@@ Line 9: / Line 9: @@
 * [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]]
 * [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]]
-* ''[[Kwai]]'' (+16875/16807) → [[Mirkwai clan #Kwai|Mirkwai clan]]
 * [[Diaschismic]] (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
 * [[Hemififths]] (+2401/2400) → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]]
 * [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan|Gamelismic clan]]
 * ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot|Alphatricot family]]
-* ''[[Monkey]]'' (+875/864) → [[Tetracot family #Monkey|Tetracot family]]
+* [[Misty]] (+3136/3125) → [[Misty family #Misty|Misty family]]
+* [[Monkey]] (+875/864) → [[Tetracot family #Monkey|Tetracot family]]
 * [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard|Buzzardsmic clan]]
-* [[Misty]] (+3136/3125) → [[Misty family #Misty|Misty family]]
-* ''[[Supers]]'' (+118098/117649) → [[Stearnsmic clan #Supers|Stearnsmic clan]]
 * ''[[Undim]]'' (+390625/388962) → [[Undim family #Septimal undim|Undim family]]
 * ''[[Quinticosiennic]]'' (+395136/390625) → [[Quintaleap family #Quinticosiennic|Quintaleap family]]
@@ Line 23: / Line 21: @@
 * [[Amity]] (+4375/4374) → [[Amity family #Septimal amity|Amity family]]
 * ''[[Countercata]]'' (+15625/15552) → [[Kleismic family #Countercata|Kleismic family]]
+* ''[[Abergravity]]'' (+177147/175000) → [[Gravity family #Abergravity|Gravity family]]
+* ''[[Supers]]'' (+118098/117649) → [[Stearnsmic clan #Supers|Stearnsmic clan]]
 * ''[[Warrior]]'' (+78732/78125) → [[Sensipent family #Warrior|Sensipent family]]
 * ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter|Escapade family]]
-Considered below are septiquarter, ketchup, undecental, leapday, mystery, hemidromeda, countriton, artoneutral, quanic and jorgensen, in the order of increasing [[TE logflat badness]].
+Considered below are septiquarter, kwai, ketchup, undecental, leapday, mystery, hemidromeda, countriton, artoneutral, quanic and jorgensen, in the order of increasing [[TE logflat badness]].
 == Septiquarter ==
@@ Line 77: / Line 77: @@
 Badness (Sintel): 1.44
+== Kwai ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Kwai]].''
+Named by [[Gene Ward Smith]] in 2004 for its "bridgeability"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10766.html Yahoo! Tuning Group | ''Kwai'']</ref>, kwai is generated by a [[3/2|perfect fifth]], and can be described as {{nowrap| 41 & 70 }}.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 5120/5103, 16875/16807
+{{Mapping|legend=1| 1 0 -50 -40 | 0 1 33 27 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.7337{{c}}, ~3/2 = 702.4600{{c}}
+: [[error map]]: {{val| -0.266 +0.239 -0.607 +1.055 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.6085{{c}}
+: error map: {{val| 0.000 +0.653 -0.234 +1.603 }}
+{{Optimal ET sequence|legend=1| 41, 111, 152, 345, 497d }}
+[[Badness]] (Sintel): 1.38
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 1375/1372, 5120/5103
+Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }}
+Optimal tunings:
+* WE: ~2 = 1199.6672{{c}}, ~3/2 = 702.4282{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6189{{c}}
+{{Optimal ET sequence|legend=0| 41, 111, 152, 497de, 649dde }}
+Badness (Sintel): 0.867
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 352/351, 540/539, 729/728, 1375/1372
+Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}
+Optimal tunings:
+* WE: ~2 = 1199.4772{{c}}, ~3/2 = 702.3379{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6409{{c}}
+{{Optimal ET sequence|legend=0| 41, 111, 152f, 415dff }}
+Badness (Sintel): 1.01
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 256/255, 352/351, 540/539, 715/714, 1089/1088
+Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}
+Optimal tunings:
+* WE: ~2 = 1199.3537{{c}}, ~3/2 = 702.2850{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6589{{c}}
+{{Optimal ET sequence|legend=0| 41, 70, 111, 152fg, 263dfg }}
+Badness (Sintel): 1.12
+===== 19-limit =====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845
+Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}
+Optimal tunings:
+* WE: ~2 = 1199.3401{{c}}, ~3/2 = 702.2705{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6548{{c}}
+{{Optimal ET sequence|legend=0| 41, 70h, 111, 152fg, 263dfgh }}
+Badness (Sintel): 1.03
+==== Hemikwai ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 540/539, 676/675, 1375/1372, 5120/5103
+Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}
+: mapping generators: ~2, ~26/15
+Optimal tunings:
+* WE: ~2 = 1199.6968{{c}}, ~26/15 = 951.0740{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3123{{c}}
+{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}
+Badness (Sintel): 1.82
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103
+Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}
+Optimal tunings:
+* WE: ~2 = 1199.6861{{c}}, ~26/15 = 951.0654{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3120{{c}}
+{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}
+Badness (Sintel): 1.31
+===== 19-limit =====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444
+Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}
+Optimal tunings:
+* WE: ~2 = 1199.6718{{c}}, ~26/15 = 951.0526{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3103{{c}}
+{{Optimal ET sequence|legend=0| 82, 111, 193, 304dh }}
+Badness (Sintel): 1.16
 == Ketchup ==
-Ketchup may be described as the {{nowrap| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its ploidacot is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament.
+Ketchup may be described as the {{nowrap| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its [[ploidacot]] is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 131: / Line 259: @@
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 289/288, 325/324, 352/351, 385/384, 561/560
+Comma list: 289/288, 325/324, 352/351, 385/384, 442/441
 Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}
@@ Line 143: / Line 271: @@
 Badness (Sintel): 0.845
-=== 19-limit ===
+=== 2.3.5.7.11.13.17.23 subgroup ===
-Subgroup: 2.3.5.7.11.13.17.19
+Subgroup: 2.3.5.7.11.13.17.23
-Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560
+Comma list: 253/252, 289/288, 325/324, 352/351, 385/384, 391/390
-Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 -12 }}
+Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 1 }}
 Optimal tunings:
-* WE: ~17/12 = 600.1639{{c}}, ~66/65 = 25.6669{{c}}
+* WE: ~17/12 = 600.1139{{c}}, ~66/65 = 25.7053{{c}}
-* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.6597{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7013{{c}}
-{{Optimal ET sequence|legend=0| 46, 94, 140h }}
+{{Optimal ET sequence|legend=0| 46, 94, 140 }}
-Badness (Sintel): 1.11
-=== 23-limit ===
+Badness (Sintel): 0.772
-Subgroup: 2.3.5.7.11.13.17.19.23
-Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384
-Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}
-Optimal tunings:
-* WE: ~17/12 = 600.1777{{c}}, ~66/65 = 25.6682{{c}}
-* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.6605{{c}}
-{{Optimal ET sequence|legend=0| 46, 94, 140h }}
-Badness (Sintel): 1.00
 == Undecental ==
@@ Line 265: / Line 378: @@
 Badness (Sintel): 0.910
-==== 19-limit ====
+=== 2.3.5.7.11.13.17.23 subgroup ===
-Subgroup: 2.3.5.7.11.13.17.19
+Subgroup: 2.3.5.7.11.13.17.23
-Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168
+Comma list: 91/90, 121/120, 136/135, 154/153, 161/160, 169/168
-Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 | 0 1 21 15 11 8 24 -3 }}
+Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -5 | 0 1 21 15 11 8 24 6 }}
 Optimal tunings:
-* WE: ~2 = 1201.0192{{c}}, ~3/2 = 704.7333{{c}}
+* WE: ~2 = 1200.5169{{c}}, ~3/2 = 704.5279{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1680{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2450{{c}}
-{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}
+{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }}
-Badness (Sintel): 1.06
-===== 23-limit =====
-Subgroup: 2.3.5.7.11.13.17.19.23
-Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 161/160, 169/168
-Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 -5 | 0 1 21 15 11 8 24 -3 6 }}
-Optimal tunings:
-* WE: ~2 = 1200.9738{{c}}, ~3/2 = 704.7120{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1695{{c}}
-{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}
+Badness (Sintel): 0.872
-Badness (Sintel): 1.01
-==== Leapling ====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168
-Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 | 0 1 21 15 11 8 24 26 }}
-Optimal tunings:
-* WE: ~2 = 1200.4745{{c}}, ~3/2 = 704.4016{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1442{{c}}
-{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}
-Badness (Sintel): 1.16
-===== 23-limit =====
-Subgroup: 2.3.5.7.11.13.17.19.23
-Comma list: 77/76, 91/90, 115/114, 121/120, 136/135, 153/152, 161/160
-Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 -5 | 0 1 21 15 11 8 24 26 6 }}
-Optimal tunings:
-* WE: ~2 = 1200.5425{{c}}, ~3/2 = 704.4319{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1349{{c}}
-{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}
-Badness (Sintel): 1.15
 == Mystery ==
@@ Line 379: / Line 447: @@
 == Hemidromeda ==
-Hemidromeda may be described as the {{nowrap| 29 & 111 }} temperament. The name ''hemidromeda'' comes from "hemi-" (Ancient Greek for "one half") and ''[[andromeda]]'', because the generator is 1/2 of andromeda's perfect twelfth (~3/1, about 1902.4 cents); the ploidacot for this temperament is alpha-dicot.
+Hemidromeda may be described as the {{nowrap| 29 & 111 }} temperament. Named by [[Xenllium]] in 2023, ''hemidromeda'' comes from ''hemi-'' (Ancient Greek for "one half") and ''[[andromeda]]'', because the generator is 1/2 of andromeda's perfect twelfth (~3/1, about 1902.4 cents); the ploidacot for this temperament is alpha-dicot.
 [[Subgroup]]: 2.3.5.7
@@ Line 477: / Line 545: @@
 Countriton may be described as the {{nowrap| 51c & 53 }} temperament. It splits the [[24/1|24th harmonic]] into nine tritone generators; its ploidacot is thus delta-enneacot. Among the possible tunings are [[157edo]] and [[210edo]], as well as [[104edo]] in the 104c val.
+Countriton was named by [[Xenllium]] in 2022 as a counterpart of [[untriton]].
 [[Subgroup]]: 2.3.5.7
@@ Line 527: / Line 597: @@
 == Artoneutral ==
 Artoneutral can be described as the {{nowrap| 87 & 94 }} temperament. It is generated by an artoneutral third of ~11/9 (or a tendoneutral sixth of ~18/11), nine of which make the [[12/1|12th harmonic]]; its ploidacot is thus beta-enneacot. [[181edo]] may be recommended as a tuning.
+Artoneutral was named by [[Flora Canou]] in 2023 for its generator's quality.
 [[Subgroup]]: 2.3.5.7

Aberschismic temperaments: Difference between revisions