@@ 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.
@@ Line 12: / Line 13: @@
 = Composite subgroup temperaments =
 == 2.3.35 subgroup ==
-=== Shaka ===
+=== Darian calendar ===
-{{See also|Kalismic temperaments}}
+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]].
-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.
+==== 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: 2.3.35.11.29.41
+[[Subgroup]]: 2.3.11.19
-Comma list: 841/840, 1189/1188, 1681/1680
+{{Mapping|legend=2| 4 5 13 18 | 0 8 5 -6 }}
-{{Mapping|legend=2|2 2 6 5 7 8|0 1 1 -1 1 1|0 0 2 2 1 1}}
+: sval mapping generators: ~6291456/5285401, ~25289/24576
-Optimal tuning (CTE): ~41/29 = 1\2, ~3/2 = 702.031, ~41/24 = 926.693
+[[Optimal tuning]] ([[CTE]]): ~6291456/5285401 = 1\4, ~25289/24576 = 50.257
-[[Support]]ing [[ET]]s: {{EDOs|22, 26, 36, 48, 70, 96, 106, 118, 140, 154, 176, 188, 224, 272, 294, 342}}
+[[Support]]ing [[ET]]s: {{EDOs|24, 596, 620, 644, 668, 692, 716}}, ...
-Scale: [[Shaka10]]
+==== 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 ==
@@ Line 89: / Line 102: @@
 === 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 152: / Line 166: @@
 {{Optimal ET sequence|legend=1| 6, 23def, 29f, 35, 41, 47 }}
+== 2.3.25 subgroup ==
+=== 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: 2.3.25
+Edo join: 17 & 12
+Comma list: [[2048/2025]]
+{{Mapping|legend=2| 1 1 7| 0 1 -4}}
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.136
+==== 2.3.23.25.41 subgroup ====
+''See also: [[Reversed meantone]]''
+Edo join: 17 & 12
+Comma list: 2048/2025, 576/575, 82/81
+{{Mapping|legend=2| 1 1 1 7 3| 0 1 6 -4 4}}
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.264
+===== Sburb =====
+This temperament sets the [[octave reduction|octave-reduced]] 413th harmonic (413/256, 827.998{{c}}) to the diminished seventh.
+Subgroup: 2.3.7.23.25.41.59
+Edo join: 17 & 12
+Comma list: 64/63, 225/224, 162/161, 82/81, 177/175
+{{Mapping|legend=2| 1 1 4 1 7 3 10| 0 1 -2 6 -4 4 -7}}
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 706.387
 == 2.9.5.11 subgroup ==
@@ Line 288: / Line 341: @@
 [[Badness]]: 0.00439
-== 2.9.11 subgroup ==
+Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]
-=== 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
+== 2.9.7.13.17 subgroup ==
+=== 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]].
+[[Subgroup]]: 2.9.7.13.17
+[[Comma list]]: 729/728, 442/441, 833/832
+{{Mapping|legend=2| 1 1 1 -1 3| 0 6 5 13 3 }}
+[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~9/7 = 433.836
+Badness (Dirichlet): 0.142
+== 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.
+[[Subgroup]]: 2.9.11
 [[Comma list]]: [[1331/1296]]
@@ Line 374: / Line 444: @@
 == 2.9.21 subgroup ==
 === A-team ===
-A-team is every other step of [[mothra]].
+A-team is every other step of [[slendric]]; the 2.9.5.21.11 extension below specifically restricts [[mothra]].
 [[Subgroup]]: 2.9.21
@@ Line 394: / Line 464: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
-==== 2.9.5.21.11 ====
+==== 2.9.5.21 ====
+''Lookalike temperament: [[Dual-fifth_temperaments#Dual-3_A-Team|Dual-3 A-Team]]''
+Subgroup: 2.9.5.21
+[[Comma]] list: 81/80, 1029/1024
+Sval mapping: {{mapping| 1 2 0 4 | 0 3 6 1 }}
+Mapping generators: ~2, ~21/16
+Optimal ([[Lp tuning|POL2]]) generator: 464.3865
+{{Optimal ET sequence|legend=1| 13, 18, 31, 44 }}
+===== 2.9.5.21.11 =====
 Subgroup: 2.9.5.21.11
@@ Line 409: / Line 494: @@
 {{Optimal ET sequence|legend=1| 5, 13, 31 }}
-== 2.15.55 subgroup ==
+==== B-team ====
-=== Spog ===
+B-team (23 & 41) is every other step of [[rodan]].
-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).
+Subgroup: 2.9.15.21.33
-[[Subgroup]]: 2.15.55
+Comma list: 245/243, 385/384, 441/440
-[[Comma list]]: [[100663296/100656875]]
+Sval mapping: {{mapping| 1 2 0 4 7 | 0 3 10 1 -5 }}
-{{Mapping|legend=2| 1 0 5 | 0 5 1 }}
+Optimal tuning (subgroup POTE): ~2 = 1\1, ~21/16 = 468.918
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.655
+{{Optimal ET sequence|legend=1| 5, 13c, 18, 23, 41, 64, 87, 151 }}
-{{Optimal ET sequence|legend=1|5, 9, 23, 32, 151, 183, 215, 247, 956, 1203, 1450, 3147, 4597 }}
+== 4.3.5 subgroup ==
+=== Tetrahanson ===
+{{Main| Tetrahanson }}
-==== 2.15.55.325 ====
+[[Subgroup]]: 4.3.5
-[[Subgroup]]: 2.15.55.325
-[[Comma list]]: [[4225/4224]], [[6656/6655]]
+[[Comma list]]: 15625/15552
-{{Mapping|legend=2| 1 0 5 6 | 0 5 1 3 }}
+{{Mapping|legend=2| 1 3 3 | 0 -6 -5 }}
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.647
+: Mapping generators: ~4, ~5/3
-[[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]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941
-==== 2.15.189.55.325 ====
+[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
-Related temperament: [[Lehmerismic_temperaments#Lux|lux]]
-[[Subgroup]]: 2.15.189.55.325
+=== Tetrameantone ===
+{{Main| Tetrameantone }}
-[[Comma list]]: [[2080/2079]], [[3025/3024]], [[4096/4095]]
+[[Subgroup]]: 4.3.5
-{{Mapping|legend=2| 1 0 6 5 6 | 0 5 2 1 3 }}
+[[Comma list]]: 81/80
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.677
+{{Mapping|legend=2| 1 1 2 | 0 -1 -4 }}
-[[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
+: Mapping generators: ~4, ~4/3
-==== 2.15.189.55.325.725 ====
+[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~4/3 = 503.761
-[[Subgroup]]: 2.15.189.55.325.725
+[[Support]]ing [[ET]]s: {{EDs|5, 9, 14, 19, 24, 43, 62, 81, 100|equave=4}}
-[[Comma list]]: [[1625/1624]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
+=== Tetramagic ===
-{{Mapping|legend=2| 1 0 6 5 6 -3 | 0 5 2 1 3 16 }}
+[[Subgroup]]: 4.3.5
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.649
+[[Comma list]]: 3125/3072
-[[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
+{{Mapping|legend=2| 1 0 1 | 0 5 1 }}
-==== 2.15.189.55.325.725.279 ====
+: Mapping generators: ~4, ~5/4
-Here are rational approximations to the intervals of the semiquartal scale.
+[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~5/4 = 380.059
-Sharp: 12/11, 25/21, 33/26, 18/13, 31/21 ~ 65/44 ~ 96/65, 50/31 ~ 29/18, 55/32, 15/8.
+[[Support]]ing [[ET]]s: {{EDs|6, 13, 19, 25, 38, 44, 63, 82|equave=4}}
-Flat: 16/15, 64/55, 31/25 ~ 36/29, 42/31 ~ 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6.
+=== Blacktetra ===
-[[Subgroup]]: 2.15.189.55.325.725.279
-[[Comma list]]: [[1625/1624]], [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
+[[Subgroup]]: 4.3.5
-{{Mapping|legend=2| 1 0 6 5 6 -3 5 | 0 5 2 1 3 16 4 }}
+[[Comma list]]: 256/243
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.638
+{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}
-[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 151, 183, 206[+725], 311
+: Mapping generators: ~4, ~16/15
-== 4.3.5 subgroup ==
+[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062
-=== Tetrahanson ===
-{{Main| Tetrahanson }}
-[[Subgroup]]: 4.3.5
+[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}
-[[Comma list]]: 15625/15552
+== 4.6.5 subgroup ==
+=== Meanquad ===
+{{Main| Meanquad }}
-{{Mapping|legend=2| 1 3 3 | 0 -6 -5 }}
+[[Subgroup]]: 4.6.5
-: Mapping generators: ~4, ~5/3
+[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}
-[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941
+{{Mapping|legend=2| 1 0 -4| 0 1 4 }}
-[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
+: mapping generators: ~4, ~6
-=== Tetrameantone ===
+[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214
-{{Main| Tetrameantone }}
-[[Subgroup]]: 4.3.5
+[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
-[[Comma list]]: 81/80
+<nowiki />* Wart for 4
-{{Mapping|legend=2| 1 1 2 | 0 -1 -4 }}
+==== 4.6.5.7 subgroup (tetrominant) ====
+[[Subgroup]]: 4.6.5.7
-: Mapping generators: ~4, ~4/3
+[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}
-[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~4/3 = 503.761
+{{Mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}
-[[Support]]ing [[ET]]s: {{EDs|5, 9, 14, 19, 24, 43, 62, 81, 100|equave=4}}
+[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622
-=== Tetramagic ===
+[[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]
-[[Subgroup]]: 4.3.5
+<nowiki />* Wart for 4
-[[Comma list]]: 3125/3072
+=== 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.
-{{Mapping|legend=2| 1 0 1 | 0 5 1 }}
+Fourwar is named after the closely related [[hemiwar]] temperament.
-: Mapping generators: ~4, ~5/4
+{{Todo|inline=1|cleanup}}
-[[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
+[ ⟨	1	0	1	]
-=== Blacktetra ===
+⟨	0	16	2	] ⟩
-[[Subgroup]]: 4.3.5
+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)
-[[Comma list]]: 256/243
+Subsets
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+</pre>
-{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}
+==== 4.6.5.7 ====
+<pre>
-: Mapping generators: ~4, ~16/15
+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)
-[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062
+Subsets
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+</pre>
-[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}
+==== 4.6.5.7.11 ====
+<pre>
-== 4.6.5 subgroup ==
+Reduced Mapping
-=== Meanquad ===
+	6	5	7	11
-{{Main| Meanquad }}
+[ ⟨	1	0	1	1	1	]
+⟨	0	16	2	5	9	] ⟩
-[[Subgroup]]: 4.6.5
+TE Generator Tunings (cents)
-[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}
+⟨2400.1097, 193.9498]
-{{Mapping|legend=2| 1 0 -4| 0 1 4 }}
+TE Step Tunings (cents)
+⟨24.18752, 48.52491]
-: mapping generators: ~4, ~6
+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)
-[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214
+Subsets
+q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
+</pre>
-[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
+==== 4.6.5.7.11.13 ====
-<nowiki />* Wart for 4
+<pre>
+Reduced Mapping
-==== 4.6.5.7 subgroup (tetrominant) ====
+	6	5	7	11	13
-[[Subgroup]]: 4.6.5.7
+[ ⟨	1	0	1	1	1	0	]
+⟨	0	16	2	5	9	23	] ⟩
-[[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
-[[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.
-<pre>
-Reduced Mapping
-	6	5
-[ ⟨	1	0	1	]
-⟨	0	16	2	] ⟩
 TE Generator Tunings (cents)
-⟨2399.3973, 193.8643]
+⟨2401.2305, 193.5378]
 TE Step Tunings (cents)
-⟨25.21211, 47.81337]
+⟨42.79107, 35.98524]
 TE Tuning Map (cents)
-⟨2399.397, 3101.829, 2787.126]
+⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
 TE Mistunings (cents)
-⟨-0.603, -0.126, 0.812]
+⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]
-Complexity	1.369085
+Complexity	1.219191
-Adjusted Error	0.692892 cents
+Adjusted Error	6.699599 cents
-TE Error	0.268047 cents/octave
+TE Error	1.810487 cents/octave
-Unison Vector
+Unison Vectors
-[8, 1, -8⟩ (393216:390625)
+[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
-q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
 </pre>
-==== 4.6.5.7 ====
+==== 4.6.5.7.11.13.17 ====
 <pre>
 Reduced Mapping
-	6	5	7
+	6	5	7	11	13	17
-[ ⟨	1	0	1	1	]
+[ ⟨	1	0	1	1	1	0	1	]
-⟨	0	16	2	5	] ⟩
+⟨	0	16	2	5	9	23	13	] ⟩
 TE Generator Tunings (cents)
-⟨2399.4195, 193.8654]
+⟨2400.4701, 193.4599]
 TE Step Tunings (cents)
-⟨25.23883, 47.79592]
+⟨43.39350, 35.55764]
 TE Tuning Map (cents)
-⟨2399.420, 3101.846, 2787.150, 3368.747]
+⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]
 TE Mistunings (cents)
-⟨-0.580, -0.109, 0.837, -0.079]
+⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]
-Complexity	1.192044
+Complexity	1.129881
-Adjusted Error	0.653313 cents
+Adjusted Error	8.082725 cents
-TE Error	0.232715 cents/octave
+TE Error	1.977443 cents/octave
 Unison Vectors
-[-2, -1, -2, 4⟩ (2401:2400)
+[0, 1, -1, 0, 1, -1, 0⟩ (66:65)
-[3, 0, -5, 2⟩ (3136:3125)
+[1, 1, 1, -1, 0, 0, -1⟩ (120:119)
-[5, 1, -3, -2⟩ (6144:6125)
+[1, 2, 0, 0, -1, -1, 0⟩ (144:143)
-[8, 1, -8, 0⟩ (393216:390625)
+[-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
-q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg
 </pre>
-==== 4.6.5.7.11 ====
+==== 4.6.5.7.11.13.17.19 ====
 <pre>
 Reduced Mapping
-	6	5	7	11
+	6	5	7	11	13	17	19
-[ ⟨	1	0	1	1	1	]
+[ ⟨	1	0	1	1	1	0	1	1	]
-⟨	0	16	2	5	9	] ⟩
+⟨	0	16	2	5	9	23	13	14	] ⟩
 TE Generator Tunings (cents)
-⟨2400.1097, 193.9498]
+⟨2399.9219, 193.3952]
 TE Step Tunings (cents)
-⟨24.18752, 48.52491]
+⟨44.14256, 35.03670]
 TE Tuning Map (cents)
-⟨2400.110, 3103.196, 2788.009, 3369.859, 4145.658]
+⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
 TE Mistunings (cents)
-⟨0.110, 1.241, 1.696, 1.033, -5.660]
+⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]
-Complexity	1.068792
+Complexity	1.058472
-Adjusted Error	2.926965 cents
+Adjusted Error	8.712222 cents
-TE Error	0.846083 cents/octave
+TE Error	2.050935 cents/octave
 Unison Vectors
-[-1, -1, -1, 0, 2⟩ (121:120)
+[0, 1, -1, 0, 1, -1, 0, 0⟩ (66:65)
-[2, 0, -2, -1, 1⟩ (176:175)
+[-1, 0, 0, 1, 1, 0, 0, -1⟩ (77:76)
-[-3, -1, 1, 1, 1⟩ (385:384)
+[2, 1, -1, 0, 0, 0, 0, -1⟩ (96:95)
-[-1, 0, 3, -3, 1⟩ (1375:1372)
+[1, 1, 1, -1, 0, 0, -1, 0⟩ (120:119)
-[-2, -1, -2, 4, 0⟩ (2401:2400)
+[0, 1, 1, 1, -1, 0, 0, -1⟩ (210:209)
-[1, 0, 1, -4, 2⟩ (2420:2401)
+[0, 0, 1, -2, 1, 0, 1, -1⟩ (935:931)
+[2, 0, -3, 1, 0, 0, -1, 1⟩ (2128:2125)
 Subsets
-q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
+q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh
 </pre>
-==== 4.6.5.7.11.13 ====
+==== 4.6.5.7.11.13.17.19.23 ====
 <pre>
 Reduced Mapping
-	6	5	7	11	13
+	6	5	7	11	13	17	19	23
-[ ⟨	1	0	1	1	1	0	]
+[ ⟨	1	0	1	1	1	0	1	1	0	]
-⟨	0	16	2	5	9	23	] ⟩
+⟨	0	16	2	5	9	23	13	14	28	] ⟩
 TE Generator Tunings (cents)
-⟨2401.2305, 193.5378]
+⟨2399.3286, 193.5316]
 TE Step Tunings (cents)
-⟨42.79107, 35.98524]
+⟨37.31613, 39.63311]
 TE Tuning Map (cents)
-⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
+⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
 TE Mistunings (cents)
-⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]
+⟨-0.671, -5.449, 0.078, -1.839, -10.205, 10.699, 10.284, 11.258, -9.389]
-Complexity	1.219191
+Complexity	1.115920
-Adjusted Error	6.699599 cents
+Adjusted Error	9.502017 cents
-TE Error	1.810487 cents/octave
+TE Error	2.100561 cents/octave
 Unison Vectors
-[0, 1, -1, 0, 1, -1⟩ (66:65)
+[0, 1, -1, 0, 1, -1, 0, 0, 0⟩ (66:65)
-[-1, -1, -1, 0, 2, 0⟩ (121:120)
+[1, 0, 0, -1, 0, -1, 0, 0, 1⟩ (92:91)
-[1, 2, 0, 0, -1, -1⟩ (144:143)
+[0, -1, 1, 0, 0, 0, 0, -1, 1⟩ (115:114)
-[2, 0, -2, -1, 1, 0⟩ (176:175)
+[1, 1, 1, -1, 0, 0, -1, 0, 0⟩ (120:119)
-[-2, 1, 1, 1, 0, -1⟩ (105:104)
+[2, 0, -2, -1, 1, 0, 0, 0, 0⟩ (176:175)
-[-3, -1, 1, 1, 1, 0⟩ (385:384)
+[-3, -1, 1, 1, 1, 0, 0, 0, 0⟩ (385:384)
-[-3, 0, 0, 1, 2, -1⟩ (847:832)
+[1, 0, -2, 1, 0, 0, 1, -1, 0⟩ (476:475)
-[1, 3, -1, 0, 0, -2⟩ (864:845)
+[1, 0, 0, -2, 1, 0, -1, 1, 0⟩ (836:833)
-[-1, 0, 3, -3, 1, 0⟩ (1375:1372)
+[0, 0, 1, -2, 1, 0, 1, -1, 0⟩ (935:931)
+[1, -1, 0, 0, 0, 0, -2, 1, 1⟩ (874:867)
 Subsets
-q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
+q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii
 </pre>
-==== 4.6.5.7.11.13.17 ====
+== 4.9.25 subgroup ==
-<pre>
+=== Meansquared ===
-Reduced Mapping
+[[Subgroup]]: 4.9.25
-	6	5	7	11	13	17
-[ ⟨	1	0	1	1	1	0	1	]
+[[Comma list]]: [[6561/6400]]
-⟨	0	16	2	5	9	23	13	] ⟩
+{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
-TE Generator Tunings (cents)
-⟨2400.4701, 193.4599]
+Mapping generators: ~4, ~9/64
-TE Step Tunings (cents)
+[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
-⟨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
+[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
-q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg
-</pre>
-==== 4.6.5.7.11.13.17.19 ====
+== 4.9.49 subgroup ==
-<pre>
+=== Archsquared ===
-Reduced Mapping
+[[Subgroup]]: 4.9.49
-	6	5	7	11	13	17	19
-[ ⟨	1	0	1	1	1	0	1	1	]
+[[Comma list]]: 4096/3969
-⟨	0	16	2	5	9	23	13	14	] ⟩
+{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}
-TE Generator Tunings (cents)
-⟨2399.9219, 193.3952]
+Mapping generators: ~4, ~9/64
-TE Step Tunings (cents)
+[[Optimal tuning]] ([[CTE]]): ~9/4 = 1419.190
-⟨44.14256, 35.03670]
+[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
-TE Tuning Map (cents)
-⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
+== 8.9.7 subgroup ==
+=== Sixscared ===
-TE Mistunings (cents)
+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."
-⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]
+[[Subgroup]]: 8.9.7
-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)
-Subsets
+[[Comma list]]: 64/63
-q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh
-</pre>
-==== 4.6.5.7.11.13.17.19.23 ====
+{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
-<pre>
-Reduced Mapping
+: sval mapping generators: ~8, ~9
-	6	5	7	11	13	17	19	23
-[ ⟨	1	0	1	1	1	0	1	1	0	]
+: [[gencom]]: [8 9/8; 64/63]
-⟨	0	16	2	5	9	23	13	14	28	] ⟩
+[[Optimal tuning]] ([[CTE]]): ~9/8 = 219.1898
-TE Generator Tunings (cents)
-⟨2399.3286, 193.5316]
+[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}
-TE Step Tunings (cents)
+[[Badness]]: 0.0215 × 10<sup>-3</sup>
-⟨37.31613, 39.63311]
+= Fractional subgroup temperaments =
-TE Tuning Map (cents)
+== 2.5/3.… subgroups ==
-⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
+=== Magicaltet ===
+{{See also| Chromatic pairs #Magicaltet }}
-TE Mistunings (cents)
-⟨-0.671, -5.449, 0.078, -1.839, -10.205, 10.699, 10.284, 11.258, -9.389]
+Magicaltet is related to [[keemic]], [[superkleismic]], and [[magic]]. The tonic and the first three generator steps make a [[magical seventh chord]], hence the name.
-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)
-Subsets
+[[Subgroup]]: 2.5/3.7.11
-q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii
-</pre>
-== 4.9.25 subgroup ==
+[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})
-=== Meansquared ===
-[[Subgroup]]: 4.9.25
-[[Comma list]]: [[6561/6400]]
+{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
+: mapping generators: ~2, ~5/3
-{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
+{{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]
-Mapping generators: ~4, ~9/64
+[[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
-[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
+{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
+: <nowiki/>* wart for 5/3
-[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
+[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
-== 4.9.49 subgroup ==
+=== Starlingtet ===
-=== Archsquared ===
+{{See also | Chromatic pairs #Starlingtet }}
-[[Subgroup]]: 4.9.49
-[[Comma list]]: 4096/3969
+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=2| 1 3 0 | 0 1 -2 }}
+[[Subgroup]]: 2.5/3.7/3
-Mapping generators: ~4, ~9/64
+[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})
-[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 219.190
+{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
-[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
+: mapping generators: ~2, ~5/3
-== 8.9.7 subgroup ==
+{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
-=== Sixscared ===
+: [[gencom]]: [2 6/5; 126/125]
-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."
-[[Subgroup]]: 8.9.7
+[[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
-[[Comma list]]: 64/63
+{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}
-{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents
-: sval mapping generators: ~8, ~9
+==== Greeley ====
+{{See also| Chromatic pairs #Greeley }}
-: [[gencom]]: [8 9/8; 64/63]
+Greeley is related to [[opossum]] as well as to [[nusecond]].
-[[Optimal tuning]] ([[CTE]]): 1\[[3ed8]] = 1600.0, ~9/8 = 219.1898
+[[Subgroup]]: 2.5/3.7/3.11/3
-[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}
+[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})
-[[Badness]]: 0.0215 × 10<sup>-3</sup>
+{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
-= Fractional subgroup temperaments =
+{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}
-== 2.5/3… subgroups ==
+: [[gencom]]: [2 11/10; 121/120 126/125]
-=== Magicaltet ===
-{{See also| Chromatic pairs #Magicaltet }}
-Magicaltet is related to [[supermagic]], [[superkleismic]], and [[magic]]. The tonic and the first three generator steps make a [[magical seventh chord]], hence the name.
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~11/10 = 155.696
-[[Subgroup]]: 2.5/3.7.11
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~11/10 = 155.776
-[[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }}
+{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
+: <nowiki/>* wart for 11/3
-{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
+[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents
-: mapping generators: ~2, ~5/3
+==== Skateboard ====
+{{See also| Chromatic pairs #Skateboard }}
-{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
+Skateboard is related to [[thrasher]].
-: [[gencom]]: [2 6/5; 100/99 385/384]
+[[Subgroup]]: 2.5/3.7/3.11.13/9
-[[Optimal tuning]]s:
+[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }})
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 877.343
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 877.351
-{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
+{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
-<nowiki />* Wart for 5/3
+{{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]
-[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
+[[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
-=== Starlingtet ===
+{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}
-{{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]]. The tonic and the first three generator steps make a [[starling tetrad]], hence the name.
+[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents
-[[Subgroup]]: 2.5/3.7/3
+=== Gariberttet ===
+Gariberttet is the 2.5/3.7/3 [[Subgroup temperament families, relationships, and genes|altergene]] of [[sirius]].
+==== Gariberttet (2.5/3.7/3.13/11 subgroup) ====
+{{See also | Chromatic pairs #Gariberttet }}
-[[Comma list]]: [[126/125]] = {{monzo| 1 -3 1 }}
+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]].
-{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
+[[Subgroup]]: 2.5/3.7/3.13/11
-: mapping generators: ~2, ~5/3
+[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})
-{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
+{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
-: [[gencom]]: [2 6/5; 126/125]
+{{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]]: ~2 = 1200.000, ~5/3 = 888.759
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~13/11 = 293.679
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 888.846
-{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}
+{{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]]: 0.8398 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
-==== Greeley ====
+==== Indium ====
-{{See also| Chromatic pairs #Greeley }}
+{{See also | Chromatic pairs #Indium }}
-Greeley is related to [[opossum]] as well as to [[nusecond]].
+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]]: 121/120 = {{monzo| -3 -1 0 2 }}, 126/125 = {{monzo| 1 -3 1 }}
+[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }})
-{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
+{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
-{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}
+{{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]
-: [[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]] [[CTE]]: ~2 = 1200.000, ~12/11 = 146.978
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~11/10 = 155.776
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/11 = 147.010
-{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
+{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*<sup>†</sup> }}
+: <nowiki/>* wart for 7/3
+: <sup>†</sup> wart for 11/3
-<nowiki />* Wart for 11/3
+[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
-[[Tp tuning#T2 tuning|RMS error]]: 1.034 cents
+==== Ammon ====
+{{See also| Chromatic pairs #Ammon }}
-==== 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.
-{{See also| Chromatic pairs #Skateboard }}
-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 }}
+: [[gencom]]: [2 13/10; 121/120 169/168 275/273]
-{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}
+[[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
-: [[gencom]]: [2 6/5; 56/55 91/90 100/99]
+{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}
-[[Optimal tuning]]s:
+[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
-* [[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 }}
+=== Sentry ===
+{{See also | Chromatic pairs #Sentry }}
-[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents
+Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
-=== Gariberttet ===
+[[Subgroup]]: 2.5/3.9/7
-Gariberttet is the 2.5/3.7/3 [[Subgroup Temperament Families, Relationships, and Genes|altergene]] of [[sirius]].
-==== Gariberttet (2.5/3.7/3.13/11 subgroup) ====
+[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})
-{{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.
+{{Mapping|legend=2| 1 0 0 | 0 2 1 }}
-[[Subgroup]]: 2.5/3.7/3.13/11
+{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
+: [[gencom]]: [2 9/7; 245/243]
-[[Comma list]]: [[275/273]] = {{monzo| 0 2 -1 -1 }}, [[847/845]] = {{monzo| 0 -1 1 -2 }}
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902
-{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
+{{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
-{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
-: [[gencom]]: [2 13/11; 275/273 847/845]
+=== Marveltwintri ===
+{{See also| Chromatic pairs #Marveltwintri }}
-[[Optimal tuning]]s:
+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]].
-* [[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* }}
+[[Subgroup]]: 2.5/3.13/9
-<nowiki />* Wart for 13/11
+[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})
-[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
+{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
-==== Indium ====
+{{Mapping|legend=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}
-{{See also | Chromatic pairs #Indium }}
+: [[gencom]]: [2 6/5; 325/324]
-Indium can be described as the 8 &amp; 33 temperament in the 2.5/3.7/3.11/3 subgroup.
+[[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
-[[Subgroup]]: 2.5/3.7/3.11/3
+{{Optimal ET sequence|legend=1| 3, 4, 11, 15, 19, 34, 53, 87, 140 }}
-[[Comma list]]: [[3025/3024]] = {{monzo| -4 2 -1 2 }}, [[3125/3087]] = {{monzo| 0 5 -3 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
-{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
+== 2.….7/3.… subgroups ==
+=== Guanyintet ===
+{{See also | Chromatic pairs #Guanyintet }}
-{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}
+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.
-: [[gencom]]: [2 12/11; 3025/3024 3125/3087]
+[[Subgroup]]: 2.5.7/3.11/3
-[[Optimal tuning]]s:
+[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -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=2| 1 0 1 3 | 0 -3 1 -5 }}
+: mapping generators: ~2, ~7/6
-<nowiki />* Wart for 7/3
+{{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]
-<sup>†</sup> Wart for 11/3
+[[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
-[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}
+: <nowiki/>* wart for 7/3
-==== Semidim ====
+[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents
-{{See also| Chromatic pairs #Semidim }}
-Semidim can be described as the 8 &amp; 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 name.
+==== 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]]: 2.5/3.7/3.11/3.13/3
+[[Subgroup]]: 2.5.7/3.11/3.13
-[[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]]: [[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 3 5 3 4 | 0 -6 -10 -3 -5 }}
+{{Mapping|legend=2| 1 0 1 3 1 | 0 -3 1 -5 12 }}
+: mapping generators: ~2, ~12/7
-{{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]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/10 = 453.121
+* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~7/6 = 270.152
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/10 = 453.242
+* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~7/6 = 270.218
-{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 71, 111, 151, 262c*}} <small> using subgroup TE </small>
+: <nowiki/>* wart for 7/3
-[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
+Badness (Sintel): 0.329
-=== Sentry ===
+==== Laz ====
-{{See also | Chromatic pairs #Sentry }}
+{{See also | Chromatic pairs #Laz }}
-Sentry, the 3 &amp; 5 temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
+Laz is related to [[avalokita]] as well as to [[winston]].
-[[Subgroup]]: 2.5/3.9/7
+[[Subgroup]]: 2.5.7/3.11/3.13/3
-[[Comma list]]: [[245/243]] = {{monzo| 0 1 -2 }}
+[[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 0 | 0 2 1 }}
+{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
-{{Mapping|legend=3| 1 0 0 0 | 0 0 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 }}
+: [[gencom]]: [2 7/6; 144/143 176/175 196/195]
-: [[gencom]]: [2 9/7; 245/243]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1\1, ~9/7 = 440.902
+* [[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| 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| 9, 31, 40, 49, 156c*†, 205c*† }}
+: <nowiki/>* wart for 7/3
+: † wart for 11/3
-<nowiki />* Wart for 5/3
+[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents
-<sup>†</sup> Wart for 9/7
+=== Kryptonite ===
+{{See also| Chromatic pairs #Kryptonite }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
+Kryptonite is related to [[krypton]].
-=== Marveltwintri ===
+[[Subgroup]]: 2.5.7/3.11/3.13/3
-{{See also| Chromatic pairs #Marveltwintri }}
-Marveltwintri can be described as the 3 &amp; 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]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 78/77 ({{monzo| 1 0 -1 -1 1 }}), 91/90 ({{monzo| -1 -2 1 0 1 }})
-[[Subgroup]]: 2.5/3.13/9
+{{Mapping|legend=2| 1 2 1 2 2 | 0 3 2 -1 1 }}
+: mapping generators: ~2, ~13/12
-[[Comma list]]: [[325/324]] = {{monzo| -2 2 1 }}
+{{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=2| 1 0 2 | 0 1 -2 }}
+[[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
-{{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| 1, …, 8, 9 }}
-: [[gencom]]: [2 6/5; 325/324]
+[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
-[[Optimal tuning]]s:
+=== Kiribati ===
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 886.886
+{{See also| Chromatic pairs #Kiribati }}
-* [[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 }}
+Kiribati is related to [[nakika]] as well as to [[octacot]].
-[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
+[[Subgroup]]: 2.9/5.7/3.11/9
-== 2.….7/3… subgroups ==
+[[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }})
-=== 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]].
+{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
+: mapping generators: ~2, ~21/20
-[[Subgroup]]: 2.5.7/3.11/3
+{{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]
-[[Comma list]]: [[176/175]], [[540/539]]
+[[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
-{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}
+{{Optimal ET sequence|legend=1| 13, 14, 27, 41 }}
-{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}
+[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
-: [[gencom]]: [2 7/6; 176/175 540/539]
+=== Mothwelltri ===
+{{See also| Chromatic pairs #Mothwelltri }}
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 270.093
+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.
-{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd }}
+[[Subgroup]]: 2.7/3.11
-[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents
+[[Comma list]]: [[99/98]] ({{monzo| -1 -2 1 }})
-==== Laz ====
+{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
-{{See also | Chromatic pairs #Laz }}
+: mapping generators: ~2, ~7/3
-Laz is related to [[georgian]] as well as to [[winston]].
+{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
+: [[gencom]]: [2 7/6; 99/98]
-[[Subgroup]]: 2.5.7/3.11/3.13/3
+[[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
-[[Comma list]]: [[144/143]], [[176/175]], [[196/195]]
+{{Optimal ET sequence|legend=1| 4, 9, 13, 22, 79 }}
-{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
+[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents
-{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}
+== 2.….9/7.… subgroups ==
+=== Marveltri ===
+{{See also| Chromatic pairs #Marveltri }}
-: [[gencom]]: [2 7/6; 144/143 176/175 196/195]
+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.
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300
+[[Subgroup]]: 2.5.9/7
-{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 58, 156bde, 205bde }}
+[[Comma list]]: 225/224 ({{monzo| -5 2 1 }})
-[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents
+{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
+: mapping generators: ~2, ~5
-=== Kryptonite ===
+{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}
-{{See also| Chromatic pairs #Kryptonite }}
+: [[gencom]]: [2 5; 225/224]
-Kryptonite is related to [[krypton]].
+[[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
-[[Subgroup]]: 2.5.7/3.11/3.13/3
+{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122, 269c* }}
+: <nowiki/>* wart for 9/7
-[[Comma list]]: 56/55, 78/77, 91/90
+[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
-{{Mapping|legend=2| 1 2 1 2 2 | 0 -3 -2 1 -1 }}
+==== Sulis ====
+Sulis is related to [[minerva]] and [[würschmidt]].
-{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}
+[[Subgroup]]: 2.5.9/7.11/9
-: [[gencom]]: [2 13/12; 56/55 78/77 91/90]
+[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/12 = 132.428
+{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]
-{{Optimal ET sequence|legend=1| 9, 63, 82bd, 91bde }}
+[[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
-[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
+{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
-=== Kiribati ===
+[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
-{{See also| Chromatic pairs #Kiribati }}
-Kiribati is related to [[nakika]] as well as to [[octacot]].
+== 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.
-[[Subgroup]]: 2.9/5.7/3.11/9
+[[Subgroup]]: 2.3.7/5
-[[Comma list]]: 100/99, 245/242
+[[Comma list]]: [[50/49]]
-{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
+{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
-{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
+[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
-: [[gencom]]: [2 21/20; 100/99 245/242]
+[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892
+=== Argentic ===
+Argentic is the 2.3.7/5 subgroup temperament tempering out [[5120/5103]].
-{{Optimal ET sequence|legend=1| 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd }}
+[[Subgroup]]: 2.3.7/5
-[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
+[[Comma list]]: [[5120/5103]] = {{monzo| 10 -6 -1 }}
-=== Mothwelltri ===
+{{Mapping|legend=2| 1 0 10 | 0 1 -6 }}
-{{See also| Chromatic pairs #Mothwelltri }}
+: mapping generators: ~2, ~3
-Mothwelltri, the 1 &amp; 4 temperament in the 2.7/3.11 subgroup, is related to [[orwell]].
+[[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
-[[Subgroup]]: 2.7/3.11
+{{Optimal ET sequence|legend=1| 12, 29, 41, 70, 321, 391, 461, 531, 601 }}
+<small> based on subgroup TE </small>
-[[Comma list]]: [[99/98]]
+Badness (Sintel): 0.119
-{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
+==== Edson (2.3.7/5.11/5.13/5 subgroup) ====
+{{See also| Chromatic pairs #Edson }}
-{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
+Edson is related to [[pele]] and [[andromeda]].
-: [[gencom]]: [2 7/6; 99/98]
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 273.174
+[[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 }}
-{{Optimal ET sequence|legend=1| 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc }}
+{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
+: mapping generators: ~2, ~3
-[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents
+{{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]
-== 2.….9/7… subgroups ==
+[[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
-=== Marveltri ===
+{{Optimal ET sequence|legend=1| 12, 17, 29 }}
-{{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.
+[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
-[[Subgroup]]: 2.5.9/7
+==== Haumea ====
+{{See also| Chromatic pairs #Haumea }}
-[[Comma list]]: 225/224
+Related temperaments include [[#Bridgetown|bridgetown]], [[namaka]], [[hemigari]], [[#Barbados|barbados]], and [[parizekmic]].
-{{Mapping|legend=2| 1 2 1 | 0 1 -2 }}
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-{{Mapping|legend=3| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }}
+[[Comma list]]: [[352/351]], [[676/675]], [[847/845]]
-: [[gencom]]: [2 5/4; 225/224]
+{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 383.638
+{{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 ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
-<nowiki />* Wart for 9/7
+{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents
-==== Sulis ====
+=== Historical ===
-Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]]
+{{distinguish|Historical temperaments}}
+{{distinguish|History (temperament)}}, which is the rank-3 version of this temperament in the full 13-limit.
-[[Subgroup]]: 2.5.9/7.11/7
+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.
-[[Comma list]]: 99/98, 176/175
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-{{Mapping|legend=2| 1 2 1 0 | 0 1 -2 2 }}]
+[[Comma list]]: 364/363, 441/440, 1001/1000
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558
+{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
-{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
-[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
+{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
-== 2.….15/11… subgroups ==
+[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
-=== Poggers ===
+=== Terrain ===
-Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]]
+{{Redirect|Terrain|the scale|Terrain (scale)}}
+{{See also| Chromatic pairs #Terrain }}
-[[Subgroup]]: 2.9.7.15/11.13
+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.
-[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]
+[[Subgroup]]: 2.7/5.9/5
-{{Mapping|legend=2| 1 1 1 -1 -1 | 0 6 5 4 13 }}
+[[Comma list]]: [[250047/250000]]
-[[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888
+{{Mapping|legend=2| 3 1 3 | 0 1 -1 }}
-[[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
+{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
+: [[gencom]]: [63/50 10/9; 250047/250000]
-== 2.….7/5… subgroups ==
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
-=== Hydrothermal ===
+{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
-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
+[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
-[[Comma list]]: [[50/49]]
+=== Tridec ===
+{{See also| Chromatic pairs #Tridec }}
+{{See also| Non-over-1 temperament #Tridec }}
-{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
+Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[#Petrtri]].
-[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
+[[Subgroup]]: 2.7/5.11/5.13/5
-[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
+[[Comma list]]: [[847/845]], [[1001/1000]]
-=== Edson ===
+{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
-Edson is the 2.3.7/5 subgroup temperament tempering out [[5120/5103]].
-==== Edson (2.3.7/5.11/5.13/5 subgroup) ====
+{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}
-{{See also| Chromatic pairs #Edson }}
+: [[gencom]]: [2 13/10; 847/845 1001/1000]
-Edson is related to [[pele]] and [[andromeda]].
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.556
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
-[[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 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents
-{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
+==== Naiadec ====
+[[Subgroup]]: 2.7/5.11/5.13/5.17/5
-: mapping generators: ~2, ~3
+[[Comma list]]: [[170/169]], [[221/220]], [[847/845]]
-{{Mapping|legend=3| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }}
+{{Mapping|legend=2| 1 2 0 1 1 | 0 -4 3 1 2 }}
-: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363]
+{{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]]s:
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.882
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~3/2 = 703.4398
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~3/2 = 703.414
-{{Optimal ET sequence|legend=1| 12, 17, 29 }}
+{{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]]: 0.5102 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.7521 cents
-==== Haumea ====
+== 2.….11/5.… subgroups ==
-{{See also| Chromatic pairs #Haumea }}
+=== Petrtri ===
+{{See also| Chromatic pairs #Petrtri }}
+{{See also| 5L 3s/Temperaments #Petrtri }}
-Related temperaments include [[#Bridgetown|bridgetown]], [[namaka]], [[hemigari]], [[#Barbados|barbados]], and [[parizekmic]].
+Petrtri can be described as 3 &amp; 5 temperament in the 2.11/5.13/5 subgroup.
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+[[Subgroup]]: 2.11/5.13/5
-[[Comma list]]: [[352/351]], [[676/675]], [[847/845]]
+[[Comma list]]: [[2200/2197]]
-{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
+{{Mapping|legend=2| 1 0 1| 0 3 1 }}
-{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}
+{{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]
-: [[gencom]]: [2 15/13; 352/351 676/675 847/845]
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 455.012
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
+{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
-{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents
-[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents
+==== Bridgetown ====
+{{See also| Chromatic pairs #Bridgetown }}
-=== Historical ===
+Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[#Haumea|haumea]] and [[#Barbados|barbados]].
-{{distinguish|Historical temperaments}}
-[[Subgroup]]: 2.3.7/5.11/5.13/5
-[[Comma list]]: 364/363, 441/440, 1001/1000
+[[Subgroup]]: 2.3.11/5.13/5
-{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
+[[Comma list]]: [[352/351]], [[676/675]]
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
+{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
-{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
+{{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]]: 0.2562 cents
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
-=== Terrain ===
+{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
-{{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.
+[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
-[[Subgroup]]: 2.7/5.9/5
+=== Hypnosis ===
+Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Alphatricot family #Alphatricot|alphatricot]]
-[[Comma list]]: [[250047/250000]]
+[[Subgroup]]: 2.3.7.11/5.13
-{{Mapping|legend=2| 3 1 3 | 0 1 -1 }}
+[[Comma list]]: 169/168, 540/539, 729/728
-{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
+{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
-: [[gencom]]: [63/50 10/9; 250047/250000]
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
+{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
-{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
-[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
+=== Trisect ===
+Trisect divides every Pythagorean interval into three, and is the much more accurate subgroup restriction of [[Augmented family #Trisected|trisected]].
-=== Tridec ===
+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]].
-{{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]].
+[[Subgroup]]: 2.3.7.11/5
-[[Subgroup]]: 2.7/5.11/5.13/5
+[[Comma list]]: 1029/1024, 4000/3993
-[[Comma list]]: [[847/845]], [[1001/1000]]
+{{Mapping|legend=2| 3 0 10 5 | 0 3 -1 -1 }}
-{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.742
-{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}
+{{Optimal ET sequence|legend=1| 15, 21, 36, 123, 159, 195, 231 }}
-: [[gencom]]: [2 13/10; 847/845 1001/1000]
+[[Tp tuning #T2 tuning|RMS error]]: ???
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.556
+==== 2.3.7.11/5.13 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13
-{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
+[[Comma list]]: 1029/1024, 1575/1573, 2080/2079
-[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents
+{{Mapping|legend=2| 3 0 10 5 0 | 0 3 -1 -1 7 }}
-== 2.….11/5… subgroups ==
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.918
-=== Petrtri ===
+{{Optimal ET sequence|legend=1| 15, 21f, 36, 87, 123, 159 }}
-{{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.
+[[Tp tuning #T2 tuning|RMS error]]: ???
-[[Subgroup]]: 2.11/5.13/5
+==== 2.3.7.11/5.13.17 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13.17
-[[Comma list]]: [[2200/2197]]
+[[Comma list]]: 273/272, 833/832, 1575/1573, 2080/2079
-{{Mapping|legend=2| 1 0 1| 0 3 1 }}
+{{Mapping|legend=2| 3 0 10 5 0 -2 | 0 3 -1 -1 7 9 }}
-{{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.820
-: [[gencom]]: [2 13/10; 2200/2197]
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123, 159 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 455.012
+[[Tp tuning #T2 tuning|RMS error]]: ???
-{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
+===== Trisector =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19
-[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents
+[[Comma list]]: 210/209, 273/272, 286/285, 595/594, 2080/2079
-==== Bridgetown ====
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 | 0 3 -1 -1 7 9 3 }}
-{{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]].
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.894
-[[Subgroup]]: 2.3.11/5.13/5
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123h, 159h }}
-[[Comma list]]: [[352/351]], [[676/675]]
+[[Tp tuning #T2 tuning|RMS error]]: ???
-{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
+===== 2.3.7.11/5.13.17.19.23 subgroup =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19.23
-{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}
+[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 595/594, 2080/2079
-: [[gencom]]: [2 15/13; 352/351 676/675]
+{{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]]): ~2 = 1\1, ~15/13 = 248.399
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 634.038
-{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
+{{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
+[[Tp tuning #T2 tuning|RMS error]]: ???
-=== Hypnosis ===
+===== 2.3.7.11/5.13.17.19.23.29 subgroup =====
-Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
+[[Subgroup]]: 2.3.7.11/5.13.17.19.23.29
-[[Subgroup]]: 2.3.7.11/5.13
+[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 320/319, 595/594, 2080/2079
-[[Comma list]]: 169/168, 540/539, 729/728
+{{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
-{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
+[[Comma list]]: {{monzo| 8 -5 }} (256/243)
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
+{{Mapping|legend=2| 5 8 0 | 0 0 1 }}
+: mapping generators: ~9/8, ~11/7
-{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
+[[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 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
+{{Optimal ET sequence|legend=1| 15, 20, 35b, 55b }}
-== 2.….11/7… subgroups ==
 === Pepperoni ===
 {{Main| Parapyth }}
@@ Line 1,452: / Line 1,612: @@
 {{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, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*<sup>†</sup> }}
+{{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
-<nowiki />* Wart for 11/7
+: <sup>†</sup> wart for 13/7
-<sup>†</sup> Wart for 13/7
 [[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
-== 2.….13/5… subgroups ==
+== 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.
@@ Line 1,496: / Line 1,653: @@
 {{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]
@@ Line 1,506: / Line 1,662: @@
 ==== Pakkanian hemipyth ====
 [[Subgroup]]: 2.3.11.13/5.17
@@ Line 1,518: / Line 1,673: @@
 {{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]].
+[[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 }}
+Comma list: [[323/322]], [[392/391]]
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
+Subgroup-val mapping: {{Mapping| 1 0 4 3 | 0 1 -2 -1 }}
-{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}
+Optimal tunings:
+* Subgroup WE: ~2 = 1199.871{{c}}, ~17/14 = 336.243{{c}}
+* Subgroup CWE: ~2 = 1200.000{{c}}, ~17/14 = 336.296{{c}}
-[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
+{{Optimal ET sequence|legend=0| 7, 18, 25 }}
-Scales: [[Oceanfront scales]]
+Badness (Sintel): 0.029
-== 2.….49/5… subgroups ==
+==== 2.25/7.17/7.19/7.23/7 subgroup ====
-=== Direct breedsmic ===
-Related temperament: [[hemithirds]], [[newt]]
-[[Subgroup]]: 2.3.49/5
+Subgroup: 2.25/7.17/7.19/7.23/7
-[[Comma list]]: 2401/2400
+Comma list: [[323/322]], [[392/391]], [[476/475]]
-{{Mapping|legend=2| 1 1 3 | 0 2 1 }}
+Subgroup-val mapping: {{Mapping| 1 -2 0 4 3 | 0 3 1 -2 -1 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966
+Optimal tunings:
+* Subgroup WE: ~2 = 1199.757{{c}}, ~17/14 = 335.428{{c}}
-{{Optimal ET sequence|legend=1|?}}
+* 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 1,577: / Line 1,863: @@
 {{Mapping|legend=2| 1 3 4 | 0 -4 -5 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,583: / Line 1,868: @@
 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 1,592: / Line 1,876: @@
 {{Mapping|legend=2| 1 3 4 4 | 0 -4 -5 1 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,598: / Line 1,881: @@
 [[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 1,611: / Line 1,893: @@
 [[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2]
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 === Semiwolf ===
@@ Line 1,649: / Line 1,930: @@
 [[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 1,678: / Line 1,959: @@
 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 1,693: / Line 1,973: @@
 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 1,710: / Line 1,988: @@
 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 1,718: / Line 1,995: @@
 * [[Substitute harmonic]] temperaments
-<!-- main article -->
+[[Category:Subgroup temperaments| ]] <!-- main article -->
+[[Category:Temperament collections]]
-[[Category:Temperament collections]][[Category:Subgroup]]
+[[Category:Rank 2]]
+{{Todo| review | cleanup }}

Subgroup temperaments: Difference between revisions