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== Temperaments ==
== Temperaments ==
Tempering out this comma in the full 17-limit gives the rank-6 '''dakotismic''' temperament, or in the 2.3.5.7.11.17 subgroup, the rank-5 '''dakotic''' temperament, enabling [[dakotismic chords]]. You may find a list of good equal temperaments that support these temperaments below.  
Tempering out this comma in the full 17-limit gives the rank-6 '''dakotismic''' temperament, or in the 2.3.5.7.11.17 subgroup, the rank-5 '''dakotic''' temperament, enabling [[dakotismic chords]]. You may find a list of good equal temperaments that support these temperaments below.  
=== Dakotic ===
[[Subgroup]]: 2.3.5.7.11.17
[[Subgroup val|Subgroup-val]] [[mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 3 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]
|}
: mapping generators: ~2, ~3, ~5, ~7, ~11
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0443{{c}}, ~3/2 = 702.2453{{c}}, ~5/4 = 385.9853{{c}}, ~7/4 = 968.3869{{c}}, ~11/8 = 551.7162{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2568{{c}}, ~5/4 = 386.0203{{c}}, ~7/4 = 968.4102{{c}}, ~11/8 = 551.7760{{c}}
{{Optimal ET sequence|legend=1| 12, 14c, 19eg, 22, 27eg, 31g, 34d, 38d, 41, 46, 58, 68, 72, 118, 171, 190g, 193, 212g, 217, 239, 311, 1051dg }}
[[Badness]] (Sintel): 0.236


=== Dakotismic ===
=== Dakotismic ===
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: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13  
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13  


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.2950{{c}}, ~5/4 = 386.0705{{c}}, ~7/4 = 968.4704{{c}}, ~11/8 = 551.8578{{c}}, ~13/8 = 840.5277{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0443{{c}}, ~3/2 = 702.2453{{c}}, ~5/4 = 385.9853{{c}}, ~7/4 = 968.3869{{c}}, ~11/8 = 551.7162{{c}}, ~13/8 = 840.3943{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2568{{c}}, ~5/4 = 386.0203{{c}}, ~7/4 = 968.4102{{c}}, ~11/8 = 551.7760{{c}}, ~13/8 = 840.4446{{c}}


{{Optimal ET sequence|legend=1| 12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg }}*
{{Optimal ET sequence|legend=1| 12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg }}*
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<nowiki>*</nowiki> [[optimal patent val]]: [[861edo|861]]
<nowiki>*</nowiki> [[optimal patent val]]: [[861edo|861]]


=== Dakotic ===
[[Badness]] (Sintel): 0.478
[[Subgroup]]: 2.3.5.7.11.17
 
[[Subgroup-val|Subgroup val]] [[mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 3 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]
|}
: mapping generators: ~2, ~3, ~5, ~7, ~11
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.2950{{c}}, ~5/4 = 386.0705{{c}}, ~7/4 = 968.4704{{c}}, ~11/8 = 551.8578{{c}}
 
{{Optimal ET sequence|legend=1| 12, 14c, 19eg, 22, 27eg, 31g, 34d, 38d, 41, 46, 58, 68, 72, 118, 171, 190g, 193, 212g, 217, 239, 311, 1051dg }}


== Etymology ==
== Etymology ==
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