@@ Line 1: / Line 1: @@
+{{Technical data page}}
 A '''subgroup temperament''' is a regular temperament defined on a [[just intonation subgroup]] that is not a full ''p''-limit group.
 For temperaments that omit various prime harmonics, see:
+* [[No-thirteens subgroup temperaments]]
 * [[No-elevens subgroup temperaments]]
 * [[No-sevens subgroup temperaments]]
@@ Line 11: / Line 13: @@
 = Composite subgroup temperaments =
-== 2.3.35 subgroup ==
-=== Shaka ===
-{{See also|Kalismic temperaments}}
-Two commas that split 2/1 in half, corresponding to convergents to sqrt(2), are the [[1682/1681|''sha''ftesburisma]] [[Square superparticular|S29]]/S41 and the [[9801/9800|''ka''lisma S99]], prompting to temper out {S29, S41, S99}, approximating /29 and /41 [[Primodality|primodal]] chords well.
-Subgroup: 2.3.35.11.29.41
-Comma list: 841/840, 1189/1188, 1681/1680
-{{Mapping|legend=2|2 2 6 5 7 8|0 1 1 -1 1 1|0 0 2 2 1 1}}
-Optimal tuning (CTE): ~41/29 = 1\2, ~3/2 = 702.031, ~41/24 = 926.693
-[[Support]]ing [[ET]]s: {{EDOs|22, 26, 36, 48, 70, 96, 106, 118, 140, 154, 176, 188, 224, 272, 294, 342}}
-Scale: [[Shaka10]]
 == 2.9.5.7 subgroup ==
 See also [[Jubilismic clan #Antikythera|antikythera]] and [[Hemimean clan #Isra|isra]].
@@ Line 89: / Line 73: @@
 === Baldy ===
 {{See also|Schismatic family #Garibaldi}}
+{{See also|No-threes subgroup temperaments #Frostburn}}
-Baldy results from taking every other generator of the [[garibaldi temperament]]. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.
+Baldy results from taking every other generator of the [[garibaldi]] temperament. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament.
 [[Subgroup]]: 2.9.5.7
@@ Line 152: / Line 137: @@
 {{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 290: / Line 314: @@
 Scales: [[penta5]], [[penta8]], [[penta11]], [[penta19]]
-== 2.9.11 subgroup ==
+== 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.
@@ Line 439: / Line 478: @@
 {{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	]
-[[Subgroup]]: 4.3.5
+⟨	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)
-[[Comma list]]: 3125/3072
+Subsets
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+</pre>
-{{Mapping|legend=2| 1 0 1 | 0 5 1 }}
+==== 4.6.5.7 ====
+<pre>
-: Mapping generators: ~4, ~5/4
+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]]): 4 = 2400.0, ~5/4 = 380.059
+Subsets
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+</pre>
-[[Support]]ing [[ET]]s: {{EDs|6, 13, 19, 25, 38, 44, 63, 82|equave=4}}
+==== 4.6.5.7.11 ====
+<pre>
-=== Blacktetra ===
+Reduced Mapping
+	6	5	7	11
-[[Subgroup]]: 4.3.5
+[ ⟨	1	0	1	1	1	]
+⟨	0	16	2	5	9	] ⟩
-[[Comma list]]: 256/243
+TE Generator Tunings (cents)
-{{Mapping|legend=2| 5 4 6 | 0 0 -1 }}
+⟨2400.1097, 193.9498]
-: Mapping generators: ~4, ~16/15
+TE Step Tunings (cents)
+⟨24.18752, 48.52491]
-[[Optimal tuning]] ([[POTE]]): 1\5ed4 = 480.0, ~16/15 = 80.4062
+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)
-[[Support]]ing [[ET]]s: {{EDs|5, 10, 15, 20, 25, 30, 55, 85, 115|equave=4}}
+Subsets
+q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
+</pre>
-== 4.6.5 subgroup ==
+==== 4.6.5.7.11.13 ====
-=== Meanquad ===
-{{Main| Meanquad }}
-[[Subgroup]]: 4.6.5
+<pre>
+Reduced Mapping
-[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }}
+	6	5	7	11	13
+[ ⟨	1	0	1	1	1	0	]
-{{Mapping|legend=2| 1 0 -4| 0 1 4 }}
+⟨	0	16	2	5	9	23	] ⟩
-: mapping generators: ~4, ~6
+TE Generator Tunings (cents)
+⟨2401.2305, 193.5378]
-[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 697.214
+TE Step Tunings (cents)
-[[Support]]ing [[ET]]s: *7, *10, *11[-5], *13[+5], *17, *24, *27[+5], *31, *38, *41, *45, *52, *55, *69
+⟨42.79107, 35.98524]
-<nowiki />* Wart for 4
+TE Tuning Map (cents)
+⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
-==== 4.6.5.7 subgroup (tetrominant) ====
-[[Subgroup]]: 4.6.5.7
+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)
-[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }}
+Subsets
+q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
+</pre>
-{{Mapping|legend=2| 1 0 -4 4 | 0 1 4 -2 }}
+==== 4.6.5.7.11.13.17 ====
+<pre>
-[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622
+Reduced Mapping
+	6	5	7	11	13	17
-[[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]
+[ ⟨	1	0	1	1	1	0	1	]
+⟨	0	16	2	5	9	23	13	] ⟩
-<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
+[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
-<pre>
+[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
-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
+== 4.9.49 subgroup ==
-q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
+=== Archsquared ===
-</pre>
+[[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
+== 8.9.7 subgroup ==
+=== Sixscared ===
+Sixscared is a tuning which still maintains some consonance, while eviscerating the rules of conventional 12-tone harmony. The familiar major, minor and perfect intervals are nowhere to be found, and octaves are far and few between, so the seventh harmonic becomes the backbone of harmony. Approximating the harmonics 7, 8, 9, Sixscared is named for the classic dad joke: "Why was six scared? Because seven ate nine."
-==== 4.6.5.7.11.13.17 ====
+[[Subgroup]]: 8.9.7
-<pre>
-Reduced Mapping
+[[Comma list]]: 64/63
-	6	5	7	11	13	17
-[ ⟨	1	0	1	1	1	0	1	]
+{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
-⟨	0	16	2	5	9	23	13	] ⟩
-TE Generator Tunings (cents)
-⟨2400.4701, 193.4599]
-TE Step Tunings (cents)
-⟨43.39350, 35.55764]
-TE Tuning Map (cents)
-⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]
-TE Mistunings (cents)
-⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]
-Complexity	1.129881
-Adjusted Error	8.082725 cents
-TE Error	1.977443 cents/octave
-Unison Vectors
-[0, 1, -1, 0, 1, -1, 0⟩ (66:65)
-[1, 1, 1, -1, 0, 0, -1⟩ (120:119)
-[1, 2, 0, 0, -1, -1, 0⟩ (144:143)
-[-2, 1, 1, 1, 0, -1, 0⟩ (105:104)
-[-1, 2, 2, 0, 0, -1, -1⟩ (225:221)
-[-1, 1, 2, -2, 0, -1, 1⟩ (1275:1274)
-Subsets
+: sval mapping generators: ~8, ~9
-q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg
-</pre>
-==== 4.6.5.7.11.13.17.19 ====
+: [[gencom]]: [8 9/8; 64/63]
-<pre>
-Reduced Mapping
+[[Optimal tuning]] ([[CTE]]): ~9/8 = 219.1898
-	6	5	7	11	13	17	19
-[ ⟨	1	0	1	1	1	0	1	1	]
+[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}
-⟨	0	16	2	5	9	23	13	14	] ⟩
+[[Badness]]: 0.0215 × 10<sup>-3</sup>
-TE Generator Tunings (cents)
-⟨2399.9219, 193.3952]
+= Fractional subgroup temperaments =
+== 2.5/3.… subgroups ==
-TE Step Tunings (cents)
+=== Magicaltet ===
-⟨44.14256, 35.03670]
+{{See also| Chromatic pairs #Magicaltet }}
-TE Tuning Map (cents)
+Magicaltet is related to [[keemic]], [[superkleismic]], and [[magic]]. The tonic and the first three generator steps make a [[magical seventh chord]], hence the name.
-⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
+[[Subgroup]]: 2.5/3.7.11
-TE Mistunings (cents)
-⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]
+[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})
-Complexity	1.058472
+{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
-Adjusted Error	8.712222 cents
+: mapping generators: ~2, ~5/3
-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
+{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
-q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh
+: [[gencom]]: [2 6/5; 100/99 385/384]
-</pre>
-==== 4.6.5.7.11.13.17.19.23 ====
+[[Optimal tuning]]s:
-<pre>
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 877.343
-Reduced Mapping
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 877.351
-	6	5	7	11	13	17	19	23
-[ ⟨	1	0	1	1	1	0	1	1	0	]
+{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
-⟨	0	16	2	5	9	23	13	14	28	] ⟩
+: <nowiki/>* wart for 5/3
-TE Generator Tunings (cents)
+[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
-⟨2399.3286, 193.5316]
+=== Starlingtet ===
-TE Step Tunings (cents)
+{{See also | Chromatic pairs #Starlingtet }}
-⟨37.31613, 39.63311]
+Starlingtet, the {{nowrap| 4 & 15 }} temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]]. The tonic and the first three generator steps make a [[starling tetrad]], hence the name.
-TE Tuning Map (cents)
-⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
+[[Subgroup]]: 2.5/3.7/3
-TE Mistunings (cents)
+[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }})
-⟨-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
+{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
-q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii
-</pre>
-== 4.9.25 subgroup ==
+: mapping generators: ~2, ~5/3
-=== Meansquared ===
-[[Subgroup]]: 4.9.25
-[[Comma list]]: [[6561/6400]]
+{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
+: [[gencom]]: [2 6/5; 126/125]
-{{Mapping|legend=2| 1 3 4 | 0 1 4 }}
+[[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
-Mapping generators: ~4, ~9/64
+{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}
-[[Optimal tuning]] ([[CTE]]): ~4 = 2\1, ~9/4 = 1394.429
+[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents
-[[Support]]ing [[ET]]s: 12, 7, 19, 5, 31, 26, 17[+25], 43, 9[-25], 33[-25], 45, 29[+25], 8[+25], 22[+25]
+==== Greeley ====
+{{See also| Chromatic pairs #Greeley }}
-== 4.9.49 subgroup ==
+Greeley is related to [[opossum]] as well as to [[nusecond]].
-=== Archsquared ===
-[[Subgroup]]: 4.9.49
-[[Comma list]]: 4096/3969
+[[Subgroup]]: 2.5/3.7/3.11/3
-{{Mapping|legend=2| 1 3 0 | 0 1 -2 }}
+[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})
-Mapping generators: ~4, ~9/64
+{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1 }}
-[[Optimal tuning]] ([[CTE]]): ~[[9/8]] = 219.190
+{{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]
-[[Support]]ing [[ET]]s: 5, 17, 22, 12, 7, 27, 32, 8, 39[+49], 29[+49], 9[+49], 19[+49], 37, 49
+[[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
-== 8.9.7 subgroup ==
+{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
-=== Sixscared ===
+: <nowiki/>* wart for 11/3
-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
+[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents
-[[Comma list]]: 64/63
+==== Skateboard ====
+{{See also| Chromatic pairs #Skateboard }}
-{{Mapping|legend=2| 1 0 2 | 0 1 -1 }}
+Skateboard is related to [[thrasher]].
-: sval mapping generators: ~8, ~9
+[[Subgroup]]: 2.5/3.7/3.11.13/9
-: [[gencom]]: [8 9/8; 64/63]
+[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }})
-[[Optimal tuning]] ([[CTE]]): 1\[[3ed8]] = 1600.0, ~9/8 = 219.1898
+{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
-[[Optimal ET sequence]]: {{val| 16 17 15 }}, {{val| 33 35 31 }}, {{val| 148 … }}, {{val| 181 … }}, {{val| 214 … }}, {{val| 247 … }}
+{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}
+: [[gencom]]: [2 6/5; 56/55 91/90 100/99]
-[[Badness]]: 0.0215 × 10<sup>-3</sup>
+[[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
-= Fractional subgroup temperaments =
+{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}
-== 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.
+[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents
-[[Subgroup]]: 2.5/3.7.11
+=== Gariberttet ===
+Gariberttet is the 2.5/3.7/3 [[Subgroup temperament families, relationships, and genes|altergene]] of [[sirius]].
-[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }})
+==== Gariberttet (2.5/3.7/3.13/11 subgroup) ====
+{{See also | Chromatic pairs #Gariberttet }}
-{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
+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 generators: ~2, ~5/3
+[[Subgroup]]: 2.5/3.7/3.13/11
-{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
+[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})
-: [[gencom]]: [2 6/5; 100/99 385/384]
+{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
-[[Optimal tuning]]s:
+{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 877.343
+: [[gencom]]: [2 13/11; 275/273 847/845]
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 877.351
-{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~13/11 = 293.679
-<nowiki/>* Wart for 5/3
+{{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]]: 1.206 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
-=== Starlingtet ===
+==== Indium ====
-{{See also | Chromatic pairs #Starlingtet }}
+{{See also | Chromatic pairs #Indium }}
-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.
+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
+[[Subgroup]]: 2.5/3.7/3.11/3
-[[Comma list]]: [[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 0 -1 | 0 1 3 }}
+{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
-: mapping generators: ~2, ~5/3
+{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}
+: [[gencom]]: [2 12/11; 3025/3024 3125/3087]
-{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/11 = 146.978
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/11 = 147.010
-: [[gencom]]: [2 6/5; 126/125]
+{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*<sup>†</sup> }}
+: <nowiki/>* wart for 7/3
+: <sup>†</sup> wart for 11/3
-[[Optimal tuning]]s:
+[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 888.759
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 888.846
-{{Optimal ET sequence|legend=1| 4, 15, 19, 23, 27 }}
+==== Ammon ====
+{{See also| Chromatic pairs #Ammon }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents
+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.
-==== Greeley ====
+[[Subgroup]]: 2.5/3.7/3.11/3.13/3
-{{See also| Chromatic pairs #Greeley }}
-Greeley is related to [[opossum]] as well as to [[nusecond]].
+[[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 }})
-[[Subgroup]]: 2.5/3.7/3.11/3
+{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
-[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }})
+{{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=2| 1 1 2 2 | 0 -2 -6 -1 }}
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/10 = 453.121
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/10 = 453.242
-{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}
+{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}
-: [[gencom]]: [2 11/10; 121/120 126/125]
+[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
-[[Optimal tuning]]s:
+=== Sentry ===
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~11/10 = 155.696
+{{See also | Chromatic pairs #Sentry }}
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~11/10 = 155.776
-{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}
+Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
-<nowiki/>* Wart for 11/3
+[[Subgroup]]: 2.5/3.9/7
-[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents
+[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})
-==== Skateboard ====
+{{Mapping|legend=2| 1 0 0 | 0 2 1 }}
-{{See also| Chromatic pairs #Skateboard }}
-Skateboard is related to [[thrasher]].
+{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
+: [[gencom]]: [2 9/7; 245/243]
-[[Subgroup]]: 2.5/3.7/3.11.13/9
+[[Optimal tuning]]s:
+* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902
-[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }})
+{{Optimal 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=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
-{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}
+=== Marveltwintri ===
+{{See also| Chromatic pairs #Marveltwintri }}
-: [[gencom]]: [2 6/5; 56/55 91/90 100/99]
+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]].
-[[Optimal tuning]]s:
+[[Subgroup]]: 2.5/3.13/9
-* [[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 }}
+[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})
-[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents
+{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
-=== Gariberttet ===
+{{Mapping|legend=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}
-Gariberttet is the 2.5/3.7/3 [[Subgroup temperament families, relationships, and genes|altergene]] of [[sirius]].
+: [[gencom]]: [2 6/5; 325/324]
-==== Gariberttet (2.5/3.7/3.13/11 subgroup) ====
+[[Optimal tuning]]s:
-{{See also | Chromatic pairs #Gariberttet }}
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 882.886
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 882.861
-Gariberttet can be described as the {{nowrap| 4 & 29 }} temperament in the 2.5/3.7/3.13/11 subgroup.
+{{Optimal ET sequence|legend=1| 3, 4, 11, 15, 19, 34, 53, 87, 140 }}
-[[Subgroup]]: 2.5/3.7/3.13/11
+[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
+== 2.….7/3.… subgroups ==
+=== Guanyintet ===
+{{See also | Chromatic pairs #Guanyintet }}
+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.
-[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }})
+[[Subgroup]]: 2.5.7/3.11/3
-{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
+[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -1 }})
-{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}
+{{Mapping|legend=2| 1 0 1 3 | 0 -3 1 -5 }}
+: mapping generators: ~2, ~7/6
-: [[gencom]]: [2 13/11; 275/273 847/845]
+{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}
+: [[gencom]]: [2 7/6; 176/175 540/539]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~13/11 = 293.679
+* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~7/6 = 270.455
+* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~7/6 = 270.093
-{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}
+: <nowiki/>* wart for 7/3
-<nowiki/>* Wart for 13/11
+[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents
-[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents
+==== Tridecimal guanyintet ====
+Guanyintet can extend to the 13th harmonic by the equivalences ([[12/11]])<sup>3</sup> = [[13/10]] and ([[15/14]])<sup>3</sup> = [[16/13]], therefore tempering out {S11/S12/S14/S15}. However, note that it is not supported by the 31 & 53 orwell extension dubbed "tridecimal orwell", but instead the less accurate [[winston]] (22f & 31), as orwell prefers slightly sharper tunings than guanyintet. [[40edo]] remains an excellent tuning.
-==== Indium ====
+[[Subgroup]]: 2.5.7/3.11/3.13
-{{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.
+[[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 }})
-[[Subgroup]]: 2.5/3.7/3.11/3
+{{Mapping|legend=2| 1 0 1 3 1 | 0 -3 1 -5 12 }}
+: mapping generators: ~2, ~12/7
-[[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 = 270.152
+* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~7/6 = 270.218
-{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
+{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 71, 111, 151, 262c*}} <small> using subgroup TE </small>
+: <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 }}
+Badness (Sintel): 0.329
-: [[gencom]]: [2 12/11; 3025/3024 3125/3087]
+==== Laz ====
+{{See also | Chromatic pairs #Laz }}
-[[Optimal tuning]]s:
+Laz is related to [[avalokita]] as well as to [[winston]].
-* [[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> }}
+[[Subgroup]]: 2.5.7/3.11/3.13/3
-<nowiki/>* Wart for 7/3
+[[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 }}
-<sup>†</sup> Wart for 11/3
+{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents
+{{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]
-==== Semidim ====
+[[Optimal tuning]]s:
-{{See also| Chromatic pairs #Semidim }}
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/7 = 930.598
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/7 = 930.700
-Semidim 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.
+{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 156c*†, 205c*† }}
+: <nowiki/>* wart for 7/3
+: † wart for 11/3
-[[Subgroup]]: 2.5/3.7/3.11/3.13/3
+[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents
-[[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 }})
+=== Kryptonite ===
+{{See also| Chromatic pairs #Kryptonite }}
-{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
+Kryptonite is related to [[krypton]].
-{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}
+[[Subgroup]]: 2.5.7/3.11/3.13/3
-: [[gencom]]: [2 13/10; 121/120 169/168 275/273]
+[[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 }})
-[[Optimal tuning]]s:
+{{Mapping|legend=2| 1 2 1 2 2 | 0 3 2 -1 1 }}
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/10 = 453.121
+: mapping generators: ~2, ~13/12
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/10 = 453.242
-{{Optimal ET sequence|legend=1| 8, 29, 37, 45 }}
+{{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]
-[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
+[[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
-=== Sentry ===
+{{Optimal ET sequence|legend=1| 1, …, 8, 9 }}
-{{See also | Chromatic pairs #Sentry }}
-Sentry, the {{nowrap| 3 & 5 }} temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
+[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
-[[Subgroup]]: 2.5/3.9/7
+=== Kiribati ===
+{{See also| Chromatic pairs #Kiribati }}
-[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }})
+Kiribati is related to [[nakika]] as well as to [[octacot]].
-{{Mapping|legend=2| 1 0 0 | 0 2 1 }}
+[[Subgroup]]: 2.9/5.7/3.11/9
-{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
+[[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }})
-: [[gencom]]: [2 9/7; 245/243]
+{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
+: mapping generators: ~2, ~21/20
+{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
+: [[gencom]]: [2 21/20; 100/99 245/242]
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]] and [[POTE]]: ~2 = 1200.000, ~9/7 = 440.902
+* [[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| 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| 13, 14, 27, 41 }}
-<nowiki/>* Wart for 5/3
+[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
-<sup>†</sup> Wart for 9/7
+=== Mothwelltri ===
+{{See also| Chromatic pairs #Mothwelltri }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents
+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.
-=== Marveltwintri ===
+[[Subgroup]]: 2.7/3.11
-{{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]]: [[99/98]] ({{monzo| -1 -2 1 }})
-[[Subgroup]]: 2.5/3.13/9
+{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
+: mapping generators: ~2, ~7/3
-[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }})
+{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
+: [[gencom]]: [2 7/6; 99/98]
-{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
+[[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=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}
+{{Optimal ET sequence|legend=1| 4, 9, 13, 22, 79 }}
-: [[gencom]]: [2 6/5; 325/324]
+[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents
-[[Optimal tuning]]s:
+== 2.….9/7.… subgroups ==
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/3 = 886.886
+=== Marveltri ===
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/3 = 886.861
+{{See also| Chromatic pairs #Marveltri }}
-{{Optimal ET sequence|legend=1| 3, 4, 11, 15, 19, 34, 53, 87, 140 }}
+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.
-[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents
+[[Subgroup]]: 2.5.9/7
-== 2.….7/3… subgroups ==
+[[Comma list]]: 225/224 ({{monzo| -5 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 5 | 0 1 -2 }}
+: mapping generators: ~2, ~5
-[[Subgroup]]: 2.5.7/3.11/3
+{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}
+: [[gencom]]: [2 5; 225/224]
-[[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, ~5/4 = 384.208
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 383.638
-{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}
+{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122, 269c* }}
+: <nowiki/>* wart for 9/7
-: mapping generators: ~2, ~12/7
+[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
-{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}
+==== Sulis ====
+Sulis is related to [[minerva]] and [[würschmidt]].
-: [[gencom]]: [2 7/6; 176/175 540/539]
+[[Subgroup]]: 2.5.9/7.11/9
+[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})
+{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]
 [[Optimal tuning]]s:
-* ([[Tp tuning|subgroup]] [[CTE]]): ~2 = 1200.000, ~12/7 = 929.545
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 386.617
-* ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1200.000, ~12/7 = 929.907
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 386.558
+{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
-{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}
+[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
-<nowiki/>* wart for 7/3
+== 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]]: 0.6028 cents
+[[Subgroup]]: 2.3.7/5
-==== Laz ====
+[[Comma list]]: [[50/49]]
-{{See also | Chromatic pairs #Laz }}
-Laz is related to [[georgian]] as well as to [[winston]].
+{{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]]: [[144/143]] ({{monzo| 4 0 0 -1 -1 }}), [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[196/195]] ({{monzo| 2 -1 2 0 -1 }}
+[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
-{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
+=== Argentic ===
+Argentic is the 2.3.7/5 subgroup temperament tempering out [[5120/5103]].
-{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}
+[[Subgroup]]: 2.3.7/5
-: [[gencom]]: [2 7/6; 144/143 176/175 196/195]
+[[Comma list]]: [[5120/5103]] = {{monzo| 10 -6 -1 }}
+{{Mapping|legend=2| 1 0 10 | 0 1 -6 }}
+: mapping generators: ~2, ~3
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~12/7 = 930.598
+* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~3/2 = 702.792
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~12/7 = 930.700
+* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~3/2 = 702.830
-{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 156c*†, 205c*† }}
+{{Optimal ET sequence|legend=1| 12, 29, 41, 70, 321, 391, 461, 531, 601 }}
+<small> based on subgroup TE </small>
-<nowiki/>* wart for 7/3
+Badness (Sintel): 0.119
-† wart for 11/3
+==== Edson (2.3.7/5.11/5.13/5 subgroup) ====
+{{See also| Chromatic pairs #Edson }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents
+Edson is related to [[pele]] and [[andromeda]].
-=== Kryptonite ===
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-{{See also| Chromatic pairs #Kryptonite }}
-Kryptonite is related to [[krypton]].
+[[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 }}
-[[Subgroup]]: 2.5.7/3.11/3.13/3
+{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
+: mapping generators: ~2, ~3
-[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 78/77 ({{monzo| 1 0 -1 -1 1 }}), 91/90 ({{monzo| -1 -2 1 0 1 }})
+{{Mapping|legend=3| 1 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=2| 1 2 1 2 2 | 0 3 2 -1 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
-: mapping generators: ~2, ~13/12
+{{Optimal ET sequence|legend=1| 12, 17, 29 }}
-{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
-: [[gencom]]: [2 13/12; 56/55 78/77 91/90]
+==== Haumea ====
+{{See also| Chromatic pairs #Haumea }}
-[[Optimal tuning]]s:
+Related temperaments include [[#Bridgetown|bridgetown]], [[namaka]], [[hemigari]], [[#Barbados|barbados]], and [[parizekmic]].
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~13/12 = 130.945
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~13/12 = 132.428
-{{Optimal ET sequence|legend=1| 1, …, 8, 9 }}
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents
+[[Comma list]]: [[352/351]], [[676/675]], [[847/845]]
-=== Kiribati ===
+{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
-{{See also| Chromatic pairs #Kiribati }}
-Kiribati is related to [[nakika]] as well as to [[octacot]].
+{{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]
-[[Subgroup]]: 2.9/5.7/3.11/9
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
-[[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }})
+{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
-{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents
-: mapping generators: ~2, ~21/20
+=== Historical ===
+{{distinguish|Historical temperaments}}
+{{distinguish|History (temperament)}}, which is the rank-3 version of this temperament in the full 13-limit.
-{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
+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.
-: [[gencom]]: [2 21/20; 100/99 245/242]
+[[Subgroup]]: 2.3.7/5.11/5.13/5
-[[Optimal tuning]]s:
+[[Comma list]]: 364/363, 441/440, 1001/1000
-* [[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 }}
+{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
-[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
-=== Mothwelltri ===
+{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
-{{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.
+[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
-[[Subgroup]]: 2.7/3.11
+=== Terrain ===
+{{Redirect|Terrain|the scale|Terrain (scale)}}
+{{See also| Chromatic pairs #Terrain }}
-[[Comma list]]: [[99/98]] ({{monzo| -1 -2 1 }})
+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| 1 0 1 | 0 1 2 }}
+[[Subgroup]]: 2.7/5.9/5
-: mapping generators: ~2, ~7/3
+[[Comma list]]: [[250047/250000]]
-{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
+{{Mapping|legend=2| 3 1 3 | 0 1 -1 }}
-: [[gencom]]: [2 7/6; 99/98]
+{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
+: [[gencom]]: [63/50 10/9; 250047/250000]
-[[Optimal tuning]]s:
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
-* [[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 }}
+{{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]]: 1.064 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
-== 2.….9/7… subgroups ==
+=== Tridec ===
-=== Marveltri ===
+{{See also| Chromatic pairs #Tridec }}
-{{See also| Chromatic pairs #Marveltri }}
+{{See also| Non-over-1 temperament #Tridec }}
-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.
+Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[#Petrtri]].
-[[Subgroup]]: 2.5.9/7
+[[Subgroup]]: 2.7/5.11/5.13/5
-[[Comma list]]: 225/224 ({{monzo| -5 2 1 }})
+[[Comma list]]: [[847/845]], [[1001/1000]]
-{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
+{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
-: mapping generators: ~2, ~5
+{{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]
-{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.556
-: [[gencom]]: [2 5; 225/224]
+{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
-[[Optimal tuning]]s:
+[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents
-* [[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* }}
+==== Naiadec ====
+[[Subgroup]]: 2.7/5.11/5.13/5.17/5
-<nowiki/>* Wart for 9/7
+[[Comma list]]: [[170/169]], [[221/220]], [[847/845]]
-[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
+{{Mapping|legend=2| 1 2 0 1 1 | 0 -4 3 1 2 }}
-==== Sulis ====
+{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 1/4 | 0 0 0 -4 3 1 2 }}
-Sulis is related to [[minerva]] and [[würschmidt]].
+: [[gencom]]: [2 13/10; 170/169 221/220 847/845]
-[[Subgroup]]: 2.5.9/7.11/9
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.882
-[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})
+{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 95<sup>t</sup>, 124<sup>t</sup> }}
+: <sup>t</sup> wart for 17/5
-{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]
+[[Tp tuning #T2 tuning|RMS error]]: 0.7521 cents
-[[Optimal tuning]]s:
+== 2.….11/5.… subgroups ==
-* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1200.000, ~5/4 = 386.617
+=== Petrtri ===
-* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1200.000, ~5/4 = 386.558
+{{See also| Chromatic pairs #Petrtri }}
+{{See also| 5L 3s/Temperaments #Petrtri }}
-{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
+Petrtri can be described as 3 &amp; 5 temperament in the 2.11/5.13/5 subgroup.
-[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
+[[Subgroup]]: 2.11/5.13/5
-== 2.….15/11… subgroups ==
+[[Comma list]]: [[2200/2197]]
-=== Poggers ===
+{{Mapping|legend=2| 1 0 1| 0 3 1 }}
-Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]]
-[[Subgroup]]: 2.9.7.15/11.13
+{{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]
-[[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 455.012
-{{Mapping|legend=2| 1 1 1 -1 -1 | 0 6 5 4 13 }}
+{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
-[[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888
+[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents
-[[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
+==== Bridgetown ====
+{{See also| Chromatic pairs #Bridgetown }}
-== 2.….7/5… subgroups ==
+Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[#Haumea|haumea]] and [[#Barbados|barbados]].
-=== Hydrothermal ===
+[[Subgroup]]: 2.3.11/5.13/5
-A tuning whose distinctively sharp (but still consonant) fifth, and flat (but still consonant) octave, lend it a mysterious, heavy atmosphere. The 6-tone (hexatonic) MOS is melodically interesting and flavorful. The 18-tone MOS is a useful 'chromatic' scale for taking subsets of.
-[[Subgroup]]: 2.3.7/5
+[[Comma list]]: [[352/351]], [[676/675]]
-[[Comma list]]: [[50/49]]
+{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
-{{Mapping|legend=2| 2 3 1 | 0 1 0 }}
+{{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]
-[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
-[[Support]]ing [[ET]]s: {{EDOs|4, 6, 8, 10, 18, 28, 46, 64, 110}}
+{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
-=== Edson ===
+[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
-Edson is the 2.3.7/5 subgroup temperament tempering out [[5120/5103]].
-==== Edson (2.3.7/5.11/5.13/5 subgroup) ====
+=== Hypnosis ===
-{{See also| Chromatic pairs #Edson }}
+Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Alphatricot family #Alphatricot|alphatricot]]
-Edson is related to [[pele]] and [[andromeda]].
+[[Subgroup]]: 2.3.7.11/5.13
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+[[Comma list]]: 169/168, 540/539, 729/728
-[[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 0 -3 8 0 | 0 3 11 -13 7 }}
-{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
-: mapping generators: ~2, ~3
+{{Optimal ET sequence|legend=1| 17, 36, 118f, 125f, 161f, 197f }}
-{{Mapping|legend=3| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
-: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363]
+=== Trisect ===
+Trisect divides every Pythagorean interval into three, and is the much more accurate subgroup restriction of [[Augmented family #Trisected|trisected]].
-[[Optimal tuning]]s:
+Extending this temperament to the full [[11-limit|11-]], [[13-limit|13-]], or [[17-limit]] through [[portent]] or [[landscape]] results in the [[weak extension]] known as [[tritikleismic]].
-* [[Tp tuning|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 }}
+[[Subgroup]]: 2.3.7.11/5
-[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
+[[Comma list]]: 1029/1024, 4000/3993
-==== Haumea ====
+{{Mapping|legend=2| 3 0 10 5 | 0 3 -1 -1 }}
-{{See also| Chromatic pairs #Haumea }}
-Related temperaments include [[#Bridgetown|bridgetown]], [[namaka]], [[hemigari]], [[#Barbados|barbados]], and [[parizekmic]].
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.742
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+{{Optimal ET sequence|legend=1| 15, 21, 36, 123, 159, 195, 231 }}
-[[Comma list]]: [[352/351]], [[676/675]], [[847/845]]
+[[Tp tuning #T2 tuning|RMS error]]: ???
-{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
+==== 2.3.7.11/5.13 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13
-{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}
+[[Comma list]]: 1029/1024, 1575/1573, 2080/2079
-: [[gencom]]: [2 15/13; 352/351 676/675 847/845]
+{{Mapping|legend=2| 3 0 10 5 0 | 0 3 -1 -1 7 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.918
-{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
+{{Optimal ET sequence|legend=1| 15, 21f, 36, 87, 123, 159 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents
+[[Tp tuning #T2 tuning|RMS error]]: ???
-=== Historical ===
+==== 2.3.7.11/5.13.17 subgroup ====
-{{distinguish|Historical temperaments}}
+[[Subgroup]]: 2.3.7.11/5.13.17
-{{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]].
+[[Comma list]]: 273/272, 833/832, 1575/1573, 2080/2079
-[[Subgroup]]: 2.3.7/5.11/5.13/5
+{{Mapping|legend=2| 3 0 10 5 0 -2 | 0 3 -1 -1 7 9 }}
-[[Comma list]]: 364/363, 441/440, 1001/1000
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.820
-{{Mapping|legend=2| 1 2 0 1 2 | 0 -6 7 2 -9 }}
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123, 159 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016
+[[Tp tuning #T2 tuning|RMS error]]: ???
-{{Optimal ET sequence|legend=1| 14, 29, 72, 101, 130, 159 }}
+===== Trisector =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19
-[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
+[[Comma list]]: 210/209, 273/272, 286/285, 595/594, 2080/2079
-=== Terrain ===
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 | 0 3 -1 -1 7 9 3 }}
-{{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.
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.894
-[[Subgroup]]: 2.7/5.9/5
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123h, 159h }}
-[[Comma list]]: [[250047/250000]]
+[[Tp tuning #T2 tuning|RMS error]]: ???
-{{Mapping|legend=2| 3 1 3 | 0 1 -1 }}
+===== 2.3.7.11/5.13.17.19.23 subgroup =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19.23
-{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
+[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 595/594, 2080/2079
-: [[gencom]]: [63/50 10/9; 250047/250000]
+{{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]]): ~63/50 = 1\3, ~10/9 = 182.461
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 634.038
-{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
+{{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
+[[Tp tuning #T2 tuning|RMS error]]: ???
-=== Tridec ===
+===== 2.3.7.11/5.13.17.19.23.29 subgroup =====
-{{See also| Chromatic pairs #Tridec }}
+[[Subgroup]]: 2.3.7.11/5.13.17.19.23.29
-{{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]].
+[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 320/319, 595/594, 2080/2079
-[[Subgroup]]: 2.7/5.11/5.13/5
+{{Mapping|legend=2| 3 0 10 5 0 -2 8 12 13 | 0 3 -1 -1 7 9 3 1 1 }}
-[[Comma list]]: [[847/845]], [[1001/1000]]
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~29/23 = 1\3, ~13/9 = 634.102
-{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
+{{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
-{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}
+[[Tp tuning #T2 tuning|RMS error]]: ???
-: [[gencom]]: [2 13/10; 847/845 1001/1000]
+== 2.….11/7.… subgroups ==
+=== Pepperoni ===
+{{Main| Parapyth }}
+{{See also| Chromatic pairs #Pepperoni }}
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.556
+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, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
+[[Subgroup]]: 2.3.11/7.13/7
-[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents
+[[Comma list]]: 352/351, 364/363
-== 2.….11/5… subgroups ==
+{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
-=== Petrtri ===
+{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
-{{See also| Chromatic pairs #Petrtri }}
+: [[gencom]]: [2 3/2; 352/351 364/363]
-{{See also| 5L 3s/Temperaments #Petrtri }}
-Petrtri can be described as 3 &amp; 5 temperament in the 2.11/5.13/5 subgroup.
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856
-[[Subgroup]]: 2.11/5.13/5
+{{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]]: [[2200/2197]]
+[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
-{{Mapping|legend=2| 1 0 1| 0 3 1 }}
+== 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.
-{{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}
+[[Subgroup]]: 2.3.13/5
-: [[gencom]]: [2 13/10; 2200/2197]
+[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 455.012
+[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
-{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
-[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents
+{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
-==== Bridgetown ====
+[[Badness]]: 0.002335
-{{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]].
+; 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]
-[[Subgroup]]: 2.3.11/5.13/5
+==== Tobago ====
+{{See also| Chromatic pairs #Tobago }}
-[[Comma list]]: [[352/351]], [[676/675]]
+Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
-{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
+[[Subgroup]]: 2.3.11.13/5
-{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}
+[[Comma list]]: [[243/242]], [[676/675]]
-: [[gencom]]: [2 15/13; 352/351 676/675]
+{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
+{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}
+: [[gencom]]: [55/39 15/13; 243/242 676/675]
-{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
-[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents
+{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
-=== Hypnosis ===
+[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents
-Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
-[[Subgroup]]: 2.3.7.11/5.13
+==== Pakkanian hemipyth ====
+[[Subgroup]]: 2.3.11.13/5.17
-[[Comma list]]: 169/168, 540/539, 729/728
+[[Comma list]]: 221/220, 243/242, 289/288
-{{Mapping|legend=2| 1 0 -3 8 0 | 0 3 11 -13 7 }}
+{{Mapping|legend=2| 2 0 -1 -2 5 | 0 2 5 3 2 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518
+[[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| 17, 36, 118f, 125f, 161f, 197f }}
+{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}
+: <nowiki />* wart for 13/5
-[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
+=== Oceanfront ===
+Related temperaments: [[Archytas clan #Superpyth|superpyth]], [[Archytas clan #Ultrapyth|ultrapyth]]
-== 2.….11/7… subgroups ==
+[[Subgroup]]: 2.3.7.13/5
-=== 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.
+[[Comma list]]: 64/63, 91/90
-[[Subgroup]]: 2.3.11/7.13/7
+{{Mapping|legend=2| 1 0 6 -5 | 0 1 -2 4 }}
-[[Comma list]]: 352/351, 364/363
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910
-{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
+{{Optimal ET sequence|legend=1| 5, 22, 27, 32, 37 }}
-{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
+[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
-: [[gencom]]: [2 3/2; 352/351 364/363]
+Scales: [[Oceanfront scales]]
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 703.856
+== 2.….49/5.… subgroups ==
+=== Direct breedsmic ===
+Related temperament: [[hemithirds]], [[newt]]
-{{Optimal ET sequence|legend=1| 5, 7, 12f, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*<sup>†</sup> }}
+[[Subgroup]]: 2.3.49/5
-<nowiki />* Wart for 11/7
+[[Comma list]]: 2401/2400
-<sup>†</sup> Wart for 13/7
+{{Mapping|legend=2| 1 1 3 | 0 2 1 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966
-== 2.….13/5… subgroups ==
+{{Optimal ET sequence|legend=1|7, 10, 17}}
-=== 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
+[[Tp tuning #T2 tuning|RMS error]]: ?
-[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
+== 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.
-[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
+[[Subgroup]]: 2.3.17/5
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
+[[Comma list]]: 136/135 ({{monzo| 3 -3 1 }})
-{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
+{{Mapping|legend=2| 1 0 -3 | 0 1 3 }}
+: mapping generators: ~2, ~3
-[[Badness]]: 0.002335
+[[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}}
-; Music
+{{Optimal ET sequence|legend=1| 5, 12, 17, 46, 63, 143 }}
-* [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 ====
+== 2.….19/7.… subgroups ==
-{{See also| Chromatic pairs #Tobago }}
+=== 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.
-Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
+[[Subgroup]]: 2.3.19/7
-[[Subgroup]]: 2.3.11.13/5
+[[Comma list]]: [[57/56]] ({{Monzo| -3 1 1 }})
-[[Comma list]]: [[243/242]], [[676/675]]
+{{Mapping|legend=2| 1 0 3 | 0 1 -1 }}
+: mapping generators: ~2, ~3
-{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}
+[[Optimal tuning]]s:
+* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1202.4345{{c}}, ~3/2 = 697.4314{{c}}
-{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}
+* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.3981{{c}}
-: [[gencom]]: [55/39 15/13; 243/242 676/675]
-[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
+{{Optimal ET sequence|legend=1| 5, 7, 12, 19, 31*, 50* }}
-{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
+<nowiki/>* wart for 19/7
-[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents
+[[Badness]] (Sintel): 0.082
-==== Pakkanian hemipyth ====
+=== 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]]: 2.3.11.13/5.17
+[[Subgroup]]: 2.17/7.19/7
-[[Comma list]]: 221/220, 243/242, 289/288
+[[Comma list]]: [[5491/5488]] ({{Monzo| -4 2 1 }})
-{{Mapping|legend=2| 2 0 -1 -2 5 | 0 2 5 3 2 }}
+{{Mapping|legend=2| 1 0 4 | 0 1 -2 }}
+: mapping generators: ~2, ~17/7
 [[Optimal tuning]]s:
-* [[Tp tuning|subgroup CTE]]: ~17/12 = 1\2, ~26/15 = 950.7656 (~15/13 = 249.2344)
+* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1200.022{{c}}, ~17/14 = 335.793{{c}}
-* [[Tp tuning|subgroup CWE]]: ~17/12 = 1\2, ~26/15 = 950.6011 (~15/13 = 249.3989)
+* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.000{{c}}, ~17/14 = 335.785{{c}}
-{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}
-<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 1,640: / Line 1,772: @@
 {{Mapping|legend=2| 1 3 4 | 0 -4 -5 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,646: / Line 1,777: @@
 Supporting ETs: *5, *6, *7[+5/2, +7/2], *9[-5/2, --7/2], *11, *16, *17[+5/2], *23[+5/2, +7/2], *21[-7/2], *27, *28[+5/2], *38, *43[-7/2], *49
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 ==== 3/2.5/2.7/2.11/2 ====
@@ Line 1,655: / Line 1,785: @@
 {{Mapping|legend=2| 1 3 4 4 | 0 -4 -5 1 }}
 : sval mapping generators: ~3/2, ~15/14
@@ Line 1,661: / Line 1,790: @@
 [[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2], *21[-7/2], *38[-11/2], *43[-7/2, -11/2], *59[-7/2, -11/2], *70[-7/2, -11/2], *75[--7/2, -11/2]
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 ==== 3/2.5/2.7/2.11/2.13/2 ====
@@ Line 1,674: / Line 1,802: @@
 [[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2]
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 === Semiwolf ===
@@ Line 1,712: / Line 1,839: @@
 [[Optimal ET sequence]]: [[8edf]], [[11edf]]
-== 3/2.5/4… subgroups ==
+== 3/2.5/4.… subgroups ==
 === Poseidon ===
 '''This temperament will be subjected to renaming due to a conflict.'''
@@ Line 1,741: / Line 1,868: @@
 Supporting ETs: *5, *6[+13], *7[-7, -13], *9, *11[+13], *13, *14, *17[-7, -13], *19[+13], *21[-7, -13], *22[-7], *23[+13], *25[-7, -13], *31[-7]
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 === Doubleton ===
@@ Line 1,756: / Line 1,882: @@
 Supporting ETs: *6, *10, *16, *14[-13], *8[+7], *22, *18[-13], *26, *24[-13], *28[+7], *20[+7], *36[-13], *12[+7, +13], *34[-13]
+: <nowiki />* wart for 3/2
-<nowiki />* Wart for 3/2
 == 5/2-equave subgroups ==
 === Hyperion ===
 [[Subgroup]]: 5/2.7.11
@@ Line 1,773: / Line 1,897: @@
 Supporting ETs: *5[-7], *8, *19[+7], *21[-7], *27[+7], *29[-7], *35[+7], *43[+7], *37[-7], *51[+7, +11], *45[-7], *59[+7, +11]
+: <nowiki />* wart for 5/2
-<nowiki />* Wart for 5/2
 = Related temperament collections =
@@ Line 1,781: / Line 1,904: @@
 * [[Substitute harmonic]] temperaments
-<!-- main article -->
+[[Category:Subgroup temperaments| ]] <!-- main article -->
+[[Category:Temperament collections]]
-[[Category:Temperament collections]][[Category:Subgroup]]
+{{Todo| review | cleanup }}

Subgroup temperaments: Difference between revisions