optimal ET sequence|legend=0| 2, 20, 22 }}


Badness (Smith): 0.038890
Badness (Sintel): 1.29


=== Hemifourths ===
=== Hemifourths ===
Line 394: Line 476:
Mapping: {{mapping| 2 0 11 12 -1 | 0 2 -4 -4 5 }}
Mapping: {{mapping| 2 0 11 12 -1 | 0 2 -4 -4 5 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~55/32 = 953.093{{c}}
: mapping generators: ~2, ~55/32
 
Optimal tunings:
* WE: ~7/5 = 597.6509{{c}}, ~55/32 = 950.8475{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~55/32 = 953.1172{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~55/32 = 953.093{{c}} -->


{{Optimal ET sequence|legend=0| 10, 24d, 34d }}
{{Optimal ET sequence|legend=0| 10, 24d, 34d }}


Badness (Smith): 0.048885
Badness (Sintel): 1.62


==== 13-limit ====
==== 13-limit ====
Line 407: Line 494:
Mapping: {{mapping| 2 0 11 12 -1 9 | 0 2 -4 -4 5 -1 }}
Mapping: {{mapping| 2 0 11 12 -1 9 | 0 2 -4 -4 5 -1 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~26/15 = 953.074{{c}}
Optimal tunings:
* WE: ~7/5 = 598.6748{{c}}, ~26/15 = 950.9691{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~26/15 = 953.1052{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~26/15 = 953.074{{c}} -->


{{Optimal ET sequence|legend=0| 10, 24d, 34d }}
{{Optimal ET sequence|legend=0| 10, 24d, 34d }}


Badness (Smith): 0.028755
Badness (Sintel): 1.19


==== 17-limit ====
==== 17-limit ====
Line 420: Line 510:
Mapping: {{mapping| 2 0 11 12 -1 9 5 | 0 2 -4 -4 5 -1 2 }}
Mapping: {{mapping| 2 0 11 12 -1 9 5 | 0 2 -4 -4 5 -1 2 }}


Optimal tuning (POTE): ~7/5 = 600.000{{c}}, ~26/15 = 953.210{{c}}
Optimal tunings:
* WE: ~7/5 = 598.8411{{c}}, ~26/15 = 951.3687{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~26/15 = 953.2169{{c}}
<!-- * POTE: ~7/5 = 600.000{{c}}, ~26/15 = 953.210{{c}} -->


{{Optimal ET sequence|legend=0| 10, 24d, 34d }}
{{Optimal ET sequence|legend=0| 10, 24d, 34d }}


Badness (Smith): 0.021790
Badness (Sintel): 1.11


== Srutal ==
== Srutal ==
Line 437: Line 530:
{{Mapping|legend=1| 2 0 11 -42 | 0 1 -2 15 }}
{{Mapping|legend=1| 2 0 11 -42 | 0 1 -2 15 }}


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~3/2 = 704.814{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 599.4046{{c}}, ~3/2 = 704.1150{{c}}
: [[error map]]: {{val| -1.191 +0.969 +1.289 +0.044 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.7646{{c}}
: error map: {{val| 0.000 +2.810 +4.157 +2.643 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~3/2 = 704.814{{c}} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 445: Line 543:
{{Optimal ET sequence|legend=1| 34d, 46, 80, 126, 206cd, 332bcd }}
{{Optimal ET sequence|legend=1| 34d, 46, 80, 126, 206cd, 332bcd }}


[[Badness]] (Smith): 0.091504
[[Badness]] (Sintel): 2.32


=== 11-limit ===
=== 11-limit ===
Line 454: Line 552:
Mapping: {{mapping| 2 0 11 -42 -28 | 0 1 -2 15 11 }}
Mapping: {{mapping| 2 0 11 -42 -28 | 0 1 -2 15 11 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~3/2 = 704.856{{c}}
Optimal tunings:
* WE: ~45/32 = 599.4413{{c}}, ~3/2 = 704.1999{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8017{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~3/2 = 704.856{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 462: Line 563:
{{Optimal ET sequence|legend=0| 34d, 46, 80, 126, 206cd }}
{{Optimal ET sequence|legend=0| 34d, 46, 80, 126, 206cd }}


Badness (Smith): 0.035315
Badness (Sintel): 1.17


=== 13-limit ===
=== 13-limit ===
Line 471: Line 572:
Mapping: {{mapping| 2 0 11 -42 -28 -18 | 0 1 -2 15 11 8 }}
Mapping: {{mapping| 2 0 11 -42 -28 -18 | 0 1 -2 15 11 8 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~3/2 = 704.881{{c}}
Optimal tunings:
* WE: ~45/32 = 599.5490{{c}}, ~3/2 = 704.3516{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8347{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~3/2 = 704.881{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 478: Line 582:
* 15-odd-limit diamond tradeoff: ~3/2 = [701.955, 711.731]
* 15-odd-limit diamond tradeoff: ~3/2 = [701.955, 711.731]


{{Optimal ET sequence|legend=0| 34d, 46, 80, 206cd, 286bcde }}
{{Optimal ET sequence|legend=0| 34d, 46, 80 }}


Badness (Smith): 0.025286
Badness (Sintel): 1.04


=== 17-limit ===
=== 17-limit ===
Line 489: Line 593:
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 | 0 1 -2 15 11 8 1 }}
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 | 0 1 -2 15 11 8 1 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~3/2 = 704.840{{c}}
Optimal tunings:
* WE: ~17/12 = 599.6459{{c}}, ~3/2 = 704.4237{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8083{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 704.840{{c}} -->


Tuning ranges:  
Tuning ranges:  
Line 495: Line 602:
* 17-odd-limit diamond tradeoff: ~3/2 = [698.955, 711.731]
* 17-odd-limit diamond tradeoff: ~3/2 = [698.955, 711.731]


{{Optimal ET sequence|legend=0| 34d, 46, 80, 126, 206cd }}
{{Optimal ET sequence|legend=0| 34d, 46, 80, 126 }}


Badness (Smith): 0.018594
Badness (Sintel): 0.947


=== 19-limit ===
=== 19-limit ===
Line 506: Line 613:
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 | 0 1 -2 15 11 8 1 20 }}
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 | 0 1 -2 15 11 8 1 20 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~3/2 = 704.905{{c}}
Optimal tunings:
* WE: ~17/12 = 599.6371{{c}}, ~3/2 = 704.4790{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8745{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 704.905{{c}} -->


{{Optimal ET sequence|legend=0| 34dh, 46, 80, 206cd }}
{{Optimal ET sequence|legend=0| 34dh, 46, 80 }}


Badness (Smith): 0.017063
Badness (Sintel): 1.04


==== Srutaloo ====
==== Srutaloo ====
Line 521: Line 631:
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 | 0 1 -2 15 11 8 1 20 6 }}
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 | 0 1 -2 15 11 8 1 20 6 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~3/2 = 704.899{{c}}
Optimal tunings:
* WE: ~17/12 = 599.6690{{c}}, ~3/2 = 704.5098{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8713{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 704.899{{c}} -->


{{Optimal ET sequence|legend=0| 34dh, 46, 80, 206cd }}
{{Optimal ET sequence|legend=0| 34dh, 46, 80 }}


Badness (Smith): 0.013555
Badness (Sintel): 0.971


===== 29-limit =====
===== 29-limit =====
Line 534: Line 647:
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 | 0 1 -2 15 11 8 1 20 6 27 }}
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 | 0 1 -2 15 11 8 1 20 6 27 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~3/2 = 704.906{{c}}
Optimal tunings:
* WE: ~17/12 = 599.6664{{c}}, ~3/2 = 704.5138{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8807{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 704.906{{c}} -->


{{Optimal ET sequence|legend=0| 34dhj, 46, 80, 206cd }}
{{Optimal ET sequence|legend=0| 34dhj, 46, 80 }}


Badness (Smith): 0.013203
Badness (Sintel): 1.10


===== 31-limit =====
===== 31-limit =====
Line 547: Line 663:
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 48 | 0 1 -2 15 11 8 1 20 6 27 -12 }}
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 48 | 0 1 -2 15 11 8 1 20 6 27 -12 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~3/2 = 704.817{{c}}
Optimal tunings:
* WE: ~17/12 = 599.8115{{c}}, ~3/2 = 704.5958{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8086{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 704.817{{c}} -->


{{Optimal ET sequence|legend=0| 46, 80, 126 }}
{{Optimal ET sequence|legend=0| 46, 80, 126 }}


Badness (Smith): 0.015073
Badness (Sintel): 1.44


== Keen ==
== Keen ==
Line 562: Line 681:
{{Mapping|legend=1| 2 0 11 -23 | 0 1 -2 9 }}
{{Mapping|legend=1| 2 0 11 -23 | 0 1 -2 9 }}


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~3/2 = 707.571{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 599.6603{{c}}, ~3/2 = 707.1707{{c}}
: [[error map]]: {{val| -0.679 +4.536 -3.033 -2.591 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 707.5294{{c}}
: error map: {{val| 0.000 +5.574 -1.373 -1.061 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~3/2 = 707.571{{c}} -->


{{Optimal ET sequence|legend=1| 22, 56, 78, 134b, 212b, 290bb }}
{{Optimal ET sequence|legend=1| 22, 56, 78, 134b }}


[[Badness]] (Smith): 0.083971
[[Badness]] (Sintel): 2.13


=== 11-limit ===
=== 11-limit ===
Line 575: Line 699:
Mapping: {{mapping| 2 0 11 -23 26 | 0 1 -2 9 -6 }}
Mapping: {{mapping| 2 0 11 -23 26 | 0 1 -2 9 -6 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~3/2 = 707.609{{c}}
Optimal tunings:
* WE: ~45/32 = 599.6286{{c}}, ~3/2 = 707.1712{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 707.5984{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~3/2 = 707.609{{c}} -->


{{Optimal ET sequence|legend=0| 22, 56, 78, 212be, 290bbe }}
{{Optimal ET sequence|legend=0| 22, 56, 78 }}


Badness (Smith): 0.045270
Badness (Sintel): 1.50


==== 13-limit ====
==== 13-limit ====
Line 588: Line 715:
Mapping: {{mapping| 2 0 11 -23 26 -18 | 0 1 -2 9 -6 8 }}
Mapping: {{mapping| 2 0 11 -23 26 -18 | 0 1 -2 9 -6 8 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~3/2 = 707.167{{c}}
Optimal tunings:
* WE: ~45/32 = 599.3498{{c}}, ~3/2 = 706.4009{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 707.1309{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~3/2 = 707.167{{c}} -->


{{Optimal ET sequence|legend=0| 22f, 34, 56f }}
{{Optimal ET sequence|legend=0| 22f, 34, 56f }}


Badness (Smith): 0.044877
Badness (Sintel): 1.85


===== 17-limit =====
===== 17-limit =====
Line 601: Line 731:
Mapping: {{mapping| 2 0 11 -23 26 -18 5 | 0 1 -2 9 -6 8 1}}
Mapping: {{mapping| 2 0 11 -23 26 -18 5 | 0 1 -2 9 -6 8 1}}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~3/2 = 707.155{{c}}
Optimal tunings:
* WE: ~17/12 = 599.4053{{c}}, ~3/2 = 706.4544{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 707.1243{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 707.155{{c}} -->


{{Optimal ET sequence|legend=0| 22f, 34, 56f }}
{{Optimal ET sequence|legend=0| 22f, 34, 56f }}


Badness (Smith): 0.030297
Badness (Sintel): 1.54


==== Keenic ====
==== Keenic ====
Line 614: Line 747:
Mapping: {{mapping| 2 0 11 -23 26 36 | 0 1 -2 9 -6 -9 }}
Mapping: {{mapping| 2 0 11 -23 26 36 | 0 1 -2 9 -6 -9 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~3/2 = 707.257{{c}}
Optimal tunings:
* WE: ~45/32 = 599.8547{{c}}, ~3/2 = 707.0858{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 707.2596{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~3/2 = 707.257{{c}} -->


{{Optimal ET sequence|legend=0| 22, 34, 56 }}
{{Optimal ET sequence|legend=0| 22, 34, 56 }}


Badness (Smith): 0.040351
Badness (Sintel): 1.67


===== 17-limit =====
===== 17-limit =====
Line 627: Line 763:
Mapping: {{mapping| 2 0 11 -23 26 36 5 | 0 1 -2 9 -6 -9 1 }}
Mapping: {{mapping| 2 0 11 -23 26 36 5 | 0 1 -2 9 -6 -9 1 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~3/2 = 707.252{{c}}
Optimal tunings:
* WE: ~17/12 = 599.8338{{c}}, ~3/2 = 707.0558{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 707.2537{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 707.252{{c}} -->


{{Optimal ET sequence|legend=0| 22, 34, 56 }}
{{Optimal ET sequence|legend=0| 22, 34, 56 }}


Badness (Smith): 0.026917
Badness (Sintel): 1.37


== Bidia ==
== Bidia ==
Retrieved from "https://en.xen.wiki/w/Diaschismic_family"