Biyatismic clan: Difference between revisions

Latest revision as of 17:36, 20 October 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The biyatismic clan of rank-3 temperaments tempers out the biyatisma, 121/120.

Temperaments discussed elsewhere are:

Sonic (+55/54 or 100/99) → Porcupine rank-3 family
Urania (+81/80) → Rastmic rank-3 clan
Bisector (+245/243) → Sensamagic family

Considered below are zeus, artemis, oxpecker, kahoupokane, big brother, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see Rank-4 temperament #Biyatismic (121/120).

Protomere

The head of this clan is protomere, named by Aura as part of a series of names ending in mere (Greek μέρος, "part") where a number of rastmas are equated with a syntonic comma; in this case, it is a single rastma, hence proto-.

The systematically derived name of the temperament from biyatisma would be biyatic.

Subgroup: 2.3.5.11

Comma list: 121/120

Subgroup-val mapping: [⟨1 0 1 2], ⟨0 1 1 1], ⟨0 0 -2 -1]]

mapping generators: ~2, ~3, ~11/10

Optimal tunings:

WE: ~2 = 1200.6628 ¢, ~3/2 = 701.8452 ¢, ~11/10 = 157.8337 ¢

error map: ⟨+0.663 +0.553 +1.190 -5.318]

CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9848 ¢, ~12/11 = 157.6099 ¢

error map: ⟨0.000 +0.030 +0.451 -6.943]

Optimal ET sequence: 7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee

Badness (Sintel): 0.245

Zeus

Main article: Zeus

See also: Porwell family § Zeus

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175

Mapping: [⟨1 0 1 4 2], ⟨0 1 1 -1 1], ⟨0 0 -2 3 1]]

Mapping to lattice: [⟨0 1 -1 2 0], ⟨0 1 1 -1 1]]

Lattice basis:

11/10, 11/8

Angle (11/10, 11/8) = 87.464 degrees

Optimal tunings:

WE: ~2 = 1200.1693 ¢, ~3/2 = 702.2521 ¢, ~12/11 = 157.1102 ¢

error map: ⟨+0.169 +0.466 +2.057 +0.761 -5.668]

CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.2478 ¢, ~12/11 = 157.1265 ¢

error map: ⟨0.000 +0.293 +1.681 +0.306 -6.197]

Minimax tuning:

11-odd-limit

[[1 0 0 0 0⟩, [11/9 10/9 -1/3 -2/9 0⟩, [22/9 2/9 1/3 -4/9 0⟩, [22/9 2/9 -2/3 5/9 0⟩, [10/3 2/3 0 -1/3 0⟩]

unchanged-interval (eigenmonzo) basis: 2.9/5.9/7

Optimal ET sequence: 15, 22, 31, 46, 53, 68, 77, 99, 130e

Badness (Sintel): 0.480

Projection pairs: 5 600/121 7 2662/375 11 120/11 to 2.3.11/5

Zeus11[22] hobbit transversal

33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3,

11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4,

11/6, 15/8, 64/33, 2

Zeus11[24] hobbit transversal

33/32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,

11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9,

11/6, 15/8, 64/33, 2

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 176/175, 351/350

Mapping: [⟨1 0 1 4 2 7], ⟨0 1 1 -1 1 -2], ⟨0 0 -2 3 -1 -1]]

Mapping to lattice: [⟨0 1 -1 2 0 -3], ⟨0 1 1 -1 1 -2]]

Lattice basis:

11/10 length = 0.7898, 11/8 length = 1.002

Angle (11/10, 11/8) = 106.7439 degrees

Optimal tunings:

WE: ~2 = 1200.2411 ¢, ~3/2 = 702.0090 ¢, ~12/11 = 156.9897 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.8818 ¢, ~12/11 = 156.9568 ¢

Minimax tuning:

13-odd-limit

[[1 0 0 0 0 0⟩, [11/9 10/9 -1/3 -2/9 0 0⟩, [22/9 2/9 1/3 -4/9 0 0⟩, [22/9 2/9 -2/3 5/9 0 0⟩, [10/3 2/3 0 -1/3 0 0⟩, [14/3 -8/3 1 1/3 0 0⟩]

unchanged-interval (eigenmonzo) basis: 2.9/5.9/7

15-odd-limit

[[1 0 0 0 0 0⟩, [0 1 0 0 0 0⟩, [11/5 1/5 2/5 -2/5 0 0⟩, [11/5 1/5 -3/5 3/5 0 0⟩, [13/5 3/5 1/5 -1/5 0 0⟩, [38/5 -12/5 1/5 -1/5 0 0⟩]

unchanged-interval (eigenmonzo) basis: 2.3.7/5

Optimal ET sequence: 15f, 22, 31, 46, 53, 77, 99, 130e

Badness (Sintel): 0.873

Projection pairs: 5 600/121 7 2662/375 11 120/11 13 1280/99 to 2.3.11/5

Zeus13[22] hobbit transversal

260/243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2

Tinia

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 121/120, 176/175

Mapping: [⟨1 0 1 4 2 2], ⟨0 1 1 -1 1 1], ⟨0 0 -2 3 -1 -1]]

Optimal tunings:

WE: ~2 = 1199.9251 ¢, ~3/2 = 699.2984 ¢, ~12/11 = 155.3569 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 699.2982 ¢, ~12/11 = 155.3484 ¢

Optimal ET sequence: 7, 9, 15, 22f, 24, 31

Badness (Sintel): 0.756

Artemis

Named by Graham Breed in 2011, artemis was found to be locally efficient in the higher limits among rank-3 extensions of marvel^[1], although it is a weak extension. However, the alternative 13-limit extension called diana is more accurate.

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224

Mapping: [⟨1 0 1 -3 2], ⟨0 1 1 4 1], ⟨0 0 -2 -4 -1]]

Optimal tunings:

WE: ~2 = 1201.2783 ¢, ~3/2 = 700.6174 ¢, ~11/10 = 158.4919 ¢

error map: ⟨+1.278 -0.059 -0.123 +0.955 -5.357]

CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.2777 ¢, ~11/10 = 158.3100 ¢

error map: ⟨0.000 -1.677 -2.656 -0.955 -9.350]

Optimal ET sequence: 9, 15d, 16d, 20, 22, 31, 53, 60e, 84e, 91e, 113e, 144ee

Badness (Sintel): 0.713

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 121/120, 196/195

Mapping: [⟨1 0 1 -3 2 -5], ⟨0 1 1 4 1 6], ⟨0 0 -2 -4 -1 -6]]

Optimal tunings:

WE: ~2 = 1201.7896 ¢, ~3/2 = 699.7509 ¢, ~11/10 = 158.9484 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 699.1687 ¢, ~11/10 = 158.7345 ¢

Optimal ET sequence: 9, 20, 22f, 29, 31, 60e, 129cddee

Badness (Sintel): 1.04

Diana

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 225/224, 275/273

Mapping: [⟨1 0 1 -3 2 7], ⟨0 1 1 4 1 -2], ⟨0 0 -2 -4 -1 -1]]

Optimal tunings:

WE: ~2 = 1200.9110 ¢, ~3/2 = 701.5110 ¢, ~11/10 = 159.1256 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.9717 ¢, ~11/10 = 158.7903 ¢

Optimal ET sequence: 22, 29, 31, 53, 82e, 84e, 113e

Badness (Sintel): 1.07

Oxpecker

Subgroup: 2.3.5.7.11

Comma list: 121/120, 126/125

Mapping: [⟨1 0 1 2 2], ⟨0 1 1 1 1], ⟨0 0 -2 -6 -1]]

Optimal tunings:

WE: ~2 = 1200.4124 ¢, ~3/2 = 701.1291 ¢, ~12/11 = 155.8292 ¢

error map: ⟨+0.412 -0.414 +3.982 -1.435 -4.781]

CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.2359 ¢, ~12/11 = 155.7399 ¢

error map: ⟨0.000 -0.719 +3.442 -2.029 -5.822]

Optimal ET sequence: 7d, 8d, 15, 23de, 24d, 31, 46, 77

Badness (Sintel): 0.840

Woodpecker

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 121/120, 126/125

Mapping: [⟨1 0 1 2 2 2], ⟨0 1 1 1 1 1], ⟨0 0 -2 -6 -1 1]]

Optimal tunings:

WE: ~2 = 1198.9113 ¢, ~3/2 = 700.9581 ¢, ~12/11 = 154.7247 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.6409 ¢, ~12/11 = 154.9115 ¢

Optimal ET sequence: 7d, 8d, 15, 23de, 24d, 31

Badness (Sintel): 1.02

Kahoupokane

Named by Tristan Bay in 2025, Kahoupokane tempers out 5120/5103 and may be described as the 29 & 46 & 53 temperament.

Subgroup: 2.3.5.7.11

Comma list: 121/120, 5120/5103

Mapping: [⟨1 0 1 11 2], ⟨0 1 1 -5 1], ⟨0 0 -2 -2 -1]]

Optimal tunings:

WE: ~2 = 1200.1911 ¢, ~3/2 = 703.1412 ¢, ~11/10 = 158.1068 ¢

error map: ⟨+0.191 +1.377 +0.996 +0.401 -5.710]

CWE: ~2 = 1200.000 ¢, ~3/2 = 703.0417 ¢, ~11/10 = 157.9917 ¢

error map: ⟨0.000 +1.087 +0.744 -0.018 -6.268]

Optimal ET sequence: 7, 17c, 24d, 29, 46, 53, 82e, 99

Badness (Sintel): 2.73

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 169/168, 352/351

Mapping: [⟨1 0 1 11 2 7], ⟨0 1 1 -5 1 -2], ⟨0 0 -2 -2 -1 -1]]

Optimal tunings:

WE: ~2 = 1200.4435 ¢, ~3/2 = 703.1443 ¢, ~11/10 = 158.4176 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.9013 ¢, ~11/10 = 158.1657 ¢

Optimal ET sequence: 7, 17c, 24d, 29, 46, 53, 82e, 99, 181eef

Badness (Sintel): 1.27

Big brother

For the 7-limit version, see Miscellaneous 7-limit temperaments #Nuwell.

Subgroup: 2.3.5.7.11

Comma list: 99/98, 121/120

Mapping: [⟨1 0 -5 -1 -1], ⟨0 1 3 2 2], ⟨0 0 4 1 2]]

mapping generators: ~2, ~3, ~11/7

Optimal tunings:

WE: ~2 = 1200.6559 ¢, ~3/2 = 700.2627 ¢, ~11/7 = 771.8821 ¢

error map: ⟨+0.656 -1.036 +0.691 +4.237 -6.372]

CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.4019 ¢, ~11/7 = 771.2671 ¢

error map: ⟨0.000 -1.553 -0.039 +3.245 -7.980]

Optimal ET sequence: 8d, 9, 14c, 17c, 22, 31, 53, 84e

Badness (Sintel): 0.609

Projection pairs: 5 2401/486, 11 98/9 to 2.3.7

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 99/98, 121/120

Mapping: [⟨1 0 3 1 3 1], ⟨0 1 3 2 2 0], ⟨0 0 -4 -1 -2 2]]

Optimal tunings:

WE: ~2 = 1199.0121 ¢, ~3/2 = 699.9867 ¢, ~11/7 = 771.9817 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 699.7360 ¢, ~11/7 = 773.0154 ¢

Optimal ET sequence: 8d, 9, 14c, 17c, 22f, 31, 79cf

Badness (Sintel): 0.889

Aphrodite

For the 7-limit version, see Miscellaneous 7-limit temperaments #Squalentine.

Subgroup: 2.3.5.7.11

Comma list: 121/120, 441/440

Mapping: [⟨1 0 1 3 2], ⟨0 1 1 0 1], ⟨0 0 -4 -3 -2]]

mapping generators: ~2, ~3, ~22/21

Optimal tunings:

WE: ~2 = 1201.0691 ¢, ~3/2 = 700.9439 ¢, ~22/21 = 78.7122 ¢

error map: ⟨+1.069 +0.058 +1.920 -1.755 -4.591]

CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.8990 ¢, ~22/21 = 78.4412 ¢

error map: ⟨0.000 -1.056 +0.820 -4.150 -7.301]

Optimal ET sequence: 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee

Badness (Sintel): 0.701

Eros

Eros fairs impressively into the 23-limit as a rank-3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but has the pleasing property that all the harmonics are on the negative side of the last generator. Specifically, -3 to 2 fifths and -5 to 0 ~23/22's will provide odd harmonics 1–23 up to octave equivalence; you can think of this as a 6×6 grid, which is a recommendable place to start looking at its structure.

Tempering out the less accurate comma 121/120 can be seen as an implication of tempering out 441/440 (S21), 484/483 (S22), and 529/528 (S23). Therefore, characteristic of any good tuning is the prime 11 being the flattest prime, with other primes having strictly less than 5 ¢ of error.

This temperament was discovered by Scott Dakota. Note that the 17-limit extension requires the 29g val for 29edo, which has the sizes of 17/16 and 18/17 swapped.

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 196/195, 352/351

Mapping: [⟨1 0 1 3 2 7], ⟨0 1 1 0 1 -2], ⟨0 0 -4 -3 -2 -2]]

Optimal tunings:

WE: ~2 = 1200.6419 ¢, ~3/2 = 701.8766 ¢, ~22/21 = 78.6564 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.5612 ¢, ~22/21 = 78.4778 ¢

Optimal ET sequence: 17c, 29, 31, 46, 60e, 77, 106de, 183dee

Badness (Sintel): 1.08

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 121/120, 154/153, 196/195, 352/351

Mapping: [⟨1 0 1 3 2 7 6], ⟨0 1 1 0 1 -2 -1], ⟨0 0 -4 -3 -2 -2 -5]]

Optimal tunings:

WE: ~2 = 1200.6172 ¢, ~3/2 = 702.1026 ¢, ~22/21 = 78.7963 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7925 ¢, ~22/21 = 78.6203 ¢

Optimal ET sequence: 17cg, 29g, 31, 46, 60e, 77, 106de

Badness (Sintel): 0.931

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 121/120, 154/153, 196/195, 286/285, 352/351

Mapping: [⟨1 0 1 3 2 7 6 9], ⟨0 1 1 0 1 -2 -1 -3], ⟨0 0 -4 -3 -2 -2 -5 0]]

Optimal tunings:

WE: ~2 = 1200.6224 ¢, ~3/2 = 702.0959 ¢, ~22/21 = 78.8004 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.6963 ¢, ~22/21 = 78.6479 ¢

Optimal ET sequence: 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de

Badness (Sintel): 1.16

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 121/120, 154/153, 161/160, 196/195, 286/285, 352/351

Mapping: [⟨1 0 1 3 2 7 6 9 3], ⟨0 1 1 0 1 -2 -1 -3 1], ⟨0 0 -4 -3 -2 -2 -5 0 -1]]

Optimal tunings:

WE: ~2 = 1200.7268 ¢, ~3/2 = 702.2463 ¢, ~22/21 = 78.8824 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.8010 ¢, ~23/22 = 78.7188 ¢

Optimal ET sequence: 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de

Badness (Sintel): 1.08

Astarte

This extension is catalogued as tridecimal aphrodite in Graham Breed's temperament finder.

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 351/350, 441/440

Mapping: [⟨1 0 1 3 2 6], ⟨0 1 1 0 1 -1], ⟨0 0 -4 -3 -2 -11]]

Optimal tunings:

WE: ~2 = 1201.0656 ¢, ~3/2 = 700.7374 ¢, ~22/21 = 78.5908 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.7005 ¢, ~22/21 = 78.3253 ¢

Optimal ET sequence: 14cf, 29ff, 31, 45ef, 46, 77, 122ee, 137def, 168deef

Badness (Sintel): 1.36

Inanna

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 121/120, 275/273

Mapping: [⟨1 0 1 3 2 1], ⟨0 1 1 0 1 2], ⟨0 0 -4 -3 -2 -7]]

Optimal tunings:

WE: ~2 = 1201.7881 ¢, ~3/2 = 699.8166 ¢, ~22/21 = 79.7282 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 699.5926 ¢, ~22/21 = 79.3822 ¢

Optimal ET sequence: 14cf, 15, 29, 31, 45ef, 60e

Badness (Sintel): 1.01

Ishtar

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 121/120, 441/440

Mapping: [⟨1 0 1 3 2 -1], ⟨0 1 1 0 1 3], ⟨0 0 -4 -3 -2 -1]]

Optimal tunings:

WE: ~2 = 1200.7875 ¢, ~3/2 = 703.8568 ¢, ~22/21 = 79.0096 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 703.7640 ¢, ~22/21 = 78.8025 ¢

Optimal ET sequence: 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def

Badness (Sintel): 1.08

References

↑ Yahoo! Tuning Group | Artemis and friends

[1] Yahoo! Tuning Group | Artemis and friends

[1]

Biyatismic clan: Difference between revisions

FloraC (talk | contribs)

Latest revision as of 17:36, 20 October 2026

Contents

Protomere

Zeus

13-limit

Tinia

Artemis

13-limit

Diana

Oxpecker

Woodpecker

Kahoupokane

13-limit

Big brother

13-limit

Aphrodite

Eros

17-limit

19-limit

23-limit

Astarte

Inanna

Ishtar

References

Navigation menu

@@ Line 1: / Line 1: @@
-The '''biyatismic clan''' of [[Rank-3 temperament|rank-3]] [[Temperament|temperaments]] [[Tempering out|tempers out]] the [[biyatisma]], 121/120 = {{monzo| -3 -1 -1 0 2 }}.
+{{Technical data page}}
+The '''biyatismic clan''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the biyatisma, [[121/120]].
 Temperaments discussed elsewhere are:
-* ''[[Sonic]]'' (+55/54 or 100/99) → [[Porcupine rank three family #Sonic|Porcupine rank-3 family]]
+* ''[[Sonic]]'' (+55/54 or 100/99) → [[Porcupine rank-3 family #Sonic|Porcupine rank-3 family]]
-* ''[[Urania]]'' (+81/80) → [[Didymus rank three family #Urania|Didymus rank-3 family]]
+* ''[[Urania]]'' (+81/80) → [[Rastmic rank-3 clan #Urania|Rastmic rank-3 clan]]
-* ''[[Big brother]]'' (+99/98) → [[Nuwell family #big Brother|Nuwell family]]
 * ''[[Bisector]]'' (+245/243) → [[Sensamagic family #Bisector|Sensamagic family]]
-Considered below are zeus, artemis, oxpecker, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].
+Considered below are zeus, artemis, oxpecker, kahoupokane, big brother, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].
 == Protomere ==
+The head of this clan is protomere, named by [[Aura]] as part of a series of names ending in ''mere'' (Greek [[wiktionary: %CE%BC%CE%AD%CF%81%CE%BF%CF%82 #Ancient Greek|μέρος]], "part") where a number of [[rastma]]s are equated with a [[syntonic comma]]; in this case, it is a single rastma, hence ''proto-''.
+The systematically derived name of the temperament from ''biyatisma'' would be ''biyatic''.
 [[Subgroup]]: 2.3.5.11
 [[Comma list]]: 121/120
-{{Mapping|legend=2| 1 0 1 2 | 0 1 1 1 | 0 0 -2 -1 }}
+{{Mapping|legend=3| 1 0 1 2 | 0 1 1 1 | 0 0 -2 -1 }}
+: mapping generators: ~2, ~3, ~11/10
-: Mapping generators: ~2, ~3, ~11/10
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.4578, ~11/10 = 157.7466
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.6628{{c}}, ~3/2 = 701.8452{{c}}, ~11/10 = 157.8337{{c}}
+: [[error map]]: {{val| +0.663 +0.553 +1.190 -5.318 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~12/11 = 157.6099{{c}}
+: error map: {{val| 0.000 +0.030 +0.451 -6.943 }}
 {{Optimal ET sequence|legend=1| 7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee }}
-[[Badness]]: 0.0297 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.245
 == Zeus ==
@@ Line 40: / Line 47: @@
 : Angle (11/10, 11/8) = 87.464 degrees
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.1530, ~11/10 = 157.0881
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1693{{c}}, ~3/2 = 702.2521{{c}}, ~12/11 = 157.1102{{c}}
+: [[error map]]: {{val| +0.169 +0.466 +2.057 +0.761 -5.668 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2478{{c}}, ~12/11 = 157.1265{{c}}
+: error map: {{val| 0.000 +0.293 +1.681 +0.306 -6.197 }}
 [[Minimax tuning]]:
 * [[11-odd-limit]]
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 10/9 -1/3 -2/9 0 }}, {{monzo| 22/9 2/9 1/3 -4/9 0 }}, {{monzo| 22/9 2/9 -2/3 5/9 0 }}, {{monzo| 10/3 2/3 0 -1/3 0 }}]
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.9/7
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7
 {{Optimal ET sequence|legend=1| 15, 22, 31, 46, 53, 68, 77, 99, 130e }}
-[[Badness]]: 0.400 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.480
 [[Projection pair]]s: 5 600/121 7 2662/375 11 120/11 to 2.3.11/5
@@ Line 68: / Line 79: @@
 Comma list: 121/120, 176/175, 351/350
-Mapping: {{mapping| 1 0 1 4 2 7 | 0 1 1 -1 1 -2 | 0 0 -2 3 -1 -1 }}
+{{Mapping|legend=0| 1 0 1 4 2 7 | 0 1 1 -1 1 -2 | 0 0 -2 3 -1 -1 }}
 Mapping to lattice: [{{val| 0 1 -1 2 0 -3 }}, {{val| 0 1 1 -1 1 -2 }}]
@@ Line 76: / Line 87: @@
 : Angle (11/10, 11/8) = 106.7439 degrees
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.8679, ~11/10 = 156.9582
+Optimal tunings:
+* WE: ~2 = 1200.2411{{c}}, ~3/2 = 702.0090{{c}}, ~12/11 = 156.9897{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8818{{c}}, ~12/11 = 156.9568{{c}}
 Minimax tuning:
 * 13-odd-limit
 : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 11/9 10/9 -1/3 -2/9 0 0 }}, {{monzo| 22/9 2/9 1/3 -4/9 0 0 }}, {{monzo| 22/9 2/9 -2/3 5/9 0 0 }}, {{monzo| 10/3 2/3 0 -1/3 0 0 }}, {{monzo| 14/3 -8/3 1 1/3 0 0 }}]
-: eigenmonzo (unchanged-interval) basis: 2.9/5.9/7
+: unchanged-interval (eigenmonzo) basis: 2.9/5.9/7
 * 15-odd-limit
 : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 11/5 1/5 2/5 -2/5 0 0 }}, {{monzo| 11/5 1/5 -3/5 3/5 0 0 }}, {{monzo| 13/5 3/5 1/5 -1/5 0 0 }}, {{monzo| 38/5 -12/5 1/5 -1/5 0 0 }}]
-: eigenmonzo (unchanged-interval) basis: 2.3.7/5
+: unchanged-interval (eigenmonzo) basis: 2.3.7/5
-{{Optimal ET sequence|legend=1| 15, 22, 31, 46, 53, 77, 99, 130e }}
+{{Optimal ET sequence|legend=0| 15f, 22, 31, 46, 53, 77, 99, 130e }}
-Badness: 0.934 × 10<sup>-3</sup>
+Badness (Sintel): 0.873
 Projection pairs: 5 600/121 7 2662/375 11 120/11 13 1280/99 to 2.3.11/5
@@ Line 100: / Line 113: @@
 Comma list: 66/65, 121/120, 176/175
-Mapping: {{mapping| 1 0 1 4 2 2 | 0 1 1 -1 1 1 | 0 0 -2 3 -1 -1 }}
+{{Mapping|legend=0| 1 0 1 4 2 2 | 0 1 1 -1 1 1 | 0 0 -2 3 -1 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.3420, ~11/10 = 155.3666
+Optimal tunings:
+* WE: ~2 = 1199.9251{{c}}, ~3/2 = 699.2984{{c}}, ~12/11 = 155.3569{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2982{{c}}, ~12/11 = 155.3484{{c}}
-{{Optimal ET sequence|legend=1| 7, 9, 15, 22f, 24, 31 }}
+{{Optimal ET sequence|legend=0| 7, 9, 15, 22f, 24, 31 }}
-Badness: 0.808 × 10<sup>-3</sup>
+Badness (Sintel): 0.756
 == Artemis ==
+Named by [[Graham Breed]] in 2011, artemis was found to be locally efficient in the higher limits among rank-3 extensions of [[marvel]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19673.html Yahoo! Tuning Group | ''Artemis and friends'']</ref>, although it is a [[weak extension]]. However, the alternative 13-limit extension called diana is more accurate.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 115: / Line 132: @@
 {{Mapping|legend=1| 1 0 1 -3 2 | 0 1 1 4 1 | 0 0 -2 -4 -1 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 699.8719, ~11/10 = 158.3232
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.2783{{c}}, ~3/2 = 700.6174{{c}}, ~11/10 = 158.4919{{c}}
+: [[error map]]: {{val| +1.278 -0.059 -0.123 +0.955 -5.357 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.2777{{c}}, ~11/10 = 158.3100{{c}}
+: error map: {{val| 0.000 -1.677 -2.656 -0.955 -9.350 }}
+{{Optimal ET sequence|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 60e, 84e, 91e, 113e, 144ee }}
-{{Optimal ET sequence|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}
+[[Badness]] (Sintel): 0.713
 === 13-limit ===
@@ Line 124: / Line 147: @@
 Comma list: 105/104, 121/120, 196/195
-Mapping: {{mapping| 1 0 1 -3 2 -5 | 0 1 1 4 1 6 | 0 0 -2 -4 -1 -6 }}
+{{Mapping|legend=0| 1 0 1 -3 2 -5 | 0 1 1 4 1 6 | 0 0 -2 -4 -1 -6 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.7090, ~11/10 = 158.7117
+Optimal tunings:
+* WE: ~2 = 1201.7896{{c}}, ~3/2 = 699.7509{{c}}, ~11/10 = 158.9484{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.1687{{c}}, ~11/10 = 158.7345{{c}}
-{{Optimal ET sequence|legend=1| 9, 20, 22f, 29, 31 }}
+{{Optimal ET sequence|legend=0| 9, 20, 22f, 29, 31, 60e, 129cddee }}
+Badness (Sintel): 1.04
 === Diana ===
@@ Line 135: / Line 162: @@
 Comma list: 121/120, 225/224, 275/273
-Mapping: {{mapping| 1 0 1 -3 2 7 | 0 1 1 4 1 -2 | 0 0 -2 -4 -1 -1 }}
+{{Mapping|legend=0| 1 0 1 -3 2 7 | 0 1 1 4 1 -2 | 0 0 -2 -4 -1 -1 }}
+Optimal tunings:
+* WE: ~2 = 1200.9110{{c}}, ~3/2 = 701.5110{{c}}, ~11/10 = 159.1256{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.9717{{c}}, ~11/10 = 158.7903{{c}}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.9789, ~11/10 = 159.0048
+{{Optimal ET sequence|legend=0| 22, 29, 31, 53, 82e, 84e, 113e }}
-{{Optimal ET sequence|legend=1| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}
+Badness (Sintel): 1.07
 == Oxpecker ==
@@ Line 148: / Line 179: @@
 {{Mapping|legend=1| 1 0 1 2 2 | 0 1 1 1 1 | 0 0 -2 -6 -1 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.8882, ~11/10 = 155.7756
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.4124{{c}}, ~3/2 = 701.1291{{c}}, ~12/11 = 155.8292{{c}}
+: [[error map]]: {{val| +0.412 -0.414 +3.982 -1.435 -4.781 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2359{{c}}, ~12/11 = 155.7399{{c}}
+: error map: {{val| 0.000 -0.719 +3.442 -2.029 -5.822 }}
 {{Optimal ET sequence|legend=1| 7d, 8d, 15, 23de, 24d, 31, 46, 77 }}
-[[Badness]]: 0.699 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.840
 === Woodpecker ===
@@ Line 159: / Line 194: @@
 Comma list: 66/65, 121/120, 126/125
-Mapping: {{mapping| 1 0 1 2 2 2 | 0 1 1 1 1 1 | 0 0 -2 -6 -1 1 }}
+{{Mapping|legend=0| 1 0 1 2 2 2 | 0 1 1 1 1 1 | 0 0 -2 -6 -1 1 }}
+Optimal tunings:
+* WE: ~2 = 1198.9113{{c}}, ~3/2 = 700.9581{{c}}, ~12/11 = 154.7247{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.6409{{c}}, ~12/11 = 154.9115{{c}}
+{{Optimal ET sequence|legend=0| 7d, 8d, 15, 23de, 24d, 31 }}
+Badness (Sintel): 1.02
+== Kahoupokane ==
+Named by [[Tristan Bay]] in 2025, Kahoupokane tempers out [[5120/5103]] and may be described as the {{nowrap| 29 & 46 & 53 }} temperament.
+[[Subgroup]]: 2.3.5.7.11
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.5946, ~11/10 = 154.8652
+[[Comma list]]: 121/120, 5120/5103
-{{Optimal ET sequence|legend=1| 7d, 8d, 15, 23de, 24d, 31 }}
+{{Mapping|legend=1| 1 0 1 11 2 | 0 1 1 -5 1 | 0 0 -2 -2 -1 }}
-Badness: 1.093 × 10<sup>-3</sup>
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1911{{c}}, ~3/2 = 703.1412{{c}}, ~11/10 = 158.1068{{c}}
+: [[error map]]: {{val| +0.191 +1.377 +0.996 +0.401 -5.710 }}
+* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.0417{{c}}, ~11/10 = 157.9917{{c}}
+: error map: {{val| 0.000 +1.087 +0.744 -0.018 -6.268 }}
-== Aphrodite ==
+{{Optimal ET sequence|legend=1| 7, 17c, 24d, 29, 46, 53, 82e, 99 }}
-Aphrodite tempers out the squalentine comma, 64827/64000, in the 7-limit. Its generators can be taken to be 2, 3, and 21/20, and it equates (21/20)<sup>3</sup> with 8/7.
-=== 7-limit (squalentine) ===
+[[Badness]] (Sintel): 2.73
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 64827/64000
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-{{Mapping|legend=1| 1 0 1 3 | 0 1 1 0 | 0 0 -4 -3 }}
+Comma list: 121/120, 169/168, 352/351
-: Mapping generators: ~2, ~3, ~21/20
+{{Mapping|legend=0| 1 0 1 11 2 7 | 0 1 1 -5 1 -2 | 0 0 -2 -2 -1 -1 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.2144, ~21/20 = 78.5694
+Optimal tunings:
+* WE: ~2 = 1200.4435{{c}}, ~3/2 = 703.1443{{c}}, ~11/10 = 158.4176{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9013{{c}}, ~11/10 = 158.1657{{c}}
-{{Optimal ET sequence|legend=1| 14c, 15, 29, 31, 46, 60, 77, 91, 122, 137d, 168d }}
+{{Optimal ET sequence|legend=0| 7, 17c, 24d, 29, 46, 53, 82e, 99, 181eef }}
-[[Badness]]: 0.943 × 10<sup>-3</sup>
+Badness (Sintel): 1.27
-[[Projection pair]]s: 5 320000/64827 7 64000/9261 to 2.3.7/5
+== Big brother ==
+: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Nuwell]].''
-=== 11-limit ===
 [[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 121/120, 441/440
+[[Comma list]]: 99/98, 121/120
-{{Mapping|legend=1| 1 0 1 3 2 | 0 1 1 0 1 | 0 0 -4 -3 -2 }}
+{{Mapping|legend=1| 1 0 -5 -1 -1 | 0 1 3 2 2 | 0 0 4 1 2 }}
+: mapping generators: ~2, ~3, ~11/7
-: Mapping generators: ~2, ~3, ~22/21
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.6559{{c}}, ~3/2 = 700.2627{{c}}, ~11/7 = 771.8821{{c}}
+: [[error map]]: {{val| +0.656 -1.036 +0.691 +4.237 -6.372 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.4019{{c}}, ~11/7 = 771.2671{{c}}
+: error map: {{val| 0.000 -1.553 -0.039 +3.245 -7.980 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.3200, ~21/20 = 78.6421
+{{Optimal ET sequence|legend=1| 8d, 9, 14c, 17c, 22, 31, 53, 84e }}
-{{Optimal ET sequence|legend=1| 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee }}
+[[Badness]] (Sintel): 0.609
-[[Badness]]: 0.583 × 10<sup>-3</sup>
+[[Projection pair]]s: <code>5 2401/486, 11 98/9</code> to 2.3.7
-==== 13-limit ====
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 121/120, 351/350, 441/440
+Comma list: 66/65, 99/98, 121/120
+{{Mapping|legend=0| 1 0 3 1 3 1 | 0 1 3 2 2 0 | 0 0 -4 -1 -2 2 }}
+Optimal tunings:
+* WE: ~2 = 1199.0121{{c}}, ~3/2 = 699.9867{{c}}, ~11/7 = 771.9817{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.7360{{c}}, ~11/7 = 773.0154{{c}}
+{{Optimal ET sequence|legend=0| 8d, 9, 14c, 17c, 22f, 31, 79cf }}
+Badness (Sintel): 0.889
+== Aphrodite ==
+: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Squalentine]].''
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 121/120, 441/440
+{{Mapping|legend=1| 1 0 1 3 2 | 0 1 1 0 1 | 0 0 -4 -3 -2 }}
+: mapping generators: ~2, ~3, ~22/21
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.0691{{c}}, ~3/2 = 700.9439{{c}}, ~22/21 = 78.7122{{c}}
+: [[error map]]: {{val| +1.069 +0.058 +1.920 -1.755 -4.591 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.8990{{c}}, ~22/21 = 78.4412{{c}}
+: error map: {{val| 0.000 -1.056 +0.820 -4.150 -7.301 }}
-Mapping: {{mapping| 1 0 1 3 2 6 | 0 1 1 0 1 -1 | 0 0 -4 -3 -2 -11 }}
+{{Optimal ET sequence|legend=1| 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.1158, ~21/20 = 78.5211
+[[Badness]] (Sintel): 0.701
-{{Optimal ET sequence|legend=1| 14cf, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}
+=== Eros ===
+Eros fairs impressively into the 23-limit as a rank-3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but has the pleasing property that all the harmonics are on the negative side of the last generator. Specifically, -3 to 2 fifths and -5 to 0 [[~]][[23/22]]'s will provide odd harmonics 1–23 up to octave equivalence; you can think of this as a 6×6 grid, which is a recommendable place to start looking at its structure.
-Badness: 1.456 × 10<sup>-3</sup>
+Tempering out the less accurate comma 121/120 can be seen as an implication of tempering out [[441/440]] ({{S|21}}), [[484/483]] ({{S|22}}), and [[529/528]] ({{S|23}}). Therefore, characteristic of any good tuning is the prime [[11/1|11]] being the flattest prime, with other primes having strictly less than 5{{cent}} of error.
-==== Eros ====
+This temperament was discovered by [[Scott Dakota]]. Note that the 17-limit extension requires the 29g val for 29edo, which has the sizes of 17/16 and 18/17 swapped.
-Eros fairs impressively into the 23-limit as a rank 3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but all the generators are positive (or only 1 into the negatives in the case of the fifth) meaning it's even simpler than it might appear and has the pleasing property of all harmonics and subharmonics being "on the same side"; specifically: -3 to 1 fifths ([[2L 3s]]) and -5 to 0 ~[[23/22]]'s will get you every prime, up to octave equivalence; you can think of this as a 5 by 6 grid if you like and is a recommendable place to start looking at its structure. Tempering the less accurate comma [[121/120|S11]] can be seen as a consequence of tempering {[[441/440|S21]], [[484/483|S22]], [[529/528|S23]]} so is very natural and given its properties certainly excusable. Therefore characteristic of any good tuning is the ~11 being the most flat prime, with other primes having strictly less than 5{{cent}} of error. This temperament was first logged on x31eq by [[Scott Dakota]].
 Subgroup: 2.3.5.7.11.13
@@ Line 222: / Line 306: @@
 Comma list: 121/120, 196/195, 352/351
-Mapping: {{mapping| 1 0 1 3 2 7 | 0 1 1 0 1 -2 | 0 0 -4 -3 -2 -2 }}
+{{Mapping|legend=0| 1 0 1 3 2 7 | 0 1 1 0 1 -2 | 0 0 -4 -3 -2 -2 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.5014, ~21/20 = 78.6143
+Optimal tunings:
+* WE: ~2 = 1200.6419{{c}}, ~3/2 = 701.8766{{c}}, ~22/21 = 78.6564{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5612{{c}}, ~22/21 = 78.4778{{c}}
-{{Optimal ET sequence|legend=1| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }}
+{{Optimal ET sequence|legend=0| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }}
-Badness: 1.150 × 10<sup>-3</sup>
+Badness (Sintel): 1.08
-===== 17-limit =====
-Note that this extension requires the 29g val for 29edo, which has the sizes of 17/16 and 18/17 swapped.
+==== 17-limit ====
 Subgroup: 2.3.5.7.11.13.17
 Comma list: 121/120, 154/153, 196/195, 352/351
-Mapping: {{mapping| 1 0 1 3 2 7 6 | 0 1 1 0 1 -2 -1 | 0 0 -4 -3 -2 -2 -5 }}
+{{Mapping|legend=0| 1 0 1 3 2 7 6 | 0 1 1 0 1 -2 -1 | 0 0 -4 -3 -2 -2 -5 }}
 Optimal tunings:
-* CTE: ~2 = 1\1, ~3/2 = 701.9299, ~22/21 = 78.2539
+* WE: ~2 = 1200.6172{{c}}, ~3/2 = 702.1026{{c}}, ~22/21 = 78.7963{{c}}
-* CWE: ~2 = 1\1, ~3/2 = 701.7925, ~22/21 = 78.6203
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7925{{c}}, ~22/21 = 78.6203{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 17cg, 29g, 31, 46, 60e, 77, 106de }}
+{{Optimal ET sequence|legend=0| 17cg, 29g, 31, 46, 60e, 77, 106de }}
-Badness:
+Badness (Sintel): 0.931
-* Smith: 0.979 × 10<sup>-3</sup>
-* Dirichlet: 0.931
-===== 19-limit =====
+==== 19-limit ====
 Subgroup: 2.3.5.7.11.13.17.19
 Comma list: 121/120, 154/153, 196/195, 286/285, 352/351
-Mapping: {{mapping| 1 0 1 3 2 7 6 9 | 0 1 1 0 1 -2 -1 -3 | 0 0 -4 -3 -2 -2 -5 0 }}
+{{Mapping|legend=0| 1 0 1 3 2 7 6 9 | 0 1 1 0 1 -2 -1 -3 | 0 0 -4 -3 -2 -2 -5 0 }}
 Optimal tunings:
-* CTE: ~2 = 1\1, ~3/2 = 701.5642, ~22/21 = 78.2353
+* WE: ~2 = 1200.6224{{c}}, ~3/2 = 702.0959{{c}}, ~22/21 = 78.8004{{c}}
-* CWE: ~2 = 1\1, ~3/2 = 701.6963, ~22/21 = 78.6479
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.6963{{c}}, ~22/21 = 78.6479{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}
+{{Optimal ET sequence|legend=0| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}
-Badness:
+Badness (Sintel): 1.16
-* Smith: 1.13 × 10<sup>-3</sup>
-* Dirichlet: 1.159
-===== 23-limit =====
+==== 23-limit ====
 Subgroup: 2.3.5.7.11.13.17.19.23
 Comma list: 121/120, 154/153, 161/160, 196/195, 286/285, 352/351
-Mapping: {{mapping| 1 0 1 3 2 7 6 9 3 | 0 1 1 0 1 -2 -1 -3 1 | 0 0 -4 -3 -2 -2 -5 0 -1 }}
+{{Mapping|legend=0| 1 0 1 3 2 7 6 9 3 | 0 1 1 0 1 -2 -1 -3 1 | 0 0 -4 -3 -2 -2 -5 0 -1 }}
 Optimal tunings:
-* CTE: ~2 = 1\1, ~3 = 1901.7115, ~23/22 = 78.2054
+* WE: ~2 = 1200.7268{{c}}, ~3/2 = 702.2463{{c}}, ~22/21 = 78.8824{{c}}
-* CWE: ~2 = 1\1, ~3 = 1901.8010, ~23/22 = 78.7188
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8010{{c}}, ~23/22 = 78.7188{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}
+{{Optimal ET sequence|legend=0| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}
-Badness:
+Badness (Sintel): 1.08
-* Smith: 0.939 × 10<sup>-3</sup>
-* Dirichlet: 1.084
+=== Astarte ===
+This extension is catalogued as tridecimal aphrodite in [[Graham Breed]]'s temperament finder.
-==== Inanna ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 121/120, 351/350, 441/440
+{{Mapping|legend=0| 1 0 1 3 2 6 | 0 1 1 0 1 -1 | 0 0 -4 -3 -2 -11 }}
+Optimal tunings:
+* WE: ~2 = 1201.0656{{c}}, ~3/2 = 700.7374{{c}}, ~22/21 = 78.5908{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.7005{{c}}, ~22/21 = 78.3253{{c}}
+{{Optimal ET sequence|legend=0| 14cf, 29ff, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}
+Badness (Sintel): 1.36
+=== Inanna ===
 Subgroup: 2.3.5.7.11.13
 Comma list: 105/104, 121/120, 275/273
-Mapping: {{mapping| 1 0 1 3 2 1 | 0 1 1 0 1 2 | 0 0 -4 -3 -2 -7 }}
+{{Mapping|legend=0| 1 0 1 3 2 1 | 0 1 1 0 1 2 | 0 0 -4 -3 -2 -7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.7754, ~21/20 = 79.6096
+Optimal tunings:
+* WE: ~2 = 1201.7881{{c}}, ~3/2 = 699.8166{{c}}, ~22/21 = 79.7282{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.5926{{c}}, ~22/21 = 79.3822{{c}}
-{{Optimal ET sequence|legend=1| 14cf, 15, 29, 31, 45ef, 60e }}
+{{Optimal ET sequence|legend=0| 14cf, 15, 29, 31, 45ef, 60e }}
-Badness: 1.077 × 10<sup>-3</sup>
+Badness (Sintel): 1.01
-==== Ishtar ====
+=== Ishtar ===
 Subgroup: 2.3.5.7.11.13
 Comma list: 91/90, 121/120, 441/440
-Mapping: {{mapping| 1 0 1 3 2 -1 | 0 1 1 0 1 3 | 0 0 -4 -3 -2 -1 }}
+{{Mapping|legend=0| 1 0 1 3 2 -1 | 0 1 1 0 1 3 | 0 0 -4 -3 -2 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.3952, ~21/20 = 78.9578
+Optimal tunings:
+* WE: ~2 = 1200.7875{{c}}, ~3/2 = 703.8568{{c}}, ~22/21 = 79.0096{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7640{{c}}, ~22/21 = 78.8025{{c}}
-{{Optimal ET sequence|legend=1| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }}
+{{Optimal ET sequence|legend=0| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }}
-Badness: 1.151 × 10<sup>-3</sup>
+Badness (Sintel): 1.08
+== References ==
-[[Category:Temperament clans]]
 [[Category:Biyatismic clan| ]] <!-- main article -->
 [[Category:Biyatismic| ]] <!-- key article -->
-[[Category:Rank 3]]
+[[Category:Temperament clans]]
+[[Category:Catalogs of rank-3 temperaments]]

Biyatismic clan: Difference between revisions

FloraC (talk | contribs)

Latest revision as of 17:36, 20 October 2026

Protomere

Zeus

13-limit

Tinia

Artemis

13-limit

Diana

Oxpecker

Woodpecker

Kahoupokane

13-limit

Big brother

13-limit

Aphrodite

Eros

17-limit

19-limit

23-limit

Astarte

Inanna

Ishtar

References

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