@@ Line 1: / Line 1: @@
-{{Technical data page}}<br><br>
+{{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 13: / 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 90: / 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 153: / 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 291: / Line 343: @@
 Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]
-== 2.9.11 subgroup ==
+== 2.9.7.13.17 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
+=== 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]].
-[[Comma list]]: [[1331/1296]]
+[[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]]
 {{Mapping|legend=2|1 1 2|0 3 2}}
@@ Line 440: / Line 507: @@
 {{Optimal ET sequence|legend=1| 5, 13c, 18, 23, 41, 64, 87, 151 }}
-== 2.15.55 subgroup ==
+== 4.3.5 subgroup ==
-=== Spog ===
+=== Tetrahanson ===
+{{Main| Tetrahanson }}
-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]]: 4.3.5
-[[Subgroup]]: 2.15.55
+[[Comma list]]: 15625/15552
-[[Comma list]]: [[100663296/100656875]]
+{{Mapping|legend=2| 1 3 3 | 0 -6 -5 }}
-{{Mapping|legend=2| 1 0 5 | 0 5 1 }}
+: Mapping generators: ~4, ~5/3
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.655
+[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941
-{{Optimal ET sequence|legend=1|5, 9, 23, 32, 151, 183, 215, 247, 956, 1203, 1450, 3147, 4597 }}
+[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
-==== 2.15.55.325 ====
+=== Tetrameantone ===
-[[Subgroup]]: 2.15.55.325
+{{Main| Tetrameantone }}
-[[Comma list]]: [[4225/4224]], [[6656/6655]]
+[[Subgroup]]: 4.3.5
-{{Mapping|legend=2| 1 0 5 6 | 0 5 1 3 }}
+[[Comma list]]: 81/80
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.647
+{{Mapping|legend=2| 1 1 2 | 0 -1 -4 }}
-[[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
+: Mapping generators: ~4, ~4/3
-==== 2.15.189.55.325 ====
+[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~4/3 = 503.761
-Related temperament: [[Lehmerismic_temperaments#Lux|lux]]
-[[Subgroup]]: 2.15.189.55.325
+[[Support]]ing [[ET]]s: {{EDs|5, 9, 14, 19, 24, 43, 62, 81, 100|equave=4}}
-[[Comma list]]: [[2080/2079]], [[3025/3024]], [[4096/4095]]
+=== Tetramagic ===
-{{Mapping|legend=2| 1 0 6 5 6 | 0 5 2 1 3 }}
+[[Subgroup]]: 4.3.5
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.677
+[[Comma list]]: 3125/3072
-[[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|legend=2| 1 0 1 | 0 5 1 }}
-==== 2.15.189.55.325.725 ====
+: Mapping generators: ~4, ~5/4
-[[Subgroup]]: 2.15.189.55.325.725
+[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~5/4 = 380.059
-[[Comma list]]: [[1625/1624]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
+[[Support]]ing [[ET]]s: {{EDs|6, 13, 19, 25, 38, 44, 63, 82|equave=4}}
-{{Mapping|legend=2| 1 0 6 5 6 -3 | 0 5 2 1 3 16 }}
+=== Blacktetra ===
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.649
+[[Subgroup]]: 4.3.5
-[[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
+[[Comma list]]: 256/243
-==== 2.15.189.55.325.725.279 ====
+{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}
-Here are rational approximations to the intervals of the semiquartal scale.
+: Mapping generators: ~4, ~16/15
-Sharp: 12/11, 25/21, 33/26, 18/13, 31/21 ~ 65/44 ~ 96/65, 50/31 ~ 29/18, 55/32, 15/8.
+[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062
-Flat: 16/15, 64/55, 31/25 ~ 36/29, 42/31 ~ 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6.
+[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}
-[[Subgroup]]: 2.15.189.55.325.725.279
-[[Comma list]]: [[1625/1624]], [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
+== 4.6.5 subgroup ==
+=== Meanquad ===
+{{Main| Meanquad }}
-{{Mapping|legend=2| 1 0 6 5 6 -3 5 | 0 5 2 1 3 16 4 }}
+[[Subgroup]]: 4.6.5
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.638
+[[Comma list]]: [[81/80]] = {{monzo| -4 4 -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|legend=2| 1 0 -4| 0 1 4 }}
-== 4.3.5 subgroup ==
+: mapping generators: ~4, ~6
-=== Tetrahanson ===
-{{Main| Tetrahanson }}
-[[Subgroup]]: 4.3.5
+[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214
-[[Comma list]]: 15625/15552
+[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
-{{Mapping|legend=2| 1 3 3 | 0 -6 -5 }}
+<nowiki />* Wart for 4
-: Mapping generators: ~4, ~5/3
+==== 4.6.5.7 subgroup (tetrominant) ====
+[[Subgroup]]: 4.6.5.7
-[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~5/3 = 882.941
+[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}
-[[Support]]ing [[ET]]s: {{EDs|19, 106, 87, 68, 11, 8, 125, 49, 30, 27, 117, 46, 41b, 79|equave=4}}
+{{Mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}
-=== Tetrameantone ===
+[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622
-{{Main| Tetrameantone }}
-[[Subgroup]]: 4.3.5
+[[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]
-[[Comma list]]: 81/80
+<nowiki />* Wart for 4
-{{Mapping|legend=2| 1 1 2 | 0 -1 -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.
-: Mapping generators: ~4, ~4/3
+Fourwar is named after the closely related [[hemiwar]] temperament.
-[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~4/3 = 503.761
+{{Todo|inline=1|cleanup}}
-[[Support]]ing [[ET]]s: {{EDs|5, 9, 14, 19, 24, 43, 62, 81, 100|equave=4}}
+<pre>
+Reduced Mapping
-=== Tetramagic ===
+	6	5
+[ ⟨	1	0	1	]
+⟨	0	16	2	] ⟩
+TE Generator Tunings (cents)
+⟨2399.3973, 193.8643]
+TE Step Tunings (cents)
+⟨25.21211, 47.81337]
+TE Tuning Map (cents)
+⟨2399.397, 3101.829, 2787.126]
+TE Mistunings (cents)
+⟨-0.603, -0.126, 0.812]
+Complexity	1.369085
+Adjusted Error	0.692892 cents
+TE Error	0.268047 cents/octave
+Unison Vector
+[8, 1, -8⟩ (393216:390625)
-[[Subgroup]]: 4.3.5
+Subsets
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+</pre>
-[[Comma list]]: 3125/3072
+==== 4.6.5.7 ====
+<pre>
+Reduced Mapping
+	6	5	7
+[ ⟨	1	0	1	1	]
+⟨	0	16	2	5	] ⟩
+TE Generator Tunings (cents)
+⟨2399.4195, 193.8654]
+TE Step Tunings (cents)
+⟨25.23883, 47.79592]
+TE Tuning Map (cents)
+⟨2399.420, 3101.846, 2787.150, 3368.747]
+TE Mistunings (cents)
+⟨-0.580, -0.109, 0.837, -0.079]
+Complexity	1.192044
+Adjusted Error	0.653313 cents
+TE Error	0.232715 cents/octave
+Unison Vectors
+[-2, -1, -2, 4⟩ (2401:2400)
+[3, 0, -5, 2⟩ (3136:3125)
+[5, 1, -3, -2⟩ (6144:6125)
+[8, 1, -8, 0⟩ (393216:390625)
-{{Mapping|legend=2| 1 0 1 | 0 5 1 }}
+Subsets
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+</pre>
-: Mapping generators: ~4, ~5/4
+==== 4.6.5.7.11 ====
+<pre>
-[[Optimal tuning]] ([[POTE]]): 4 = 2400.0, ~5/4 = 380.059
+Reduced Mapping
+	6	5	7	11
-[[Support]]ing [[ET]]s: {{EDs|6, 13, 19, 25, 38, 44, 63, 82|equave=4}}
+[ ⟨	1	0	1	1	1	]
+⟨	0	16	2	5	9	] ⟩
-=== Blacktetra ===
+TE Generator Tunings (cents)
-[[Subgroup]]: 4.3.5
+⟨2400.1097, 193.9498]
-[[Comma list]]: 256/243
+TE Step Tunings (cents)
+⟨24.18752, 48.52491]
-{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}
+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)
-: Mapping generators: ~4, ~16/15
+Subsets
+q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
+</pre>
-[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062
+==== 4.6.5.7.11.13 ====
-[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}
+<pre>
+Reduced Mapping
-== 4.6.5 subgroup ==
+	6	5	7	11	13
-=== Meanquad ===
+[ ⟨	1	0	1	1	1	0	]
-{{Main| Meanquad }}
+⟨	0	16	2	5	9	23	] ⟩
-[[Subgroup]]: 4.6.5
+TE Generator Tunings (cents)
+⟨2401.2305, 193.5378]
-[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}
+TE Step Tunings (cents)
-{{Mapping|legend=2| 1 0 -4| 0 1 4 }}
+⟨42.79107, 35.98524]
-: mapping generators: ~4, ~6
+TE Tuning Map (cents)
+⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
-[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214
+TE Mistunings (cents)
+⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]
+Complexity	1.219191
+Adjusted Error	6.699599 cents
+TE Error	1.810487 cents/octave
+Unison Vectors
+[0, 1, -1, 0, 1, -1⟩ (66:65)
+[-1, -1, -1, 0, 2, 0⟩ (121:120)
+[1, 2, 0, 0, -1, -1⟩ (144:143)
+[2, 0, -2, -1, 1, 0⟩ (176:175)
+[-2, 1, 1, 1, 0, -1⟩ (105:104)
+[-3, -1, 1, 1, 1, 0⟩ (385:384)
+[-3, 0, 0, 1, 2, -1⟩ (847:832)
+[1, 3, -1, 0, 0, -2⟩ (864:845)
+[-1, 0, 3, -3, 1, 0⟩ (1375:1372)
-[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
+Subsets
+q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
+</pre>
-<nowiki />* Wart for 4
+==== 4.6.5.7.11.13.17 ====
+<pre>
-==== 4.6.5.7 subgroup (tetrominant) ====
+Reduced Mapping
-[[Subgroup]]: 4.6.5.7
+	6	5	7	11	13	17
+[ ⟨	1	0	1	1	1	0	1	]
-[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}
+⟨	0	16	2	5	9	23	13	] ⟩
-{{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]
+⟨2400.4701, 193.4599]
 TE Step Tunings (cents)
-⟨25.21211, 47.81337]
+⟨43.39350, 35.55764]
 TE Tuning Map (cents)
-⟨2399.397, 3101.829, 2787.126]
+⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]
 TE Mistunings (cents)
-⟨-0.603, -0.126, 0.812]
+⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]
-Complexity	1.369085
+Complexity	1.129881
-Adjusted Error	0.692892 cents
+Adjusted Error	8.082725 cents
-TE Error	0.268047 cents/octave
+TE Error	1.977443 cents/octave
-Unison Vector
+Unison Vectors
-[8, 1, -8⟩ (393216:390625)
+[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
-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 ====
+==== 4.6.5.7.11.13.17.19 ====
 <pre>
 Reduced Mapping
-	6	5	7
+	6	5	7	11	13	17	19
-[ ⟨	1	0	1	1	]
+[ ⟨	1	0	1	1	1	0	1	1	]
-⟨	0	16	2	5	] ⟩
+⟨	0	16	2	5	9	23	13	14	] ⟩
 TE Generator Tunings (cents)
-⟨2399.4195, 193.8654]
+⟨2399.9219, 193.3952]
 TE Step Tunings (cents)
-⟨25.23883, 47.79592]
+⟨44.14256, 35.03670]
 TE Tuning Map (cents)
-⟨2399.420, 3101.846, 2787.150, 3368.747]
+⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
 TE Mistunings (cents)
-⟨-0.580, -0.109, 0.837, -0.079]
+⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]
-Complexity	1.192044
+Complexity	1.058472
-Adjusted Error	0.653313 cents
+Adjusted Error	8.712222 cents
-TE Error	0.232715 cents/octave
+TE Error	2.050935 cents/octave
 Unison Vectors
-[-2, -1, -2, 4⟩ (2401:2400)
+[0, 1, -1, 0, 1, -1, 0, 0⟩ (66:65)
-[3, 0, -5, 2⟩ (3136:3125)
+[-1, 0, 0, 1, 1, 0, 0, -1⟩ (77:76)
-[5, 1, -3, -2⟩ (6144:6125)
+[2, 1, -1, 0, 0, 0, 0, -1⟩ (96:95)
-[8, 1, -8, 0⟩ (393216:390625)
+[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
-q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh
 </pre>
-==== 4.6.5.7.11 ====
+==== 4.6.5.7.11.13.17.19.23 ====
 <pre>
 Reduced Mapping
-	6	5	7	11
+	6	5	7	11	13	17	19	23
-[ ⟨	1	0	1	1	1	]
+[ ⟨	1	0	1	1	1	0	1	1	0	]
-⟨	0	16	2	5	9	] ⟩
+⟨	0	16	2	5	9	23	13	14	28	] ⟩
 TE Generator Tunings (cents)
-⟨2400.1097, 193.9498]
+⟨2399.3286, 193.5316]
 TE Step Tunings (cents)
-⟨24.18752, 48.52491]
+⟨37.31613, 39.63311]
 TE Tuning Map (cents)
-⟨2400.110, 3103.196, 2788.009, 3369.859, 4145.658]
+⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
 TE Mistunings (cents)
-⟨0.110, 1.241, 1.696, 1.033, -5.660]
+⟨-0.671, -5.449, 0.078, -1.839, -10.205, 10.699, 10.284, 11.258, -9.389]
-Complexity	1.068792
+Complexity	1.115920
-Adjusted Error	2.926965 cents
+Adjusted Error	9.502017 cents
-TE Error	0.846083 cents/octave
+TE Error	2.100561 cents/octave
 Unison Vectors
-[-1, -1, -1, 0, 2⟩ (121:120)
+[0, 1, -1, 0, 1, -1, 0, 0, 0⟩ (66:65)
-[2, 0, -2, -1, 1⟩ (176:175)
+[1, 0, 0, -1, 0, -1, 0, 0, 1⟩ (92:91)
-[-3, -1, 1, 1, 1⟩ (385:384)
+[0, -1, 1, 0, 0, 0, 0, -1, 1⟩ (115:114)
-[-1, 0, 3, -3, 1⟩ (1375:1372)
+[1, 1, 1, -1, 0, 0, -1, 0, 0⟩ (120:119)
-[-2, -1, -2, 4, 0⟩ (2401:2400)
+[2, 0, -2, -1, 1, 0, 0, 0, 0⟩ (176:175)
-[1, 0, 1, -4, 2⟩ (2420:2401)
+[-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
-q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
+q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii
 </pre>
-==== 4.6.5.7.11.13 ====
+== 4.9.25 subgroup ==
+=== Meansquared ===
+[[Subgroup]]: 4.9.25
+[[Comma list]]: [[6561/6400]]
+{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
+Mapping generators: ~4, ~9/64
-<pre>
+[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
-Reduced Mapping
-	6	5	7	11	13
-[ ⟨	1	0	1	1	1	0	]
-⟨	0	16	2	5	9	23	] ⟩
-TE Generator Tunings (cents)
-⟨2401.2305, 193.5378]
-TE Step Tunings (cents)
-⟨42.79107, 35.98524]
-TE Tuning Map (cents)
-⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
-TE Mistunings (cents)
-⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]
-Complexity	1.219191
-Adjusted Error	6.699599 cents
-TE Error	1.810487 cents/octave
-Unison Vectors
-[0, 1, -1, 0, 1, -1⟩ (66:65)
-[-1, -1, -1, 0, 2, 0⟩ (121:120)
-[1, 2, 0, 0, -1, -1⟩ (144:143)
-[2, 0, -2, -1, 1, 0⟩ (176:175)
-[-2, 1, 1, 1, 0, -1⟩ (105:104)
-[-3, -1, 1, 1, 1, 0⟩ (385:384)
-[-3, 0, 0, 1, 2, -1⟩ (847:832)
-[1, 3, -1, 0, 0, -2⟩ (864:845)
-[-1, 0, 3, -3, 1, 0⟩ (1375:1372)
-Subsets
+[[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, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
-</pre>
+== 4.9.49 subgroup ==
+=== Archsquared ===
+[[Subgroup]]: 4.9.49
+[[Comma list]]: 4096/3969
+{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}
+Mapping generators: ~4, ~9/64
+[[Optimal tuning]] ([[CTE]]): ~9/4 = 1419.190
+[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
-==== 4.6.5.7.11.13.17 ====
+== 8.9.7 subgroup ==
-<pre>
+=== Sixscared ===
-Reduced Mapping
+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."
-	6	5	7	11	13	17
-[ ⟨	1	0	1	1	1	0	1	]
+[[Subgroup]]: 8.9.7
-⟨	0	16	2	5	9	23	13	] ⟩
-TE Generator Tunings (cents)
-⟨2400.4701, 193.4599]
-TE Step Tunings (cents)
-⟨43.39350, 35.55764]
-TE Tuning Map (cents)
-⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]
-TE Mistunings (cents)
-⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]
-Complexity	1.129881
-Adjusted Error	8.082725 cents
-TE Error	1.977443 cents/octave
-Unison Vectors
-[0, 1, -1, 0, 1, -1, 0⟩ (66:65)
-[1, 1, 1, -1, 0, 0, -1⟩ (120:119)
-[1, 2, 0, 0, -1, -1, 0⟩ (144:143)
-[-2, 1, 1, 1, 0, -1, 0⟩ (105:104)
-[-1, 2, 2, 0, 0, -1, -1⟩ (225:221)
-[-1, 1, 2, -2, 0, -1, 1⟩ (1275:1274)
-Subsets
+[[Comma list]]: 64/63
-q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg
-</pre>
-==== 4.6.5.7.11.13.17.19 ====
+{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
-<pre>
-Reduced Mapping
+: sval mapping generators: ~8, ~9
-	6	5	7	11	13	17	19
-[ ⟨	1	0	1	1	1	0	1	1	]
+: [[gencom]]: [8 9/8; 64/63]
-⟨	0	16	2	5	9	23	13	14	] ⟩
+[[Optimal tuning]] ([[CTE]]): ~9/8 = 219.1898
-TE Generator Tunings (cents)
-⟨2399.9219, 193.3952]
+[[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>
-⟨44.14256, 35.03670]
+= Fractional subgroup temperaments =
-TE Tuning Map (cents)
+== 2.5/3.… subgroups ==
-⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
+=== Magicaltet ===
+{{See also| Chromatic pairs #Magicaltet }}
-TE Mistunings (cents)
-⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]
+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	1.058472
+[[Subgroup]]: 2.5/3.7.11
-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]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})
-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 5 2 | 0 1 -3 2 }}
-<pre>
+: mapping generators: ~2, ~5/3
-Reduced Mapping
-	6	5	7	11	13	17	19	23
+{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
-[ ⟨	1	0	1	1	1	0	1	1	0	]
+: [[gencom]]: [2 6/5; 100/99 385/384]
-⟨	0	16	2	5	9	23	13	14	28	] ⟩
+[[Optimal tuning]]s:
-TE Generator Tunings (cents)
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 877.343
-⟨2399.3286, 193.5316]
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 877.351
-TE Step Tunings (cents)
+{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
-⟨37.31613, 39.63311]
+: <nowiki/>* wart for 5/3
-TE Tuning Map (cents)
+[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
-⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
+=== Starlingtet ===
-TE Mistunings (cents)
+{{See also | Chromatic pairs #Starlingtet }}
-⟨-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)
-Subsets
+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.
-q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii
-</pre>
-== 4.9.25 subgroup ==
+[[Subgroup]]: 2.5/3.7/3
-=== Meansquared ===
-[[Subgroup]]: 4.9.25
-[[Comma list]]: [[6561/6400]]
+[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})
-{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
+{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
-Mapping generators: ~4, ~9/64
+: mapping generators: ~2, ~5/3
-[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
+{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
+: [[gencom]]: [2 6/5; 126/125]
-[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
+[[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
-== 4.9.49 subgroup ==
+{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}
-=== Archsquared ===
-[[Subgroup]]: 4.9.49
-[[Comma list]]: 4096/3969
+[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents
-{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}
+==== Greeley ====
+{{See also| Chromatic pairs #Greeley }}
-Mapping generators: ~4, ~9/64
+Greeley is related to [[opossum]] as well as to [[nusecond]].
-[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 219.190
+[[Subgroup]]: 2.5/3.7/3.11/3
-[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
+[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})
-== 8.9.7 subgroup ==
+{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
-=== 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."
-[[Subgroup]]: 8.9.7
+{{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]
-[[Comma list]]: 64/63
+[[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
-{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
+{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
+: <nowiki/>* wart for 11/3
-: sval mapping generators: ~8, ~9
+[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents
-: [[gencom]]: [8 9/8; 64/63]
+==== Skateboard ====
+{{See also| Chromatic pairs #Skateboard }}
-[[Optimal tuning]] ([[CTE]]): 1\[[3ed8]] = 1600.0, ~9/8 = 219.1898
+Skateboard is related to [[thrasher]].
-[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}
+[[Subgroup]]: 2.5/3.7/3.11.13/9
-[[Badness]]: 0.0215 × 10<sup>-3</sup>
+[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }})
-= Fractional subgroup temperaments =
+{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
-== 2.5/3… subgroups ==
-=== 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.
+{{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]
-[[Subgroup]]: 2.5/3.7.11
+[[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
-[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})
+{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}
-{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
+[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents
-: mapping generators: ~2, ~5/3
+=== Gariberttet ===
+Gariberttet is the 2.5/3.7/3 [[Subgroup temperament families, relationships, and genes|altergene]] of [[sirius]].
-{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
+==== Gariberttet (2.5/3.7/3.13/11 subgroup) ====
+{{See also | Chromatic pairs #Gariberttet }}
-: [[gencom]]: [2 6/5; 100/99 385/384]
+Gariberttet can be described as the {{nowrap| 4 & 29 }} temperament in the 2.5/3.7/3.13/11 subgroup. Extensions to the full 7-, 11-, and 13-limits include [[quasitemp]].
-[[Optimal tuning]]s:
+[[Subgroup]]: 2.5/3.7/3.13/11
-* [[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* }}
+[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})
-<nowiki/>* Wart for 5/3
+{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
-[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
+{{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]
-=== Starlingtet ===
+[[Optimal tuning]]s:
-{{See also | Chromatic pairs #Starlingtet }}
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~13/11 = 293.679
-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.
+{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}
+: <nowiki/>* wart for 13/11
-[[Subgroup]]: 2.5/3.7/3
+[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
+==== Indium ====
+{{See also | Chromatic pairs #Indium }}
-[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})
+Indium can be described as the {{nowrap| 8 & 33 }} temperament in the 2.5/3.7/3.11/3 subgroup.
-{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
+[[Subgroup]]: 2.5/3.7/3.11/3
-: mapping generators: ~2, ~5/3
+[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }})
-{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
+{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
-: [[gencom]]: [2 6/5; 126/125]
+{{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]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 888.759
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/11 = 146.978
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 888.846
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/11 = 147.010
-{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}
+{{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]]: 0.8398 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
-==== Greeley ====
+==== Ammon ====
-{{See also| Chromatic pairs #Greeley }}
+{{See also| Chromatic pairs #Ammon }}
-Greeley is related to [[opossum]] as well as to [[nusecond]].
+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
+[[Subgroup]]: 2.5/3.7/3.11/3.13/3
-[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})
+[[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 1 2 2 | 0 -2 -6 -1 }}
+{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
-{{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 -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]
-: [[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, ~13/10 = 453.121
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~11/10 = 155.776
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/10 = 453.242
-{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
+{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}
-<nowiki/>* Wart for 11/3
+[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
-[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents
+=== Sentry ===
+{{See also | Chromatic pairs #Sentry }}
-==== Skateboard ====
+Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
-{{See also| Chromatic pairs #Skateboard }}
-Skateboard is related to [[thrasher]].
+[[Subgroup]]: 2.5/3.9/7
-[[Subgroup]]: 2.5/3.7/3.11.13/9
+[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})
-[[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 0 | 0 2 1 }}
-{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
+{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
+: [[gencom]]: [2 9/7; 245/243]
-{{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]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 886.158
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 886.158
-{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}
+{{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]]: 2.396 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
-=== Gariberttet ===
+=== Marveltwintri ===
-Gariberttet is the 2.5/3.7/3 [[Subgroup temperament families, relationships, and genes|altergene]] of [[sirius]].
+{{See also| Chromatic pairs #Marveltwintri }}
-==== Gariberttet (2.5/3.7/3.13/11 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]].
-{{See also | Chromatic pairs #Gariberttet }}
-Gariberttet can be described as the {{nowrap| 4 & 29 }} temperament in the 2.5/3.7/3.13/11 subgroup.
+[[Subgroup]]: 2.5/3.13/9
-[[Subgroup]]: 2.5/3.7/3.13/11
+[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})
-[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})
+{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
-{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
+{{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]
-{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}
+[[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
-: [[gencom]]: [2 13/11; 275/273 847/845]
+{{Optimal ET sequence|legend=1| 3, 4, 11, 15, 19, 34, 53, 87, 140 }}
-[[Optimal tuning]]s:
+[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
-* [[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* }}
+== 2.….7/3.… subgroups ==
+=== Guanyintet ===
+{{See also | Chromatic pairs #Guanyintet }}
-<nowiki/>* Wart for 13/11
+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.
-[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
+[[Subgroup]]: 2.5.7/3.11/3
-==== Indium ====
+[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -1 }})
-{{See also | Chromatic pairs #Indium }}
-Indium can be described as the {{nowrap| 8 & 33 }} temperament in the 2.5/3.7/3.11/3 subgroup.
+{{Mapping|legend=2| 1 0 1 3 | 0 -3 1 -5 }}
+: mapping generators: ~2, ~7/6
-[[Subgroup]]: 2.5/3.7/3.11/3
+{{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]
-[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -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
-{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}
+: <nowiki/>* wart for 7/3
-{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents
-: [[gencom]]: [2 12/11; 3025/3024 3125/3087]
+==== Tridecimal guanyintet ====
+Guanyintet can extend to the 13th harmonic by the equivalences ([[12/11]])<sup>3</sup> = [[13/10]] and ([[15/14]])<sup>3</sup> = [[16/13]], therefore tempering out {S11/S12/S14/S15}. However, note that it is not supported by the 31 & 53 orwell extension dubbed "tridecimal orwell", but instead the less accurate [[winston]] (22f & 31), as orwell prefers slightly sharper tunings than guanyintet. [[40edo]] remains an excellent tuning.
-[[Optimal tuning]]s:
+[[Subgroup]]: 2.5.7/3.11/3.13
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~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> }}
+[[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 }})
-<nowiki/>* Wart for 7/3
+{{Mapping|legend=2| 1 0 1 3 1 | 0 -3 1 -5 12 }}
+: mapping generators: ~2, ~12/7
-<sup>†</sup> Wart for 11/3
+[[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
-[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 71, 111, 151, 262c*}} <small> using subgroup TE </small>
+: <nowiki/>* wart for 7/3
-==== Ammon ====
+Badness (Sintel): 0.329
-{{See also| Chromatic pairs #Ammon }}
-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 name.
+==== Laz ====
+{{See also | Chromatic pairs #Laz }}
-It was formerly known as "semidim" but renamed to avoid confusion with another temperament of the same name.
+Laz is related to [[avalokita]] as well as to [[winston]].
-[[Subgroup]]: 2.5/3.7/3.11/3.13/3
+[[Subgroup]]: 2.5.7/3.11/3.13/3
-[[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]]: [[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 3 5 3 4 | 0 -6 -10 -3 -5 }}
+{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
-{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}
+{{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]
-: [[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, ~12/7 = 930.598
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/10 = 453.242
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/7 = 930.700
-{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}
+{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 156c*†, 205c*† }}
+: <nowiki/>* wart for 7/3
+: † wart for 11/3
-[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents
-=== Sentry ===
+=== Kryptonite ===
-{{See also | Chromatic pairs #Sentry }}
+{{See also| Chromatic pairs #Kryptonite }}
-Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
+Kryptonite is related to [[krypton]].
-[[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]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 78/77 ({{monzo| 1 0 -1 -1 1 }}), 91/90 ({{monzo| -1 -2 1 0 1 }})
-{{Mapping|legend=2| 1 0 0 | 0 2 1 }}
+{{Mapping|legend=2| 1 2 1 2 2 | 0 3 2 -1 1 }}
+: mapping generators: ~2, ~13/12
-{{Mapping|legend=3| 1 0 0 0 | 0 0 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]
-: [[gencom]]: [2 9/7; 245/243]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902
+* [[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| 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| 1, …, 8, 9 }}
-<nowiki/>* Wart for 5/3
+[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
-<sup>†</sup> Wart for 9/7
+=== Kiribati ===
+{{See also| Chromatic pairs #Kiribati }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
+Kiribati is related to [[nakika]] as well as to [[octacot]].
-=== Marveltwintri ===
+[[Subgroup]]: 2.9/5.7/3.11/9
-{{See also| Chromatic pairs #Marveltwintri }}
-Marveltwintri can be described as the {{nowrap| 3 & 4 }} temperament in the 2.5/3.13/9 subgroup. The tonic and the first two generator steps make a [[marveltwin triad]], hence the name.
+[[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }})
-[[Subgroup]]: 2.5/3.13/9
+{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
+: mapping generators: ~2, ~21/20
-[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})
+{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
+: [[gencom]]: [2 21/20; 100/99 245/242]
-{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
+[[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=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}
+{{Optimal ET sequence|legend=1| 13, 14, 27, 41 }}
-: [[gencom]]: [2 6/5; 325/324]
+[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
-[[Optimal tuning]]s:
+=== Mothwelltri ===
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 886.886
+{{See also| Chromatic pairs #Mothwelltri }}
-* [[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 }}
+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.
-[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
+[[Subgroup]]: 2.7/3.11
-== 2.….7/3… subgroups ==
+[[Comma list]]: [[99/98]] ({{monzo| -1 -2 1 }})
-=== Guanyintet ===
-{{See also | Chromatic pairs #Guanyintet }}
-Guanyintet, the {{nowrap| 4 & 9 }} temperament in the 2.5.7/3.11/3 subgroup, is related to [[guanyin]] as well as to [[orwell]]. The tonic and the first three generator steps make a [[guanyin tetrad]], hence the name.
+{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
+: mapping generators: ~2, ~7/3
-[[Subgroup]]: 2.5.7/3.11/3
+{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
+: [[gencom]]: [2 7/6; 99/98]
-[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -1 }})
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~7/6 = 273.695
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~7/6 = 273.174
-{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}
+{{Optimal ET sequence|legend=1| 4, 9, 13, 22, 79 }}
-: mapping generators: ~2, ~12/7
+[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents
-{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}
+== 2.….9/7.… subgroups ==
+=== Marveltri ===
+{{See also| Chromatic pairs #Marveltri }}
-: [[gencom]]: [2 7/6; 176/175 540/539]
+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]]s:
+[[Subgroup]]: 2.5.9/7
-* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~12/7 = 929.545
-* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~12/7 = 929.907
-{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}
+[[Comma list]]: 225/224 ({{monzo| -5 2 1 }})
-<nowiki/>* wart for 7/3
+{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
+: mapping generators: ~2, ~5
-[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents
+{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}
+: [[gencom]]: [2 5; 225/224]
-==== Laz ====
+[[Optimal tuning]]s:
-{{See also | Chromatic pairs #Laz }}
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 384.208
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 383.638
-Laz is related to [[georgian]] as well as to [[winston]].
+{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122, 269c* }}
+: <nowiki/>* wart for 9/7
-[[Subgroup]]: 2.5.7/3.11/3.13/3
+[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
-[[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 }}
+==== Sulis ====
+Sulis is related to [[minerva]] and [[würschmidt]].
-{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
+[[Subgroup]]: 2.5.9/7.11/9
-{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}
+[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})
-: [[gencom]]: [2 7/6; 144/143 176/175 196/195]
+{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/7 = 930.598
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 386.617
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/7 = 930.700
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 386.558
-{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 156c*†, 205c*† }}
+{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
-<nowiki/>* wart for 7/3
+[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
-† wart for 11/3
+== 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.
-[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents
+[[Subgroup]]: 2.3.7/5
-=== Kryptonite ===
+[[Comma list]]: [[50/49]]
-{{See also| Chromatic pairs #Kryptonite }}
-Kryptonite is related to [[krypton]].
+{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
-[[Subgroup]]: 2.5.7/3.11/3.13/3
+[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
-[[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 }})
+[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
-{{Mapping|legend=2| 1 2 1 2 2 | 0 3 2 -1 1 }}
+=== Argentic ===
+Argentic is the 2.3.7/5 subgroup temperament tempering out [[5120/5103]].
-: mapping generators: ~2, ~13/12
+[[Subgroup]]: 2.3.7/5
-{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}
+[[Comma list]]: [[5120/5103]] = {{monzo| 10 -6 -1 }}
-: [[gencom]]: [2 13/12; 56/55 78/77 91/90]
+{{Mapping|legend=2| 1 0 10 | 0 1 -6 }}
+: mapping generators: ~2, ~3
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/12 = 130.945
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~3/2 = 702.792
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/12 = 132.428
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~3/2 = 702.830
-{{Optimal ET sequence|legend=1| 1, …, 8, 9 }}
+{{Optimal ET sequence|legend=1| 12, 29, 41, 70, 321, 391, 461, 531, 601 }}
+<small> based on subgroup TE </small>
-[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
+Badness (Sintel): 0.119
-=== Kiribati ===
+==== Edson (2.3.7/5.11/5.13/5 subgroup) ====
-{{See also| Chromatic pairs #Kiribati }}
+{{See also| Chromatic pairs #Edson }}
-Kiribati is related to [[nakika]] as well as to [[octacot]].
+Edson is related to [[pele]] and [[andromeda]].
-[[Subgroup]]: 2.9/5.7/3.11/9
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-[[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }})
+[[Comma list]]: [[196/195]] = {{monzo| 2 -1 2 0 -1 }}, [[352/351]] = {{monzo| 5 -3 0 1 -1 }}, [[364/363]] = {{monzo| 2 -1 1 -2 1 }}
-{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
+{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
+: mapping generators: ~2, ~3
-: mapping generators: ~2, ~21/20
+{{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]
-{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
+[[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
-: [[gencom]]: [2 21/20; 100/99 245/242]
+{{Optimal ET sequence|legend=1| 12, 17, 29 }}
-[[Optimal tuning]]s:
+[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
-* [[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 }}
+==== Haumea ====
+{{See also| Chromatic pairs #Haumea }}
-[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
+Related temperaments include [[#Bridgetown|bridgetown]], [[namaka]], [[hemigari]], [[#Barbados|barbados]], and [[parizekmic]].
-=== Mothwelltri ===
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-{{See also| Chromatic pairs #Mothwelltri }}
-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.
+[[Comma list]]: [[352/351]], [[676/675]], [[847/845]]
-[[Subgroup]]: 2.7/3.11
+{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
-[[Comma list]]: [[99/98]] ({{monzo| -1 -2 1 }})
+{{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]
-{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
-: mapping generators: ~2, ~7/3
+{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
-{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents
-: [[gencom]]: [2 7/6; 99/98]
+=== Historical ===
+{{distinguish|Historical temperaments}}
+{{distinguish|History (temperament)}}, which is the rank-3 version of this temperament in the full 13-limit.
-[[Optimal tuning]]s:
+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.
-* [[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| 4, 9, 13, 22, 79 }}
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents
+[[Comma list]]: 364/363, 441/440, 1001/1000
-== 2.….9/7… subgroups ==
+{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
-=== Marveltri ===
-{{See also| Chromatic pairs #Marveltri }}
-Marveltri, the {{nowrap| 3 & 13 }} temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed {{nowrap| 22 & 47 }} temperament. The tonic and the first two generator steps make a [[marvel triad]], hence the name.
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
-[[Subgroup]]: 2.5.9/7
+{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
-[[Comma list]]: 225/224 ({{monzo| -5 2 1 }})
+[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
-{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
+=== Terrain ===
+{{Redirect|Terrain|the scale|Terrain (scale)}}
+{{See also| Chromatic pairs #Terrain }}
-: mapping generators: ~2, ~5
+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.
-{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}
+[[Subgroup]]: 2.7/5.9/5
-: [[gencom]]: [2 5; 225/224]
+[[Comma list]]: [[250047/250000]]
-[[Optimal tuning]]s:
+{{Mapping|legend=2| 3 1 3 | 0 1 -1 }}
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 384.208
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 383.638
-{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122, 269c* }}
+{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
+: [[gencom]]: [63/50 10/9; 250047/250000]
-<nowiki/>* Wart for 9/7
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
-[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
+{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
-==== Sulis ====
+[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
-Sulis is related to [[minerva]] and [[würschmidt]].
-[[Subgroup]]: 2.5.9/7.11/9
+=== Tridec ===
+{{See also| Chromatic pairs #Tridec }}
+{{See also| Non-over-1 temperament #Tridec }}
-[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})
+Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[#Petrtri]].
-{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]
+[[Subgroup]]: 2.7/5.11/5.13/5
-[[Optimal tuning]]s:
+[[Comma list]]: [[847/845]], [[1001/1000]]
-* [[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 }}
+{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
-[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
+{{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]
-== 2.….15/11… subgroups ==
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.556
-=== Poggers ===
+{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
-Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]]
-[[Subgroup]]: 2.9.7.15/11.13
+[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents
-[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]
+==== Naiadec ====
+[[Subgroup]]: 2.7/5.11/5.13/5.17/5
-{{Mapping|legend=2| 1 1 1 -1 -1 | 0 6 5 4 13 }}
+[[Comma list]]: [[170/169]], [[221/220]], [[847/845]]
-[[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888
+{{Mapping|legend=2| 1 2 0 1 1 | 0 -4 3 1 2 }}
-[[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| 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]
-== 2.….7/5… subgroups ==
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.882
-=== Hydrothermal ===
+{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 95<sup>t</sup>, 124<sup>t</sup> }}
-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.
+: <sup>t</sup> wart for 17/5
-[[Subgroup]]: 2.3.7/5
+[[Tp tuning #T2 tuning|RMS error]]: 0.7521 cents
-[[Comma list]]: [[50/49]]
+== 2.….11/5.… subgroups ==
+=== Petrtri ===
+{{See also| Chromatic pairs #Petrtri }}
+{{See also| 5L 3s/Temperaments #Petrtri }}
-{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
+Petrtri can be described as 3 &amp; 5 temperament in the 2.11/5.13/5 subgroup.
-[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
+[[Subgroup]]: 2.11/5.13/5
-[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
+[[Comma list]]: [[2200/2197]]
-=== Edson ===
+{{Mapping|legend=2| 1 0 1| 0 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 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}
-{{See also| Chromatic pairs #Edson }}
+: [[gencom]]: [2 13/10; 2200/2197]
-Edson is related to [[pele]] and [[andromeda]].
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 455.012
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
-[[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]]: 0.0749 cents
-{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
+==== Bridgetown ====
+{{See also| Chromatic pairs #Bridgetown }}
-: mapping generators: ~2, ~3
+Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[#Haumea|haumea]] and [[#Barbados|barbados]].
-{{Mapping|legend=3| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }}
+[[Subgroup]]: 2.3.11/5.13/5
-: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363]
+[[Comma list]]: [[352/351]], [[676/675]]
-[[Optimal tuning]]s:
+{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
-* [[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 }}
+{{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]]: 0.5102 cents
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
-==== Haumea ====
+{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
-{{See also| Chromatic pairs #Haumea }}
-Related temperaments include [[#Bridgetown|bridgetown]], [[namaka]], [[hemigari]], [[#Barbados|barbados]], and [[parizekmic]].
+[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+=== Hypnosis ===
+Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Alphatricot family #Alphatricot|alphatricot]]
-[[Comma list]]: [[352/351]], [[676/675]], [[847/845]]
+[[Subgroup]]: 2.3.7.11/5.13
-{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
+[[Comma list]]: 169/168, 540/539, 729/728
-{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}
+{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
-: [[gencom]]: [2 15/13; 352/351 676/675 847/845]
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
+{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
-{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
-[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents
+=== Trisect ===
+Trisect divides every Pythagorean interval into three, and is the much more accurate subgroup restriction of [[Augmented family #Trisected|trisected]].
-=== Historical ===
+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]].
-{{distinguish|Historical temperaments}}
-{{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]]: 2.3.7.11/5
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+[[Comma list]]: 1029/1024, 4000/3993
-[[Comma list]]: 364/363, 441/440, 1001/1000
+{{Mapping|legend=2| 3 0 10 5 | 0 3 -1 -1 }}
-{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.742
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
+{{Optimal ET sequence|legend=1| 15, 21, 36, 123, 159, 195, 231 }}
-{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
+[[Tp tuning #T2 tuning|RMS error]]: ???
-[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
+==== 2.3.7.11/5.13 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13
-=== Terrain ===
+[[Comma list]]: 1029/1024, 1575/1573, 2080/2079
-{{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.
+{{Mapping|legend=2| 3 0 10 5 0 | 0 3 -1 -1 7 }}
-[[Subgroup]]: 2.7/5.9/5
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.918
-[[Comma list]]: [[250047/250000]]
+{{Optimal ET sequence|legend=1| 15, 21f, 36, 87, 123, 159 }}
-{{Mapping|legend=2| 3 1 3 | 0 1 -1 }}
+[[Tp tuning #T2 tuning|RMS error]]: ???
-{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
+==== 2.3.7.11/5.13.17 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13.17
-: [[gencom]]: [63/50 10/9; 250047/250000]
+[[Comma list]]: 273/272, 833/832, 1575/1573, 2080/2079
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
+{{Mapping|legend=2| 3 0 10 5 0 -2 | 0 3 -1 -1 7 9 }}
-{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.820
-[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123, 159 }}
-=== Tridec ===
+[[Tp tuning #T2 tuning|RMS error]]: ???
-{{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]].
+===== Trisector =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19
-[[Subgroup]]: 2.7/5.11/5.13/5
+[[Comma list]]: 210/209, 273/272, 286/285, 595/594, 2080/2079
-[[Comma list]]: [[847/845]], [[1001/1000]]
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 | 0 3 -1 -1 7 9 3 }}
-{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.894
-{{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, 21fg, 36, 123h, 159h }}
-: [[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
+===== 2.3.7.11/5.13.17.19.23 subgroup =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19.23
-{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
+[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 595/594, 2080/2079
-[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 12 | 0 3 -1 -1 7 9 3 1 }}
-== 2.….11/5… subgroups ==
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 634.038
-=== Petrtri ===
+{{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
-{{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
+===== 2.3.7.11/5.13.17.19.23.29 subgroup =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19.23.29
-[[Comma list]]: [[2200/2197]]
+[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 320/319, 595/594, 2080/2079
-{{Mapping|legend=2| 1 0 1| 0 3 1 }}
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 12 13 | 0 3 -1 -1 7 9 3 1 1 }}
-{{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]]): ~29/23 = 1\3, ~13/9 = 634.102
-: [[gencom]]: [2 13/10; 2200/2197]
+{{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
-[[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 }}
+== 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.
-[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents
+[[Subgroup]]: 2.3.11/7
-==== Bridgetown ====
+[[Comma list]]: {{monzo| 8 -5 }} (256/243)
-{{See also| Chromatic pairs #Bridgetown }}
-Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[#Haumea|haumea]] and [[#Barbados|barbados]].
+{{Mapping|legend=2| 5 8 0 | 0 0 1 }}
+: mapping generators: ~9/8, ~11/7
-[[Subgroup]]: 2.3.11/5.13/5
+[[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 }}
-[[Comma list]]: [[352/351]], [[676/675]]
+{{Optimal ET sequence|legend=1| 15, 20, 35b, 55b }}
-{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
+=== Pepperoni ===
+{{Main| Parapyth }}
+{{See also| Chromatic pairs #Pepperoni }}
-{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}
+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.
-: [[gencom]]: [2 15/13; 352/351 676/675]
+[[Subgroup]]: 2.3.11/7.13/7
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
+[[Comma list]]: 352/351, 364/363
-{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
+{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
+{{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]
-=== Hypnosis ===
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856
-Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
-[[Subgroup]]: 2.3.7.11/5.13
+{{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
-[[Comma list]]: 169/168, 540/539, 729/728
+[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
-{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
+== 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.
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
+[[Subgroup]]: 2.3.13/5
-{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
+[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
+[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
-== 2.….11/7… subgroups ==
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
-=== 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.
+{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
-[[Subgroup]]: 2.3.11/7.13/7
+[[Badness]]: 0.002335
-[[Comma list]]: 352/351, 364/363
+; 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]
-{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
+==== Tobago ====
+{{See also| Chromatic pairs #Tobago }}
-{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
+Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
-: [[gencom]]: [2 3/2; 352/351 364/363]
+[[Subgroup]]: 2.3.11.13/5
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856
+[[Comma list]]: [[243/242]], [[676/675]]
-{{Optimal ET sequence|legend=1| 5, 7, 12f, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*<sup>†</sup> }}
+{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}
-<nowiki />* Wart for 11/7
+{{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]
-<sup>†</sup> Wart for 13/7
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
-[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
+{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
-== 2.….13/5… subgroups ==
+[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents
-=== Barbados ===
-The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.
-[[Subgroup]]: 2.3.13/5
+==== Pakkanian hemipyth ====
+[[Subgroup]]: 2.3.11.13/5.17
-[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
+[[Comma list]]: 221/220, 243/242, 289/288
-[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
+{{Mapping|legend=2| 2 0 -1 -2 5 | 0 2 5 3 2 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
+[[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| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
+{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}
+: <nowiki />* wart for 13/5
-[[Badness]]: 0.002335
+=== Oceanfront ===
+Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]
-; Music
+[[Subgroup]]: 2.3.7.13/5
-* [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 ====
+[[Comma list]]: 64/63, 91/90
-{{See also| Chromatic pairs #Tobago }}
-Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
+{{Mapping|legend=2| 1 0 6 -5 | 0 1 -2 4 }}
-[[Subgroup]]: 2.3.11.13/5
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
-[[Comma list]]: [[243/242]], [[676/675]]
+{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}
-{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}
+[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
-{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}
+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====
-: [[gencom]]: [55/39 15/13; 243/242 676/675]
+Comma basis: 225000/224939, 43940/43923
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
+edo join: 29 & 146
-{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
+{{Mapping|legend=2| 1 1 1 1 | 0 17 4 11 }}
+: mapping generators: ~2, ~169/165
-[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents
+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}}
-==== Pakkanian hemipyth ====
+edos: 29, 465, 494, 436, 523, 407, 378, 349, 320, 291, 30[-3], 262, 28[+3], 233
-[[Subgroup]]: 2.3.11.13/5.17
+Badness (Sintel): 0.080
-[[Comma list]]: 221/220, 243/242, 289/288
+== 2.….49/5.… subgroups ==
+=== Direct breedsmic ===
+Related temperament: [[hemithirds]], [[newt]]
-{{Mapping|legend=2| 2 0 -1 -2 5 | 0 2 5 3 2 }}
+[[Subgroup]]: 2.3.49/5
-[[Optimal tuning]]s:
+[[Comma list]]: 2401/2400
-* [[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* }}
+{{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 }}
-[[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 1,643: / Line 1,863: @@
 {{Mapping|legend=2| 1 3 4 | 0 -4 -5 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,649: / 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 1,658: / Line 1,876: @@
 {{Mapping|legend=2| 1 3 4 4 | 0 -4 -5 1 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,664: / 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 1,677: / 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 1,715: / 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 1,744: / 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 1,759: / 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 1,776: / 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 1,784: / 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