@@ Line 3: / Line 3: @@
 For temperaments that omit various prime harmonics, see:
-* [[No-thirteens subgroup temperaments]]
 * [[No-elevens subgroup temperaments]]
 * [[No-sevens subgroup temperaments]]
@@ Line 13: / Line 12: @@
 = Composite subgroup temperaments =
+== 2.3.35 subgroup ==
+=== Darian calendar ===
+Darian calendar is described as 24 & 668 temperament in the 2.3.11.19 [[subgroup]] and is named after a certain calendar layout by the same name. The generator is close to the [[36/35]] quartertone, and this allows an extension to the 2.3.35.11.19 subgroup. 5 of them make [[11/8]], 8 of them make [[3/2]], and 6 of them make [[32/19]].
+==== 2.3.11.19 subgroup ====
+The temperament is simplest in this subgroup, although there is a tradeoff of breaking up the simplicity of the 36/35 quartertone.
+[[Subgroup]]: 2.3.11.19
+{{Mapping|legend=2| 4 5 13 18 | 0 8 5 -6 }}
+: sval mapping generators: ~6291456/5285401, ~25289/24576
+[[Optimal tuning]] ([[CTE]]): ~6291456/5285401 = 1\4, ~25289/24576 = 50.257
+[[Support]]ing [[ET]]s: {{EDOs|24, 596, 620, 644, 668, 692, 716}}, ...
+==== 2.3.35.11.19 subgroup ====
+edo does not map 36/35 consistently, with its own [[direct approximation]] being 27 steps while the direct approximations of its constituent odd harmonics do not sum to that same amount: 3/2, 8/5, and 8/7 are 391, 453, and 129 steps, respectively, and 391 + 391 + 453 + 129 - 668 - 668 = 28, ≠ 27.
+Subgroup: 2.3.35.11.19
+Sval mapping: {{mapping| 4 0 5 13 18 | 0 1 8 5 -6 }}
+: sval mapping generators: ~2240/1881, ~36/35
+Optimal tuning (CTE): ~2240/1881 = 1\4, ~36/35 = 50.288
+[[Support]]ing [[ET]]s: {{EDOs|24, 668}}, ...
 == 2.9.5.7 subgroup ==
 See also [[Jubilismic clan #Antikythera|antikythera]] and [[Hemimean clan #Isra|isra]].
@@ Line 75: / Line 104: @@
 {{See also|No-threes subgroup temperaments #Frostburn}}
-Baldy results from taking every other generator of the [[garibaldi temperament]]. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.
+Baldy results from taking every other generator of the [[garibaldi]] temperament. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.
 [[Subgroup]]: 2.9.5.7
@@ Line 138: / Line 167: @@
 {{Optimal ET sequence|legend=1| 6, 23def, 29f, 35, 41, 47 }}
-== 2.9.5.11 subgroup ==
+== 2.3.25 subgroup ==
-=== Glacial ===
-{{See also| Chromatic pairs #Glacial }}
+=== Shrub ===
+This is a restriction of diaschismic which omits the tritone to produce a diatonic scale. True to its name, it generates a [[shrubmajor]] third (~425c) in quarter-comma tuning.
-[[Subgroup]]: 2.9.5.11.13
+Subgroup: 2.3.25
-[[Comma list]]: 45/44, 65/64, 81/80
+Edo join: 17 & 12
-{{Mapping|legend=2| 1 0 -4 -6 10 | 0 1 2 3 -2 }}
+Comma list: [[2048/2025]]
-{{Mapping|legend=3| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }}
+{{Mapping|legend=2| 1 1 7| 0 1 -4}}
-: [[gencom]]: [2 9/8; 45/44 65/64 81/80]
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.136
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151
+==== 2.3.23.25.41 subgroup ====
+''See also: [[Reversed meantone]]''
-{{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }}
+Edo join: 17 & 12
-[[Tp tuning #T2 tuning|RMS error]]: 2.887 cents
+Comma list: 2048/2025, 576/575, 82/81
-Music:
+{{Mapping|legend=2| 1 1 1 7 3| 0 1 6 -4 4}}
-* ''[[Thundersnow]]'' - [[Sevish]] (2021)
-== 2.9.7 subgroup ==
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.264
-=== Mabon ===
-Derived from a [http://individual.utoronto.ca/kalendis/leap/index.htm#se calendar leap cycle built for the autumn equinox], hence the name. Defined as the 11 & 62 temperament.
-Subgroup: 2.9.7
+===== Sburb =====
+This temperament sets the [[octave reduction|octave-reduced]] 413th harmonic (413/256, 827.998{{c}}) to the diminished seventh.
-Comma basis: 44957696/43046721
+Subgroup: 2.3.7.23.25.41.59
-Sval mapping: [{{val|1 1 -3}}, {{val|0 3 8}}]
+Edo join: 17 & 12
-Optimal tuning (CTE): ~729/448 = 870.792
+Comma list: 64/63, 225/224, 162/161, 82/81, 177/175
-{{Optimal ET sequence|legend=1|7d, 11, 18d, 29, 40, 62}}, ...
+{{Mapping|legend=2| 1 1 4 1 7 3 10| 0 1 -2 6 -4 4 -7}}
-==== 2.9.7.11 subgroup ====
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 706.387
-Subgroup: 2.9.7.11
-Comma basis: 896/891, 1331/1296
+== 2.9.5.11 subgroup ==
+=== Glacial ===
+{{See also| Chromatic pairs #Glacial }}
-Sval mapping: [{{val|1 1 -3 2}}, {{val|0 3 8 2}}]
+[[Subgroup]]: 2.9.5.11.13
-Optimal tuning (CTE): ~16/11 = 870.966
+[[Comma list]]: 45/44, 65/64, 81/80
-{{Optimal ET sequence|legend=1| 7d, 11, 40, 51, 62 }}
+{{Mapping|legend=2| 1 0 -4 -6 10 | 0 1 2 3 -2 }}
-== 2.9.7.11 subgroup ==
+{{Mapping|legend=3| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }}
-=== Apparatus ===
-[[Subgroup]]: 2.9.7.11
-[[Comma list]]: 41503/41472, 322102/321489
+: [[gencom]]: [2 9/8; 45/44 65/64 81/80]
-{{Mapping|legend=2| 1 5 3 5 | 0 -19 -2 -16 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151
-: mapping generators: ~2, ~77/72
+{{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }}
-{{Mapping|legend=3| 1 5/2 0 3 5 | 0 -19/2 0 -2 -16 }}
+[[Tp tuning #T2 tuning|RMS error]]: 2.887 cents
-: [[gencom]]: [2 77/72; 41503/41472 322102/321489]
+Music:
+* ''[[Thundersnow]]'' - [[Sevish]] (2021)
-[[Optimal tuning]] ([[CTE]]): ~77/72 = 115.5685
+== 2.9.7 subgroup ==
+=== Mabon ===
+Derived from a [http://individual.utoronto.ca/kalendis/leap/index.htm#se calendar leap cycle built for the autumn equinox], hence the name. Defined as the 11 & 62 temperament.
-{{Optimal ET sequence|legend=1| 10e, 21, 31, 52, 83, 135, 353, 488, 623 }}
+Subgroup: 2.9.7
-[[Badness]]: 0.00263
+Comma basis: 44957696/43046721
-=== Joan ===
+Sval mapping: [{{val|1 1 -3}}, {{val|0 3 8}}]
-{{See also| Chromatic pairs #Joan }}
-Joan is related to [[casablanca]] as well as to [[orwell]].
+Optimal tuning (CTE): ~729/448 = 870.792
-[[Subgroup]]: 2.9.7.11
+{{Optimal ET sequence|legend=1|7d, 11, 18d, 29, 40, 62}}, ...
-[[Comma list]]: 99/98, 9317/9216
+==== 2.9.7.11 subgroup ====
+Subgroup: 2.9.7.11
-{{Mapping|legend=2| 1 0 1 3 | 0 7 4 1 }}
+Comma basis: 896/891, 1331/1296
-{{Mapping|legend=3| 1 0 0 1 3 | 0 7/2 0 4 1 }}
+Sval mapping: [{{val|1 1 -3 2}}, {{val|0 3 8 2}}]
-: [[gencom]]: [2 11/8; 99/98 9317/9216]
+Optimal tuning (CTE): ~16/11 = 870.966
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents
+{{Optimal ET sequence|legend=1| 7d, 11, 40, 51, 62 }}
-{{Optimal ET sequence|legend=1| 11, 20, 31, 42, 115bd, 157bd }}
+== 2.9.7.11 subgroup ==
+=== Apparatus ===
+[[Subgroup]]: 2.9.7.11
-[[Tp tuning #T2 tuning|RMS error]]: 1.424 cents
+[[Comma list]]: 41503/41472, 322102/321489
-=== Machine ===
+{{Mapping|legend=2| 1 5 3 5 | 0 -19 -2 -16 }}
-Machine is every other step of [[supra]], most interesting for its scale patterns.
-[[Subgroup]]: 2.9.7.11
+: mapping generators: ~2, ~77/72
-[[Comma list]]: 64/63, 99/98
+{{Mapping|legend=3| 1 5/2 0 3 5 | 0 -19/2 0 -2 -16 }}
-{{Mapping|legend=2| 1 0 6 13 | 0 1 -1 -3 }}
+: [[gencom]]: [2 77/72; 41503/41472 322102/321489]
-: sval mapping generators: ~2, ~9
+[[Optimal tuning]] ([[CTE]]): ~77/72 = 115.5685
-{{Mapping|legend=3| 1 3/2 0 3 4 | 0 1/2 0 -1 -3 }}
+{{Optimal ET sequence|legend=1| 10e, 21, 31, 52, 83, 135, 353, 488, 623 }}
-: [[gencom]]: [2 8/7; 64/63 99/98]
+[[Badness]]: 0.00263
-[[Optimal tuning]]s:
+=== Joan ===
-* [[CTE]]: ~2 = 1\1, ~9/8 = 216.9128
+{{See also| Chromatic pairs #Joan }}
-* [[POTE]]: ~2 = 1\1, ~9/8 = 214.3843
-{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }}
+Joan is related to [[casablanca]] as well as to [[orwell]].
-[[Badness]]: 0.00233
+[[Subgroup]]: 2.9.7.11
-=== Penta a.k.a. mechanism ===
+[[Comma list]]: 99/98, 9317/9216
-Penta or mechanism is the 8 &amp; 11 temperament in the 2.9.7.11 subgroup.
-[[Subgroup]]: 2.9.7.11
+{{Mapping|legend=2| 1 0 1 3 | 0 7 4 1 }}
-[[Comma list]]: 896/891, 26411/26244
+{{Mapping|legend=3| 1 0 0 1 3 | 0 7/2 0 4 1 }}
-{{Mapping|legend=2| 1 0 -1 6 | 0 5 6 -4 }}
+: [[gencom]]: [2 11/8; 99/98 9317/9216]
-: sval mapping generators: ~2, ~14/9
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents
-{{Mapping|legend=3| 1 5/2 0 5 2 | 0 -5/2 0 -6 4 }}
+{{Optimal ET sequence|legend=1| 11, 20, 31, 42, 115bd, 157bd }}
-: [[gencom]]: [2 9/7; 896/891 26411/26244]
+[[Tp tuning #T2 tuning|RMS error]]: 1.424 cents
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/9 = 761.3782
+=== Machine ===
+Machine is every other step of [[supra]], most interesting for its scale patterns.
-{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}
+[[Subgroup]]: 2.9.7.11
-[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
+[[Comma list]]: 64/63, 99/98
-[[Badness]]: 0.00439
+{{Mapping|legend=2| 1 0 6 13 | 0 1 -1 -3 }}
-Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]
+: sval mapping generators: ~2, ~9
-== 2.9.11 subgroup ==
+{{Mapping|legend=3| 1 3/2 0 3 4 | 0 1/2 0 -1 -3 }}
-=== Demon ===
-Demon is a temperament which equates 3 [[11/9]] with [[16/9]], or equivalently 3 [[18/11]] with [[9/8]], tempering out [[1331/1296]]. This results in [[11/9]] being tuned flat to a supraminor third, and [[27/22]] being tuned sharp to a submajor third. It was discovered by [[User:CompactStar|CompactStar]] while searching for temperaments assosciated with the [[7L 4s]] ("daemotonic") MOS, known for its lack of representation of simple temperaments. The optimal tuning for demon temperament is near the basic tuning of 7L 4s (13\18), and indeed [[18edo]] supports demon temperament.
-[[Subgroup]]: 2.9.11
+: [[gencom]]: [2 8/7; 64/63 99/98]
-[[Comma list]]: [[1331/1296]]
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~9/8 = 216.9128
+* [[POTE]]: ~2 = 1\1, ~9/8 = 214.3843
-{{Mapping|legend=2|1 1 2|0 3 2}}
+{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }}
-[[Optimal tuning]] ([[CTE]]): ~[[18/11]] = 870.060
+[[Badness]]: 0.00233
-{{Optimal ET sequence|legend=1|4, 7, 11, 18, 29, 76e}}
+=== Penta a.k.a. mechanism ===
+Penta or mechanism is the 8 &amp; 11 temperament in the 2.9.7.11 subgroup.
-=== Genius ===
+[[Subgroup]]: 2.9.7.11
-Named after the genius in Roman religion, following the demon (daimon) in Greek mythology.
+[[Comma list]]: 896/891, 26411/26244
-[[Subgroup]]: 2.9.11
+{{Mapping|legend=2| 1 0 -1 6 | 0 5 6 -4 }}
-[[Comma list]]: [[131769/131072]]
+: sval mapping generators: ~2, ~14/9
-{{Mapping|legend=2|1 1 4|0 4 -1}}
+{{Mapping|legend=3| 1 5/2 0 5 2 | 0 -5/2 0 -6 4 }}
-[[Optimal tuning]] ([[CTE]]): ~[[16/11]] = 650.863
+: [[gencom]]: [2 9/7; 896/891 26411/26244]
-{{Optimal ET sequence|legend=1|9, 11, 24, 59, 83, 142, 225, 367}}[-11], 592[-11], 959[-9, --11], 1326[-9, --11]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/9 = 761.3782
-== 2.9.15.7 subgroup ==
+{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}
-=== Stacks (a.k.a. 2magic) ===
-Stacks, the 11 &amp; 30 temperament in the 2.9.15.7.11.13 subgroup, is every other step of [[magic]].
-[[Subgroup]]: 2.9.15.7
+[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
-[[Comma list]]: 225/224, 245/243
+[[Badness]]: 0.00439
-{{Mapping|legend=2| 1 0 2 -1 | 0 5 3 6 }}
+Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]
-: sval mapping generators: ~2, ~14/9
+== 2.9.7.13.17 subgroup ==
-{{Mapping|legend=3| 1 5/2 5/2 5 | 0 -5/2 -1/2 -6 }}
+=== Novisept ===
+Novisept is generated by a one-cent-flat 9/7, such that stacking 5 of them gives you 7/4. It can be formed by doubling both generator and period of [[gizzard]].
-: [[gencom]]: [2 9/7; 225/224 245/243]
+[[Subgroup]]: 2.9.7.13.17
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~14/9 = 760.704
+[[Comma list]]: 729/728, 442/441, 833/832
-{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 71, 93, 112c, 134c, 175c }}
+{{Mapping|legend=2| 1 1 1 -1 3| 0 6 5 13 3 }}
-[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
+[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~9/7 = 433.836
-==== 2.9.15.7.11 ====
+Badness (Dirichlet): 0.142
-Subgroup: 2.9.15.7.11
-Comma list: 100/99, 225/224, 245/243
+== 2.9.11 subgroup ==
+=== Demon ===
+Demon is a temperament which equates 3 [[11/9]] with [[16/9]], or equivalently 3 [[18/11]] with [[9/8]], tempering out [[1331/1296]]. This results in [[11/9]] being tuned flat to a supraminor third, and [[27/22]] being tuned sharp to a submajor third. It was discovered by [[User:CompactStar|CompactStar]] while searching for temperaments assosciated with the [[7L 4s]] ("daemotonic") MOS, known for its lack of representation of simple temperaments. The optimal tuning for demon temperament is near the basic tuning of 7L 4s (13\18), and indeed [[18edo]] supports demon temperament.
-Sval mapping: {{mapping| 1 0 2 -1 6 | 0 5 3 6 -4 }}
+[[Subgroup]]: 2.9.11
-Gencom mapping: {{mapping| 1 5/2 5/2 5 2 | 0 -5/2 -1/2 -6 4 }}
+[[Comma list]]: [[1331/1296]]
-: gencom: [2 9/7; 100/99 225/224 245/243]
+{{Mapping|legend=2|1 1 2|0 3 2}}
-Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.393
+[[Optimal tuning]] ([[CTE]]): ~[[18/11]] = 870.060
-Optimal ET sequence: {{Optimal ET sequence| 8, 11, 30, 41, 52, 93, 145, 342bce }}
+{{Optimal ET sequence|legend=1|4, 7, 11, 18, 29, 76e}}
-RMS error: 1.226 cents
+=== Genius ===
-==== 2.9.15.7.11.13 ====
+Named after the genius in Roman religion, following the demon (daimon) in Greek mythology.
-Subgroup: 2.9.15.7.11.13
-Comma list: 100/99, 105/104, 144/143, 196/195
+[[Subgroup]]: 2.9.11
-Sval mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 3 6 -4 9 }}
+[[Comma list]]: [[131769/131072]]
-Gencom mapping: {{mapping| 1 5/2 5/2 5 2 7 | 0 -5/2 -1/2 -6 4 -9 }}
+{{Mapping|legend=2|1 1 4|0 4 -1}}
-: gencom: [2 9/7; 100/99 105/104 144/143 196/195]
+[[Optimal tuning]] ([[CTE]]): ~[[16/11]] = 650.863
-Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.023
+{{Optimal ET sequence|legend=1|9, 11, 24, 59, 83, 142, 225, 367}}[-11], 592[-11], 959[-9, --11], 1326[-9, --11]
-Optimal ET sequence: {{Optimal ET sequence| 11, 30, 41, 153cdef, 194cdef, 235cdef }}
+== 2.9.15.7 subgroup ==
+=== Stacks (a.k.a. 2magic) ===
+Stacks, the 11 &amp; 30 temperament in the 2.9.15.7.11.13 subgroup, is every other step of [[magic]].
-RMS error: 1.540 cents
+[[Subgroup]]: 2.9.15.7
-== 2.9.21 subgroup ==
+[[Comma list]]: 225/224, 245/243
-=== A-team ===
-A-team is every other step of [[slendric]]; the 2.9.5.21.11 extension below specifically restricts [[mothra]].
-[[Subgroup]]: 2.9.21
+{{Mapping|legend=2| 1 0 2 -1 | 0 5 3 6 }}
-[[Comma list]]: 1029/1024
+: sval mapping generators: ~2, ~14/9
-{{Mapping|legend=2| 1 2 4 | 0 3 1 }}
+{{Mapping|legend=3| 1 5/2 5/2 5 | 0 -5/2 -1/2 -6 }}
-: sval mapping generators: ~2, ~21/16
+: [[gencom]]: [2 9/7; 225/224 245/243]
-{{Mapping|legend=3| 1 1 0 3 | 0 3/2 0 -1/2 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~14/9 = 760.704
-: [[gencom]]: [2 21/16; 1029/1024]
+{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 71, 93, 112c, 134c, 175c }}
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~21/16 = 467.375
+[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
-{{Optimal ET sequence|legend=1| 5, 13, 18, 41, 59, 77, 95 }}
+==== 2.9.15.7.11 ====
+Subgroup: 2.9.15.7.11
-[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
+Comma list: 100/99, 225/224, 245/243
-==== 2.9.5.21 ====
+Sval mapping: {{mapping| 1 0 2 -1 6 | 0 5 3 6 -4 }}
-''Lookalike temperament: [[Dual-fifth_temperaments#Dual-3_A-Team|Dual-3 A-Team]]''
-Subgroup: 2.9.5.21
+Gencom mapping: {{mapping| 1 5/2 5/2 5 2 | 0 -5/2 -1/2 -6 4 }}
-[[Comma]] list: 81/80, 1029/1024
+: gencom: [2 9/7; 100/99 225/224 245/243]
-Sval mapping: {{mapping| 1 2 0 4 | 0 3 6 1 }}
+Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.393
-Mapping generators: ~2, ~21/16
+Optimal ET sequence: {{Optimal ET sequence| 8, 11, 30, 41, 52, 93, 145, 342bce }}
-Optimal ([[Lp tuning|POL2]]) generator: 464.3865
+RMS error: 1.226 cents
-{{Optimal ET sequence|legend=1| 13, 18, 31, 44 }}
+==== 2.9.15.7.11.13 ====
+Subgroup: 2.9.15.7.11.13
-===== 2.9.5.21.11 =====
+Comma list: 100/99, 105/104, 144/143, 196/195
-Subgroup: 2.9.5.21.11
-Comma list: 81/80, 99/98, 385/384
+Sval mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 3 6 -4 9 }}
-Sval mapping: {{mapping| 1 2 0 4 5 | 0 3 6 1 -4 }}
+Gencom mapping: {{mapping| 1 5/2 5/2 5 2 7 | 0 -5/2 -1/2 -6 4 -9 }}
-Gencom mapping: {{mapping| 1 1 0 3 5 | 0 3/2 6 -1/2 -4 }}
+: gencom: [2 9/7; 100/99 105/104 144/143 196/195]
-: gencom: [2 21/16; 81/80 99/98 385/384]
+Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.023
-Optimal tuning (subgroup POTE): ~2 = 1\1, ~21/16 = 463.956
+Optimal ET sequence: {{Optimal ET sequence| 11, 30, 41, 153cdef, 194cdef, 235cdef }}
-{{Optimal ET sequence|legend=1| 5, 13, 31 }}
+RMS error: 1.540 cents
-==== B-team ====
+== 2.9.21 subgroup ==
-B-team (23 & 41) is every other step of [[rodan]].
+=== A-team ===
+A-team is every other step of [[slendric]]; the 2.9.5.21.11 extension below specifically restricts [[mothra]].
-Subgroup: 2.9.15.21.33
+[[Subgroup]]: 2.9.21
-Comma list: 245/243, 385/384, 441/440
+[[Comma list]]: 1029/1024
-Sval mapping: {{mapping| 1 2 0 4 7 | 0 3 10 1 -5 }}
+{{Mapping|legend=2| 1 2 4 | 0 3 1 }}
-Optimal tuning (subgroup POTE): ~2 = 1\1, ~21/16 = 468.918
+: sval mapping generators: ~2, ~21/16
-{{Optimal ET sequence|legend=1| 5, 13c, 18, 23, 41, 64, 87, 151 }}
+{{Mapping|legend=3| 1 1 0 3 | 0 3/2 0 -1/2 }}
-== 4.3.5 subgroup ==
+: [[gencom]]: [2 21/16; 1029/1024]
-=== Tetrahanson ===
-{{Main| Tetrahanson }}
-[[Subgroup]]: 4.3.5
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~21/16 = 467.375
-[[Comma list]]: 15625/15552
+{{Optimal ET sequence|legend=1| 5, 13, 18, 41, 59, 77, 95 }}
-{{Mapping|legend=2| 1 3 3 | 0 -6 -5 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
-: Mapping generators: ~4, ~5/3
+==== 2.9.5.21 ====
+''Lookalike temperament: [[Dual-fifth_temperaments#Dual-3_A-Team|Dual-3 A-Team]]''
-[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941
+Subgroup: 2.9.5.21
-[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
+[[Comma]] list: 81/80, 1029/1024
-=== Tetrameantone ===
+Sval mapping: {{mapping| 1 2 0 4 | 0 3 6 1 }}
-{{Main| Tetrameantone }}
-[[Subgroup]]: 4.3.5
+Mapping generators: ~2, ~21/16
-[[Comma list]]: 81/80
+Optimal ([[Lp tuning|POL2]]) generator: 464.3865
-{{Mapping|legend=2| 1 1 2 | 0 -1 -4 }}
+{{Optimal ET sequence|legend=1| 13, 18, 31, 44 }}
-: Mapping generators: ~4, ~4/3
+===== 2.9.5.21.11 =====
+Subgroup: 2.9.5.21.11
-[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~4/3 = 503.761
+Comma list: 81/80, 99/98, 385/384
-[[Support]]ing [[ET]]s: {{EDs|5, 9, 14, 19, 24, 43, 62, 81, 100|equave=4}}
+Sval mapping: {{mapping| 1 2 0 4 5 | 0 3 6 1 -4 }}
-=== Tetramagic ===
+Gencom mapping: {{mapping| 1 1 0 3 5 | 0 3/2 6 -1/2 -4 }}
-[[Subgroup]]: 4.3.5
+: gencom: [2 21/16; 81/80 99/98 385/384]
-[[Comma list]]: 3125/3072
+Optimal tuning (subgroup POTE): ~2 = 1\1, ~21/16 = 463.956
-{{Mapping|legend=2| 1 0 1 | 0 5 1 }}
+{{Optimal ET sequence|legend=1| 5, 13, 31 }}
-: Mapping generators: ~4, ~5/4
+==== B-team ====
+B-team (23 & 41) is every other step of [[rodan]].
-[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~5/4 = 380.059
+Subgroup: 2.9.15.21.33
-[[Support]]ing [[ET]]s: {{EDs|6, 13, 19, 25, 38, 44, 63, 82|equave=4}}
+Comma list: 245/243, 385/384, 441/440
-=== Blacktetra ===
+Sval mapping: {{mapping| 1 2 0 4 7 | 0 3 10 1 -5 }}
-[[Subgroup]]: 4.3.5
+Optimal tuning (subgroup POTE): ~2 = 1\1, ~21/16 = 468.918
-[[Comma list]]: 256/243
+{{Optimal ET sequence|legend=1| 5, 13c, 18, 23, 41, 64, 87, 151 }}
-{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}
+== 2.75.85 subgroup ==
+=== MVP archagall ===
+By tempering out the comma [[24576/24565]] in the 2.75.85 subgroup, we have three [[85/64]]'s up and one octave down as a [[75/64]] and we have two [[128/85]]'s up and one octave down as a [[17/15]] whole tone. It is because of this combination of accuracy, efficiency and mapping-wise simplicity and its corresponding explanatory power in what this comma does that the comma has been named the ''archagallisma''. The ''MVP'' stands for ''minimum viable product'', as this is the core of what the archagall logic achieves, with further extensions adding to the subgroup while avoiding significantly impacting its accuracy. This is a highly accurate temperament that could be considered to be encoding the "high-accuracy logic" of [[superpyth]] and which is inescapably related to the [[17L 5s]] scale form as it is the 17 & 22 temperament (or less accurately, the 5 & 17 temperament) in the 2.75.85 subgroup.
-: Mapping generators: ~4, ~16/15
+[[Subgroup]]: 2.75.85
-[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062
+[[Comma list]]: 24576/24565 ({{monzo| 13 1 -3 }})
-[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}
+{{Mapping|legend=2| 1 2 5 | 0 3 1 }}
+: mapping generators: ~2, ~85/32
-== 4.6.5 subgroup ==
+[[Optimal tuning]]s:
-=== Meanquad ===
+* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.9692{{c}}, ~85/64 = 491.5853{{c}}
-{{Main| Meanquad }}
+* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~85/64 = 491.5794{{c}}
-[[Subgroup]]: 4.6.5
+{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 61, 83, 310, 393, 476, 1345, 1821, 4118*, 5939*, 7760* }}
-[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}
+== 2.75.9/7.85 subgroup ==
+=== Archagall ===
+A fairly natural way to extend [[#MVP archagall|MVP archagall]] is by tempering out [[2025/2023]] ([[S-expression|S15/S17]]), which equates a stack of two [[17/15]]'s with [[9/7]] without much damage. As 9/7 was not previously in the subgroup, this does not decrease the rank of the temperament and qualifies a proper and natural extension. We can equally get the same temperament by tempering out S15/S16 instead (equating a stack of three [[16/15]]'s with [[17/14]]); however, [[16/15]] is not in the subgroup, so it is preferred to think of it as adding 2025/2023.
-{{Mapping|legend=2| 1 0 -4| 0 1 4 }}
+[[Subgroup]]: 2.75.9/7.85
-: mapping generators: ~4, ~6
+[[Comma list]]: 2025/2023 ({{monzo| 2 -2 1 0 }}), 24576/24565 ({{monzo| 13 1 0 -3 }})
-[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214
+{{Mapping|legend=2| 1 2 6 5 | 0 3 -4 1 }}
+: mapping generators: ~2, ~85/32
-[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
+[[Optimal tuning]]s:
+* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1200.0241{{c}}, ~85/64 = 491.3358{{c}}
+* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~85/64 = 491.3290{{c}}
+{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 83, 105, 127, 403, 530, 657, 784, 1441* }}
-<nowiki />* Wart for 4
+== 4.3.5 subgroup ==
+=== Tetrahanson ===
+{{Main| Tetrahanson }}
-==== 4.6.5.7 subgroup (tetrominant) ====
+[[Subgroup]]: 4.3.5
-[[Subgroup]]: 4.6.5.7
-[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}
+[[Comma list]]: 15625/15552
-{{Mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}
+{{Mapping|legend=2| 1 3 3 | 0 -6 -5 }}
-[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622
+: Mapping generators: ~4, ~5/3
-[[Support]]ing [[ET]]s: *7, *10, *17, *24, *27[+5], *31, *38[+7], *41, *44[+5], *55[+7], *58[+5, +7], *65[+5, +7], *75[+5, +7]
+[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941
-<nowiki />* Wart for 4
+[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
-=== Fourwar ===
+=== Tetrameantone ===
-The 23-limit version of Fourwar was created first, as an attempt to approximate subgroup 4.6.5.7.11.13.17.19.23 as accurately as possible using 25 to 35 notes per equave. Then the lower limit versions were created by simply extrapolating the temperament downwards.
+{{Main| Tetrameantone }}
-Fourwar is named after the closely related [[hemiwar]] temperament.
+[[Subgroup]]: 4.3.5
-<pre>
+[[Comma list]]: 81/80
-Reduced Mapping
-	6	5
-[ ⟨	1	0	1	]
-⟨	0	16	2	] ⟩
-TE Generator Tunings (cents)
-⟨2399.3973, 193.8643]
-TE Step Tunings (cents)
-⟨25.21211, 47.81337]
-TE Tuning Map (cents)
-⟨2399.397, 3101.829, 2787.126]
-TE Mistunings (cents)
-⟨-0.603, -0.126, 0.812]
-Complexity	1.369085
-Adjusted Error	0.692892 cents
-TE Error	0.268047 cents/octave
-Unison Vector
-[8, 1, -8⟩ (393216:390625)
-Subsets
+{{Mapping|legend=2| 1 1 2 | 0 -1 -4 }}
-q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
-</pre>
-==== 4.6.5.7 ====
+: Mapping generators: ~4, ~4/3
-<pre>
-Reduced Mapping
-	6	5	7
-[ ⟨	1	0	1	1	]
-⟨	0	16	2	5	] ⟩
-TE Generator Tunings (cents)
-⟨2399.4195, 193.8654]
-TE Step Tunings (cents)
-⟨25.23883, 47.79592]
-TE Tuning Map (cents)
-⟨2399.420, 3101.846, 2787.150, 3368.747]
-TE Mistunings (cents)
-⟨-0.580, -0.109, 0.837, -0.079]
-Complexity	1.192044
-Adjusted Error	0.653313 cents
-TE Error	0.232715 cents/octave
-Unison Vectors
-[-2, -1, -2, 4⟩ (2401:2400)
-[3, 0, -5, 2⟩ (3136:3125)
-[5, 1, -3, -2⟩ (6144:6125)
-[8, 1, -8, 0⟩ (393216:390625)
-Subsets
+[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~4/3 = 503.761
-q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
-</pre>
+[[Support]]ing [[ET]]s: {{EDs|5, 9, 14, 19, 24, 43, 62, 81, 100|equave=4}}
+=== Tetramagic ===
+[[Subgroup]]: 4.3.5
+[[Comma list]]: 3125/3072
+{{Mapping|legend=2| 1 0 1 | 0 5 1 }}
+: Mapping generators: ~4, ~5/4
-==== 4.6.5.7.11 ====
+[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~5/4 = 380.059
-<pre>
-Reduced Mapping
+[[Support]]ing [[ET]]s: {{EDs|6, 13, 19, 25, 38, 44, 63, 82|equave=4}}
-	6	5	7	11
-[ ⟨	1	0	1	1	1	]
-⟨	0	16	2	5	9	] ⟩
-TE Generator Tunings (cents)
-⟨2400.1097, 193.9498]
-TE Step Tunings (cents)
-⟨24.18752, 48.52491]
-TE Tuning Map (cents)
-⟨2400.110, 3103.196, 2788.009, 3369.859, 4145.658]
-TE Mistunings (cents)
-⟨0.110, 1.241, 1.696, 1.033, -5.660]
-Complexity	1.068792
-Adjusted Error	2.926965 cents
-TE Error	0.846083 cents/octave
-Unison Vectors
-[-1, -1, -1, 0, 2⟩ (121:120)
-[2, 0, -2, -1, 1⟩ (176:175)
-[-3, -1, 1, 1, 1⟩ (385:384)
-[-1, 0, 3, -3, 1⟩ (1375:1372)
-[-2, -1, -2, 4, 0⟩ (2401:2400)
-[1, 0, 1, -4, 2⟩ (2420:2401)
-Subsets
+=== Blacktetra ===
-q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
-</pre>
-==== 4.6.5.7.11.13 ====
+[[Subgroup]]: 4.3.5
-<pre>
+[[Comma list]]: 256/243
-Reduced Mapping
-	6	5	7	11	13
+{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}
-[ ⟨	1	0	1	1	1	0	]
-⟨	0	16	2	5	9	23	] ⟩
+: Mapping generators: ~4, ~16/15
-TE Generator Tunings (cents)
+[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062
-⟨2401.2305, 193.5378]
+[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}
-TE Step Tunings (cents)
-⟨42.79107, 35.98524]
+== 4.6.5 subgroup ==
+=== Meanquad ===
-TE Tuning Map (cents)
+{{Main| Meanquad }}
-⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
+[[Subgroup]]: 4.6.5
-TE Mistunings (cents)
-⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]
+[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}
-Complexity	1.219191
-Adjusted Error	6.699599 cents
-TE Error	1.810487 cents/octave
-Unison Vectors
-[0, 1, -1, 0, 1, -1⟩ (66:65)
-[-1, -1, -1, 0, 2, 0⟩ (121:120)
-[1, 2, 0, 0, -1, -1⟩ (144:143)
-[2, 0, -2, -1, 1, 0⟩ (176:175)
-[-2, 1, 1, 1, 0, -1⟩ (105:104)
-[-3, -1, 1, 1, 1, 0⟩ (385:384)
-[-3, 0, 0, 1, 2, -1⟩ (847:832)
-[1, 3, -1, 0, 0, -2⟩ (864:845)
-[-1, 0, 3, -3, 1, 0⟩ (1375:1372)
-Subsets
+{{Mapping|legend=2| 1 0 -4| 0 1 4 }}
-q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
-</pre>
-==== 4.6.5.7.11.13.17 ====
+: mapping generators: ~4, ~6
-<pre>
-Reduced Mapping
-	6	5	7	11	13	17
-[ ⟨	1	0	1	1	1	0	1	]
-⟨	0	16	2	5	9	23	13	] ⟩
-TE Generator Tunings (cents)
-⟨2400.4701, 193.4599]
-TE Step Tunings (cents)
-⟨43.39350, 35.55764]
-TE Tuning Map (cents)
-⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]
-TE Mistunings (cents)
-⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]
-Complexity	1.129881
-Adjusted Error	8.082725 cents
-TE Error	1.977443 cents/octave
-Unison Vectors
-[0, 1, -1, 0, 1, -1, 0⟩ (66:65)
-[1, 1, 1, -1, 0, 0, -1⟩ (120:119)
-[1, 2, 0, 0, -1, -1, 0⟩ (144:143)
-[-2, 1, 1, 1, 0, -1, 0⟩ (105:104)
-[-1, 2, 2, 0, 0, -1, -1⟩ (225:221)
-[-1, 1, 2, -2, 0, -1, 1⟩ (1275:1274)
-Subsets
+[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214
-q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg
-</pre>
+[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
+<nowiki />* Wart for 4
+==== 4.6.5.7 subgroup (tetrominant) ====
+[[Subgroup]]: 4.6.5.7
+[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}
+{{Mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}
+[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622
-==== 4.6.5.7.11.13.17.19 ====
+[[Support]]ing [[ET]]s: *7, *10, *17, *24, *27[+5], *31, *38[+7], *41, *44[+5], *55[+7], *58[+5, +7], *65[+5, +7], *75[+5, +7]
-<pre>
-Reduced Mapping
+<nowiki />* Wart for 4
-	6	5	7	11	13	17	19
-[ ⟨	1	0	1	1	1	0	1	1	]
+=== Fourwar ===
-⟨	0	16	2	5	9	23	13	14	] ⟩
+The 23-limit version of Fourwar was created first, as an attempt to approximate subgroup 4.6.5.7.11.13.17.19.23 as accurately as possible using 25 to 35 notes per equave. Then the lower limit versions were created by simply extrapolating the temperament downwards.
-TE Generator Tunings (cents)
+Fourwar is named after the closely related [[hemiwar]] temperament.
-⟨2399.9219, 193.3952]
+{{Todo|inline=1|cleanup}}
-TE Step Tunings (cents)
-⟨44.14256, 35.03670]
+<pre>
+Reduced Mapping
+	6	5
+[ ⟨	1	0	1	]
+⟨	0	16	2	] ⟩
+TE Generator Tunings (cents)
+⟨2399.3973, 193.8643]
+TE Step Tunings (cents)
+⟨25.21211, 47.81337]
 TE Tuning Map (cents)
-⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
+⟨2399.397, 3101.829, 2787.126]
 TE Mistunings (cents)
-⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]
+⟨-0.603, -0.126, 0.812]
-Complexity	1.058472
+Complexity	1.369085
-Adjusted Error	8.712222 cents
+Adjusted Error	0.692892 cents
-TE Error	2.050935 cents/octave
+TE Error	0.268047 cents/octave
-Unison Vectors
+Unison Vector
-[0, 1, -1, 0, 1, -1, 0, 0⟩ (66:65)
+[8, 1, -8⟩ (393216:390625)
-[-1, 0, 0, 1, 1, 0, 0, -1⟩ (77:76)
-[2, 1, -1, 0, 0, 0, 0, -1⟩ (96:95)
-[1, 1, 1, -1, 0, 0, -1, 0⟩ (120:119)
-[0, 1, 1, 1, -1, 0, 0, -1⟩ (210:209)
-[0, 0, 1, -2, 1, 0, 1, -1⟩ (935:931)
-[2, 0, -3, 1, 0, 0, -1, 1⟩ (2128:2125)
 Subsets
-q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
 </pre>
-==== 4.6.5.7.11.13.17.19.23 ====
+==== 4.6.5.7 ====
 <pre>
 Reduced Mapping
-	6	5	7	11	13	17	19	23
+	6	5	7
-[ ⟨	1	0	1	1	1	0	1	1	0	]
+[ ⟨	1	0	1	1	]
-⟨	0	16	2	5	9	23	13	14	28	] ⟩
+⟨	0	16	2	5	] ⟩
 TE Generator Tunings (cents)
-⟨2399.3286, 193.5316]
+⟨2399.4195, 193.8654]
 TE Step Tunings (cents)
-⟨37.31613, 39.63311]
+⟨25.23883, 47.79592]
 TE Tuning Map (cents)
-⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
+⟨2399.420, 3101.846, 2787.150, 3368.747]
 TE Mistunings (cents)
-⟨-0.671, -5.449, 0.078, -1.839, -10.205, 10.699, 10.284, 11.258, -9.389]
+⟨-0.580, -0.109, 0.837, -0.079]
-Complexity	1.115920
+Complexity	1.192044
-Adjusted Error	9.502017 cents
+Adjusted Error	0.653313 cents
-TE Error	2.100561 cents/octave
+TE Error	0.232715 cents/octave
 Unison Vectors
-[0, 1, -1, 0, 1, -1, 0, 0, 0⟩ (66:65)
+[-2, -1, -2, 4⟩ (2401:2400)
-[1, 0, 0, -1, 0, -1, 0, 0, 1⟩ (92:91)
+[3, 0, -5, 2⟩ (3136:3125)
-[0, -1, 1, 0, 0, 0, 0, -1, 1⟩ (115:114)
+[5, 1, -3, -2⟩ (6144:6125)
-[1, 1, 1, -1, 0, 0, -1, 0, 0⟩ (120:119)
+[8, 1, -8, 0⟩ (393216:390625)
-[2, 0, -2, -1, 1, 0, 0, 0, 0⟩ (176:175)
-[-3, -1, 1, 1, 1, 0, 0, 0, 0⟩ (385:384)
-[1, 0, -2, 1, 0, 0, 1, -1, 0⟩ (476:475)
-[1, 0, 0, -2, 1, 0, -1, 1, 0⟩ (836:833)
-[0, 0, 1, -2, 1, 0, 1, -1, 0⟩ (935:931)
-[1, -1, 0, 0, 0, 0, -2, 1, 1⟩ (874:867)
 Subsets
-q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
 </pre>
-== 4.9.25 subgroup ==
+==== 4.6.5.7.11 ====
-=== Meansquared ===
+<pre>
-[[Subgroup]]: 4.9.25
+Reduced Mapping
+	6	5	7	11
-[[Comma list]]: [[6561/6400]]
+[ ⟨	1	0	1	1	1	]
+⟨	0	16	2	5	9	] ⟩
-{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
+TE Generator Tunings (cents)
-Mapping generators: ~4, ~9/64
+⟨2400.1097, 193.9498]
-[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
+TE Step Tunings (cents)
+⟨24.18752, 48.52491]
-[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
+TE Tuning Map (cents)
-== 4.9.49 subgroup ==
+⟨2400.110, 3103.196, 2788.009, 3369.859, 4145.658]
-=== Archsquared ===
-[[Subgroup]]: 4.9.49
+TE Mistunings (cents)
+⟨0.110, 1.241, 1.696, 1.033, -5.660]
+Complexity	1.068792
+Adjusted Error	2.926965 cents
+TE Error	0.846083 cents/octave
+Unison Vectors
+[-1, -1, -1, 0, 2⟩ (121:120)
+[2, 0, -2, -1, 1⟩ (176:175)
+[-3, -1, 1, 1, 1⟩ (385:384)
+[-1, 0, 3, -3, 1⟩ (1375:1372)
+[-2, -1, -2, 4, 0⟩ (2401:2400)
+[1, 0, 1, -4, 2⟩ (2420:2401)
-[[Comma list]]: 4096/3969
+Subsets
+q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
+</pre>
-{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}
+==== 4.6.5.7.11.13 ====
-Mapping generators: ~4, ~9/64
+<pre>
+Reduced Mapping
-[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 219.190
+	6	5	7	11	13
+[ ⟨	1	0	1	1	1	0	]
-[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
+⟨	0	16	2	5	9	23	] ⟩
-== 8.9.7 subgroup ==
+TE Generator Tunings (cents)
-=== Sixscared ===
+⟨2401.2305, 193.5378]
-Sixscared is a tuning which still maintains some consonance, while eviscerating the rules of conventional 12-tone harmony. The familiar major, minor and perfect intervals are nowhere to be found, and octaves are far and few between, so the seventh harmonic becomes the backbone of harmony. Approximating the harmonics 7, 8, 9, Sixscared is named for the classic dad joke: "Why was six scared? Because seven ate nine."
+TE Step Tunings (cents)
-[[Subgroup]]: 8.9.7
+⟨42.79107, 35.98524]
-[[Comma list]]: 64/63
+TE Tuning Map (cents)
+⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
-{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
+TE Mistunings (cents)
-: sval mapping generators: ~8, ~9
+⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]
-: [[gencom]]: [8 9/8; 64/63]
+Complexity	1.219191
+Adjusted Error	6.699599 cents
+TE Error	1.810487 cents/octave
+Unison Vectors
+[0, 1, -1, 0, 1, -1⟩ (66:65)
+[-1, -1, -1, 0, 2, 0⟩ (121:120)
+[1, 2, 0, 0, -1, -1⟩ (144:143)
+[2, 0, -2, -1, 1, 0⟩ (176:175)
+[-2, 1, 1, 1, 0, -1⟩ (105:104)
+[-3, -1, 1, 1, 1, 0⟩ (385:384)
+[-3, 0, 0, 1, 2, -1⟩ (847:832)
+[1, 3, -1, 0, 0, -2⟩ (864:845)
+[-1, 0, 3, -3, 1, 0⟩ (1375:1372)
-[[Optimal tuning]] ([[CTE]]): 1\[[3ed8]] = 1600.0, ~9/8 = 219.1898
+Subsets
+q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
+</pre>
-[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}
+==== 4.6.5.7.11.13.17 ====
+<pre>
-[[Badness]]: 0.0215 × 10<sup>-3</sup>
+Reduced Mapping
+	6	5	7	11	13	17
-= Fractional subgroup temperaments =
+[ ⟨	1	0	1	1	1	0	1	]
-== 2.5/3… subgroups ==
+⟨	0	16	2	5	9	23	13	] ⟩
-=== Magicaltet ===
-{{See also| Chromatic pairs #Magicaltet }}
+TE Generator Tunings (cents)
+⟨2400.4701, 193.4599]
+TE Step Tunings (cents)
+⟨43.39350, 35.55764]
+TE Tuning Map (cents)
+⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]
+TE Mistunings (cents)
+⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]
+Complexity	1.129881
+Adjusted Error	8.082725 cents
+TE Error	1.977443 cents/octave
+Unison Vectors
+[0, 1, -1, 0, 1, -1, 0⟩ (66:65)
+[1, 1, 1, -1, 0, 0, -1⟩ (120:119)
+[1, 2, 0, 0, -1, -1, 0⟩ (144:143)
+[-2, 1, 1, 1, 0, -1, 0⟩ (105:104)
+[-1, 2, 2, 0, 0, -1, -1⟩ (225:221)
+[-1, 1, 2, -2, 0, -1, 1⟩ (1275:1274)
-Magicaltet is related to [[supermagic]], [[superkleismic]], and [[magic]]. The tonic and the first three generator steps make a [[magical seventh chord]], hence the name.
+Subsets
+q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg
+</pre>
-[[Subgroup]]: 2.5/3.7.11
+==== 4.6.5.7.11.13.17.19 ====
+<pre>
-[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})
+Reduced Mapping
+	6	5	7	11	13	17	19
-{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
+[ ⟨	1	0	1	1	1	0	1	1	]
+⟨	0	16	2	5	9	23	13	14	] ⟩
-: mapping generators: ~2, ~5/3
+TE Generator Tunings (cents)
-{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
+⟨2399.9219, 193.3952]
-: [[gencom]]: [2 6/5; 100/99 385/384]
+TE Step Tunings (cents)
+⟨44.14256, 35.03670]
-[[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 877.343
+TE Tuning Map (cents)
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 877.351
+⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
+TE Mistunings (cents)
+⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]
+Complexity	1.058472
+Adjusted Error	8.712222 cents
+TE Error	2.050935 cents/octave
+Unison Vectors
+[0, 1, -1, 0, 1, -1, 0, 0⟩ (66:65)
+[-1, 0, 0, 1, 1, 0, 0, -1⟩ (77:76)
+[2, 1, -1, 0, 0, 0, 0, -1⟩ (96:95)
+[1, 1, 1, -1, 0, 0, -1, 0⟩ (120:119)
+[0, 1, 1, 1, -1, 0, 0, -1⟩ (210:209)
+[0, 0, 1, -2, 1, 0, 1, -1⟩ (935:931)
+[2, 0, -3, 1, 0, 0, -1, 1⟩ (2128:2125)
-{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
+Subsets
+q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh
+</pre>
-<nowiki/>* Wart for 5/3
+==== 4.6.5.7.11.13.17.19.23 ====
+<pre>
-[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
+Reduced Mapping
+	6	5	7	11	13	17	19	23
-=== Starlingtet ===
+[ ⟨	1	0	1	1	1	0	1	1	0	]
-{{See also | Chromatic pairs #Starlingtet }}
+⟨	0	16	2	5	9	23	13	14	28	] ⟩
-Starlingtet, the {{nowrap| 4 & 15 }} temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]]. The tonic and the first three generator steps make a [[starling tetrad]], hence the name.
+TE Generator Tunings (cents)
+⟨2399.3286, 193.5316]
-[[Subgroup]]: 2.5/3.7/3
+TE Step Tunings (cents)
-[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})
+⟨37.31613, 39.63311]
-{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
+TE Tuning Map (cents)
+⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
-: mapping generators: ~2, ~5/3
+TE Mistunings (cents)
+⟨-0.671, -5.449, 0.078, -1.839, -10.205, 10.699, 10.284, 11.258, -9.389]
+Complexity	1.115920
+Adjusted Error	9.502017 cents
+TE Error	2.100561 cents/octave
+Unison Vectors
+[0, 1, -1, 0, 1, -1, 0, 0, 0⟩ (66:65)
+[1, 0, 0, -1, 0, -1, 0, 0, 1⟩ (92:91)
+[0, -1, 1, 0, 0, 0, 0, -1, 1⟩ (115:114)
+[1, 1, 1, -1, 0, 0, -1, 0, 0⟩ (120:119)
+[2, 0, -2, -1, 1, 0, 0, 0, 0⟩ (176:175)
+[-3, -1, 1, 1, 1, 0, 0, 0, 0⟩ (385:384)
+[1, 0, -2, 1, 0, 0, 1, -1, 0⟩ (476:475)
+[1, 0, 0, -2, 1, 0, -1, 1, 0⟩ (836:833)
+[0, 0, 1, -2, 1, 0, 1, -1, 0⟩ (935:931)
+[1, -1, 0, 0, 0, 0, -2, 1, 1⟩ (874:867)
-{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
+Subsets
+q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii
+</pre>
-: [[gencom]]: [2 6/5; 126/125]
+== 4.9.25 subgroup ==
+=== Meansquared ===
+[[Subgroup]]: 4.9.25
-[[Optimal tuning]]s:
+[[Comma list]]: [[6561/6400]]
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 888.759
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 888.846
-{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}
+{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents
+Mapping generators: ~4, ~9/64
-==== Greeley ====
+[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
-{{See also| Chromatic pairs #Greeley }}
-Greeley is related to [[opossum]] as well as to [[nusecond]].
+[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
-[[Subgroup]]: 2.5/3.7/3.11/3
+== 4.9.49 subgroup ==
+=== Archsquared ===
+[[Subgroup]]: 4.9.49
-[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})
+[[Comma list]]: 4096/3969
-{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
+{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}
-{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}
+Mapping generators: ~4, ~9/64
-: [[gencom]]: [2 11/10; 121/120 126/125]
+[[Optimal tuning]] ([[CTE]]): ~9/4 = 1419.190
-[[Optimal tuning]]s:
+[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~11/10 = 155.696
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~11/10 = 155.776
-{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
+== 8.9.7 subgroup ==
+=== Sixscared ===
+Sixscared is a tuning which still maintains some consonance, while eviscerating the rules of conventional 12-tone harmony. The familiar major, minor and perfect intervals are nowhere to be found, and octaves are far and few between, so the seventh harmonic becomes the backbone of harmony. Approximating the harmonics 7, 8, 9, Sixscared is named for the classic dad joke: "Why was six scared? Because seven ate nine."
-<nowiki/>* Wart for 11/3
+[[Subgroup]]: 8.9.7
-[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents
+[[Comma list]]: 64/63
-==== Skateboard ====
+{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
-{{See also| Chromatic pairs #Skateboard }}
-Skateboard is related to [[thrasher]].
+: sval mapping generators: ~8, ~9
-[[Subgroup]]: 2.5/3.7/3.11.13/9
+: [[gencom]]: [8 9/8; 64/63]
-[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }})
+[[Optimal tuning]] ([[CTE]]): ~9/8 = 219.1898
-{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
+[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}
-{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}
+[[Badness]]: 0.0215 × 10<sup>-3</sup>
-: [[gencom]]: [2 6/5; 56/55 91/90 100/99]
+= Fractional subgroup temperaments =
+== 2.5/3.… subgroups ==
+=== Magicaltet ===
+{{See also| Chromatic pairs #Magicaltet }}
-[[Optimal tuning]]s:
+Magicaltet is related to [[keemic]], [[superkleismic]], and [[magic]]. The tonic and the first three generator steps make a [[magical seventh chord]], hence the name.
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 886.158
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 886.158
-{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}
+[[Subgroup]]: 2.5/3.7.11
-[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents
+[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})
-=== Gariberttet ===
+{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
-Gariberttet is the 2.5/3.7/3 [[Subgroup temperament families, relationships, and genes|altergene]] of [[sirius]].
+: mapping generators: ~2, ~5/3
-==== Gariberttet (2.5/3.7/3.13/11 subgroup) ====
+{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
-{{See also | Chromatic pairs #Gariberttet }}
+: [[gencom]]: [2 6/5; 100/99 385/384]
-Gariberttet can be described as the {{nowrap| 4 & 29 }} temperament in the 2.5/3.7/3.13/11 subgroup.
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 877.343
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 877.351
-[[Subgroup]]: 2.5/3.7/3.13/11
+{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
+: <nowiki/>* wart for 5/3
-[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})
+[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
-{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
+=== Starlingtet ===
+{{See also | Chromatic pairs #Starlingtet }}
-{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}
+Starlingtet, the {{nowrap| 4 & 15 }} temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]]. The tonic and the first three generator steps make a [[starling tetrad]], hence the name.
-: [[gencom]]: [2 13/11; 275/273 847/845]
+[[Subgroup]]: 2.5/3.7/3
-[[Optimal tuning]]s:
+[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})
-* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~13/11 = 293.679
-{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}
+{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
-<nowiki/>* Wart for 13/11
+: mapping generators: ~2, ~5/3
-[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
+{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
+: [[gencom]]: [2 6/5; 126/125]
-==== Indium ====
+[[Optimal tuning]]s:
-{{See also | Chromatic pairs #Indium }}
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 888.759
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 888.846
-Indium can be described as the {{nowrap| 8 & 33 }} temperament in the 2.5/3.7/3.11/3 subgroup.
+{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}
-[[Subgroup]]: 2.5/3.7/3.11/3
+[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents
-[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }})
+==== Greeley ====
+{{See also| Chromatic pairs #Greeley }}
-{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
+Greeley is related to [[opossum]] as well as to [[nusecond]].
-{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}
+[[Subgroup]]: 2.5/3.7/3.11/3
-: [[gencom]]: [2 12/11; 3025/3024 3125/3087]
+[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})
-[[Optimal tuning]]s:
+{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/11 = 146.978
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/11 = 147.010
-{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*<sup>†</sup> }}
+{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}
+: [[gencom]]: [2 11/10; 121/120 126/125]
-<nowiki/>* Wart for 7/3
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~11/10 = 155.696
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~11/10 = 155.776
-<sup>†</sup> Wart for 11/3
+{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
+: <nowiki/>* wart for 11/3
-[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
+[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents
-==== Ammon ====
+==== Skateboard ====
-{{See also| Chromatic pairs #Ammon }}
+{{See also| Chromatic pairs #Skateboard }}
-Ammon can be described as the {{nowrap| 8 & 29 }} temperament in the 2.5/3.7/3.11/3.13/3 subgroup. It extends [[tridec]], and is related to [[ammonite]]. It is generated by a semidiminished fourth, hence the old name ''semidim'', which has been rejected since 2025 to avoid confusion with another temperament of the same name.
+Skateboard is related to [[thrasher]].
-[[Subgroup]]: 2.5/3.7/3.11/3.13/3
+[[Subgroup]]: 2.5/3.7/3.11.13/9
-[[Comma list]]: [[121/120]] ({{monzo| -3 -1 0 2 }}), [[169/168]] ({{monzo| -3 0 -1 0 2 }}), [[275/273]] ({{monzo| 0 2 -1 1 -1 }})
+[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }})
-{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
+{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
-{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}
+{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}
+: [[gencom]]: [2 6/5; 56/55 91/90 100/99]
-: [[gencom]]: [2 13/10; 121/120 169/168 275/273]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/10 = 453.121
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 886.158
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/10 = 453.242
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 886.158
-{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}
+{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}
-[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
+[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents
-=== Sentry ===
+=== Gariberttet ===
-{{See also | Chromatic pairs #Sentry }}
+Gariberttet is the 2.5/3.7/3 [[Subgroup temperament families, relationships, and genes|altergene]] of [[sirius]].
-Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
+==== Gariberttet (2.5/3.7/3.13/11 subgroup) ====
+{{See also | Chromatic pairs #Gariberttet }}
-[[Subgroup]]: 2.5/3.9/7
+Gariberttet can be described as the {{nowrap| 4 & 29 }} temperament in the 2.5/3.7/3.13/11 subgroup. Extensions to the full 7-, 11-, and 13-limits include [[quasitemp]].
-[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})
+[[Subgroup]]: 2.5/3.7/3.13/11
-{{Mapping|legend=2| 1 0 0 | 0 2 1 }}
+[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})
-{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
+{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
-: [[gencom]]: [2 9/7; 245/243]
+{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}
+: [[gencom]]: [2 13/11; 275/273 847/845]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~13/11 = 293.679
-{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145*, 166<sup>†</sup>, 197*<sup>†</sup>, 215<sup>†</sup>, 264*<sup>†</sup> }}
+{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}
+: <nowiki/>* wart for 13/11
-<nowiki/>* Wart for 5/3
+[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
-<sup>†</sup> Wart for 9/7
+==== Indium ====
+{{See also | Chromatic pairs #Indium }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
+Indium can be described as the {{nowrap| 8 & 33 }} temperament in the 2.5/3.7/3.11/3 subgroup.
-=== Marveltwintri ===
+[[Subgroup]]: 2.5/3.7/3.11/3
-{{See also| Chromatic pairs #Marveltwintri }}
-Marveltwintri can be described as the {{nowrap| 3 & 4 }} temperament in the 2.5/3.13/9 subgroup. The tonic and the first two generator steps make a [[marveltwin triad]], hence the name.
+[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }})
-[[Subgroup]]: 2.5/3.13/9
+{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
-[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})
+{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}
+: [[gencom]]: [2 12/11; 3025/3024 3125/3087]
-{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/11 = 146.978
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/11 = 147.010
-{{Mapping|legend=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}
+{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*<sup>†</sup> }}
+: <nowiki/>* wart for 7/3
+: <sup>†</sup> wart for 11/3
-: [[gencom]]: [2 6/5; 325/324]
+[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
-[[Optimal tuning]]s:
+==== Ammon ====
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 886.886
+{{See also| Chromatic pairs #Ammon }}
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 886.861
-{{Optimal ET sequence|legend=1| 3, 4, 11, 15, 19, 34, 53, 87, 140 }}
+Ammon can be described as the {{nowrap| 8 & 29 }} temperament in the 2.5/3.7/3.11/3.13/3 subgroup. It extends [[tridec]], and is related to [[ammonite]]. It is generated by a semidiminished fourth, hence the old name ''semidim'', which has been rejected since 2025 to avoid confusion with another temperament of the same name.
-[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
+[[Subgroup]]: 2.5/3.7/3.11/3.13/3
-== 2.….7/3… subgroups ==
+[[Comma list]]: [[121/120]] ({{monzo| -3 -1 0 2 }}), [[169/168]] ({{monzo| -3 0 -1 0 2 }}), [[275/273]] ({{monzo| 0 2 -1 1 -1 }})
-=== Guanyintet ===
-{{See also | Chromatic pairs #Guanyintet }}
-Guanyintet, the {{nowrap| 4 & 9 }} temperament in the 2.5.7/3.11/3 subgroup, is related to [[guanyin]] as well as to [[orwell]]. The tonic and the first three generator steps make a [[guanyin tetrad]], hence the name.
+{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
-[[Subgroup]]: 2.5.7/3.11/3
+{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}
+: [[gencom]]: [2 13/10; 121/120 169/168 275/273]
-[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -1 }})
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/10 = 453.121
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/10 = 453.242
-{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}
+{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}
-: mapping generators: ~2, ~12/7
+[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
-{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}
+=== Sentry ===
+{{See also | Chromatic pairs #Sentry }}
-: [[gencom]]: [2 7/6; 176/175 540/539]
+Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
-[[Optimal tuning]]s:
+[[Subgroup]]: 2.5/3.9/7
-* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~12/7 = 929.545
-* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~12/7 = 929.907
-{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}
+[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})
-<nowiki/>* wart for 7/3
+{{Mapping|legend=2| 1 0 0 | 0 2 1 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents
+{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
+: [[gencom]]: [2 9/7; 245/243]
-==== Laz ====
+[[Optimal tuning]]s:
-{{See also | Chromatic pairs #Laz }}
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902
-Laz is related to [[avalokita]] as well as to [[winston]].
+{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145*, 166<sup>†</sup>, 197*<sup>†</sup>, 215<sup>†</sup>, 264*<sup>†</sup> }}
+: <nowiki/>* wart for 5/3
+: <sup>†</sup> wart for 9/7
+[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
+=== Marveltwintri ===
+{{See also| Chromatic pairs #Marveltwintri }}
-[[Subgroup]]: 2.5.7/3.11/3.13/3
+Marveltwintri can be described as the {{nowrap| 3 & 4 }} temperament in the 2.5/3.13/9 subgroup. The tonic and the first two generator steps make a [[marveltwin triad]], hence the name. [[Cata]] is a very natural extension of this temperament to the [[2.3.5.13 subgroup|2.3.5.13-subgroup]].
-[[Comma list]]: [[144/143]] ({{monzo| 4 0 0 -1 -1 }}), [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[196/195]] ({{monzo| 2 -1 2 0 -1 }}
+[[Subgroup]]: 2.5/3.13/9
-{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
+[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})
-{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}
+{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
-: [[gencom]]: [2 7/6; 144/143 176/175 196/195]
+{{Mapping|legend=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}
+: [[gencom]]: [2 6/5; 325/324]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/7 = 930.598
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 882.886
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/7 = 930.700
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 882.861
-{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 156c*†, 205c*† }}
+{{Optimal ET sequence|legend=1| 3, 4, 11, 15, 19, 34, 53, 87, 140 }}
-<nowiki/>* wart for 7/3
+[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
-† wart for 11/3
+== 2.….7/3.… subgroups ==
+=== Guanyintet ===
+{{See also | Chromatic pairs #Guanyintet }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents
+Guanyintet, the {{nowrap| 4 & 9 }} temperament in the 2.5.7/3.11/3 subgroup, is the main rank-2 chain of [[guanyin]] and a restriction of [[orwell]]. It is defined by tempering out [[1728/1715]] ({{S|6/S7}}) and [[540/539]] (S12/S14), which imply [[176/175]] (S8/S10) as well as S11/S15 being tempered out. The tonic and the first three generator steps make a [[guanyin tetrad]], hence the name.
-=== Kryptonite ===
+[[Subgroup]]: 2.5.7/3.11/3
-{{See also| Chromatic pairs #Kryptonite }}
-Kryptonite is related to [[krypton]].
+[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -1 }})
-[[Subgroup]]: 2.5.7/3.11/3.13/3
+{{Mapping|legend=2| 1 0 1 3 | 0 -3 1 -5 }}
+: mapping generators: ~2, ~7/6
-[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 78/77 ({{monzo| 1 0 -1 -1 1 }}), 91/90 ({{monzo| -1 -2 1 0 1 }})
+{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}
+: [[gencom]]: [2 7/6; 176/175 540/539]
-{{Mapping|legend=2| 1 2 1 2 2 | 0 3 2 -1 1 }}
+[[Optimal tuning]]s:
+* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~7/6 = 270.455
+* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~7/6 = 270.093
-: mapping generators: ~2, ~13/12
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}
+: <nowiki/>* wart for 7/3
-{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents
-: [[gencom]]: [2 13/12; 56/55 78/77 91/90]
+==== Tridecimal guanyintet ====
+Guanyintet can extend to the 13th harmonic by the equivalences ([[12/11]])<sup>3</sup> = [[13/10]] and ([[15/14]])<sup>3</sup> = [[16/13]], therefore tempering out {S11/S12/S14/S15}. However, note that it is not supported by the 31 & 53 orwell extension dubbed "tridecimal orwell", but instead the less accurate [[winston]] (22f & 31), as orwell prefers slightly sharper tunings than guanyintet. [[40edo]] remains an excellent tuning.
-[[Optimal tuning]]s:
+[[Subgroup]]: 2.5.7/3.11/3.13
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/12 = 130.945
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/12 = 132.428
-{{Optimal ET sequence|legend=1| 1, …, 8, 9 }}
+[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 0 }}), [[540/539]] ({{monzo| 2 1 -2 -1 0 }}), [[1573/1568]] ({{monzo| -5 0 -2 2 1 }})
-[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
+{{Mapping|legend=2| 1 0 1 3 1 | 0 -3 1 -5 12 }}
+: mapping generators: ~2, ~12/7
-=== Kiribati ===
+[[Optimal tuning]]s:
-{{See also| Chromatic pairs #Kiribati }}
+* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~7/6 = 270.152
+* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~7/6 = 270.218
-Kiribati is related to [[nakika]] as well as to [[octacot]].
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 71, 111, 151, 262c*}} <small> using subgroup TE </small>
+: <nowiki/>* wart for 7/3
-[[Subgroup]]: 2.9/5.7/3.11/9
+Badness (Sintel): 0.329
-[[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }})
+==== Laz ====
+{{See also | Chromatic pairs #Laz }}
-{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
+Laz is related to [[avalokita]] as well as to [[winston]].
+[[Subgroup]]: 2.5.7/3.11/3.13/3
-: mapping generators: ~2, ~21/20
+[[Comma list]]: [[144/143]] ({{monzo| 4 0 0 -1 -1 }}), [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[196/195]] ({{monzo| 2 -1 2 0 -1 }}
-{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
+{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
-: [[gencom]]: [2 21/20; 100/99 245/242]
+{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}
+: [[gencom]]: [2 7/6; 144/143 176/175 196/195]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~21/20 = 87.776
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/7 = 930.598
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~21/20 = 87.892
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/7 = 930.700
-{{Optimal ET sequence|legend=1| 13, 14, 27, 41 }}
+{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 156c*†, 205c*† }}
+: <nowiki/>* wart for 7/3
+: † wart for 11/3
-[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents
-=== Mothwelltri ===
+=== Kryptonite ===
-{{See also| Chromatic pairs #Mothwelltri }}
+{{See also| Chromatic pairs #Kryptonite }}
-Mothwelltri, the {{nowrap| 1 & 4 }} temperament in the 2.7/3.11 subgroup, is related to [[orwell]]. The tonic and the first two generator steps make a [[mothwellsmic triad]], hence the name.
+Kryptonite is related to [[krypton]].
-[[Subgroup]]: 2.7/3.11
+[[Subgroup]]: 2.5.7/3.11/3.13/3
-[[Comma list]]: [[99/98]] ({{monzo| -1 -2 1 }})
+[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 78/77 ({{monzo| 1 0 -1 -1 1 }}), 91/90 ({{monzo| -1 -2 1 0 1 }})
-{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
+{{Mapping|legend=2| 1 2 1 2 2 | 0 3 2 -1 1 }}
+: mapping generators: ~2, ~13/12
-: mapping generators: ~2, ~7/3
+{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}
+: [[gencom]]: [2 13/12; 56/55 78/77 91/90]
-{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
-: [[gencom]]: [2 7/6; 99/98]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~7/6 = 273.695
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/12 = 130.945
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~7/6 = 273.174
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/12 = 132.428
-{{Optimal ET sequence|legend=1| 4, 9, 13, 22, 79 }}
+{{Optimal ET sequence|legend=1| 1, …, 8, 9 }}
-[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents
+[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
-== 2.….9/7… subgroups ==
+=== Kiribati ===
-=== Marveltri ===
+{{See also| Chromatic pairs #Kiribati }}
-{{See also| Chromatic pairs #Marveltri }}
-Marveltri, the {{nowrap| 3 & 13 }} temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed {{nowrap| 22 & 47 }} temperament. The tonic and the first two generator steps make a [[marvel triad]], hence the name.
+Kiribati is related to [[nakika]] as well as to [[octacot]].
-[[Subgroup]]: 2.5.9/7
+[[Subgroup]]: 2.9/5.7/3.11/9
-[[Comma list]]: 225/224 ({{monzo| -5 2 1 }})
+[[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }})
-{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
+{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
+: mapping generators: ~2, ~21/20
-: mapping generators: ~2, ~5
+{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
+: [[gencom]]: [2 21/20; 100/99 245/242]
-{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}
-: [[gencom]]: [2 5; 225/224]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 384.208
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~21/20 = 87.776
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 383.638
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~21/20 = 87.892
-{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122, 269c* }}
+{{Optimal ET sequence|legend=1| 13, 14, 27, 41 }}
-<nowiki/>* Wart for 9/7
+[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
-[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
+=== Mothwelltri ===
+{{See also| Chromatic pairs #Mothwelltri }}
-==== Sulis ====
+Mothwelltri, the {{nowrap| 1 & 4 }} temperament in the 2.7/3.11 subgroup, is related to [[orwell]]. The tonic and the first two generator steps make a [[mothwellsmic triad]], hence the name.
-Sulis is related to [[minerva]] and [[würschmidt]].
-[[Subgroup]]: 2.5.9/7.11/9
+[[Subgroup]]: 2.7/3.11
-[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})
+[[Comma list]]: [[99/98]] ({{monzo| -1 -2 1 }})
-{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]
+{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
+: mapping generators: ~2, ~7/3
+{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
+: [[gencom]]: [2 7/6; 99/98]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 386.617
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~7/6 = 273.695
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 386.558
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~7/6 = 273.174
-{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
+{{Optimal ET sequence|legend=1| 4, 9, 13, 22, 79 }}
-[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
+[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents
-== 2.….7/5… subgroups ==
+== 2.….9/7.… subgroups ==
+=== Marveltri ===
+{{See also| Chromatic pairs #Marveltri }}
-=== Hydrothermal ===
+Marveltri, the {{nowrap| 3 & 13 }} temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed {{nowrap| 22 & 47 }} temperament. The tonic and the first two generator steps make a [[marvel triad]], hence the name.
-A tuning whose distinctively sharp (but still consonant) fifth, and flat (but still consonant) octave, lend it a mysterious, heavy atmosphere. The 6-tone (hexatonic) MOS is melodically interesting and flavorful. The 18-tone MOS is a useful 'chromatic' scale for taking subsets of.
-[[Subgroup]]: 2.3.7/5
+[[Subgroup]]: 2.5.9/7
-[[Comma list]]: [[50/49]]
+[[Comma list]]: 225/224 ({{monzo| -5 2 1 }})
-{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
+{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
+: mapping generators: ~2, ~5
-[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
+{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}
+: [[gencom]]: [2 5; 225/224]
-[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 384.208
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 383.638
-=== Edson ===
+{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122, 269c* }}
-Edson is the 2.3.7/5 subgroup temperament tempering out [[5120/5103]].
+: <nowiki/>* wart for 9/7
-==== Edson (2.3.7/5.11/5.13/5 subgroup) ====
+[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
-{{See also| Chromatic pairs #Edson }}
-Edson is related to [[pele]] and [[andromeda]].
+==== Sulis ====
+Sulis is related to [[minerva]] and [[würschmidt]].
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+[[Subgroup]]: 2.5.9/7.11/9
-[[Comma list]]: [[196/195]] = {{monzo| 2 -1 2 0 -1 }}, [[352/351]] = {{monzo| 5 -3 0 1 -1 }}, [[364/363]] = {{monzo| 2 -1 1 -2 1 }}
+[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})
-{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
+{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]
-: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 386.617
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 386.558
-{{Mapping|legend=3| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }}
+{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
-: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363]
+[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
-[[Optimal tuning]]s:
+== 2.….7/5.… subgroups ==
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~3/2 = 703.4398
+=== Hydrothermal ===
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~3/2 = 703.414
+A tuning whose distinctively sharp (but still consonant) fifth, and flat (but still consonant) octave, lend it a mysterious, heavy atmosphere. The 6-tone (hexatonic) MOS is melodically interesting and flavorful. The 18-tone MOS is a useful 'chromatic' scale for taking subsets of.
-{{Optimal ET sequence|legend=1| 12, 17, 29 }}
+[[Subgroup]]: 2.3.7/5
-[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
+[[Comma list]]: [[50/49]]
-==== Haumea ====
+{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
-{{See also| Chromatic pairs #Haumea }}
-Related temperaments include [[#Bridgetown|bridgetown]], [[namaka]], [[hemigari]], [[#Barbados|barbados]], and [[parizekmic]].
+[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
-[[Comma list]]: [[352/351]], [[676/675]], [[847/845]]
+=== Argentic ===
+Argentic is the 2.3.7/5 subgroup temperament tempering out [[5120/5103]].
-{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
+[[Subgroup]]: 2.3.7/5
-{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}
+[[Comma list]]: [[5120/5103]] = {{monzo| 10 -6 -1 }}
-: [[gencom]]: [2 15/13; 352/351 676/675 847/845]
+{{Mapping|legend=2| 1 0 10 | 0 1 -6 }}
+: mapping generators: ~2, ~3
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~3/2 = 702.792
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~3/2 = 702.830
-{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
+{{Optimal ET sequence|legend=1| 12, 29, 41, 70, 321, 391, 461, 531, 601 }}
+<small> based on subgroup TE </small>
-[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents
+Badness (Sintel): 0.119
-=== Historical ===
+==== Edson (2.3.7/5.11/5.13/5 subgroup) ====
-{{distinguish|Historical temperaments}}
+{{See also| Chromatic pairs #Edson }}
-{{distinguish|History (temperament)}}, which is the rank-3 version of this temperament in the full 13-limit.
-Historical is essentially an analogue of [[miracle]] that splits [[4/3]] in six rather than [[3/2]]. It tempers out the comma S10/S11 = [[4000/3993]] to set [[11/10]] equal to one-third of 4/3, and S13/S15 = [[676/675]] to equate [[15/13]] to one-half of 4/3, and tempers out S21 = [[441/440]] to split 11/10 into two instances of [[22/21]]~[[21/20]]. [[Sextilifourths]] adds the [[schismic]] mapping of prime 5 (reached by eight fourths) to complete the 13-limit.
+Edson is related to [[pele]] and [[andromeda]].
 [[Subgroup]]: 2.3.7/5.11/5.13/5
-[[Comma list]]: 364/363, 441/440, 1001/1000
+[[Comma list]]: [[196/195]] = {{monzo| 2 -1 2 0 -1 }}, [[352/351]] = {{monzo| 5 -3 0 1 -1 }}, [[364/363]] = {{monzo| 2 -1 1 -2 1 }}
-{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
+{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
+: mapping generators: ~2, ~3
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
+{{Mapping|legend=3| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }}
+: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363]
-{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~3/2 = 703.4398
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~3/2 = 703.414
-[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
+{{Optimal ET sequence|legend=1| 12, 17, 29 }}
-=== Terrain ===
+[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
-{{Redirect|Terrain|the scale|Terrain (scale)}}
-{{See also| Chromatic pairs #Terrain }}
-Terrain, the 6 &amp; 21 temperament in the 2.7/5.9/5 subgroup, is related to [[domain (temperament)|domain]]. It is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1–7/5–9/5 and 1–9/7–9/5 chords are characteristic.
+==== Haumea ====
+{{See also| Chromatic pairs #Haumea }}
-[[Subgroup]]: 2.7/5.9/5
+Related temperaments include [[#Bridgetown|bridgetown]], [[namaka]], [[hemigari]], [[#Barbados|barbados]], and [[parizekmic]].
-[[Comma list]]: [[250047/250000]]
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-{{Mapping|legend=2| 3 1 3 | 0 1 -1 }}
+[[Comma list]]: [[352/351]], [[676/675]], [[847/845]]
-{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
+{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
-: [[gencom]]: [63/50 10/9; 250047/250000]
+{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}
+: [[gencom]]: [2 15/13; 352/351 676/675 847/845]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
-{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
+{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents
-=== Tridec ===
+=== Historical ===
-{{See also| Chromatic pairs #Tridec }}
+{{distinguish|Historical temperaments}}
-{{See also| Non-over-1 temperament #Tridec }}
+{{distinguish|History (temperament)}}, which is the rank-3 version of this temperament in the full 13-limit.
-Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[#Petrtri]].
+Historical is essentially an analogue of [[miracle]] that splits [[4/3]] in six rather than [[3/2]]. It tempers out the comma S10/S11 = [[4000/3993]] to set [[11/10]] equal to one-third of 4/3, and S13/S15 = [[676/675]] to equate [[15/13]] to one-half of 4/3, and tempers out S21 = [[441/440]] to split 11/10 into two instances of [[22/21]]~[[21/20]]. [[Sextilifourths]] adds the [[schismic]] mapping of prime 5 (reached by eight fourths) to complete the 13-limit.
-[[Subgroup]]: 2.7/5.11/5.13/5
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-[[Comma list]]: [[847/845]], [[1001/1000]]
+[[Comma list]]: 364/363, 441/440, 1001/1000
-{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
+{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
-{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
-: [[gencom]]: [2 13/10; 847/845 1001/1000]
+{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.556
+[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
-{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
+=== Terrain ===
+{{Redirect|Terrain|the scale|Terrain (scale)}}
+{{See also| Chromatic pairs #Terrain }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents
+Terrain, the 6 &amp; 21 temperament in the 2.7/5.9/5 subgroup, is related to [[domain (temperament)|domain]]. It is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1–7/5–9/5 and 1–9/7–9/5 chords are characteristic.
-== 2.….11/5… subgroups ==
+[[Subgroup]]: 2.7/5.9/5
-=== Petrtri ===
+[[Comma list]]: [[250047/250000]]
-{{See also| Chromatic pairs #Petrtri }}
-{{See also| 5L 3s/Temperaments #Petrtri }}
-Petrtri can be described as 3 &amp; 5 temperament in the 2.11/5.13/5 subgroup.
+{{Mapping|legend=2| 3 1 3 | 0 1 -1 }}
-[[Subgroup]]: 2.11/5.13/5
+{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
+: [[gencom]]: [63/50 10/9; 250047/250000]
-[[Comma list]]: [[2200/2197]]
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
-{{Mapping|legend=2| 1 0 1| 0 3 1 }}
+{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
-{{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
-: [[gencom]]: [2 13/10; 2200/2197]
+=== Tridec ===
+{{See also| Chromatic pairs #Tridec }}
+{{See also| Non-over-1 temperament #Tridec }}
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 455.012
+Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[#Petrtri]].
-{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
+[[Subgroup]]: 2.7/5.11/5.13/5
-[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents
+[[Comma list]]: [[847/845]], [[1001/1000]]
-==== Bridgetown ====
+{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
-{{See also| Chromatic pairs #Bridgetown }}
-Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[#Haumea|haumea]] and [[#Barbados|barbados]].
+{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}
+: [[gencom]]: [2 13/10; 847/845 1001/1000]
-[[Subgroup]]: 2.3.11/5.13/5
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.556
-[[Comma list]]: [[352/351]], [[676/675]]
+{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
-{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents
-{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}
+==== Naiadec ====
+[[Subgroup]]: 2.7/5.11/5.13/5.17/5
-: [[gencom]]: [2 15/13; 352/351 676/675]
+[[Comma list]]: [[170/169]], [[221/220]], [[847/845]]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
+{{Mapping|legend=2| 1 2 0 1 1 | 0 -4 3 1 2 }}
-{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
+{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 1/4 | 0 0 0 -4 3 1 2 }}
+: [[gencom]]: [2 13/10; 170/169 221/220 847/845]
-[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.882
-=== Hypnosis ===
+{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 95<sup>t</sup>, 124<sup>t</sup> }}
-Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
+: <sup>t</sup> wart for 17/5
-[[Subgroup]]: 2.3.7.11/5.13
+[[Tp tuning #T2 tuning|RMS error]]: 0.7521 cents
-[[Comma list]]: 169/168, 540/539, 729/728
+== 2.….11/5.… subgroups ==
+=== Petrtri ===
+{{See also| Chromatic pairs #Petrtri }}
+{{See also| 5L 3s/Temperaments #Petrtri }}
-{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
+Petrtri can be described as 3 &amp; 5 temperament in the 2.11/5.13/5 subgroup.
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
+[[Subgroup]]: 2.11/5.13/5
-{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
+[[Comma list]]: [[2200/2197]]
-[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
+{{Mapping|legend=2| 1 0 1| 0 3 1 }}
-== 2.….11/7… subgroups ==
+{{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}
-=== Pepperoni ===
+: [[gencom]]: [2 13/10; 2200/2197]
-{{Main| Parapyth }}
-{{See also| Chromatic pairs #Pepperoni }}
-Pepperoni is generated by a fifth and can be described as the 5 &amp; 12 temperament in the 2.3.11/7.13/7 subgroup. It is the single-chain retraction of [[parapyth]]. The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 455.012
-[[Subgroup]]: 2.3.11/7.13/7
+{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
-[[Comma list]]: 352/351, 364/363
+[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents
-{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
+==== Bridgetown ====
+{{See also| Chromatic pairs #Bridgetown }}
-{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
+Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[#Haumea|haumea]] and [[#Barbados|barbados]].
-: [[gencom]]: [2 3/2; 352/351 364/363]
+[[Subgroup]]: 2.3.11/5.13/5
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856
+[[Comma list]]: [[352/351]], [[676/675]]
-{{Optimal ET sequence|legend=1| 5, 7, 12f, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*<sup>†</sup> }}
+{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
-<nowiki />* Wart for 11/7
+{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}
+: [[gencom]]: [2 15/13; 352/351 676/675]
-<sup>†</sup> Wart for 13/7
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
-[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
+{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
-== 2.….13/5… subgroups ==
+[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
-=== Barbados ===
-The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.
-[[Subgroup]]: 2.3.13/5
+=== Hypnosis ===
+Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Alphatricot family #Alphatricot|alphatricot]]
-[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
+[[Subgroup]]: 2.3.7.11/5.13
-[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
+[[Comma list]]: 169/168, 540/539, 729/728
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
+{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
-{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
-[[Badness]]: 0.002335
+{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
-; Music
+[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
-* [http://micro.soonlabel.com/gene_ward_smith/Others/Sevish/Sevish%20-%20Desert%20Island%20Rain.mp3 ''Desert Island Rain''] in 313edo tuned Barbados[9], by [https://soundcloud.com/sevish/desert-island-rain Sevish]
-==== Tobago ====
+=== Trisect ===
-{{See also| Chromatic pairs #Tobago }}
+Trisect divides every Pythagorean interval into three, and is the much more accurate subgroup restriction of [[Augmented family #Trisected|trisected]].
+Extending this temperament to the full [[11-limit|11-]], [[13-limit|13-]], or [[17-limit]] through [[portent]] or [[landscape]] results in the [[weak extension]] known as [[tritikleismic]].
+[[Subgroup]]: 2.3.7.11/5
+[[Comma list]]: 1029/1024, 4000/3993
+{{Mapping|legend=2| 3 0 10 5 | 0 3 -1 -1 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.742
+{{Optimal ET sequence|legend=1| 15, 21, 36, 123, 159, 195, 231 }}
+[[Tp tuning #T2 tuning|RMS error]]: ???
+==== 2.3.7.11/5.13 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13
+[[Comma list]]: 1029/1024, 1575/1573, 2080/2079
-Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
+{{Mapping|legend=2| 3 0 10 5 0 | 0 3 -1 -1 7 }}
-[[Subgroup]]: 2.3.11.13/5
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.918
-[[Comma list]]: [[243/242]], [[676/675]]
+{{Optimal ET sequence|legend=1| 15, 21f, 36, 87, 123, 159 }}
-{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}
+[[Tp tuning #T2 tuning|RMS error]]: ???
-{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}
+==== 2.3.7.11/5.13.17 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13.17
-: [[gencom]]: [55/39 15/13; 243/242 676/675]
+[[Comma list]]: 273/272, 833/832, 1575/1573, 2080/2079
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
+{{Mapping|legend=2| 3 0 10 5 0 -2 | 0 3 -1 -1 7 9 }}
-{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.820
-[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123, 159 }}
-==== Pakkanian hemipyth ====
+[[Tp tuning #T2 tuning|RMS error]]: ???
-[[Subgroup]]: 2.3.11.13/5.17
+===== Trisector =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19
-[[Comma list]]: 221/220, 243/242, 289/288
+[[Comma list]]: 210/209, 273/272, 286/285, 595/594, 2080/2079
-{{Mapping|legend=2| 2 0 -1 -2 5 | 0 2 5 3 2 }}
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 | 0 3 -1 -1 7 9 3 }}
-[[Optimal tuning]]s:
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.894
-* [[Tp tuning|subgroup CTE]]: ~17/12 = 1\2, ~26/15 = 950.7656 (~15/13 = 249.2344)
-* [[Tp tuning|subgroup CWE]]: ~17/12 = 1\2, ~26/15 = 950.6011 (~15/13 = 249.3989)
-{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123h, 159h }}
+[[Tp tuning #T2 tuning|RMS error]]: ???
+===== 2.3.7.11/5.13.17.19.23 subgroup =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19.23
+[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 595/594, 2080/2079
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 12 | 0 3 -1 -1 7 9 3 1 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 634.038
+{{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
+[[Tp tuning #T2 tuning|RMS error]]: ???
+===== 2.3.7.11/5.13.17.19.23.29 subgroup =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19.23.29
+[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 320/319, 595/594, 2080/2079
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 12 13 | 0 3 -1 -1 7 9 3 1 1 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~29/23 = 1\3, ~13/9 = 634.102
+{{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
+[[Tp tuning #T2 tuning|RMS error]]: ???
+== 2.….11/7.… subgroups ==
+=== Blackweed ===
+Blackweed is a [[restriction]] of undecimal [[blackwood]] as it tempers out 256/243 alike but in the 2.3.11/7 subgroup. 20edo is close to the optimum, which has 4\20 as the period and 420{{c}} as the generator.
+[[Subgroup]]: 2.3.11/7
+[[Comma list]]: {{monzo| 8 -5 }} (256/243)
+{{Mapping|legend=2| 5 8 0 | 0 0 1 }}
+: mapping generators: ~9/8, ~11/7
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[WE]]: ~8/7 = 238.851{{c}}, ~11/7 = 782.457{{c}}
+: [[error map]]: {{val| -5.746 +8.852 -0.035 }}
+* [[Tp tuning|subgroup]] [[CWE]]: ~8/7 = 240.000{{c}}, ~11/7 = 784.967{{c}}
+: error map: {{val| 0.000 +18.045 +2.475 }}
+{{Optimal ET sequence|legend=1| 15, 20, 35b, 55b }}
+=== Pepperoni ===
+{{Main| Parapyth }}
+{{See also| Chromatic pairs #Pepperoni }}
+Pepperoni is generated by a fifth and can be described as the 5 &amp; 12 temperament in the 2.3.11/7.13/7 subgroup. It is the single-chain retraction of [[parapyth]]. The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
+[[Subgroup]]: 2.3.11/7.13/7
+[[Comma list]]: 352/351, 364/363
+{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
+{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
+: [[gencom]]: [2 3/2; 352/351 364/363]
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856
+{{Optimal ET sequence|legend=1| 5, 7, 12f, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*<sup>†</sup> }}
+: <nowiki />* wart for 11/7
+: <sup>†</sup> wart for 13/7
+[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
+== 2.….13/5.… subgroups ==
+=== Barbados ===
+The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.
+[[Subgroup]]: 2.3.13/5
+[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
+[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
+{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
+[[Badness]]: 0.002335
+; Music
+* [http://micro.soonlabel.com/gene_ward_smith/Others/Sevish/Sevish%20-%20Desert%20Island%20Rain.mp3 ''Desert Island Rain''] in 313edo tuned Barbados[9], by [https://soundcloud.com/sevish/desert-island-rain Sevish]
+==== Tobago ====
+{{See also| Chromatic pairs #Tobago }}
+Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
+[[Subgroup]]: 2.3.11.13/5
+[[Comma list]]: [[243/242]], [[676/675]]
+{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}
+{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}
+: [[gencom]]: [55/39 15/13; 243/242 676/675]
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
+{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents
+==== Pakkanian hemipyth ====
+[[Subgroup]]: 2.3.11.13/5.17
+[[Comma list]]: 221/220, 243/242, 289/288
+{{Mapping|legend=2| 2 0 -1 -2 5 | 0 2 5 3 2 }}
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup CTE]]: ~17/12 = 1\2, ~26/15 = 950.7656 (~15/13 = 249.2344)
+* [[Tp tuning|subgroup CWE]]: ~17/12 = 1\2, ~26/15 = 950.6011 (~15/13 = 249.3989)
+{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}
+: <nowiki />* wart for 13/5
+=== Oceanfront ===
+Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]
+[[Subgroup]]: 2.3.7.13/5
+[[Comma list]]: 64/63, 91/90
+{{Mapping|legend=2| 1 0 6 -5 | 0 1 -2 4 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
+{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}
+[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
+Scales: [[Oceanfront scales]]
+=== Seventeen-cot ===
+Seventeen-cot is a rank-2 temperament in the 2.3.13/5 and 2.3.11/5.13/5 subgroups. It tempers out the [[Tendoartisma]] in the 2.3.13/5 subgroup. It can be generated with a ~2/1 octave and a ~2250/2197 or ~169/165 generator which is a 17th of a ~3/2 perfect fifth. It can be described as the 29 & 146 temperament in these subgroups.
+====2.3.13/5 subgroup====
+Comma basis: {{monzo| -6 -11 17 }} (2.3.13/5)
+edo join: 29 & 146
+{{Mapping|legend=2| 1 1 1 | 0 17 11 }}
+: mapping generators: ~2, ~2250/2197
+{{Todo|inline=1|correct maths|comment=Optimal tunings and error maps showed below is not yet precise enough.}}
+Optimal tunings:
+* WE: ~2 = 1200.000{{c}}, ~2250/2197 = 41.291{{c}}
+: error map: {{val| +0.000 +0.001 -0.007}}
+* CWE: ~2 = 1200.000{{c}}, ~2250/2197 = 41.292{{c}}
+: error map: {{val| +0.000 +0.001 -0.007}}
+edos: 29, 465, 494, 436, 523, 407, 378, 349, 30[-3], 28[+3], 320, 291, 59[-3], 262
+Badness (Sintel): 0.064
+====2.3.11/5.13/5 subgroup====
+Comma basis: 225000/224939, 43940/43923
+edo join: 29 & 146
+{{Mapping|legend=2| 1 1 1 1 | 0 17 4 11 }}
+: mapping generators: ~2, ~169/165
+Optimal tunings:
+* WE: ~2 = 1199.993{{c}}, ~169/165 = 41.292{{c}}
+: error map: {{val| -0.007 -0.000 +0.157 -0.010}}
+* CWE: ~2 = 1200.000{{c}}, ~169/165 = 41.292{{c}}
+: error map: {{val| +0.000 +0.005 +0.163 -0.005}}
+edos: 29, 465, 494, 436, 523, 407, 378, 349, 320, 291, 30[-3], 262, 28[+3], 233
+Badness (Sintel): 0.080
+== 2.….49/5.… subgroups ==
+=== Direct breedsmic ===
+Related temperament: [[hemithirds]], [[newt]]
+[[Subgroup]]: 2.3.49/5
+[[Comma list]]: 2401/2400
+{{Mapping|legend=2| 1 1 3 | 0 2 1 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966
+{{Optimal ET sequence|legend=1|7, 10, 17}}
+[[Tp tuning #T2 tuning|RMS error]]: ?
+== 2.….17/5.… subgroups ==
+=== Fiventeen ===
+Fiventeen tempers out [[136/135]] ({{monzo| 3 -3 1 }}) in 2.3.17/5. It equates [[17/15]] with [[9/8]], so it implies a [[supersoft]] [[pentic]] [[pentad]] of [[~]]30:34:40:45:51. [[17edo]] makes a good tuning especially for its size, which gives a [[supersoft]] pentic scale corresponding approximately to a just [[20/17]] tuning, although [[80edo]] might be preferred for an approximately just [[51/40]] to optimize plausibility slightly more, and [[97edo]] (= 80 + 17) and  [[114edo]] (= 97 + 17) do even better in striking a balance between 80edo's more stable tuning and that having 20/17 more accurate (as in 17edo) is useful because of the more convincing suggestion of the two 15:17:20 chords present in the fiventeen pentad. The same is true of the related rank-3 temperament diatic, for which the [[optimal ET sequence]] is much more characteristic of optimized tunings, finding [[34edo]], then [[80edo]], then [[114edo]] (= 34 + 80) and even [[194edo|194bc-edo]] (= 80 + 114), though because of its focus on primes 5 and 17 it misses 97edo as a tuning, and slightly less optimized though still interesting [[63edo]] and [[143edo]] (= 63 + 80) tunings are found in the optimal ET sequence for fiventeen.
+[[Subgroup]]: 2.3.17/5
+[[Comma list]]: 136/135 ({{monzo| 3 -3 1 }})
+{{Mapping|legend=2| 1 0 -3 | 0 1 3 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.2838{{c}}, ~3/2 = 704.4600{{c}}
+* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5286{{c}}
+{{Optimal ET sequence|legend=1| 5, 12, 17, 46, 63, 143 }}
+== 2.….19/7.… subgroups ==
+=== Surprise ===
+This temperament was named by [[User:VectorGraphics|Vector]] in 2025, as he was surprised that the temperament of [[57/56]] did not have a name. This is the [[rank-2 temperament|rank-2]] version of the temperament; Vector surmises that the name ''hendrix'' would be more thoughtfully given to the [[rank-3]] version.
+[[Subgroup]]: 2.3.19/7
+[[Comma list]]: [[57/56]] ({{Monzo| -3 1 1 }})
+{{Mapping|legend=2| 1 0 3 | 0 1 -1 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1202.4345{{c}}, ~3/2 = 697.4314{{c}}
+* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.3981{{c}}
+{{Optimal ET sequence|legend=1| 5, 7, 12, 19, 31*, 50* }}
+<nowiki/>* wart for 19/7
+[[Badness]] (Sintel): 0.082
+=== Supramin ===
+This is a remarkable low-complexity microtemperament that contains the 14:17:19 triad within just four generator steps. An excellent tuning is [[25edo]], which provides an accurate yet tone-efficient tuning of this temperament. It was named by [[User:Overthink|Overthink]] in 2026 after the fact that the generator is a [[17/14]] supraminor third, two of which reach [[28/19]]. It is related to [[cohemimabila]].
+[[Subgroup]]: 2.17/7.19/7
+[[Comma list]]: [[5491/5488]] ({{Monzo| -4 2 1 }})
+{{Mapping|legend=2| 1 0 4 | 0 1 -2 }}
+: mapping generators: ~2, ~17/7
+[[Optimal tuning]]s:
+* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1200.022{{c}}, ~17/14 = 335.793{{c}}
+* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.000{{c}}, ~17/14 = 335.785{{c}}
-<nowiki />* Wart for 13/5
+{{Optimal ET sequence|legend=1| 7, 18, 25 }}
-=== Oceanfront ===
+[[Badness]] (Sintel): 0.005
-Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]
-[[Subgroup]]: 2.3.7.13/5
+==== Supramine ====
+This extension approximates the 14:17:19:23:25 pentad in just six generator steps, at the cost of some accuracy. 25edo remains a strong tuning.
-[[Comma list]]: 64/63, 91/90
+Subgroup: 2.17/7.19/7.23/7
-{{Mapping|legend=2| 1 0 6 -5 | 0 1 -2 4 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
+Comma list: [[323/322]], [[392/391]]
-{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}
+Subgroup-val mapping: {{Mapping| 1 0 4 3 | 0 1 -2 -1 }}
-[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
+Optimal tunings:
+* Subgroup WE: ~2 = 1199.871{{c}}, ~17/14 = 336.243{{c}}
+* Subgroup CWE: ~2 = 1200.000{{c}}, ~17/14 = 336.296{{c}}
-Scales: [[Oceanfront scales]]
+{{Optimal ET sequence|legend=0| 7, 18, 25 }}
-== 2.….49/5… subgroups ==
+Badness (Sintel): 0.029
-=== Direct breedsmic ===
-Related temperament: [[hemithirds]], [[newt]]
-[[Subgroup]]: 2.3.49/5
+==== 2.25/7.17/7.19/7.23/7 subgroup ====
-[[Comma list]]: 2401/2400
+Subgroup: 2.25/7.17/7.19/7.23/7
-{{Mapping|legend=2| 1 1 3 | 0 2 1 }}
+Comma list: [[323/322]], [[392/391]], [[476/475]]
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966
+Subgroup-val mapping: {{Mapping| 1 -2 0 4 3 | 0 3 1 -2 -1 }}
-{{Optimal ET sequence|legend=1|?}}
+Optimal tunings:
+* Subgroup WE: ~2 = 1199.757{{c}}, ~17/14 = 335.428{{c}}
+* Subgroup CWE: ~2 = 1200.000{{c}}, ~17/14 = 335.479{{c}}
-[[Tp tuning #T2 tuning|RMS error]]: ?
+{{Optimal ET sequence|legend=0| 7, 18, 25 }}
+Badness (Sintel): 0.053
-== 3/2.5/2… subgroups ==
+== 3/2.5/2.… subgroups ==
 {{Main|Half-prime subgroup}}
@@ Line 1,541: / Line 1,897: @@
 {{Mapping|legend=2| 1 3 4 | 0 -4 -5 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,547: / Line 1,902: @@
 Supporting ETs: *5, *6, *7[+5/2, +7/2], *9[-5/2, --7/2], *11, *16, *17[+5/2], *23[+5/2, +7/2], *21[-7/2], *27, *28[+5/2], *38, *43[-7/2], *49
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 ==== 3/2.5/2.7/2.11/2 ====
@@ Line 1,556: / Line 1,910: @@
 {{Mapping|legend=2| 1 3 4 4 | 0 -4 -5 1 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,562: / Line 1,915: @@
 [[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2], *21[-7/2], *38[-11/2], *43[-7/2, -11/2], *59[-7/2, -11/2], *70[-7/2, -11/2], *75[--7/2, -11/2]
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 ==== 3/2.5/2.7/2.11/2.13/2 ====
@@ Line 1,575: / Line 1,927: @@
 [[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2]
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 === Semiwolf ===
@@ Line 1,613: / Line 1,964: @@
 [[Optimal ET sequence]]: [[8edf]], [[11edf]]
-== 3/2.5/4… subgroups ==
+== 3/2.5/4.… subgroups ==
 === Poseidon ===
 '''This temperament will be subjected to renaming due to a conflict.'''
@@ Line 1,642: / Line 1,993: @@
 Supporting ETs: *5, *6[+13], *7[-7, -13], *9, *11[+13], *13, *14, *17[-7, -13], *19[+13], *21[-7, -13], *22[-7], *23[+13], *25[-7, -13], *31[-7]
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 === Doubleton ===
@@ Line 1,657: / Line 2,007: @@
 Supporting ETs: *6, *10, *16, *14[-13], *8[+7], *22, *18[-13], *26, *24[-13], *28[+7], *20[+7], *36[-13], *12[+7, +13], *34[-13]
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 == 5/2-equave subgroups ==
 === Hyperion ===
 [[Subgroup]]: 5/2.7.11
@@ Line 1,674: / Line 2,022: @@
 Supporting ETs: *5[-7], *8, *19[+7], *21[-7], *27[+7], *29[-7], *35[+7], *43[+7], *37[-7], *51[+7, +11], *45[-7], *59[+7, +11]
+: <nowiki />* wart for 5/2
-<nowiki />* Wart for 5/2
 = Related temperament collections =
@@ Line 1,682: / Line 2,029: @@
 * [[Substitute harmonic]] temperaments
-<!-- main article -->
+[[Category:Subgroup temperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Pages with mostly numerical content]][[Category:Subgroup]]
+[[Category:Rank 2]]
+{{Todo| review | cleanup }}

Subgroup temperaments: Difference between revisions