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 ==
== Rank-2 temperaments ==
Line 710: Line 710:
=== Complexity 20 ===
=== Complexity 20 ===
* [[Frigg]] {{multival|rank=3| 20 10 22 -5 -7 2 25 7 -24 7 }}
* [[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:Lists of temperaments]]
[[Category:Exterior algebra]]
[[Category:Exterior algebra]]

Latest revision as of 13:25, 30 September 2026

Below are listed wedgies for 7-limit rank-2, 11-limit rank-3, and 13-limit rank-4 temperaments in the order of increasing complexities of the 2.3, 2.3.5, and 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

Complexity 0

Complexity 1

Complexity 2

Complexity 3

Complexity 4

Complexity 5

Complexity 6

Complexity 7

Complexity 8

Complexity 9

Complexity 10

Complexity 11

Complexity 12

Complexity 13

Complexity 14

Complexity 15

Complexity 16

Complexity 17

  • Semisept ⟨⟨17 6 15 -30 -24 18]]
  • Maquiloid ⟨⟨17 -6 13 -49 -27 47]]
  • Maquila ⟨⟨17 -6 22 -49 -13 68]]
  • Hyperkleismic ⟨⟨17 16 3 -14 -43 -38]]
  • Oolong ⟨⟨17 18 20 -11 -16 -4]]
  • Majo ⟨⟨17 23 -26 -3 -89 -125]]
  • Maja ⟨⟨17 23 27 -3 -5 -2]]
  • Slendi ⟨⟨17 28 8 5 -35 -60]]
  • Mitonic ⟨⟨17 35 -21 16 -81 -147]]

Complexity 18

Complexity 19

Complexity 20

Complexity 21

Complexity 22

Complexity 23

Complexity 24

Higher complexity

Rank-3 temperaments

Complexity 0

  • Rabic ⟨⟨⟨0 0 0 24 0 0 38 0 0 83]]]
  • Erato ⟨⟨⟨0 0 1 0 4 10 0 4 13 12]]]
  • Negric ⟨⟨⟨0 0 4 0 -3 2 0 -14 -8 13]]]
  • Supernatural ⟨⟨⟨0 0 5 0 1 12 0 -10 5 25]]]
  • Catakleismoid ⟨⟨⟨0 0 6 0 5 22 0 -6 18 37]]]
  • Sensigh ⟨⟨⟨0 0 7 0 9 13 0 -2 1 5]]]
  • Ennealimmic ⟨⟨⟨0 0 18 0 27 18 0 1 -22 -34]]]
  • Thalia ⟨⟨⟨0 1 0 4 0 1 4 0 5 16]]]
  • Calliope ⟨⟨⟨0 1 0 4 0 -6 4 0 -6 0]]]
  • Melpomene ⟨⟨⟨0 1 1 4 4 4 4 4 7 12]]]
  • Clio ⟨⟨⟨0 1 1 4 4 -8 4 4 -12 -16]]]
  • Polyhymnia ⟨⟨⟨0 1 -1 4 -4 3 4 -4 11 32]]]
  • Euterpe ⟨⟨⟨0 1 2 4 8 2 4 8 1 -4]]]
  • Terpsichore ⟨⟨⟨0 1 -2 4 -8 -7 4 -8 -2 20]]]
  • Orthoschismic ⟨⟨⟨0 1 -2 -8 16 5 -15 30 17 -61]]]
  • Urania ⟨⟨⟨0 2 0 8 0 -5 8 0 -1 16]]]
  • Varda ⟨⟨⟨0 2 2 -4 -4 8 -11 -11 14 16]]]
  • Augustus ⟨⟨⟨0 2 -2 -4 4 -6 -11 11 3 -39]]]
  • Tiberius ⟨⟨⟨0 2 4 -4 -8 -8 -11 -22 -17 -10]]]
  • Claudius ⟨⟨⟨0 2 -4 -4 8 -2 -11 22 15 -41]]]
  • Sonic ⟨⟨⟨0 3 0 5 0 -4 1 0 4 8]]]
  • Tikal ⟨⟨⟨0 3 3 5 5 5 1 1 10 15]]]
  • Altierran ⟨⟨⟨0 5 1 -40 -8 6 -75 -15 24 -102]]]
  • Schisnex ⟨⟨⟨0 6 0 -48 0 -3 -90 0 16 -173]]]
  • Isimud ⟨⟨⟨0 6 0 5 0 21 -6 0 54 66]]]
  • Enlil ⟨⟨⟨0 6 -6 5 -5 -1 -6 6 36 29]]]
  • Enki ⟨⟨⟨0 12 6 10 5 -8 -12 -6 12 2]]]

Complexity 1

  • Cassaschismic ⟨⟨⟨1 0 0 14 -23 0 25 -33 0 113]]]
  • Vulcan ⟨⟨⟨1 0 -1 2 2 2 6 9 6 6]]]
  • Ares ⟨⟨⟨1 0 2 2 2 -4 6 2 -12 -8]]]
  • Androschismic ⟨⟨⟨1 0 -2 14 34 28 25 62 50 18]]]
  • Pele ⟨⟨⟨1 1 1 6 10 4 10 17 7 2]]]
  • Laka ⟨⟨⟨1 1 -1 6 -15 -9 10 -18 -8 42]]]
  • Akea ⟨⟨⟨1 1 -2 6 -7 5 10 -3 17 52]]]
  • Lono ⟨⟨⟨1 1 3 6 6 -12 10 6 -24 -24]]]
  • Nickel ⟨⟨⟨1 -1 1 -2 -2 4 2 -2 0 8]]]
  • Potassium ⟨⟨⟨1 2 1 -2 -2 -2 -5 -2 1 -6]]]
  • Apollo ⟨⟨⟨1 2 2 -2 2 8 -5 2 14 6]]]
  • Malcolm ⟨⟨⟨1 2 -2 -2 -7 -18 -5 -3 -16 -29]]]
  • Prodigy ⟨⟨⟨1 2 3 -2 -6 -6 -5 -13 -11 -4]]]
  • Marvel ⟨⟨⟨1 2 -3 -2 1 -4 -5 12 9 -19]]]
  • Minerva ⟨⟨⟨1 2 4 -2 -2 4 -5 -9 2 8]]]
  • Thrasher ⟨⟨⟨1 3 2 2 2 2 -1 2 8 6]]]
  • Treecreeper ⟨⟨⟨1 3 -2 2 -7 -17 -1 -3 -11 -13]]]
  • Starnova ⟨⟨⟨1 3 -4 2 -3 -1 -1 8 20 13]]]
  • Thrush ⟨⟨⟨1 3 5 2 2 -4 -1 -5 -10 -8]]]
  • Aplonis ⟨⟨⟨1 3 -5 2 -7 -11 -1 4 7 1]]]
  • Keemic ⟨⟨⟨1 -3 2 -3 2 0 5 2 -16 -16]]]
  • Ulmo ⟨⟨⟨1 -4 -2 -7 -7 14 1 -3 14 28]]]
  • Beyla ⟨⟨⟨1 -4 3 -7 6 -3 1 6 -27 -48]]]
  • Manwe ⟨⟨⟨1 -6 -4 -3 -3 6 12 8 0 12]]]
  • Ganesha ⟨⟨⟨1 10 4 -1 -2 -16 -22 -9 -2 -35]]]

Complexity 2

  • Parahemif ⟨⟨⟨2 0 0 -13 -5 0 -15 -1 0 -31]]]
  • Selenium ⟨⟨⟨2 0 -2 -1 -1 -1 4 10 4 -3]]]
  • Sensamagic ⟨⟨⟨2 -1 -1 -5 3 -4 0 14 -7 -35]]]
  • Shrusus ⟨⟨⟨2 -1 3 -5 -5 10 0 -8 4 20]]]
  • Octarod ⟨⟨⟨2 -1 4 -5 4 8 0 4 -2 -10]]]
  • Sensawer ⟨⟨⟨2 -1 -4 -5 -14 -3 0 -6 3 15]]]
  • Fiesta ⟨⟨⟨2 2 0 0 0 0 1 7 7 0]]]
  • Kahoupokane ⟨⟨⟨2 2 1 12 -1 -7 20 3 -7 28]]]
  • Kapo ⟨⟨⟨2 2 -1 12 3 9 20 14 24 54]]]
  • Festival ⟨⟨⟨2 2 2 0 -4 -4 1 -4 -5 2]]]
  • Namaka ⟨⟨⟨2 2 2 12 -9 -21 20 -12 -32 18]]]
  • Jamboree ⟨⟨⟨2 2 -2 0 -6 -6 1 2 3 3]]]
  • Jubilismic ⟨⟨⟨2 2 4 0 4 4 1 4 2 -2]]]
  • Mirwomo ⟨⟨⟨2 -2 0 3 -5 5 15 -1 1 36]]]
  • Draco ⟨⟨⟨2 -2 2 -9 -9 18 -4 -12 16 36]]]
  • Albus ⟨⟨⟨2 -2 6 -9 12 15 -4 12 0 -30]]]
  • Snape ⟨⟨⟨2 -2 -6 -9 -22 -5 -4 -14 2 19]]]
  • Nakika ⟨⟨⟨2 3 4 4 4 -2 5 4 -4 -2]]]
  • Octosand ⟨⟨⟨2 3 -4 4 -14 -13 5 -6 1 23]]]
  • Zeus ⟨⟨⟨2 -3 1 -1 -1 2 11 3 -10 4]]]
  • Spectacle ⟨⟨⟨2 4 0 -4 -5 -10 -10 -1 -2 -23]]]
  • Hestia ⟨⟨⟨2 4 0 -4 7 14 -10 18 36 -1]]]
  • Artemis ⟨⟨⟨2 4 1 -4 -1 0 -10 3 11 -11]]]
  • Fantastic ⟨⟨⟨2 4 6 -4 0 12 -10 -7 16 14]]]
  • Varuna ⟨⟨⟨2 4 6 8 12 0 9 12 -3 -6]]]
  • Mandos ⟨⟨⟨2 -4 0 -5 -5 10 7 -1 2 20]]]
  • Baffin ⟨⟨⟨2 -4 8 7 -4 -20 26 -18 -68 -11]]]
  • Belobog ⟨⟨⟨2 5 8 0 -4 -10 -6 -18 -21 -12]]]
  • Siebog ⟨⟨⟨2 5 -8 0 -6 -15 -6 16 16 -18]]]
  • Cuckoo ⟨⟨⟨2 6 0 4 -5 -15 -2 -1 -3 -7]]]
  • Oxpecker ⟨⟨⟨2 6 1 4 -1 -5 -2 3 10 5]]]
  • Loki ⟨⟨⟨2 6 8 -8 -4 20 -21 -18 30 30]]]
  • Thor ⟨⟨⟨2 -8 -6 -14 -10 -2 2 5 -14 -25]]]
  • Heimdall ⟨⟨⟨2 -8 -24 -14 -37 -20 2 4 8 9]]]

Complexity 3

  • Gamel ⟨⟨⟨3 0 3 1 -11 -1 10 -14 -10 32]]]
  • Hypnos ⟨⟨⟨3 0 3 -11 13 11 -9 24 9 -49]]]
  • Portent ⟨⟨⟨3 0 -3 1 -4 1 10 11 10 17]]]
  • Uni ⟨⟨⟨3 1 1 -7 5 4 -5 16 7 -29]]]
  • Turan ⟨⟨⟨3 1 -1 -7 -20 -9 -5 -19 -8 11]]]
  • Orwellian ⟨⟨⟨3 -1 -2 -3 0 -2 6 15 -1 -15]]]
  • Guanyin ⟨⟨⟨3 -1 5 -3 -3 6 6 -6 -8 12]]]
  • Demeter ⟨⟨⟨3 2 1 -3 -12 -7 -1 -11 -7 7]]]
  • Krypton ⟨⟨⟨3 2 -1 -3 -3 -3 -1 8 5 -9]]]
  • Androboh ⟨⟨⟨3 5 6 2 6 6 0 6 10 4]]]
  • Gariboh ⟨⟨⟨3 5 -7 2 -13 -17 0 6 10 4]]]
  • Morfil ⟨⟨⟨3 6 4 -6 -7 -6 -15 -10 0 -15]]]
  • Landy ⟨⟨⟨3 6 9 6 6 -6 4 -1 -14 -10]]]
  • Bragi ⟨⟨⟨3 -12 2 -21 9 -22 3 20 -82 -149]]]
  • Hanuman ⟨⟨⟨3 12 3 11 1 -7 -2 5 22 19]]]

Complexity 4

  • Big brother ⟨⟨⟨4 1 2 -5 -2 2 1 6 1 -7]]]
  • Jove ⟨⟨⟨4 2 0 -1 -10 -5 5 -2 -1 13]]]
  • Freyr ⟨⟨⟨4 2 -2 -1 -35 -18 5 -37 -16 53]]]
  • Lif ⟨⟨⟨4 2 -4 -1 22 10 5 58 34 -42]]]
  • Agni ⟨⟨⟨4 2 -6 -1 -3 -3 5 23 19 -2]]]
  • Zisa ⟨⟨⟨4 2 16 -1 -8 0 5 -36 -38 19]]]
  • Bisector ⟨⟨⟨4 -2 2 -10 -2 6 0 6 -3 -15]]]
  • Aphrodite ⟨⟨⟨4 3 2 3 -2 -3 9 6 0 9]]]
  • Hagrid ⟨⟨⟨4 -4 0 -18 -10 10 -8 -2 2 -11]]]
  • Triglav ⟨⟨⟨4 10 1 0 -6 -15 -12 2 8 -18]]]
  • Semihemimean ⟨⟨⟨4 10 14 0 8 20 -12 -6 27 24]]]

Complexity 5

  • Lux ⟨⟨⟨5 2 -4 13 -1 10 30 25 34 71]]]
  • Sophia ⟨⟨⟨5 -3 6 0 25 -15 21 43 -51 -105]]]
  • Persephone ⟨⟨⟨5 -3 11 -12 9 21 2 6 -8 -18]]]
  • Indra ⟨⟨⟨5 4 -3 -3 -9 -9 0 10 8 -6]]]
  • Trimyna ⟨⟨⟨5 5 5 1 -8 -9 4 -7 -11 5]]]
  • Vidar ⟨⟨⟨5 -20 -4 -35 -1 -24 5 25 -96 -174]]]

Complexity 6

  • Nexiquart ⟨⟨⟨6 0 0 -51 -3 0 -64 16 0 -168]]]
  • Hades ⟨⟨⟨6 0 6 -10 2 10 1 10 -1 -17]]]
  • Pessoal ⟨⟨⟨6 -2 4 6 18 -10 31 40 -34 -53]]]
  • History ⟨⟨⟨6 6 6 7 2 -5 14 10 -4 7]]]
  • Trismegiboh ⟨⟨⟨6 10 -1 4 -7 -11 0 12 20 8]]]
  • Tyr ⟨⟨⟨6 12 0 12 -3 -6 8 16 32 36]]]
  • Odin ⟨⟨⟨6 12 18 12 24 12 8 17 10 2]]]
  • Skadi ⟨⟨⟨6 14 1 -4 -11 -25 -22 1 6 -41]]]

Complexity 8

  • Freya ⟨⟨⟨8 4 -6 -2 -13 -8 10 21 18 11]]]
  • Baldur ⟨⟨⟨8 4 12 -2 14 10 10 22 -4 -23]]]
  • Sif ⟨⟨⟨8 -10 -2 -8 8 -12 33 45 -48 -78]]]

Complexity 9

  • Galaxy ⟨⟨⟨9 -14 -16 -14 -20 5 34 35 6 21]]]

Complexity 10

  • Minos ⟨⟨⟨10 2 6 -11 -8 5 6 8 -2 -4]]]
  • Linus ⟨⟨⟨10 10 20 -10 10 30 -11 4 26 7]]]

Complexity 12

  • Vili ⟨⟨⟨12 6 28 -3 6 10 15 -14 -42 -4]]]
  • Lycoris ⟨⟨⟨12 -10 2 -46 -22 26 -16 2 1 -37]]]

Complexity 15

  • House ⟨⟨⟨15 30 6 30 24 36 20 76 144 120]]]

Complexity 18

  • Van gogh ⟨⟨⟨18 2 20 -34 2 38 -8 19 11 -35]]]

Complexity 20

  • Frigg ⟨⟨⟨20 10 22 -5 -7 2 25 7 -24 7]]]

Rank-4 temperaments

Complexity 0

  • Akua ⟨⟨⟨⟨0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0]]]]

Complexity 1

  • Gentle ⟨⟨⟨⟨1 1 1 0 0 0 -4 -7 -3 0 -7 -12 -5 0 -1]]]]
  • Valinorsmic ⟨⟨⟨⟨1 1 1 -2 -2 0 0 -3 -3 6 4 -1 -5 10 12]]]]
  • Symbiotic ⟨⟨⟨⟨1 -1 0 0 1 -1 9 12 -12 -9 8 13 -13 -8 21]]]]
  • Martwin ⟨⟨⟨⟨1 -1 0 1 2 -2 1 4 -4 2 -7 -2 2 12 26]]]]
  • Ancient ⟨⟨⟨⟨1 -1 0 1 -4 4 1 -1 1 3 -7 4 -4 -24 -3]]]]
  • Zaxa ⟨⟨⟨⟨1 -1 -1 1 1 0 1 -2 3 -3 -7 -12 5 -5 -26]]]]
  • Olympic ⟨⟨⟨⟨1 -2 -1 0 1 -2 -5 -2 -1 5 -17 -12 7 17 26]]]]

Complexity 2

  • Semiporwellismic ⟨⟨⟨⟨2 0 2 1 3 -1 -3 3 3 6 -14 -4 14 19 27]]]]
  • Briggs ⟨⟨⟨⟨2 2 4 -2 0 4 -4 2 10 -2 -3 7 13 -7 -11]]]]
  • Tannic ⟨⟨⟨⟨2 -2 1 -2 -2 2 -4 -4 0 3 -11 -16 -5 -10]]]]

Complexity 4

  • Topsy ⟨⟨⟨⟨4 -3 -1 -7 -5 2 0 0 0 0 -6 -6 3 3 0]]]]
  • Kalimera ⟨⟨⟨⟨4 4 4 -4 -6 -2 -8 -16 -8 4 -6 -15 -9 6 6]]]]

Complexity 5

  • Quartismic ⟨⟨⟨⟨5 1 3 0 -5 -1 -6 -18 0 -6 -24 -27 9 -24 -54]]]]