595/594: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Name = dakotisma
+| Color name = 17o1uzy2, soluzoyo 2nd
 | Comma = yes
 }}
@@ Line 36: / Line 37: @@
 == 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 this temperament 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.
+=== Dakotismic ===
 [[Subgroup]]: 2.3.5.7.11.13.17
-[[Mapping]]:
+[[Mapping]]: <br>
-<br>[{{val| 1 0 0 0 0 0 1 }},
+{| class="right-all"
-<br>{{val| 0 1 0 0 0 0 3 }},
+|-
-<br>{{val| 0 0 1 0 0 0 -1 }},
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 1 || ],
-<br>{{val| 0 0 0 1 0 0 -1 }},
+|-
-<br>{{val| 0 0 0 0 1 0 1 }},
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 3 || ],
-<br>{{val| 0 0 0 0 0 1 0 }}]
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
-Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
-{{Val list|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 tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578, ~13/8 = 840.5277
+{{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 }}*
 <nowiki>*</nowiki> [[optimal patent val]]: [[861edo|861]]
+=== Dakotic ===
+[[Subgroup]]: 2.3.5.7.11.17
+[[Sval]] [[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 || ]]
+|}
+: sval mapping generators: ~2, ~3, ~5, ~7, ~11
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578
+{{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 ==
@@ Line 58: / Line 93: @@
 [[Category:Dakotismic]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]