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Trisedodge family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~144/125 = 240.0000{{c}}, ~864/625 = 553.8249{{c}} (~25/24 = 73.8249{{c}})
* [[WE]]: ~144/125 = 239.9482{{c}}, ~864/625 = 553.8881{{c}} (~25/24 = 73.9917{{c}})
* [[POTE]]: ~144/125 = 240.0000{{c}}, ~864/625 = 554.0077{{c}} (~25/24 = 74.0077{{c}})
: [[error map]]: {{val| -0.259 -0.342 +1.100 }}
* [[CWE]]: ~144/125 = 240.0000{{c}}, ~864/625 = 553.9342{{c}} (~25/24 = 73.9342{{c}})
: error map: {{val| 0.000 -0.152 +1.555 }}


{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 340c, 405c, 470c, 535c, 600c }}
{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 340c, 405c, …, 600c }}


[[Badness]] (Smith): 0.252724
[[Badness]] (Sintel): 5.93


=== Countdown ===
=== Countdown ===
Line 36: Line 38:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/48 = 240.0000{{c}}, ~11/8 = 553.7951{{c}} (~25/24 = 73.7951{{c}})
* WE: ~55/48 = 240.0000{{c}}, ~11/8 = 553.9041{{c}} (~25/24 = 74.0952{{c}})
* POTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.1247{{c}} (~25/24 = 74.1247{{c}})
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.0109{{c}} (~25/24 = 74.0109{{c}})


{{Optimal ET sequence|legend=0| 15, 35, 50, 65, 210e, 275e, 340ce }}
{{Optimal ET sequence|legend=0| 15, 35, 50, 65, 210e, 275e, 340ce }}


RMS error: 0.3198 cents
Badness (Sintel): 0.794


== Septimal trisedodge ==
== Septimal trisedodge ==
Line 51: Line 53:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~144/125 = 240.0000{{c}}, ~175/128 = 554.5146{{c}} (~25/24 = 74.5146{{c}})
* [[WE]]: ~144/125 = 239.7187{{c}}, ~175/128 = 554.2976{{c}} (~25/24 = 74.8601{{c}})
* [[POTE]]: ~144/125 = 240.0000{{c}}, ~175/128 = 554.9480{{c}} (~25/24 = 74.9480{{c}})
: [[error map]]: {{val| -1.406 +0.656 +0.312 +2.374 }}
* [[CWE]]: ~144/125 = 240.0000{{c}}, ~175/128 = 554.8511{{c}} (~25/24 = 74.8511{{c}})
: error map: {{val| 0.000 +2.598 +3.388 +6.621 }}


{{Optimal ET sequence|legend=1| 15, 50d, 65d, 80 }}
{{Optimal ET sequence|legend=1| 15, 50d, 65d, 80 }}


Badness (Smith): 0.137695
Badness (Sintel): 3.48


=== 11-limit ===
=== 11-limit ===
Line 66: Line 70:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.4664{{c}} (~25/24 = 74.4664{{c}})
* WE: ~55/48 = 239.7335{{c}}, ~11/8 = 554.3239{{c}} (~25/24 = 74.8569{{c}})
* POTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.9401{{c}} (~25/24 = 74.9401{{c}})
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.8505{{c}} (~25/24 = 74.8505{{c}})


{{Optimal ET sequence|legend=0| 15, 50d, 65d, 80 }}
{{Optimal ET sequence|legend=0| 15, 50d, 65d, 80 }}


Badness (Smith): 0.043508
Badness (Sintel): 1.44


==== 13-limit ====
==== 13-limit ====
Line 81: Line 85:


Optimal tunings:
Optimal tunings:
* CTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.6802{{c}} (~25/24 = 74.6802{{c}})
* WE: ~55/48 = 239.7764{{c}}, ~11/8 = 554.1429{{c}} (~25/24 = 74.5902{{c}})
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.6627{{c}} (~25/24 = 74.6627{{c}})
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.6627{{c}} (~25/24 = 74.6627{{c}})


{{Optimal ET sequence|legend=0| 15f, 50df, 65d, 80, 145d }}
{{Optimal ET sequence|legend=0| 15f, 50df, 65d, 80, 145d }}


Badness (Smith): 0.0446
Badness (Sintel): 1.84


==== 17-limit ====
==== 17-limit ====
Line 93: Line 97:
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 176/175, 351/350, 1040/1029, 1331/1323, 256/255
Comma list: 176/175, 256/255, 351/350, 1040/1029, 1331/1323


Mapping: {{mapping| 5 1 7 21 15 37 32 | 0 3 2 -3 1 -8 -5 }}
Mapping: {{mapping| 5 1 7 21 15 37 32 | 0 3 2 -3 1 -8 -5 }}


Optimal tunings:
Optimal tunings:
* CTE: ~55/48 = 240.000{{c}}, ~11/8 = 554.722{{c}} (~25/24 = 74.722{{c}})
* CTE: ~55/48 = 239.7935{{c}}, ~11/8 = 554.1209{{c}} (~25/24 = 74.5340{{c}})
* CWE: ~55/48 = 240.000{{c}}, ~11/8 = 554.614{{c}} (~25/24 = 74.614{{c}})
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.6141{{c}} (~25/24 = 74.6141{{c}})


{{Optimal ET sequence|legend=0| 15f, 50dfg, 65d, 80, 145d }}
{{Optimal ET sequence|legend=0| 15f, 50dfg, 65d, 80, 145d }}


Badness (Sintel): 1.609
Badness (Sintel): 1.61


==== 19-limit ====
==== 19-limit ====
Line 110: Line 114:
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 176/175, 351/350, 1040/1029, 1331/1323, 256/255, 190/189,
Comma list: 176/175, 190/189, 256/255, 351/350, 1040/1029, 1331/1323


Mapping: {{mapping| 5 1 7 21 15 37 32 12 | 0 3 2 -3 1 -8 -5 4 }}
Mapping: {{mapping| 5 1 7 21 15 37 32 12 | 0 3 2 -3 1 -8 -5 4 }}


Optimal tunings:
Optimal tunings:
* CTE: ~55/48 = 240.000{{c}}, ~11/8 = 554.698{{c}} (~25/24 = 74.698{{c}})
* WE: ~55/48 = 239.8147{{c}}, ~11/8 = 554.2353{{c}} (~25/24 = 74.6060{{c}})
* CWE: ~55/48 = 240.000{{c}}, ~11/8 = 554.667{{c}} (~25/24 = 74.667{{c}})
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.6675{{c}} (~25/24 = 74.6675{{c}})


{{Optimal ET sequence|legend=0| 15f, 65d, 80 }}
{{Optimal ET sequence|legend=0| 15f, 65d, 80 }}


Badness (Sintel): 1.542
Badness (Sintel): 1.54


==== 23-limit ====
==== 23-limit ====
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Subgroup: 2.3.5.7.11.13.17.19.23
Subgroup: 2.3.5.7.11.13.17.19.23


Comma list: 176/175, 351/350, 1040/1029, 1331/1323, 256/255, 190/189, 253/252
Comma list: 176/175, 190/189, 253/252, 256/255, 351/350, 1040/1029, 1331/1323


Mapping: {{mapping| 5 1 7 21 15 37 32 12 18 | 0 3 2 -3 1 -8 -5 4 2 }}
Mapping: {{mapping| 5 1 7 21 15 37 32 12 18 | 0 3 2 -3 1 -8 -5 4 2 }}


Optimal tunings:
Optimal tunings:
* CTE: ~23/20 = 240.0000{{c}}, ~11/8 = 554.689{{c}} (~24/23 = 74.689{{c}})
* WE: ~23/20 = 239.8299{{c}}, ~11/8 = 554.2946{{c}} (~24/23 = 74.6347{{c}})
* CWE: ~23/20 = 240.0000{{c}}, ~11/8 = 554.688{{c}} (~24/23 = 74.688{{c}})
* CWE: ~23/20 = 240.0000{{c}}, ~11/8 = 554.6878{{c}} (~24/23 = 74.6878{{c}})


{{Optimal ET sequence|legend=0| 15f, 65d, 80 }}
{{Optimal ET sequence|legend=0| 15f, 65d, 80 }}


Badness (Sintel): 1.463
Badness (Sintel): 1.46


==== 29-limit ====
==== 29-limit ====
Line 144: Line 148:
Subgroup: 2.3.5.7.11.13.17.19.23.29
Subgroup: 2.3.5.7.11.13.17.19.23.29


Comma list: 176/175, 351/350, 1040/1029, 1331/1323, 256/255, 190/189, 253/252, 232/231
Comma list: 176/175, 190/189, 232/231, 253/252, 256/255, 351/350, 1040/1029, 1331/1323


Mapping: {{mapping| 5 1 7 21 15 37 32 12 18 22 | 0 3 2 -3 1 -8 -5 4 2 1 }}
Mapping: {{mapping| 5 1 7 21 15 37 32 12 18 22 | 0 3 2 -3 1 -8 -5 4 2 1 }}


Optimal tunings:
Optimal tunings:
* CTE: ~23/20 = 240.000{{c}}, ~11/8 = 554.673{{c}} (~24/23 = 74.673{{c}})
* WE: ~23/20 = 239.8259{{c}}, ~11/8 = 554.2822{{c}} (~24/23 = 74.6304{{c}})
* CWE: ~23/20 = 240.000{{c}}, ~11/8 = 554.684{{c}} (~24/23 = 74.684{{c}})
* CWE: ~23/20 = 240.0000{{c}}, ~11/8 = 554.6835{{c}} (~24/23 = 74.6835{{c}})


{{Optimal ET sequence|legend=0| 15f, 65d, 80 }}
{{Optimal ET sequence|legend=0| 15f, 65d, 80 }}


Badness (Sintel): 1.380
Badness (Sintel): 1.38


==== Trisey ====
==== Trisey ====
Line 166: Line 170:


Optimal tunings:
Optimal tunings:
* CTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.7405{{c}} (~25/24 = 74.7405{{c}})
* WE: ~55/48 = 239.7425{{c}}, ~11/8 = 554.6648{{c}} (~25/24 = 75.1797{{c}})
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 555.1626{{c}} (~25/24 = 75.1626{{c}})
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 555.1626{{c}} (~25/24 = 75.1626{{c}})


{{Optimal ET sequence|legend=0| 15, 80, 175bcde, 255bcdde }}
{{Optimal ET sequence|legend=0| 15, 80, 175bcde, 255bcdde }}


Badness (Smith): 0.0380
Badness (Sintel): 1.57


== Coblack ==
== Coblack ==
Line 183: Line 187:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~8/7 = 240.0000{{c}}, ~48/35 = 553.8429{{c}} (~21/20 = 73.8429{{c}})
* [[WE]]: ~8/7 = 240.2499{{c}}, ~48/35 = 553.6203{{c}} (~21/20 = 73.1204{{c}})
* [[POTE]]: ~8/7 = 240.000{{c}}, ~48/35 = 553.044{{c}} (~21/20 = 73.044{{c}})
: [[error map]]: {{val| +1.250 -0.844 +2.676 -5.327 }}
* [[CWE]]: ~8/7 = 240.0000{{c}}, ~48/35 = 553.2893{{c}} (~21/20 = 73.2893{{c}})
: error map: {{val| 0.000 -2.087 +0.265 -8.826 }}


{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }}
{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 115d }}


[[Badness]] (Smith): 0.107282
[[Badness]] (Sintel): 2.71


=== 11-limit ===
=== 11-limit ===
Line 198: Line 204:


Optimal tunings:  
Optimal tunings:  
* CTE: ~8/7 = 240.0000{{c}}, ~11/8 = 553.7951{{c}} (~21/20 = 73.7951{{c}})
* WE: ~8/7 = 240.1524{{c}}, ~11/8 = 553.6154{{c}} (~21/20 = 73.3106{{c}})
* POTE: ~8/7 = 240.000{{c}}, ~11/8 = 553.264{{c}} (~21/20 = 73.264{{c}})
* CWE: ~8/7 = 240.0000{{c}}, ~11/8 = 553.3989{{c}} (~21/20 = 73.3989{{c}})


{{Optimal ET sequence|legend=0| 15, 35, 50, 65, 115d }}
{{Optimal ET sequence|legend=0| 15, 35, 50, 65, 115d }}


Badness (Smith): 0.045070
Badness (Sintel): 1.49


== References ==
== References ==
Retrieved from "https://en.xen.wiki/w/Trisedodge_family"