@@ Line 1: / Line 1: @@
+{{Technical data page}}
 A '''subgroup temperament''' is a regular temperament defined on a [[just intonation subgroup]] that is not a full ''p''-limit group.
 For temperaments that omit various prime harmonics, see:
+* [[No-thirteens subgroup temperaments]]
 * [[No-elevens subgroup temperaments]]
 * [[No-sevens subgroup temperaments]]
@@ Line 10: / Line 12: @@
 Below are some temperaments for composite subgroups and fractional subgroups. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]].
-= Integer subgroup temperaments =
+= Composite subgroup temperaments =
-== 2.3.35 subgroup ==
-=== Shaka ===
-{{See also|Kalismic temperaments}}
-Two commas that split 2/1 in half, corresponding to convergents to sqrt(2), are the [[1682/1681|''sha''ftesburisma]] [[Square superparticular|S29]]/S41 and the [[9801/9800|''ka''lisma S99]], prompting to temper out {S29, S41, S99}, approximating /29 and /41 [[Primodality|primodal]] chords well.
-Subgroup: 2.3.35.11.29.41
-Comma list: 841/840, 1189/1188, 1681/1680
-{{Mapping|legend=2|2 2 6 5 7 8|0 1 1 -1 1 1|0 0 2 2 1 1}}
-Optimal tuning (CTE): ~41/29 = 1\2, ~3/2 = 702.031, ~41/24 = 926.693
-[[Support]]ing [[ET]]s: {{EDOs|22, 26, 36, 48, 70, 96, 106, 118, 140, 154, 176, 188, 224, 272, 294, 342}}
-Scale: [[Shaka10]]
 == 2.9.5.7 subgroup ==
 See also [[Jubilismic clan #Antikythera|antikythera]] and [[Hemimean clan #Isra|isra]].
@@ Line 89: / Line 73: @@
 === Baldy ===
 {{See also|Schismatic family #Garibaldi}}
+{{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 105: / Line 90: @@
 ==== 2.9.5.7.13 ====
-Subgroup: 2.9.5.7.13
+{{See also|Chromatic pairs #Baldy}}
+Baldy is every other step of [[garibaldi]], without the mapping of prime 11. It can be described as the 6 &amp; 35 temperament.
+[[Subgroup]]: 2.9.5.7.13
+[[Comma list]]: [[225/224]], [[325/324]], [[640/637]]
+{{Mapping|legend=2| 1 0 15 25 -28 | 0 1 -4 -7 10 }}
+{{Mapping|legend=3| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }}
-Comma list: 225/224, 325/324, 640/637
+: [[gencom]]: [2 9/8; 225/224 325/324 640/637]
-{{Mapping|legend=2| 1 3 3 4 2 | 0 1 -4 -7 10 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.090
-Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.090
+{{Optimal ET sequence|legend=1| 6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd }}
-{{Optimal ET sequence|legend=1| 6, 29f, 35, 41, 47 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.5999 cents
 Related temperament: [[Schismatic family #Garibaldi|Cassandra]]
@@ Line 143: / Line 138: @@
 {{Optimal ET sequence|legend=1| 6, 23def, 29f, 35, 41, 47 }}
-== 2.9.7 subgroup ==
+== 2.3.25 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.
-Subgroup: 2.9.7
+=== 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.
-Comma basis: 44957696/43046721
+Subgroup: 2.3.25
-Sval mapping: [{{val|1 1 -3}}, {{val|0 3 8}}]
+Edo join: 17 & 12
-Optimal tuning (CTE): ~729/448 = 870.792
+Comma list: [[2048/2025]]
-{{Optimal ET sequence|legend=1|7d, 11, 18d, 29, 40, 62}}, ...
+{{Mapping|legend=2| 1 1 7| 0 1 -4}}
-==== 2.9.7.11 subgroup ====
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.136
-Subgroup: 2.9.7.11
-Comma basis: 896/891, 1331/1296
+==== 2.3.23.25.41 subgroup ====
+''See also: [[Reversed meantone]]''
-Sval mapping: [{{val|1 1 -3 2}}, {{val|0 3 8 2}}]
+Edo join: 17 & 12
-Optimal tuning (CTE): ~16/11 = 870.966
+Comma list: 2048/2025, 576/575, 82/81
-{{Optimal ET sequence|legend=1| 7d, 11, 40, 51, 62 }}
+{{Mapping|legend=2| 1 1 1 7 3| 0 1 6 -4 4}}
-== 2.9.7.11 subgroup ==
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.264
-=== Machine ===
-Machine is every other step of [[supra]], most interesting for its scale patterns.
-[[Subgroup]]: 2.9.7.11
+===== Sburb =====
+This temperament sets the [[octave reduction|octave-reduced]] 413th harmonic (413/256, 827.998{{c}}) to the diminished seventh.
-[[Comma list]]: 64/63, 99/98
+Subgroup: 2.3.7.23.25.41.59
-{{Mapping|legend=2| 1 0 6 13 | 0 1 -1 -3 }}
+Edo join: 17 & 12
-: sval mapping generators: ~2, ~9
+Comma list: 64/63, 225/224, 162/161, 82/81, 177/175
-{{Mapping|legend=3| 1 3/2 0 3 4 | 0 1/2 0 -1 -3 }}
+{{Mapping|legend=2| 1 1 4 1 7 3 10| 0 1 -2 6 -4 4 -7}}
-: [[gencom]]: [2 8/7; 64/63 99/98]
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 706.387
-[[Optimal tuning]]s:
+== 2.9.5.11 subgroup ==
-* [[CTE]]: ~2 = 1\1, ~9/8 = 216.9128
+=== Glacial ===
-* [[POTE]]: ~2 = 1\1, ~9/8 = 214.3843
+{{See also| Chromatic pairs #Glacial }}
-{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }}
+[[Subgroup]]: 2.9.5.11.13
-[[Badness]]: 0.00233
+[[Comma list]]: 45/44, 65/64, 81/80
-=== Penta a.k.a. mechanism ===
+{{Mapping|legend=2| 1 0 -4 -6 10 | 0 1 2 3 -2 }}
-Penta or mechanism is the 8 &amp; 11 temperament in the 2.9.7.11 subgroup.
-[[Subgroup]]: 2.9.7.11
+{{Mapping|legend=3| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }}
-[[Comma list]]: 896/891, 26411/26244
+: [[gencom]]: [2 9/8; 45/44 65/64 81/80]
-{{Mapping|legend=2| 1 0 -1 6 | 0 5 6 -4 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151
-: sval mapping generators: ~2, ~14/9
+{{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }}
-{{Mapping|legend=3| 1 5/2 0 5 2 | 0 -5/2 0 -6 4 }}
+[[Tp tuning #T2 tuning|RMS error]]: 2.887 cents
-: [[gencom]]: [2 9/7; 896/891 26411/26244]
+Music:
+* ''[[Thundersnow]]'' - [[Sevish]] (2021)
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/9 = 761.3782
+== 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.
+Subgroup: 2.9.7
+Comma basis: 44957696/43046721
+Sval mapping: [{{val|1 1 -3}}, {{val|0 3 8}}]
+Optimal tuning (CTE): ~729/448 = 870.792
+{{Optimal ET sequence|legend=1|7d, 11, 18d, 29, 40, 62}}, ...
+==== 2.9.7.11 subgroup ====
+Subgroup: 2.9.7.11
+Comma basis: 896/891, 1331/1296
-{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}
+Sval mapping: [{{val|1 1 -3 2}}, {{val|0 3 8 2}}]
-[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
+Optimal tuning (CTE): ~16/11 = 870.966
-[[Badness]]: 0.00439
+{{Optimal ET sequence|legend=1| 7d, 11, 40, 51, 62 }}
+== 2.9.7.11 subgroup ==
 === Apparatus ===
 [[Subgroup]]: 2.9.7.11
@@ Line 234: / Line 245: @@
 [[Badness]]: 0.00263
-== 2.9.11 subgroup ==
+=== Joan ===
-=== Demon ===
+{{See also| Chromatic pairs #Joan }}
-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
+Joan is related to [[casablanca]] as well as to [[orwell]].
-[[Comma list]]: [[1331/1296]]
+[[Subgroup]]: 2.9.7.11
-{{Mapping|legend=2|1 1 2|0 3 2}}
+[[Comma list]]: 99/98, 9317/9216
-[[Optimal tuning]] ([[CTE]]): ~[[18/11]] = 870.060
+{{Mapping|legend=2| 1 0 1 3 | 0 7 4 1 }}
-{{Optimal ET sequence|legend=1|4, 7, 11, 18, 29, 76e}}
+{{Mapping|legend=3| 1 0 0 1 3 | 0 7/2 0 4 1 }}
-=== Genius ===
+: [[gencom]]: [2 11/8; 99/98 9317/9216]
-Named after the genius in Roman religion, following the demon (daimon) in Greek mythology.
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents
-[[Subgroup]]: 2.9.11
+{{Optimal ET sequence|legend=1| 11, 20, 31, 42, 115bd, 157bd }}
-[[Comma list]]: [[131769/131072]]
+[[Tp tuning #T2 tuning|RMS error]]: 1.424 cents
-{{Mapping|legend=2|1 1 4|0 4 -1}}
+=== Machine ===
+Machine is every other step of [[supra]], most interesting for its scale patterns.
-[[Optimal tuning]] ([[CTE]]): ~[[16/11]] = 650.863
+[[Subgroup]]: 2.9.7.11
-{{Optimal ET sequence|legend=1|9, 11, 24, 59, 83, 142, 225, 367}}[-11], 592[-11], 959[-9, --11], 1326[-9, --11]
+[[Comma list]]: 64/63, 99/98
-== 2.9.15.7 subgroup ==
+{{Mapping|legend=2| 1 0 6 13 | 0 1 -1 -3 }}
-=== 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
+: sval mapping generators: ~2, ~9
-[[Comma list]]: 225/224, 245/243
+{{Mapping|legend=3| 1 3/2 0 3 4 | 0 1/2 0 -1 -3 }}
-{{Mapping|legend=2| 1 0 2 -1 | 0 5 3 6 }}
+: [[gencom]]: [2 8/7; 64/63 99/98]
-: sval mapping generators: ~2, ~14/9
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~9/8 = 216.9128
+* [[POTE]]: ~2 = 1\1, ~9/8 = 214.3843
-{{Mapping|legend=3| 1 5/2 5/2 5 | 0 -5/2 -1/2 -6 }}
+{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }}
-: [[gencom]]: [2 9/7; 225/224 245/243]
+[[Badness]]: 0.00233
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~14/9 = 760.704
+=== Penta a.k.a. mechanism ===
+Penta or mechanism is the 8 &amp; 11 temperament in the 2.9.7.11 subgroup.
-{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 71, 93, 112c, 134c, 175c }}
+[[Subgroup]]: 2.9.7.11
-[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
+[[Comma list]]: 896/891, 26411/26244
-==== 2.9.15.7.11 ====
+{{Mapping|legend=2| 1 0 -1 6 | 0 5 6 -4 }}
-Subgroup: 2.9.15.7.11
-Comma list: 100/99, 225/224, 245/243
+: sval mapping generators: ~2, ~14/9
-Sval mapping: {{mapping| 1 0 2 -1 6 | 0 5 3 6 -4 }}
+{{Mapping|legend=3| 1 5/2 0 5 2 | 0 -5/2 0 -6 4 }}
-Gencom mapping: {{mapping| 1 5/2 5/2 5 2 | 0 -5/2 -1/2 -6 4 }}
+: [[gencom]]: [2 9/7; 896/891 26411/26244]
-: gencom: [2 9/7; 100/99 225/224 245/243]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/9 = 761.3782
-Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.393
+{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}
-Optimal ET sequence: {{Optimal ET sequence| 8, 11, 30, 41, 52, 93, 145, 342bce }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
-RMS error: 1.226 cents
+[[Badness]]: 0.00439
-==== 2.9.15.7.11.13 ====
+Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]
-Subgroup: 2.9.15.7.11.13
-Comma list: 100/99, 105/104, 144/143, 196/195
+== 2.9.7.13.17 subgroup ==
-Sval mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 3 6 -4 9 }}
+=== 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 mapping: {{mapping| 1 5/2 5/2 5 2 7 | 0 -5/2 -1/2 -6 4 -9 }}
+[[Subgroup]]: 2.9.7.13.17
-: gencom: [2 9/7; 100/99 105/104 144/143 196/195]
+[[Comma list]]: 729/728, 442/441, 833/832
-Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.023
+{{Mapping|legend=2| 1 1 1 -1 3| 0 6 5 13 3 }}
-Optimal ET sequence: {{Optimal ET sequence| 11, 30, 41, 153cdef, 194cdef, 235cdef }}
+[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~9/7 = 433.836
-RMS error: 1.540 cents
+Badness (Dirichlet): 0.142
-== 2.9.21 subgroup ==
+== 2.9.11 subgroup ==
-=== A-team ===
+=== Demon ===
-A-team is every other step of [[mothra]].
+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]]: 2.9.21
+[[Subgroup]]: 2.9.11
-[[Comma list]]: 1029/1024
+[[Comma list]]: [[1331/1296]]
-{{Mapping|legend=2| 1 2 4 | 0 3 1 }}
+{{Mapping|legend=2|1 1 2|0 3 2}}
-: sval mapping generators: ~2, ~21/16
+[[Optimal tuning]] ([[CTE]]): ~[[18/11]] = 870.060
-{{Mapping|legend=3| 1 1 0 3 | 0 3/2 0 -1/2 }}
+{{Optimal ET sequence|legend=1|4, 7, 11, 18, 29, 76e}}
-: [[gencom]]: [2 21/16; 1029/1024]
+=== Genius ===
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~21/16 = 467.375
+Named after the genius in Roman religion, following the demon (daimon) in Greek mythology.
-{{Optimal ET sequence|legend=1| 5, 13, 18, 41, 59, 77, 95 }}
+[[Subgroup]]: 2.9.11
-[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
+[[Comma list]]: [[131769/131072]]
-==== 2.9.5.21.11 ====
+{{Mapping|legend=2|1 1 4|0 4 -1}}
-Subgroup: 2.9.5.21.11
-Comma list: 81/80, 99/98, 385/384
+[[Optimal tuning]] ([[CTE]]): ~[[16/11]] = 650.863
-Sval mapping: {{mapping| 1 2 0 4 5 | 0 3 6 1 -4 }}
+{{Optimal ET sequence|legend=1|9, 11, 24, 59, 83, 142, 225, 367}}[-11], 592[-11], 959[-9, --11], 1326[-9, --11]
-Gencom mapping: {{mapping| 1 1 0 3 5 | 0 3/2 6 -1/2 -4 }}
+== 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]].
-: gencom: [2 21/16; 81/80 99/98 385/384]
+[[Subgroup]]: 2.9.15.7
-Optimal tuning (subgroup POTE): ~2 = 1\1, ~21/16 = 463.956
+[[Comma list]]: 225/224, 245/243
-{{Optimal ET sequence|legend=1| 5, 13, 31 }}
+{{Mapping|legend=2| 1 0 2 -1 | 0 5 3 6 }}
-== 2.15.55 subgroup ==
+: sval mapping generators: ~2, ~14/9
-=== Spog ===
-This temperament produces [[Slendro_clan#Superpelog|superpelog]]-like [[5L 4s|semiquartal]] scales while being more accurate ([[Subgroup temperaments#2.15.189.55.325.725.279|see]] rational approximations to their intervals).
+{{Mapping|legend=3| 1 5/2 5/2 5 | 0 -5/2 -1/2 -6 }}
-[[Subgroup]]: 2.15.55
+: [[gencom]]: [2 9/7; 225/224 245/243]
-[[Comma list]]: [[100663296/100656875]]
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~14/9 = 760.704
-{{Mapping|legend=2| 1 0 5 | 0 5 1 }}
+{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 71, 93, 112c, 134c, 175c }}
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.655
+[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
-{{Optimal ET sequence|legend=1|5, 9, 23, 32, 151, 183, 215, 247, 956, 1203, 1450, 3147, 4597 }}
+==== 2.9.15.7.11 ====
+Subgroup: 2.9.15.7.11
-==== 2.15.55.325 ====
+Comma list: 100/99, 225/224, 245/243
-[[Subgroup]]: 2.15.55.325
-[[Comma list]]: [[4225/4224]], [[6656/6655]]
+Sval mapping: {{mapping| 1 0 2 -1 6 | 0 5 3 6 -4 }}
-{{Mapping|legend=2| 1 0 5 6 | 0 5 1 3 }}
+Gencom mapping: {{mapping| 1 5/2 5/2 5 2 | 0 -5/2 -1/2 -6 4 }}
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.647
+: gencom: [2 9/7; 100/99 225/224 245/243]
-[[Support]]ing [[ET]]s: 5, 9, 13[-15], 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311
+Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.393
-==== 2.15.189.55.325 ====
+Optimal ET sequence: {{Optimal ET sequence| 8, 11, 30, 41, 52, 93, 145, 342bce }}
-Related temperament: [[Lehmerismic_temperaments#Lux|lux]]
-[[Subgroup]]: 2.15.189.55.325
+RMS error: 1.226 cents
-[[Comma list]]: [[2080/2079]], [[3025/3024]], [[4096/4095]]
+==== 2.9.15.7.11.13 ====
+Subgroup: 2.9.15.7.11.13
-{{Mapping|legend=2| 1 0 6 5 6 | 0 5 2 1 3 }}
+Comma list: 100/99, 105/104, 144/143, 196/195
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.677
+Sval mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 3 6 -4 9 }}
-[[Support]]ing [[ET]]s: 5, 9, 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311
+Gencom mapping: {{mapping| 1 5/2 5/2 5 2 7 | 0 -5/2 -1/2 -6 4 -9 }}
-==== 2.15.189.55.325.725 ====
+: gencom: [2 9/7; 100/99 105/104 144/143 196/195]
-[[Subgroup]]: 2.15.189.55.325.725
+Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.023
-[[Comma list]]: [[1625/1624]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
+Optimal ET sequence: {{Optimal ET sequence| 11, 30, 41, 153cdef, 194cdef, 235cdef }}
-{{Mapping|legend=2| 1 0 6 5 6 -3 | 0 5 2 1 3 16 }}
+RMS error: 1.540 cents
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.649
+== 2.9.21 subgroup ==
+=== A-team ===
+A-team is every other step of [[slendric]]; the 2.9.5.21.11 extension below specifically restricts [[mothra]].
-[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119,  142[+725], 151, 183, 206[+725], 311
+[[Subgroup]]: 2.9.21
-==== 2.15.189.55.325.725.279 ====
+[[Comma list]]: 1029/1024
-Here are rational approximations to the intervals of the semiquartal scale.
+{{Mapping|legend=2| 1 2 4 | 0 3 1 }}
-Sharp: 12/11, 25/21, 33/26, 18/13, 31/21 ~ 65/44 ~ 96/65, 50/31 ~ 29/18, 55/32, 15/8.
+: sval mapping generators: ~2, ~21/16
-Flat: 16/15, 64/55, 31/25 ~ 36/29, 42/31 ~ 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6.
+{{Mapping|legend=3| 1 1 0 3 | 0 3/2 0 -1/2 }}
-[[Subgroup]]: 2.15.189.55.325.725.279
-[[Comma list]]: [[1625/1624]], [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
+: [[gencom]]: [2 21/16; 1029/1024]
-{{Mapping|legend=2| 1 0 6 5 6 -3 5 | 0 5 2 1 3 16 4 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~21/16 = 467.375
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.638
+{{Optimal ET sequence|legend=1| 5, 13, 18, 41, 59, 77, 95 }}
-[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 151, 183, 206[+725], 311
+[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
-== 4.3.5 subgroup ==
+==== 2.9.5.21 ====
-=== Tetrahanson ===
+''Lookalike temperament: [[Dual-fifth_temperaments#Dual-3_A-Team|Dual-3 A-Team]]''
-{{Main| Tetrahanson }}
-[[Subgroup]]: 4.3.5
+Subgroup: 2.9.5.21
-[[Comma list]]: 15625/15552
+[[Comma]] list: 81/80, 1029/1024
-{{Mapping|legend=2| 1 3 3 | 0 -6 -5 }}
+Sval mapping: {{mapping| 1 2 0 4 | 0 3 6 1 }}
-: Mapping generators: ~4, ~5/3
+Mapping generators: ~2, ~21/16
-[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941
+Optimal ([[Lp tuning|POL2]]) generator: 464.3865
-[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
+{{Optimal ET sequence|legend=1| 13, 18, 31, 44 }}
-=== Tetrameantone ===
+===== 2.9.5.21.11 =====
-{{Main| Tetrameantone }}
+Subgroup: 2.9.5.21.11
-[[Subgroup]]: 4.3.5
+Comma list: 81/80, 99/98, 385/384
-[[Comma list]]: 81/80
+Sval mapping: {{mapping| 1 2 0 4 5 | 0 3 6 1 -4 }}
-{{Mapping|legend=2| 1 1 2 | 0 -1 -4 }}
+Gencom mapping: {{mapping| 1 1 0 3 5 | 0 3/2 6 -1/2 -4 }}
-: Mapping generators: ~4, ~4/3
+: gencom: [2 21/16; 81/80 99/98 385/384]
-[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~4/3 = 503.761
+Optimal tuning (subgroup POTE): ~2 = 1\1, ~21/16 = 463.956
-[[Support]]ing [[ET]]s: {{EDs|5, 9, 14, 19, 24, 43, 62, 81, 100|equave=4}}
+{{Optimal ET sequence|legend=1| 5, 13, 31 }}
-=== Tetramagic ===
-[[Subgroup]]: 4.3.5
+==== B-team ====
+B-team (23 & 41) is every other step of [[rodan]].
-[[Comma list]]: 3125/3072
+Subgroup: 2.9.15.21.33
-{{Mapping|legend=2| 1 0 1 | 0 5 1 }}
+Comma list: 245/243, 385/384, 441/440
-: Mapping generators: ~4, ~5/4
+Sval mapping: {{mapping| 1 2 0 4 7 | 0 3 10 1 -5 }}
-[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~5/4 = 380.059
+Optimal tuning (subgroup POTE): ~2 = 1\1, ~21/16 = 468.918
-[[Support]]ing [[ET]]s: {{EDs|6, 13, 19, 25, 38, 44, 63, 82|equave=4}}
+{{Optimal ET sequence|legend=1| 5, 13c, 18, 23, 41, 64, 87, 151 }}
-=== Blacktetra ===
+== 4.3.5 subgroup ==
+=== Tetrahanson ===
+{{Main| Tetrahanson }}
 [[Subgroup]]: 4.3.5
-[[Comma list]]: 256/243
+[[Comma list]]: 15625/15552
-{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}
+{{Mapping|legend=2| 1 3 3 | 0 -6 -5 }}
-: Mapping generators: ~4, ~16/15
+: Mapping generators: ~4, ~5/3
-[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062
+[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941
-[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}
+[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
-== 4.6.5 subgroup ==
+=== Tetrameantone ===
-=== Meanquad ===
+{{Main| Tetrameantone }}
-{{Main| Meanquad }}
-[[Subgroup]]: 4.6.5
+[[Subgroup]]: 4.3.5
-[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}
+[[Comma list]]: 81/80
-{{Mapping|legend=2| 1 0 -4| 0 1 4 }}
+{{Mapping|legend=2| 1 1 2 | 0 -1 -4 }}
-: mapping generators: ~4, ~6
+: Mapping generators: ~4, ~4/3
-[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214
+[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~4/3 = 503.761
-[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
+[[Support]]ing [[ET]]s: {{EDs|5, 9, 14, 19, 24, 43, 62, 81, 100|equave=4}}
-<nowiki>*</nowiki> wart for 4
+=== Tetramagic ===
-==== 4.6.5.7 subgroup (tetrominant) ====
+[[Subgroup]]: 4.3.5
-[[Subgroup]]: 4.6.5.7
+[[Comma list]]: 3125/3072
+{{Mapping|legend=2| 1 0 1 | 0 5 1 }}
-[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}
+: Mapping generators: ~4, ~5/4
-{{Mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}
+[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~5/4 = 380.059
-[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622
+[[Support]]ing [[ET]]s: {{EDs|6, 13, 19, 25, 38, 44, 63, 82|equave=4}}
-[[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]
+=== Blacktetra ===
-<nowiki>*</nowiki> wart for 4
+[[Subgroup]]: 4.3.5
-=== Fourwar ===
+[[Comma list]]: 256/243
-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.
-Fourwar is named after the closely related [[hemiwar]] temperament.
+{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}
-<pre>
+: Mapping generators: ~4, ~16/15
-Reduced Mapping
-	6	5
+[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062
-[ ⟨	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
+[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}
-q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
-</pre>
-==== 4.6.5.7 ====
+== 4.6.5 subgroup ==
-<pre>
+=== Meanquad ===
-Reduced Mapping
+{{Main| Meanquad }}
-	6	5	7
-[ ⟨	1	0	1	1	]
+[[Subgroup]]: 4.6.5
-⟨	0	16	2	5	] ⟩
+[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}
-TE Generator Tunings (cents)
-⟨2399.4195, 193.8654]
+{{Mapping|legend=2| 1 0 -4| 0 1 4 }}
-TE Step Tunings (cents)
+: mapping generators: ~4, ~6
-⟨25.23883, 47.79592]
+[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214
-TE Tuning Map (cents)
-⟨2399.420, 3101.846, 2787.150, 3368.747]
+[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
-TE Mistunings (cents)
+<nowiki />* Wart for 4
-⟨-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
+==== 4.6.5.7 subgroup (tetrominant) ====
-q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+[[Subgroup]]: 4.6.5.7
-</pre>
-==== 4.6.5.7.11 ====
+[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}
-<pre>
-Reduced Mapping
+{{Mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}
-	6	5	7	11
-[ ⟨	1	0	1	1	1	]
+[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622
-⟨	0	16	2	5	9	] ⟩
+[[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]
+<nowiki />* Wart for 4
+=== Fourwar ===
+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.
+Fourwar is named after the closely related [[hemiwar]] temperament.
+{{Todo|inline=1|cleanup}}
+<pre>
+Reduced Mapping
+	6	5
+[ ⟨	1	0	1	]
+⟨	0	16	2	] ⟩
 TE Generator Tunings (cents)
-⟨2400.1097, 193.9498]
+⟨2399.3973, 193.8643]
 TE Step Tunings (cents)
-⟨24.18752, 48.52491]
+⟨25.21211, 47.81337]
 TE Tuning Map (cents)
-⟨2400.110, 3103.196, 2788.009, 3369.859, 4145.658]
+⟨2399.397, 3101.829, 2787.126]
 TE Mistunings (cents)
-⟨0.110, 1.241, 1.696, 1.033, -5.660]
+⟨-0.603, -0.126, 0.812]
-Complexity	1.068792
+Complexity	1.369085
-Adjusted Error	2.926965 cents
+Adjusted Error	0.692892 cents
-TE Error	0.846083 cents/octave
+TE Error	0.268047 cents/octave
-Unison Vectors
+Unison Vector
-[-1, -1, -1, 0, 2⟩ (121:120)
+[8, 1, -8⟩ (393216:390625)
-[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
-q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
 </pre>
-==== 4.6.5.7.11.13 ====
+==== 4.6.5.7 ====
 <pre>
 Reduced Mapping
-	6	5	7	11	13
+	6	5	7
-[ ⟨	1	0	1	1	1	0	]
+[ ⟨	1	0	1	1	]
-⟨	0	16	2	5	9	23	] ⟩
+⟨	0	16	2	5	] ⟩
 TE Generator Tunings (cents)
-⟨2401.2305, 193.5378]
+⟨2399.4195, 193.8654]
 TE Step Tunings (cents)
-⟨42.79107, 35.98524]
+⟨25.23883, 47.79592]
 TE Tuning Map (cents)
-⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
+⟨2399.420, 3101.846, 2787.150, 3368.747]
 TE Mistunings (cents)
-⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]
+⟨-0.580, -0.109, 0.837, -0.079]
-Complexity	1.219191
+Complexity	1.192044
-Adjusted Error	6.699599 cents
+Adjusted Error	0.653313 cents
-TE Error	1.810487 cents/octave
+TE Error	0.232715 cents/octave
 Unison Vectors
-[0, 1, -1, 0, 1, -1⟩ (66:65)
+[-2, -1, -2, 4⟩ (2401:2400)
-[-1, -1, -1, 0, 2, 0⟩ (121:120)
+[3, 0, -5, 2⟩ (3136:3125)
-[1, 2, 0, 0, -1, -1⟩ (144:143)
+[5, 1, -3, -2⟩ (6144:6125)
-[2, 0, -2, -1, 1, 0⟩ (176:175)
+[8, 1, -8, 0⟩ (393216:390625)
-[-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
-q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
 </pre>
-==== 4.6.5.7.11.13.17 ====
+==== 4.6.5.7.11 ====
 <pre>
 Reduced Mapping
-	6	5	7	11	13	17
+	6	5	7	11
-[ ⟨	1	0	1	1	1	0	1	]
+[ ⟨	1	0	1	1	1	]
-⟨	0	16	2	5	9	23	13	] ⟩
+⟨	0	16	2	5	9	] ⟩
 TE Generator Tunings (cents)
-⟨2400.4701, 193.4599]
+⟨2400.1097, 193.9498]
 TE Step Tunings (cents)
-⟨43.39350, 35.55764]
+⟨24.18752, 48.52491]
 TE Tuning Map (cents)
-⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]
+⟨2400.110, 3103.196, 2788.009, 3369.859, 4145.658]
 TE Mistunings (cents)
-⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]
+⟨0.110, 1.241, 1.696, 1.033, -5.660]
-Complexity	1.129881
+Complexity	1.068792
-Adjusted Error	8.082725 cents
+Adjusted Error	2.926965 cents
-TE Error	1.977443 cents/octave
+TE Error	0.846083 cents/octave
 Unison Vectors
-[0, 1, -1, 0, 1, -1, 0⟩ (66:65)
+[-1, -1, -1, 0, 2⟩ (121:120)
-[1, 1, 1, -1, 0, 0, -1⟩ (120:119)
+[2, 0, -2, -1, 1⟩ (176:175)
-[1, 2, 0, 0, -1, -1, 0⟩ (144:143)
+[-3, -1, 1, 1, 1⟩ (385:384)
-[-2, 1, 1, 1, 0, -1, 0⟩ (105:104)
+[-1, 0, 3, -3, 1⟩ (1375:1372)
-[-1, 2, 2, 0, 0, -1, -1⟩ (225:221)
+[-2, -1, -2, 4, 0⟩ (2401:2400)
-[-1, 1, 2, -2, 0, -1, 1⟩ (1275:1274)
+[1, 0, 1, -4, 2⟩ (2420:2401)
 Subsets
-q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg
+q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
 </pre>
-==== 4.6.5.7.11.13.17.19 ====
+==== 4.6.5.7.11.13 ====
 <pre>
 Reduced Mapping
-	6	5	7	11	13	17	19
+	6	5	7	11	13
-[ ⟨	1	0	1	1	1	0	1	1	]
+[ ⟨	1	0	1	1	1	0	]
-⟨	0	16	2	5	9	23	13	14	] ⟩
+⟨	0	16	2	5	9	23	] ⟩
 TE Generator Tunings (cents)
-⟨2399.9219, 193.3952]
+⟨2401.2305, 193.5378]
 TE Step Tunings (cents)
-⟨44.14256, 35.03670]
+⟨42.79107, 35.98524]
 TE Tuning Map (cents)
-⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
+⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
 TE Mistunings (cents)
-⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]
+⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]
-Complexity	1.058472
+Complexity	1.219191
-Adjusted Error	8.712222 cents
+Adjusted Error	6.699599 cents
-TE Error	2.050935 cents/octave
+TE Error	1.810487 cents/octave
 Unison Vectors
-[0, 1, -1, 0, 1, -1, 0, 0⟩ (66:65)
+[0, 1, -1, 0, 1, -1⟩ (66:65)
-[-1, 0, 0, 1, 1, 0, 0, -1⟩ (77:76)
+[-1, -1, -1, 0, 2, 0⟩ (121:120)
-[2, 1, -1, 0, 0, 0, 0, -1⟩ (96:95)
+[1, 2, 0, 0, -1, -1⟩ (144:143)
-[1, 1, 1, -1, 0, 0, -1, 0⟩ (120:119)
+[2, 0, -2, -1, 1, 0⟩ (176:175)
-[0, 1, 1, 1, -1, 0, 0, -1⟩ (210:209)
+[-2, 1, 1, 1, 0, -1⟩ (105:104)
-[0, 0, 1, -2, 1, 0, 1, -1⟩ (935:931)
+[-3, -1, 1, 1, 1, 0⟩ (385:384)
-[2, 0, -3, 1, 0, 0, -1, 1⟩ (2128:2125)
+[-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
-q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh
+q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
 </pre>
-==== 4.6.5.7.11.13.17.19.23 ====
+==== 4.6.5.7.11.13.17 ====
 <pre>
 Reduced Mapping
-	6	5	7	11	13	17	19	23
+	6	5	7	11	13	17
-[ ⟨	1	0	1	1	1	0	1	1	0	]
+[ ⟨	1	0	1	1	1	0	1	]
-⟨	0	16	2	5	9	23	13	14	28	] ⟩
+⟨	0	16	2	5	9	23	13	] ⟩
 TE Generator Tunings (cents)
-⟨2399.3286, 193.5316]
+⟨2400.4701, 193.4599]
 TE Step Tunings (cents)
-⟨37.31613, 39.63311]
+⟨43.39350, 35.55764]
 TE Tuning Map (cents)
-⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
+⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]
 TE Mistunings (cents)
-⟨-0.671, -5.449, 0.078, -1.839, -10.205, 10.699, 10.284, 11.258, -9.389]
+⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]
-Complexity	1.115920
+Complexity	1.129881
-Adjusted Error	9.502017 cents
+Adjusted Error	8.082725 cents
-TE Error	2.100561 cents/octave
+TE Error	1.977443 cents/octave
 Unison Vectors
-[0, 1, -1, 0, 1, -1, 0, 0, 0⟩ (66:65)
+[0, 1, -1, 0, 1, -1, 0⟩ (66:65)
-[1, 0, 0, -1, 0, -1, 0, 0, 1⟩ (92:91)
+[1, 1, 1, -1, 0, 0, -1⟩ (120:119)
-[0, -1, 1, 0, 0, 0, 0, -1, 1⟩ (115:114)
+[1, 2, 0, 0, -1, -1, 0⟩ (144:143)
-[1, 1, 1, -1, 0, 0, -1, 0, 0⟩ (120:119)
+[-2, 1, 1, 1, 0, -1, 0⟩ (105:104)
-[2, 0, -2, -1, 1, 0, 0, 0, 0⟩ (176:175)
+[-1, 2, 2, 0, 0, -1, -1⟩ (225:221)
-[-3, -1, 1, 1, 1, 0, 0, 0, 0⟩ (385:384)
+[-1, 1, 2, -2, 0, -1, 1⟩ (1275:1274)
-[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
+q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg
 </pre>
-== 4.9.25 subgroup ==
+==== 4.6.5.7.11.13.17.19 ====
-=== Meansquared ===
+<pre>
-[[Subgroup]]: 4.9.25
+Reduced Mapping
+	6	5	7	11	13	17	19
-[[Comma list]]: [[6561/6400]]
+[ ⟨	1	0	1	1	1	0	1	1	]
+⟨	0	16	2	5	9	23	13	14	] ⟩
-{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
+TE Generator Tunings (cents)
-Mapping generators: ~4, ~9/64
+⟨2399.9219, 193.3952]
-[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
+TE Step Tunings (cents)
+⟨44.14256, 35.03670]
-[[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 ==
+⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
-=== Archsquared ===
-[[Subgroup]]: 4.9.49
+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)
-[[Comma list]]: 4096/3969
+Subsets
+q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh
+</pre>
-{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}
+==== 4.6.5.7.11.13.17.19.23 ====
+<pre>
-Mapping generators: ~4, ~9/64
+Reduced Mapping
+	6	5	7	11	13	17	19	23
-[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 219.190
+[ ⟨	1	0	1	1	1	0	1	1	0	]
+⟨	0	16	2	5	9	23	13	14	28	] ⟩
-[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
+TE Generator Tunings (cents)
-== 8.9.7 subgroup ==
+⟨2399.3286, 193.5316]
-=== 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."
+TE Step Tunings (cents)
+⟨37.31613, 39.63311]
-[[Subgroup]]: 8.9.7
+TE Tuning Map (cents)
-[[Comma list]]: 64/63
+⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
-{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
+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)
-: sval mapping generators: ~8, ~9
+Subsets
+q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii
+</pre>
-: [[gencom]]: [8 9/8; 64/63]
+== 4.9.25 subgroup ==
+=== Meansquared ===
+[[Subgroup]]: 4.9.25
-[[Optimal tuning]] ([[CTE]]): 1\[[3ed8]] = 1600.0, ~9/8 = 219.1898
+[[Comma list]]: [[6561/6400]]
-[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}
+{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
-[[Badness]]: 0.0215 × 10<sup>-3</sup>
+Mapping generators: ~4, ~9/64
-= Fractional subgroup temperaments =
+[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
-== 2.5/3… subgroups ==
-=== Magicaltet ===
+[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
-{{See also| Chromatic pairs #Magicaltet }}
-Magicaltet is related to [[supermagic]], [[superkleismic]], and [[magic]].
+== 4.9.49 subgroup ==
+=== Archsquared ===
+[[Subgroup]]: 4.9.49
-[[Subgroup]]: 2.5/3.7.11
+[[Comma list]]: 4096/3969
-[[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }}
+{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}
-{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
+Mapping generators: ~4, ~9/64
-: mapping generators: ~2, ~5/3
+[[Optimal tuning]] ([[CTE]]): ~9/4 = 1419.190
-{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
+[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
-: [[gencom]]: [2 6/5; 100/99 385/384]
+== 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."
-[[Optimal tuning]]s:
+[[Subgroup]]: 8.9.7
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~5/3 = 877.3426
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~5/3 = 877.351
-{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
+[[Comma list]]: 64/63
-<nowiki>*</nowiki> wart for 5/3
+{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
-[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
+: sval mapping generators: ~8, ~9
-=== Starlingtet ===
+: [[gencom]]: [8 9/8; 64/63]
-{{See also | Chromatic pairs #Starlingtet }}
-Starlingtet, the 4 &amp; 15 temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]].
+[[Optimal tuning]] ([[CTE]]): ~9/8 = 219.1898
-[[Subgroup]]: 2.5/3.7/3
+[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}
-[[Comma list]]: [[126/125]]
+[[Badness]]: 0.0215 × 10<sup>-3</sup>
-{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
+= Fractional subgroup temperaments =
+== 2.5/3.… subgroups ==
+=== Magicaltet ===
+{{See also| Chromatic pairs #Magicaltet }}
-{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
+Magicaltet is related to [[keemic]], [[superkleismic]], and [[magic]]. The tonic and the first three generator steps make a [[magical seventh chord]], hence the name.
-: [[gencom]]: [2 6/5; 126/125]
+[[Subgroup]]: 2.5/3.7.11
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 311.154
+[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})
-{{Optimal ET sequence|legend=1| 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b }}
+{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
+: mapping generators: ~2, ~5/3
-[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents
+{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
+: [[gencom]]: [2 6/5; 100/99 385/384]
-==== Greeley ====
+[[Optimal tuning]]s:
-{{See also| Chromatic pairs #Greeley }}
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 877.343
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 877.351
-Related temperaments: [[Porcupine family #Opossum|Opossum]], [[Starling temperaments #Nusecond|Nusecond]]
+{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
+: <nowiki/>* wart for 5/3
-[[Subgroup]]: 2.5/3.7/3.11/3
+[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
-[[Comma list]]: 121/120, 126/125
+=== Starlingtet ===
+{{See also | Chromatic pairs #Starlingtet }}
-{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
+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.
-{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}
+[[Subgroup]]: 2.5/3.7/3
-: [[gencom]]: [2 11/10; 121/120 126/125]
+[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~11/10 = 155.776
+{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
-{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131†, 208*† }}
+: mapping generators: ~2, ~5/3
-<nowiki>*</nowiki> wart for 5/3
+{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
+: [[gencom]]: [2 6/5; 126/125]
-<nowiki>†</nowiki> wart for 11/3
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 888.759
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 888.846
-[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents
+{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}
-==== Skateboard ====
+[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents
-{{See also| Chromatic pairs #Skateboard }}
-Skateboard is related to [[thrasher]].
+==== Greeley ====
+{{See also| Chromatic pairs #Greeley }}
-[[Subgroup]]: 2.5/3.7/3.11.13/9
+Greeley is related to [[opossum]] as well as to [[nusecond]].
-[[Comma list]]: 56/55, 91/90, 100/99
+[[Subgroup]]: 2.5/3.7/3.11/3
-{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
+[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})
-{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}
+{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
+{{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]
+[[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
+{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
+: <nowiki/>* wart for 11/3
+[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents
+==== Skateboard ====
+{{See also| Chromatic pairs #Skateboard }}
+Skateboard is related to [[thrasher]].
+[[Subgroup]]: 2.5/3.7/3.11.13/9
+[[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 0 -1 2 2 | 0 1 3 2 -2 }}
+{{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]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 313.842
+[[Optimal tuning]]s:
+* [[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 }}
@@ Line 910: / Line 964: @@
 [[Tp tuning #T2 tuning|RMS error]]: 2.396 cents
+=== Gariberttet ===
+Gariberttet is the 2.5/3.7/3 [[Subgroup temperament families, relationships, and genes|altergene]] of [[sirius]].
-=== Gariberttet ===
 ==== Gariberttet (2.5/3.7/3.13/11 subgroup) ====
 {{See also | Chromatic pairs #Gariberttet }}
-Gariberttet can be described as the 4 &amp; 29 temperament in the 2.5/3.7/3.13/11 subgroup.
+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]].
 [[Subgroup]]: 2.5/3.7/3.13/11
-[[Comma list]]: [[275/273]], [[847/845]]
+[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})
 {{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
 {{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]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/11 = 293.679
+[[Optimal tuning]]s:
+* [[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, 143d, 237bd, 380bd }}
+{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}
+: <nowiki/>* wart for 13/11
 [[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
@@ Line 936: / Line 992: @@
 {{See also | Chromatic pairs #Indium }}
-Indium can be described as the 8 &amp; 33 temperament in the 2.5/3.7/3.11/3 subgroup.
+Indium can be described as the {{nowrap| 8 & 33 }} temperament in the 2.5/3.7/3.11/3 subgroup.
 [[Subgroup]]: 2.5/3.7/3.11/3
-[[Comma list]]: [[3025/3024]], [[3125/3087]]
+[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }})
 {{Mapping|legend=2| 1 0 0 2 | 0 6 10 -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]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~12/11 = 147.010
+[[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
-{{Optimal ET sequence|legend=1| 33, 41, 49, 57, 106, 204, 253 }}
+{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*<sup>†</sup> }}
+: <nowiki/>* wart for 7/3
+: <sup>†</sup> wart for 11/3
 [[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
-==== Semidim ====
+==== Ammon ====
-{{See also| Chromatic pairs #Semidim }}
+{{See also| Chromatic pairs #Ammon }}
-Semidim can be described as the 8 &amp; 29 temperament in the 2.5/3.7/3.11/3.13/3 subgroup.
+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.
 [[Subgroup]]: 2.5/3.7/3.11/3.13/3
-[[Comma list]]: [[121/120]], [[169/168]], [[275/273]]
+[[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 }})
 {{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
 {{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]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 453.242
+[[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
-{{Optimal ET sequence|legend=1| 5, 8, 13, 21, 29, 37, 44, 45, 188bde }}
+{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}
 [[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
@@ Line 978: / Line 1,038: @@
 {{See also | Chromatic pairs #Sentry }}
-Sentry, the 3 &amp; 5 temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
+Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
 [[Subgroup]]: 2.5/3.9/7
-[[Comma list]]: [[245/243]]
+[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})
 {{Mapping|legend=2| 1 0 0 | 0 2 1 }}
 {{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
 : [[gencom]]: [2 9/7; 245/243]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~9/7 = 440.902
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902
-{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc }}
+{{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
@@ Line 999: / Line 1,061: @@
 {{See also| Chromatic pairs #Marveltwintri }}
-Marveltwintri can be described as the 3 &amp; 4 temperament in the 2.5/3.13/9 subgroup.
+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]].
 [[Subgroup]]: 2.5/3.13/9
-[[Comma list]]: [[325/324]]
+[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})
 {{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
 {{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]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 317.139
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 882.886
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 882.861
-{{Optimal ET sequence|legend=1| 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b }}
+{{Optimal ET sequence|legend=1| 3, 4, 11, 15, 19, 34, 53, 87, 140 }}
 [[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
-== 2.….7/3… subgroups ==
+== 2.….7/3.… subgroups ==
 === Guanyintet ===
 {{See also | Chromatic pairs #Guanyintet }}
-Guanyintet, the 4 &amp; 9 temperament in the 2.5.7/3.11/3 subgroup, is related to [[guanyin]] as well as to [[orwell]].
+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.
 [[Subgroup]]: 2.5.7/3.11/3
-[[Comma list]]: [[176/175]], [[540/539]]
+[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -1 }})
-{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}
+{{Mapping|legend=2| 1 0 1 3 | 0 -3 1 -5 }}
+: mapping generators: ~2, ~7/6
 {{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]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 270.093
+[[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
-{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd }}
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}
+: <nowiki/>* wart for 7/3
 [[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents
+==== 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.
+[[Subgroup]]: 2.5.7/3.11/3.13
+[[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 }})
+{{Mapping|legend=2| 1 0 1 3 1 | 0 -3 1 -5 12 }}
+: mapping generators: ~2, ~12/7
+[[Optimal tuning]]s:
+* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~7/6 = 270.152
+* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~7/6 = 270.218
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 71, 111, 151, 262c*}} <small> using subgroup TE </small>
+: <nowiki/>* wart for 7/3
+Badness (Sintel): 0.329
 ==== Laz ====
 {{See also | Chromatic pairs #Laz }}
-Laz is related to [[georgian]] as well as to [[winston]].
+Laz is related to [[avalokita]] as well as to [[winston]].
 [[Subgroup]]: 2.5.7/3.11/3.13/3
-[[Comma list]]: [[144/143]], [[176/175]], [[196/195]]
+[[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=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
 {{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]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/7 = 930.598
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/7 = 930.700
-{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 58, 156bde, 205bde }}
+{{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]]: 0.8790 cents
@@ Line 1,069: / Line 1,155: @@
 [[Subgroup]]: 2.5.7/3.11/3.13/3
-[[Comma list]]: 56/55, 78/77, 91/90
+[[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 2 1 2 2 | 0 -3 -2 1 -1 }}
+{{Mapping|legend=2| 1 2 1 2 2 | 0 3 2 -1 1 }}
+: mapping generators: ~2, ~13/12
 {{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]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/12 = 132.428
+[[Optimal tuning]]s:
+* [[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| 9, 63, 82bd, 91bde }}
+{{Optimal ET sequence|legend=1| 1, …, 8, 9 }}
 [[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
@@ Line 1,090: / Line 1,178: @@
 [[Subgroup]]: 2.9/5.7/3.11/9
-[[Comma list]]: 100/99, 245/242
+[[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }})
 {{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
+: mapping generators: ~2, ~21/20
 {{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]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~21/20 = 87.776
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~21/20 = 87.892
-{{Optimal ET sequence|legend=1| 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd }}
+{{Optimal ET sequence|legend=1| 13, 14, 27, 41 }}
 [[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
@@ Line 1,107: / Line 1,197: @@
 {{See also| Chromatic pairs #Mothwelltri }}
-Mothwelltri, the 1 &amp; 4 temperament in the 2.7/3.11 subgroup, is related to [[orwell]].
+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.
 [[Subgroup]]: 2.7/3.11
-[[Comma list]]: [[99/98]]
+[[Comma list]]: [[99/98]] ({{monzo| -1 -2 1 }})
 {{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]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 273.174
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~7/6 = 273.695
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~7/6 = 273.174
-{{Optimal ET sequence|legend=1| 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc }}
+{{Optimal ET sequence|legend=1| 4, 9, 13, 22, 79 }}
 [[Tp tuning #T2 tuning|RMS error]]: 1.064 cents
-== 2.….9/7… subgroups ==
+== 2.….9/7.… subgroups ==
 === Marveltri ===
 {{See also| Chromatic pairs #Marveltri }}
-Marveltri, the 3 &amp; 13 temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed 22 &amp; 47 temperament.
+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.
 [[Subgroup]]: 2.5.9/7
-[[Comma list]]: 225/224
+[[Comma list]]: 225/224 ({{monzo| -5 2 1 }})
-{{Mapping|legend=2| 1 2 1 | 0 1 -2 }}
+{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
+: mapping generators: ~2, ~5
-{{Mapping|legend=3| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }}
+{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}
+: [[gencom]]: [2 5; 225/224]
-: [[gencom]]: [2 5/4; 225/224]
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 384.208
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 383.638
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 383.638
-{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}
-<nowiki>*</nowiki> wart for 9/7
+{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122, 269c* }}
+: <nowiki/>* wart for 9/7
 [[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
 ==== Sulis ====
-Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]]
+Sulis is related to [[minerva]] and [[würschmidt]].
-[[Subgroup]]: 2.5.9/7.11/7
+[[Subgroup]]: 2.5.9/7.11/9
-[[Comma list]]: 99/98, 176/175
+[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})
-{{Mapping|legend=2| 1 2 1 0 | 0 1 -2 2 }}]
+{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558
+[[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
 {{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
@@ Line 1,165: / Line 1,259: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
-== 2.….15/11… subgroups ==
+== 2.….7/5.… subgroups ==
+=== Hydrothermal ===
+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.
-=== Poggers ===
+[[Subgroup]]: 2.3.7/5
-Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]]
-[[Subgroup]]: 2.9.7.15/11.13
+[[Comma list]]: [[50/49]]
-[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]
+{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
-{{Mapping|legend=2| 1 1 1 -1 -1 | 0 6 5 4 13 }}
+[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
-[[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888
+[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
-[[Support]]ing [[ET]]s: 8[+9, +7, +13], 11, 14[-13], 19[+9, +7, ++13], 25[-13], 36, 47, 58, 61[-13], 69[+13], 80[+13], 83, 91[+9, +7, +13], 105
+=== Argentic ===
+Argentic is the 2.3.7/5 subgroup temperament tempering out [[5120/5103]].
-== 2.….7/5… subgroups ==
+[[Subgroup]]: 2.3.7/5
-=== Hydrothermal ===
-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
+[[Comma list]]: [[5120/5103]] = {{monzo| 10 -6 -1 }}
-[[Comma list]]: [[50/49]]
+{{Mapping|legend=2| 1 0 10 | 0 1 -6 }}
+: mapping generators: ~2, ~3
-{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
+[[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 tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
+{{Optimal ET sequence|legend=1| 12, 29, 41, 70, 321, 391, 461, 531, 601 }}
+<small> based on subgroup TE </small>
-[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
+Badness (Sintel): 0.119
-=== Edson ===
+==== Edson (2.3.7/5.11/5.13/5 subgroup) ====
 {{See also| Chromatic pairs #Edson }}
@@ Line 1,205: / Line 1,302: @@
 {{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
 : mapping generators: ~2, ~3
 {{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]
@@ Line 1,220: / Line 1,315: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
-=== Haumea ===
+==== Haumea ====
 {{See also| Chromatic pairs #Haumea }}
-Related temperaments include [[bridgetown]], [[namaka]], [[hemigari]], [[barbados]], and [[parizekmic]].
+Related temperaments include [[#Bridgetown|bridgetown]], [[namaka]], [[hemigari]], [[#Barbados|barbados]], and [[parizekmic]].
 [[Subgroup]]: 2.3.7/5.11/5.13/5
@@ Line 1,232: / Line 1,327: @@
 {{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]
@@ Line 1,243: / Line 1,337: @@
 === Historical ===
 {{distinguish|Historical temperaments}}
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+{{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.
+[[Subgroup]]: 2.3.7/5.11/5.13/5
 [[Comma list]]: 364/363, 441/440, 1001/1000
@@ Line 1,256: / Line 1,354: @@
 === Terrain ===
+{{Redirect|Terrain|the scale|Terrain (scale)}}
 {{See also| Chromatic pairs #Terrain }}
@@ Line 1,264: / Line 1,363: @@
 [[Comma list]]: [[250047/250000]]
-{{Mapping|legend=2| 3 4 0 | 0 -1 1 }}
+{{Mapping|legend=2| 3 1 3 | 0 1 -1 }}
 {{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
 : [[gencom]]: [63/50 10/9; 250047/250000]
@@ Line 1,278: / Line 1,376: @@
 === Tridec ===
 {{See also| Chromatic pairs #Tridec }}
+{{See also| Non-over-1 temperament #Tridec }}
 Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[#Petrtri]].
@@ Line 1,288: / Line 1,387: @@
 {{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]
@@ Line 1,297: / Line 1,395: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents
-== 2.….11/5… subgroups ==
+==== Naiadec ====
+[[Subgroup]]: 2.7/5.11/5.13/5.17/5
-=== Bridgetown ===
+[[Comma list]]: [[170/169]], [[221/220]], [[847/845]]
-{{See also| Chromatic pairs #Bridgetown }}
-Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[haumea]] and [[barbados]].
-[[Subgroup]]: 2.3.11/5.13/5
-[[Comma list]]: [[352/351]], [[676/675]]
-{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
-{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}
+{{Mapping|legend=2| 1 2 0 1 1 | 0 -4 3 1 2 }}
-: [[gencom]]: [2 15/13; 352/351 676/675]
+{{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]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.882
-{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
+{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 95<sup>t</sup>, 124<sup>t</sup> }}
+: <sup>t</sup> wart for 17/5
-[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.7521 cents
+== 2.….11/5.… subgroups ==
 === Petrtri ===
 {{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.
@@ Line 1,332: / Line 1,426: @@
 {{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}
 : [[gencom]]: [2 13/10; 2200/2197]
@@ Line 1,341: / Line 1,434: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents
-=== Hypnosis ===
+==== Bridgetown ====
-Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
+{{See also| Chromatic pairs #Bridgetown }}
-[[Subgroup]]: 2.3.7.11/5.13
+Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[#Haumea|haumea]] and [[#Barbados|barbados]].
-[[Comma list]]: 169/168, 540/539, 729/728
+[[Subgroup]]: 2.3.11/5.13/5
-{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
+[[Comma list]]: [[352/351]], [[676/675]]
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
+{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
-{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
+{{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]
-[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
-== 2.….11/7… subgroups ==
+{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
-=== 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.
+[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
-[[Subgroup]]: 2.3.11/7.13/7
+=== Hypnosis ===
+Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Alphatricot family #Alphatricot|alphatricot]]
-[[Comma list]]: 352/351, 364/363
+[[Subgroup]]: 2.3.7.11/5.13
-{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
+[[Comma list]]: 169/168, 540/539, 729/728
-{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
+{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
-: [[gencom]]: [2 3/2; 352/351 364/363]
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856
+{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
-{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*† }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
-<nowiki>*</nowiki> wart for 11/7
+=== Trisect ===
+Trisect divides every Pythagorean interval into three, and is the much more accurate subgroup restriction of [[Augmented family #Trisected|trisected]].
-<nowiki>†</nowiki> wart for 13/7
+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]].
-[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
+[[Subgroup]]: 2.3.7.11/5
+[[Comma list]]: 1029/1024, 4000/3993
-== 2.….13/5… subgroups ==
+{{Mapping|legend=2| 3 0 10 5 | 0 3 -1 -1 }}
-=== Barbados ===
-[[Subgroup]]: 2.3.13/5
-[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.742
-[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
+{{Optimal ET sequence|legend=1| 15, 21, 36, 123, 159, 195, 231 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
+[[Tp tuning #T2 tuning|RMS error]]: ???
-{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
+==== 2.3.7.11/5.13 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13
-[[Badness]]: 0.002335
+[[Comma list]]: 1029/1024, 1575/1573, 2080/2079
-<nowiki>*</nowiki> wart for 3/2
+{{Mapping|legend=2| 3 0 10 5 0 | 0 3 -1 -1 7 }}
-==== Tobago ====
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.918
-{{See also| Chromatic pairs #Tobago }}
-Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
+{{Optimal ET sequence|legend=1| 15, 21f, 36, 87, 123, 159 }}
-[[Subgroup]]: 2.3.11.13/5
+[[Tp tuning #T2 tuning|RMS error]]: ???
-[[Comma list]]: [[243/242]], [[676/675]]
+==== 2.3.7.11/5.13.17 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13.17
-{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}
+[[Comma list]]: 273/272, 833/832, 1575/1573, 2080/2079
-{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}
+{{Mapping|legend=2| 3 0 10 5 0 -2 | 0 3 -1 -1 7 9 }}
-: [[gencom]]: [55/39 15/13; 243/242 676/675]
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.820
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123, 159 }}
-{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
+[[Tp tuning #T2 tuning|RMS error]]: ???
-[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents
+===== Trisector =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19
-==== Pakkanian hemipyth ====
+[[Comma list]]: 210/209, 273/272, 286/285, 595/594, 2080/2079
-[[Subgroup]]: 2.3.11.13/5.17
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 | 0 3 -1 -1 7 9 3 }}
-[[Comma list]]: 221/220, 243/242, 289/288
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.894
-{{Mapping|legend=2| 2 0 -1 -2 5 | 0 2 5 3 2 }}
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123h, 159h }}
-[[Optimal tuning]]s:
+[[Tp tuning #T2 tuning|RMS error]]: ???
-* [[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)
+===== 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 ==
+=== 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
-{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}
+{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
-<nowiki>*</nowiki> wart for 13/5
+{{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]]
+== 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]].
+[[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}}
-=== Oceanfront ===
+{{Optimal ET sequence|legend=1| 7, 18, 25 }}
-Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]
-[[Subgroup]]: 2.3.7.13/5
+[[Badness]] (Sintel): 0.005
-[[Comma list]]: 64/63, 91/90
+==== 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.
-{{Mapping|legend=2| 1 0 6 -5 | 0 1 -2 4 }}
+Subgroup: 2.17/7.19/7.23/7
-[[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 1,492: / Line 1,772: @@
 {{Mapping|legend=2| 1 3 4 | 0 -4 -5 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,498: / Line 1,777: @@
 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>*</nowiki> wart for 3/2
 ==== 3/2.5/2.7/2.11/2 ====
@@ Line 1,507: / Line 1,785: @@
 {{Mapping|legend=2| 1 3 4 4 | 0 -4 -5 1 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,513: / Line 1,790: @@
 [[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>*</nowiki> wart for 3/2
 ==== 3/2.5/2.7/2.11/2.13/2 ====
@@ Line 1,526: / Line 1,802: @@
 [[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2]
+: <nowiki />* wart for 3/2
-<nowiki>*</nowiki> wart for 3/2
 === Semiwolf ===
@@ Line 1,564: / Line 1,839: @@
 [[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 1,593: / Line 1,868: @@
 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>*</nowiki> wart for 3/2
 === Doubleton ===
@@ Line 1,608: / Line 1,882: @@
 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>*</nowiki> wart for 3/2
 == 5/2-equave subgroups ==
 === Hyperion ===
 [[Subgroup]]: 5/2.7.11
@@ Line 1,625: / Line 1,897: @@
 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>*</nowiki> wart for 5/2
 = Related temperament collections =
@@ Line 1,633: / Line 1,904: @@
 * [[Substitute harmonic]] temperaments
-<!-- main article -->
+[[Category:Subgroup temperaments| ]] <!-- main article -->
+[[Category:Temperament collections]]
-[[Category:Temperament collections]][[Category:Subgroup]]
+{{Todo| review | cleanup }}

Subgroup temperaments: Difference between revisions