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{{Technical data page}}
{{Technical data page}}
The '''trisedodge family''' tempers out the [[trisedodge comma]], 30958682112/30517578125 = {{monzo| 19 10 -15 }}.
The '''trisedodge family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[trisedodge comma]] ({{monzo|legend=1| 19 10 -15 }}, [[ratio]]: 30 958 682 112 / 30 517 578 125).


Named by [[Petr Pařízek]] in 2011, ''trisedodge'' (originally spelt ''trisedoge'') means that three semidiminished [[octave]]s add up to [[7/1]], and that an octave is made of 5 [[period]]s<ref name="naming">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.  
Named by [[Petr Pařízek]] in 2011, ''trisedodge'' (originally spelt ''trisedoge'') means that three semidiminished [[octave]]s add up to [[7/1]], and that an octave is made of 5 [[period]]s<ref name="naming">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.  
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{{Mapping|legend=1| 5 1 7 | 0 3 2 }}
{{Mapping|legend=1| 5 1 7 | 0 3 2 }}
: mapping generators: ~144/125, ~864/625
: mapping generators: ~144/125, ~864/625


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~144/125 = 1\5, ~864/625 = 553.8249 (~25/24 = 73.8249)
* [[CTE]]: ~144/125 = 240.0000{{c}}, ~864/625 = 553.8249{{c}} (~25/24 = 73.8249{{c}})
* [[POTE]]: ~144/125 = 1\5, ~864/625 = 554.0077 (~25/24 = 74.0077)
* [[POTE]]: ~144/125 = 240.0000{{c}}, ~864/625 = 554.0077{{c}} (~25/24 = 74.0077{{c}})


{{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, 470c, 535c, 600c }}


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


=== Countdown ===
=== Countdown ===
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Comma list: 4000/3993, 6912/6875
Comma list: 4000/3993, 6912/6875


Sval mapping: {{mapping| 5 1 7 15 | 0 3 2 1 }}
Subgroup-val mapping: {{mapping| 5 1 7 15 | 0 3 2 1 }}


[[Optimal tuning]]s:  
Optimal tunings:  
* CTE: ~55/48 = 1\5, ~11/8 = 553.7951 (~25/24 = 73.7951)
* CTE: ~55/48 = 240.0000{{c}}, ~11/8 = 553.7951{{c}} (~25/24 = 73.7951{{c}})
* POTE: ~55/48 = 1\5, ~11/8 = 554.1247 (~25/24 = 74.1247)
* POTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.1247{{c}} (~25/24 = 74.1247{{c}})


{{Optimal ET sequence|legend=1| 15, 35, 50, 65, 210e, 275e, 340ce }}
{{Optimal ET sequence|legend=0| 15, 35, 50, 65, 210e, 275e, 340ce }}


RMS error: 0.3198 cents
RMS error: 0.3198 cents
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~144/125 = 1\5, ~175/128 = 554.5146 (~25/24 = 74.5146)
* [[CTE]]: ~144/125 = 240.0000{{c}}, ~175/128 = 554.5146{{c}} (~25/24 = 74.5146{{c}})
* [[POTE]]: ~144/125 = 1\5, ~175/128 = 554.9480 (~25/24 = 74.9480)
* [[POTE]]: ~144/125 = 240.0000{{c}}, ~175/128 = 554.9480{{c}} (~25/24 = 74.9480{{c}})


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


Badness: 0.137695
Badness (Smith): 0.137695


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~55/48 = 1\5, ~11/8 = 554.4664 (~25/24 = 74.4664)
* CTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.4664{{c}} (~25/24 = 74.4664{{c}})
* POTE: ~55/48 = 1\5, ~11/8 = 554.9401 (~25/24 = 74.9401)
* POTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.9401{{c}} (~25/24 = 74.9401{{c}})


{{Optimal ET sequence|legend=1| 15, 50d, 65d, 80 }}
{{Optimal ET sequence|legend=0| 15, 50d, 65d, 80 }}


Badness: 0.043508
Badness (Smith): 0.043508


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:
Optimal tunings:
* CTE: ~55/48 = 1\5, ~11/8 = 554.6802 (~25/24 = 74.6802)
* CTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.6802{{c}} (~25/24 = 74.6802{{c}})
* CWE: ~55/48 = 1\5, ~11/8 = 554.6627 (~25/24 = 74.6627)
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.6627{{c}} (~25/24 = 74.6627{{c}})


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


Badness: 0.0446
Badness (Smith): 0.0446


==== 17-limit ====
==== 17-limit ====
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Optimal tunings:
Optimal tunings:
* CTE: ~55/48 = 1\5, ~11/8 = 554.722 (~25/24 = 74.722)
* CTE: ~55/48 = 240.000{{c}}, ~11/8 = 554.722{{c}} (~25/24 = 74.722{{c}})
* CWE: ~55/48 = 1\5, ~11/8 = 554.614 (~25/24 = 74.614)
* CWE: ~55/48 = 240.000{{c}}, ~11/8 = 554.614{{c}} (~25/24 = 74.614{{c}})


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


Badness (Sintel): 1.609
Badness (Sintel): 1.609
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Optimal tunings:
Optimal tunings:
* CTE: ~55/48 = 1\5, ~11/8 = 554.698 (~25/24 = 74.698)
* CTE: ~55/48 = 240.000{{c}}, ~11/8 = 554.698{{c}} (~25/24 = 74.698{{c}})
* CWE: ~55/48 = 1\5, ~11/8 = 554.667 (~25/24 = 74.667)
* CWE: ~55/48 = 240.000{{c}}, ~11/8 = 554.667{{c}} (~25/24 = 74.667{{c}})


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


Badness (Sintel): 1.542
Badness (Sintel): 1.542
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Optimal tunings:
Optimal tunings:
* CTE: ~23/20 = 1\5, ~11/8 = 554.689 (~24/23 = 74.689)
* CTE: ~23/20 = 240.0000{{c}}, ~11/8 = 554.689{{c}} (~24/23 = 74.689{{c}})
* CWE: ~23/20 = 1\5, ~11/8 = 554.688 (~24/23 = 74.688)
* CWE: ~23/20 = 240.0000{{c}}, ~11/8 = 554.688{{c}} (~24/23 = 74.688{{c}})
 
Optimal ET sequence: {{Optimal ET sequence| 15f, 65d, 80 }}


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


Badness (Sintel): 1.463
Badness (Sintel): 1.463
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Optimal tunings:
Optimal tunings:
* CTE: ~23/20 = 1\5, ~11/8 = 554.673 (~24/23 = 74.673)
* CTE: ~23/20 = 240.000{{c}}, ~11/8 = 554.673{{c}} (~24/23 = 74.673{{c}})
* CWE: ~23/20 = 1\5, ~11/8 = 554.684 (~24/23 = 74.684)
* CWE: ~23/20 = 240.000{{c}}, ~11/8 = 554.684{{c}} (~24/23 = 74.684{{c}})
 
Optimal ET sequence: {{Optimal ET sequence| 15f, 65d, 80 }}


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


Badness (Sintel): 1.380
Badness (Sintel): 1.380
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Optimal tunings:
Optimal tunings:
* CTE: ~55/48 = 1\5, ~11/8 = 554.7405 (~25/24 = 74.7405)
* CTE: ~55/48 = 240.0000{{c}}, ~11/8 = 554.7405{{c}} (~25/24 = 74.7405{{c}})
* CWE: ~55/48 = 1\5, ~11/8 = 555.1626 (~25/24 = 75.1626)
* CWE: ~55/48 = 240.0000{{c}}, ~11/8 = 555.1626{{c}} (~25/24 = 75.1626{{c}})


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


Badness: 0.0380
Badness (Smith): 0.0380


== Coblack ==
== Coblack ==
{{See also| Cloudy clan #Coblack }}
In addition to 126/125, the coblack temperament tempers out the [[cloudy comma]], 16807/16384, which is the amount by which five septimal supermajor seconds ([[8/7]]) fall short of an octave. Coblack was also named by Petr Pařízek, who considered it a counterpart of [[blackwood]]<ref name="naming"/>.  
In addition to 126/125, the coblack temperament tempers out the [[cloudy comma]], 16807/16384, which is the amount by which five septimal supermajor seconds ([[8/7]]) fall short of an octave. Coblack was also named by Petr Pařízek, who considered it a counterpart of [[blackwood]]<ref name="naming"/>.  


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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~8/7 = 1\5, ~48/35 = 553.8429 (~21/20 = 73.8429)
* [[CTE]]: ~8/7 = 240.0000{{c}}, ~48/35 = 553.8429{{c}} (~21/20 = 73.8429{{c}})
* [[POTE]]: ~8/7 = 1\5, ~48/35 = 553.044 (~21/20 = 73.044)
* [[POTE]]: ~8/7 = 240.000{{c}}, ~48/35 = 553.044{{c}} (~21/20 = 73.044{{c}})


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


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


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~8/7 = 1\5, ~11/8 = 553.7951 (~21/20 = 73.7951)
* CTE: ~8/7 = 240.0000{{c}}, ~11/8 = 553.7951{{c}} (~21/20 = 73.7951{{c}})
* POTE: ~8/7 = 1\5, ~11/8 = 553.264 (~21/20 = 73.264)
* POTE: ~8/7 = 240.000{{c}}, ~11/8 = 553.264{{c}} (~21/20 = 73.264{{c}})


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


Badness: 0.045070
Badness (Smith): 0.045070


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