595/594: Difference between revisions

Line 36:

== 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]]:

[{{val| 1 0 0 0 0 0 1 }},

[{{val| 1 0 0 0 0 0 1 }}

{{val| 0 1 0 0 0 0 3 }},

{{val| 0 1 0 0 0 0 3 }}

{{val| 0 0 1 0 0 0 -1 }},

{{val| 0 0 1 0 0 0 -1 }}

{{val| 0 0 0 1 0 0 -1 }},

{{val| 0 0 0 1 0 0 -1 }}

{{val| 0 0 0 0 1 0 1 }},

{{val| 0 0 0 0 1 0 1 }}

{{val| 0 0 0 0 0 1 0 }}]

{{val| 0 0 0 0 0 1 0 }}]

Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

[[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

{{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 }}*

<nowiki>*</nowiki> [[optimal patent val]]: [[861edo|861]]

=== Dakotic ===

[[Subgroup]]: 2.3.5.7.11.17

[[Sval]] [[mapping]]:

[{{val| 1 0 0 0 0 1 }}

{{val| 0 1 0 0 0 3 }}

{{val| 0 0 1 0 0 -1 }}

{{val| 0 0 0 1 0 -1 }}

{{val| 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

{{Val list|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 36: / Line 36: @@
 == 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 }},
+[{{val| 1 0 0 0 0 0 1 }}<br>
-<br>{{val| 0 1 0 0 0 0 3 }},
+{{val| 0 1 0 0 0 0 3 }}<br>
-<br>{{val| 0 0 1 0 0 0 -1 }},
+{{val| 0 0 1 0 0 0 -1 }}<br>
-<br>{{val| 0 0 0 1 0 0 -1 }},
+{{val| 0 0 0 1 0 0 -1 }}<br>
-<br>{{val| 0 0 0 0 1 0 1 }},
+{{val| 0 0 0 0 1 0 1 }}<br>
-<br>{{val| 0 0 0 0 0 1 0 }}]
+{{val| 0 0 0 0 0 1 0 }}]
 Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+[[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
 {{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 }}*
 <nowiki>*</nowiki> [[optimal patent val]]: [[861edo|861]]
+=== Dakotic ===
+[[Subgroup]]: 2.3.5.7.11.17
+[[Sval]] [[mapping]]: <br>
+[{{val| 1 0 0 0 0 1 }}<br>
+{{val| 0 1 0 0 0 3 }}<br>
+{{val| 0 0 1 0 0 -1 }}<br>
+{{val| 0 0 0 1 0 -1 }}<br>
+{{val| 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
+{{Val list|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 ==