Catalog of temperaments by wedgie: Difference between revisions

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Below are listed [[wedgie]]s for [[7-limit]] [[rank-2 temperament|rank-2]] ~~and~~ [[11-limit]] [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] in the order of increasing ~~complexity~~ of the [[3-limit|2.3 ~~subgroup~~]] or [[5-limit|2.3.5 subgroup]], where ''complexity'' means how many parts the subgroup is split into, and equals the first entry of the wedgie.

Below are listed [[wedgie]]s for [[7-limit]] [[rank-2 temperament|rank-2]], [[11-limit]] [[rank-3 temperament|rank-3]], and [[13-limit]] [[rank-4 temperament|rank-4]] [[regular temperament|temperaments]] in the order of increasing complexities of the [[3-limit|2.3]], [[5-limit|2.3.5]], and [[7-limit|2.3.5.7 subgroup]], respectively, where ''complexity'' means how many parts the subgroup is split into, and equals the first entry of the wedgie.

== Rank-2 temperaments ==

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=== Complexity 20 ===

* [[Frigg]] {{multival|rank=3| 20 10 22 -5 -7 2 25 7 -24 7 }}

== Rank-4 temperaments ==

=== Complexity 0 ===

* [[Akua]] {{multival|rank=4| 0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0 }}

=== Complexity 1 ===

* [[Gentle]] {{multival|rank=4| 1 1 1 0 0 0 -4 -7 -3 0 -7 -12 -5 0 -1 }}

* [[Valinorsmic]] {{multival|rank=4| 1 1 1 -2 -2 0 0 -3 -3 6 4 -1 -5 10 12 }}

* [[Symbiotic]] {{multival|rank=4| 1 -1 0 0 1 -1 9 12 -12 -9 8 13 -13 -8 21 }}

* [[Martwin]] {{multival|rank=4| 1 -1 0 1 2 -2 1 4 -4 2 -7 -2 2 12 26 }}

* [[Ancient]] {{multival|rank=4| 1 -1 0 1 -4 4 1 -1 1 3 -7 4 -4 -24 -3 }}

* [[Zaxa]] {{multival|rank=4| 1 -1 -1 1 1 0 1 -2 3 -3 -7 -12 5 -5 -26 }}

* [[Olympic]] {{multival|rank=4| 1 -2 -1 0 1 -2 -5 -2 -1 5 -17 -12 7 17 26 }}

=== Complexity 2 ===

* [[Semiporwellismic]] {{multival|rank=4| 2 0 2 1 3 -1 -3 3 3 6 -14 -4 14 19 27 }}

* [[Briggs]] {{multival|rank=4| 2 2 4 -2 0 4 -4 2 10 -2 -3 7 13 -7 -11 }}

* [[Tannic]] {{multival|rank=4| 2 -2 1 -2 -2 2 -4 -4 0 3 -11 -16 -5 -10 }}

=== Complexity 4 ===

* [[Topsy]] {{multival|rank=4| 4 -3 -1 -7 -5 2 0 0 0 0 -6 -6 3 3 0 }}

* [[Kalimera]] {{multival|rank=4| 4 4 4 -4 -6 -2 -8 -16 -8 4 -6 -15 -9 6 6 }}

=== Complexity 5 ===

* [[Quartismic]] {{multival|rank=4| 5 1 3 0 -5 -1 -6 -18 0 -6 -24 -27 9 -24 -54 }}

[[Category:Lists of temperaments]]

[[Category:Exterior algebra]]

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-Below are listed [[wedgie]]s for [[7-limit]] [[rank-2 temperament|rank-2]] and [[11-limit]] [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] in the order of increasing complexity of the [[3-limit|2.3 subgroup]] or [[5-limit|2.3.5 subgroup]], where ''complexity'' means how many parts the subgroup is split into, and equals the first entry of the wedgie.
+Below are listed [[wedgie]]s for [[7-limit]] [[rank-2 temperament|rank-2]], [[11-limit]] [[rank-3 temperament|rank-3]], and [[13-limit]] [[rank-4 temperament|rank-4]] [[regular temperament|temperaments]] in the order of increasing complexities of the [[3-limit|2.3]], [[5-limit|2.3.5]], and [[7-limit|2.3.5.7 subgroup]], respectively, where ''complexity'' means how many parts the subgroup is split into, and equals the first entry of the wedgie.
 == Rank-2 temperaments ==
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 === Complexity 20 ===
 * [[Frigg]] {{multival|rank=3| 20 10 22 -5 -7 2 25 7 -24 7 }}
+== Rank-4 temperaments ==
+=== Complexity 0 ===
+* [[Akua]] {{multival|rank=4| 0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5  0 }}
+=== Complexity 1 ===
+* [[Gentle]] {{multival|rank=4| 1 1 1 0 0 0 -4 -7 -3 0 -7 -12 -5 0 -1 }}
+* [[Valinorsmic]] {{multival|rank=4| 1 1 1 -2 -2 0 0 -3 -3 6 4 -1 -5 10 12 }}
+* [[Symbiotic]] {{multival|rank=4| 1 -1 0 0 1 -1 9 12 -12 -9 8 13 -13 -8 21 }}
+* [[Martwin]] {{multival|rank=4| 1 -1  0 1 2 -2 1 4 -4 2 -7 -2 2 12 26 }}
+* [[Ancient]] {{multival|rank=4| 1 -1  0 1 -4 4 1 -1 1 3 -7 4 -4 -24 -3 }}
+* [[Zaxa]] {{multival|rank=4| 1 -1 -1 1 1 0 1 -2 3 -3 -7 -12 5 -5 -26 }}
+* [[Olympic]] {{multival|rank=4| 1 -2 -1 0 1 -2 -5 -2 -1 5 -17 -12 7 17 26 }}
+=== Complexity 2 ===
+* [[Semiporwellismic]] {{multival|rank=4| 2 0 2 1 3 -1 -3 3 3 6 -14 -4 14 19 27 }}
+* [[Briggs]] {{multival|rank=4| 2 2 4 -2 0 4 -4 2 10 -2 -3 7 13 -7 -11 }}
+* [[Tannic]] {{multival|rank=4| 2 -2 1 -2 -2 2 -4 -4 0 3 -11 -16 -5 -10 }}
+=== Complexity 4 ===
+* [[Topsy]] {{multival|rank=4| 4 -3 -1 -7 -5 2 0 0 0 0 -6 -6 3 3 0 }}
+* [[Kalimera]] {{multival|rank=4| 4 4 4 -4 -6 -2 -8 -16 -8 4 -6 -15 -9 6 6 }}
+=== Complexity 5 ===
+* [[Quartismic]] {{multival|rank=4| 5 1 3 0 -5 -1 -6 -18 0 -6 -24 -27 9 -24 -54 }}
 [[Category:Lists of temperaments]]
 [[Category:Exterior algebra]]