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-'''Landscape microtemperaments''' are [[Rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the [[landscape comma]] ({{monzo| -4 6 -6 3 }} = 250047/250000).
+{{Technical data page}}
+This is a collection of [[rank-2 temperament|rank-2]] '''landscape microtemperaments''', which [[tempering out|temper out]] the [[landscape comma]] ({{monzo|legend=1| -4 6 -6 3 }}, [[ratio]]: 250047/250000). For the [[rank-3 temperament]], see [[Landscape family #Landscape]].
-Landscape rank-2 temperaments discussed elsewhere are:
+Temperaments discussed elsewhere are:
-* [[Augene]] (+64/63 or 126/125) → [[Augmented family #Augene|Augmented family]]
+* [[Augene]] (+64/63 or 126/125) → [[Augmented family #Septimal augmented (augene)|Augmented family]]
-* ''[[Compton]]'' (+225/224) → [[Compton family #Compton|Compton family]]
+* [[Misty]] (+3136/3125 or 5120/5103) → [[Misty family]]
+* ''[[Term (temperament)|Term]]'' (+32805/32768) → [[Schismatic family #Term|Schismatic family]]
+* ''[[Sextile]]'' (+33554432/33480783) → [[Garischismic clan #Sextile|Garischismic clan]]
+* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]]
+* [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]]
+* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Domain|Vulture family]]
+* ''[[Chromat]]'' (10976/10935) → [[Hemimage temperaments #Chromat|Hemimage temperaments]]
 * ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic|Kleismic family]]
+* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
+* ''[[Caleb]]'' (+33075/32768) → [[Mirwomo temperaments #Caleb|Mirwomo temperaments]]
 * ''[[Trisensory]]'' (+1728/1715) → [[Sensipent family #Trisensory|Sensipent family]]
-* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]]
-* ''[[Misty]]'' (+3136/3125 or 5120/5103) → [[Misty family]]
 * ''[[Nessafof]]'' (+6144/6125) → [[Porwell temperaments #Nessafof|Porwell temperaments]]
-* ''[[Chromat]]'' (10976/10935) → [[Hemimage temperaments #Chromat|Hemimage temperaments]]
+* [[Mutt]] (+65625/65536) → [[Horwell temperaments #Mutt|Horwell temperaments]]
-* ''[[Term]]'' (+32805/32768) → [[Schismatic family #Term|Schismatic family]]
-* ''[[Caleb]]'' (+33075/32768) → [[Mirwomo temperaments #Caleb|Mirwomo temperaments]]
-* [[Mutt temperament|Mutt]] (+65625/65536) → [[Horwell temperaments #Mutt|Horwell temperaments]]
 * ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]]
 * ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]]
-* ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Tricot family #Tritricot|Tricot family]]
+* ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortonic family #Domain|Minortonic family]]
+* ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]]
-Considered below are sextile, septichrome, pnict, domain, avicenna, terture, akjayland and terture.
+Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, zinc, magnesium, poe, and chromium in the order of increasing [[badness]].
-== Sextile ==
+== Septichrome ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 250047/250000, 33554432/33480783
+[[Comma list]]: 250047/250000, 2460375/2458624
-{{Mapping|legend=1| 6 0 71 150 | 0 1 -6 -14 }}
+{{Mapping|legend=1| 3 3 1 0 | 0 5 17 24 }}
+: mapping generators: ~63/50, ~243/224
-: mapping generators: ~4096/3645, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 400.0100{{c}}, ~243/224 = 140.3702{{c}}
+: [[error map]]: {{val| +0.030 -0.074 -0.010 +0.059 }}
+* [[CWE]]: ~63/50 = 400.0000{{c}}, ~243/224 = 140.3685{{c}}
+: error map: {{val| 0.000 -0.113 -0.050 +0.017 }}
-{{Multival|legend=1| 6 -36 -84 -71 -150 -94 }}
+{{Optimal ET sequence|legend=1| 60, 111, 171, 795, 966, 1137, 1308, 5403b, 6711b, 8019bc }}
-[[Optimal tuning]] ([[CTE]]): ~4096/3645 = 1\6, ~3/2 = 702.2347
+[[Badness]] (Sintel): 0.426
-{{Optimal ET sequence|legend=1| 12, 234d, 246d, 258, 270, 1362c, 1632c, 1902c, 2172c, 2442bc, 2712bc }}
+=== Semiseptichrome ===
-[[Badness]]: 0.070097
-=== 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 5632/5625, 9801/9800, 151263/151250
+Comma list: 9801/9800, 151263/151250, 234375/234256
-Mapping: {{mapping| 6 0 71 150 230 | 0 1 -6 -14 -22 }}
+Mapping: {{mapping| 6 1 -15 -24 -32 | 0 5 17 24 31 }}
+: mapping generators: ~55/49, ~375/308
-Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2225
+Optimal tunings:
+* WE: ~55/49 = 200.0058{{c}}, ~375/308 = 340.3742{{c}} (~1760/1701 = 59.6375{{c}})
+* CWE: ~55/49 = 200.0000{{c}}, ~375/308 = 340.3661{{c}} (~1760/1701 = 59.6339{{c}})
-{{Optimal ET sequence|legend=1| 12, 246dee, 258e, 270, 822, 1092, 1362c }}
+{{Optimal ET sequence|legend=0| 60e, 222cdee, 282, 342, 966, 1308, 1650, 4608b, 6258bc }}
-Badness: 0.029677
+Badness (Sintel): 0.642
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 1716/1715, 2080/2079, 5632/5625, 10648/10647
+Comma list: 1716/1715, 2080/2079, 34398/34375, 85293/85184
-Mapping: {{mapping| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }}
+Mapping: {{mapping| 6 1 -15 -24 -32 -68 | 0 5 17 24 31 53 }}
-Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2141
+Optimal tunings:
+* WE: ~55/49 = 199.9936{{c}}, ~375/308 = 340.3707{{c}} (~121/117 = 59.6165{{c}})
+* CWE: ~55/49 = 200.0000{{c}}, ~375/308 = 340.3802{{c}} (~121/117 = 59.6198{{c}})
-{{Optimal ET sequence|legend=1| 12f, 258ef, 270, 552, 822, 1092, 1914cde }}
+{{Optimal ET sequence|legend=0| 282, 342f, 624 }}
-Badness: 0.0191
+Badness (Sintel): 1.64
 ==== 17-limit ====
-Subgroup: 2.3.5.7.11.13.17
+Subgroup: 2.3.5.7.11.13
-Comma list: 936/935, 1701/1700, 1716/1715, 5632/5625, 7744/7735
+Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952
-Mapping: {{mapping| 6 0 71 150 230 279 -4 | 0 1 -6 -14 -22 -27 3 }}
+Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 | 0 5 17 24 31 53 15 }}
-Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2117
+Optimal tunings:
+* WE: ~55/49 = 199.9865{{c}}, ~375/308 = 340.3619{{c}} (~88/85 = 59.6111{{c}})
+* CWE: ~55/49 = 200.0000{{c}}, ~375/308 = 340.3821{{c}} (~88/85 = 59.6179{{c}})
-{{Optimal ET sequence|legend=1| 12f, 270, 552g }}
+{{Optimal ET sequence|legend=0| 282, 342f, 624 }}
-Badness: 0.0209
+Badness (Sintel): 1.39
 ==== 19-limit ====
 Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 936/935, 1216/1215, 1701/1700, 1716/1715, 2376/2375, 4200/4199
+Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 23409/23408
+Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 34 | 0 5 17 24 31 53 15 -5 }}
+Optimal tunings:
+* WE: ~55/49 = 199.9837{{c}}, ~162/133 = 340.3589{{c}} (~88/85 = 59.6084{{c}})
+* CWE: ~55/49 = 200.0000{{c}}, ~162/133 = 340.3844{{c}} (~88/85 = 59.6156{{c}})
+{{Optimal ET sequence|legend=0| 282, 342f, 624 }}
+Badness (Sintel): 1.35
+==== 23-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 936/935, 1701/1700, 1716/1715, 1863/1862, 2024/2023, 2025/2023, 2376/2375
+Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 34 -12 | 0 5 17 24 31 53 15 -5 23 }}
+Optimal tunings:
+* WE: ~55/49 = 199.9829{{c}}, ~162/133 = 340.3576{{c}} (~88/85 = 59.6081{{c}})
+* CWE: ~55/49 = 200.0000{{c}}, ~162/133 = 340.3844{{c}} (~88/85 = 59.6156{{c}})
+{{Optimal ET sequence|legend=0| 282, 342f, 624 }}
+Badness (Sintel): 1.14
+== Akjayland ==
+{{See also| 21st-octave temperaments }}
+Named by [[Eliora]] in 2022, akjayland tempers out the [[akjaysma]] in addition to landscape comma, and thereby features a period of 1\21.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 250047/250000, {{monzo| 43 -1 -13 -4 }}
+{{Mapping|legend=1| 21 1 38 102 | 0 3 1 -4 }}
+: mapping generators: ~1323/1280, ~131072/91875
-Mapping: {{mapping| 6 0 71 150 230 279 -4 35 | 0 1 -6 -14 -22 -27 3 -1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~1323/1280 = 57.1426{{c}}, ~131072/91875 = 614.9336{{c}}
+: [[error map]]: {{val| -0.005 -0.012 +0.039 -0.013 }}
+* [[CWE]]: ~1323/1280 = 57.1429{{c}}, ~131072/91875 = 614.9360{{c}}
+: error map: {{val| 0.000 -0.004 +0.051 +0.002 }}
-Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2118
+{{Optimal ET sequence|legend=1| 84, 273, 357, 441, 966, 1407, 1848, 7833, 9681, 11529, 13377c }}
-{{Optimal ET sequence|legend=1| 12f, 270, 552g, 822gg }}
+[[Badness]] (Sintel): 0.838
-Badness: 0.0156
+=== Vasca ===
+Vasca can be described as the {{nowrap| 357 & 525 }} temperament, extended as high as the 23-limit. It tempers out the {{monzo| 95 0 0 0 0 0 0 0 -21 }}, and sets a stack of twenty-one [[23/16]]'s equal with eleven octaves. The name derives from elements vanadium (23) and scandium (21), since this uses the 23rd harmonic, which itself is extremely well represented in 21edo.
-=== Sextilia ===
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 102487/102400, {{monzo| 39 -4 -11 -5 2 }}
+Mapping: {{mapping| 21 4 39 98 58 | 0 6 2 -8 3 3 }}
+: mapping generators: ~1323/1280, ~6615/5632
+Optimal tunings:
+* WE: ~1323/1280 = 57.1436{{c}}, ~6615/5632 = 278.9017{{c}}
+* CWE: ~1323/1280 = 57.1429{{c}}, ~6615/5632 = 278.8985{{c}}
+{{Optimal ET sequence|legend=0| 168, 357, 525, 882, 1407, 2289e }}
+Badness (Sintel): 3.14
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 1001/1000, 4096/4095, 4459/4455, 20449/20412
+Comma list: 3025/3024, 4096/4095, 14641/14625, 85750/85683
-Mapping: {{mapping| 6 0 71 150 230 -149 | 0 1 -6 -14 -22 18 }}
+Mapping: {{mapping| 21 4 39 98 58 107 | 0 6 2 -8 3 -6 }}
-Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2296
+Optimal tunings:
+* WE: ~336/325 = 57.1426{{c}}, ~168/143 = 278.9047{{c}}
+* CWE: ~336/325 = 57.1429{{c}}, ~168/143 = 278.9060{{c}}
-{{Optimal ET sequence|legend=1| 12, 258e, 270 }}
+{{Optimal ET sequence|legend=0| 168, 357, 525, 882 }}
-Badness: 0.0391
+Badness (Sintel): 2.28
 ==== 17-limit ====
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 715/714, 1001/1000, 1701/1700, 4096/4095, 4459/4455
+Comma list: 2601/2600, 3025/3024, 4096/4095, 8624/8619, 14641/14625
-Mapping: {{mapping| 6 0 71 150 230 -149 -4 | 0 1 -6 -14 -22 18 3 }}
+Mapping: {{mapping| 21 4 39 98 58 107 120 | 0 6 2 -8 3 -6 -7 }}
-Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2264
+Optimal tunings:
+* WE: ~336/325 = 57.1429{{c}}, ~168/143 = 278.9037{{c}}
+* CWE: ~336/325 = 57.1429{{c}}, ~168/143 = 278.9036{{c}}
-{{Optimal ET sequence|legend=1| 12, 258e, 270 }}
+{{Optimal ET sequence|legend=0| 168, 357, 525, 882 }}
-Badness: 0.0384
+Badness (Sintel): 1.62
 ==== 19-limit ====
 Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 715/714, 1001/1000, 1216/1215, 1701/1700, 1729/1728, 2912/2907
+Comma list: 2376/2375, 2601/2600, 2926/2925, 3025/3024, 3213/3211, 4096/4095
-Mapping: {{mapping| 6 0 71 150 230 -149 -4 35 | 0 1 -6 -14 -22 18 3 -1 }}
+Mapping: {{mapping| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }}
+Optimal tunings:
+* WE: ~336/325 = 57.1425{{c}}, ~168/143 = 278.8960{{c}}
+* CWE: ~336/325 = 57.1429{{c}}, ~168/143 = 278.8976{{c}}
-Optimal tuning (CTE): ~55/49 = 1\6, ~3/2 = 702.2266
+{{Optimal ET sequence|legend=0| 168h, 357, 525, 882, 1407 }}
-{{Optimal ET sequence|legend=1| 12, 258e, 270 }}
+Badness (Sintel): 1.64
-Badness: 0.0252
+==== 23-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23
-== Septichrome ==
+Comma list: 1496/1495, 2376/2375, 2601/2600, 2646/2645, 2926/2925, 3025/3024, 3213/3211
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 250047/250000, 2460375/2458624
+Mapping: {{mapping| 21 4 39 98 58 107 120 16 95 | 0 6 2 -8 3 -6 -7 15 0 }}
-{{Mapping|legend=1| 3 3 1 0 | 0 5 17 24 }}
+Optimal tunings:
+* WE: ~336/325 = 57.1422{{c}}, ~168/143 = 278.8949{{c}}
+* CWE: ~336/325 = 57.1429{{c}}, ~168/143 = 278.8980{{c}}
-{{Multival|legend=1| 15 51 72 46 72 24 }}
+{{Optimal ET sequence|legend=0| 168h, 357, 525, 882, 1407 }}
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~243/224 = 140.367
+Badness (Sintel): 1.43
-{{Optimal ET sequence|legend=1| 60, 111, 171, 795, 966, 1137, 1308, 5403b, 6711b, 8019bc }}
+== Pnict ==
+[[Subgroup]]: 2.3.5.7
-[[Badness]]: 0.016814
+[[Comma list]]: 250047/250000, 2100875/2097152
-=== Semiseptichrome ===
+{{Mapping|legend=1| 3 -3 1 12 | 0 13 10 -6 }}
-Subgroup: 2.3.5.7.11
+: mapping generators: ~63/50, ~147/128
-Comma list: 9801/9800, 151263/151250, 234375/234256
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 400.0312{{c}}, ~147/128 = 238.6196{{c}} (~192/175 = 161.4116{{c}})
+: [[error map]]: {{val| +0.094 +0.006 -0.087 -0.169 }}
+* [[CWE]]: ~63/50 = 400.0000{{c}}, ~147/128 = 238.6038{{c}} (~192/175 = 161.3962{{c}})
+: error map: {{val| 0.000 -0.106 -0.276 -0.449 }}
-Mapping: {{mapping| 6 1 -15 -24 -32 | 0 5 17 24 31 }}
+{{Optimal ET sequence|legend=1| 15, 141, 156, 171, 2409cd, 2580cd, …, 4461bccddd, 4632bccddd }}
-: mapping generators: ~55/49, ~375/308
+[[Badness]] (Sintel): 1.16
-Optimal tuning (CTE): ~55/49 = 1\6, ~375/308 = 340.3687 (~1760/1701 = 59.6313)
+== Atomic ==
+: ''For the 5-limit version, see [[Very high accuracy temperaments #Atomic]].''
-Optimal ET sequence: {{Optimal ET sequence| 60e, 222cdee, 282, 342, 966, 1308, 1650, 4608b, 6258bc }}
+Atomic tempers out the [[atom]], {{monzo| 161 -84 -12 }}, and in the [[7-limit]] the [[nommisma]], {{monzo| -55 30 2 1 }}, so that a stack of two [[schisma]]s gives the [[garischisma]], from which intervals of [[7/1|7]] can be derived. It may be described as the {{nowrap| 12 & 612 }} temperament, with a [[ploidacot]] signature of dodecaploid monocot.
-Badness: 0.0194
+[[Subgroup]]: 2.3.5.7
-==== 13-limit ====
+[[Comma list]]: 250047/250000, {{monzo| -55 30 2 1 }}
-Subgroup: 2.3.5.7.11.13
-Comma list: 1716/1715, 2080/2079, 34398/34375, 85293/85184
+{{Mapping|legend=1| 12 0 161 338 | 0 1 -7 -16 }}
-Mapping: {{mapping| 6 1 -15 -24 -32 -68 | 0 5 17 24 31 53 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~30375/28672 = 99.999866{{c}}, ~3/2 = 701.948670{{c}} (~32805/32768 = 1.949605{{c}})
+: [[error map]]: {{val| -0.0016 -0.0079  +0.0353 -0.0241 }}
+* [[CWE]]: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.949698{{c}} (~32805/32768 = 1.949698{{c}})
+: error map: {{val| 0.0000 -0.0053 +0.0384 -0.0211 }}
-Optimal tuning (CTE): ~55/49 = 1\6, ~375/308 = 340.3778 (~121/117 = 59.6222)
+{{Optimal ET sequence|legend=1| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
-Optimal ET sequence: {{Optimal ET sequence| 282, 342f, 624 }}
+[[Badness]] (Sintel): 1.16
-Badness: 0.0397
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-==== 17-limit ====
+Comma list: 9801/9800, 151263/151250, 184549376/184528125
-Subgroup: 2.3.5.7.11.13
-Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952
+Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }}
-Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 | 0 5 17 24 31 53 15 }}
+Optimal tunings:
+* WE: ~30375/28672 = 99.999760{{c}}, ~3/2 = 701.946301{{c}} (~32805/32768 = 1.947983{{c}})
+* CWE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.948121{{c}} (~32805/32768 = 1.948121{{c}})
-Optimal tuning (CTE): ~55/49 = 1\6, ~375/308 = 340.3763 (~88/85 = 59.6237)
+{{Optimal ET sequence|legend=0| 12, …, 600e, 612, 1236, 1848 }}
-Optimal ET sequence: {{Optimal ET sequence| 282, 342f, 624 }}
+Badness (Sintel): 0.530
-Badness: 0.0272
+==== Minutes ====
+Minutes (600e & 2460) splits the 1/12-octave period into five 1/60-octave parts.
-==== 19-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 23409/23408
+Comma list: 9801/9800, 151263/151250, 371293/371250, 184549376/184528125
+Mapping: {{mapping| 60 0 805 1690 2585 1173 | 0 1 7 -16 -25 -10 }}
+: mapping generators: ~2704/2673, ~3
+Optimal tunings:
+* WE: ~2704/2673 = 19.999967{{c}}, ~3/2 = 701.946866{{c}}
+* CWE: ~2704/2673 = 20.000000{{c}}, ~3/2 = 701.948111{{c}}
+{{Optimal ET sequence|legend=0| 600e, …, 1860, 2460, 6780, 9240 }}
-Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 34 | 0 5 17 24 31 53 15 -5 }}
+Badness (Sintel): 2.82
-Optimal tuning (CTE): ~55/49 = 1\6, ~162/133 = 340.3767 (~88/85 = 59.6233)
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
-Optimal ET sequence: {{Optimal ET sequence| 282, 342f, 624 }}
+Comma list: 9801/9800, 12376/12375, 28561/28560, 151263/151250, 11275335/11275264
-Badness: 0.0222
+Mapping: {{mapping| 60 0 805 1690 2585 1173 1957 | 0 1 7 -16 -25 -10 -18 }}
-==== 23-limit ====
+Optimal tunings:
-Subgroup: 2.3.5.7.11.13.17.19.23
+* WE: ~2704/2673 = 19.999974{{c}}, ~3/2 = 701.946956{{c}}
+* CWE: ~2704/2673 = 20.000000{{c}}, ~3/2 = 701.947926{{c}}
-Comma list: 936/935, 1701/1700, 1716/1715, 1863/1862, 2024/2023, 2025/2023, 2376/2375
+{{Optimal ET sequence|legend=0| 600e, …, 1860, 2460, 6780, 9240 }}
-Mapping: {{mapping| 6 1 -15 -24 -32 -68 -1 34 -12 | 0 5 17 24 31 53 15 -5 23 }}
+Badness (Sintel): 1.67
-Optimal tuning (CTE): ~55/49 = 1\6, ~162/133 = 340.3757 (~88/85 = 59.6243)
+===== 19-limit =====
+Subgroup: 2.3.5.7.11.13.17.19
-Optimal ET sequence: {{Optimal ET sequence| 282, 342f, 624 }}
+Comma list: 9801/9800, 12376/12375, 12636/12635, 23409/23408, 28561/28560, 151263/151250
-Badness: 0.0160
+Mapping: {{mapping| 60 60 385 730 1085 573 877 -61 | 0 1 7 -16 -25 -10 -18 9 }}
-== Pnict ==
+Optimal tunings:
-[[Subgroup]]: 2.3.5.7
+* WE: ~2704/2673 = 19.999962{{c}}, ~3/2 = 701.946354{{c}}
+* CWE: ~2704/2673 = 20.000000{{c}}, ~3/2 = 701.947751{{c}}
-[[Comma list]]: 250047/250000, 2100875/2097152
+{{Optimal ET sequence|legend=0| 600e, 1860, 2460, 4320, 6780, 9240 }}
-{{Mapping|legend=1| 3 10 11 6 | 0 -13 -10 6 }}
+Badness (Sintel): 1.50
-{{Multival|legend=1| 39 30 -18 -43 -138 -126 }}
+==== Hafnium ====
+Hafnium (1224 & 4320), named after the 72nd element, splits the 1/12-octave period into six 1/72-octave parts. Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these primes are also prescribed. In the add-37 version, [[37/22]] is mapped to exact 3\4.
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~192/175 = 161.399
+Subgroup: 2.3.5.7.11.13
-{{Optimal ET sequence|legend=1| 15, 141, 156, 171, 2409cd, 2580cd, …, 4461bccddd, 4632bccddd }}
+Comma list: 9801/9800, 151263/151250, 184549376/184528125, 308915776/308828625
-[[Badness]]: 0.045660
+Mapping: {{mapping| 72 0 966 2028 3102 2777 | 0 1 -7 -16 -25 -22 }}
+: mapping generators: ~105/104, ~3
-== Domain ==
+Optimal tunings:
-{{See also| Minortonic family }}
+* WE: ~105/104 = 16.666629{{c}}, ~3/2 = 701.945668{{c}}
+* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947388{{c}}
-[[Subgroup]]: 2.3.5.7
+{{Optimal ET sequence|legend=0| 1224, 3096e, 4320, 5544, 9864c }}
-[[Comma list]]: 250047/250000, 645700815/645657712
+Badness (Sintel): 4.76
-{{Mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
-{{Multival|legend=1| 51 105 108 48 28 -44 }}
+Comma list: 9801/9800, 12376/12375, 151263/151250, 1713660/1713481, 97144749/97140736
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.467
+Mapping: {{mapping| 72 0 966 2028 3102 2777 979 | 0 1 -7 -16 -25 -22 -6 }}
+: mapping generators: ~105/104, ~3
-{{Optimal ET sequence|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 2190, 11943, 13962, 15981, 18000, 20019, 22038 }}
+Optimal tunings:
+* WE: ~105/104 = 16.666615{{c}}, ~3/2 = 701.944968{{c}}
+* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947293{{c}}
-[[Badness]]: 0.013979
+{{Optimal ET sequence|legend=0| 1224, 3096e, 4320, 5544, 9864c }}
-== Avicenna ==
+Badness (Sintel): 2.73
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 250047/250000, 29360128/29296875
+===== 2.3.5.7.11.13.17.31 subgroup =====
+Subgroup: 2.3.5.7.11.13.17.31
-{{Mapping|legend=1| 3 2 8 16 | 0 8 -3 -22 }}
+Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625
-{{Multival|legend=1| 24 -9 -66 -70 -172 -128 }}
+Subgroup-val mapping: {{mapping| 72 0 966 2028 3102 2777 979 -328 | 0 1 -7 -16 -25 -22 -6 6 }}
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~1024/945 = 137.768
+Optimal tunings:
+* WE: ~105/104 = 16.666643{{c}}, ~3/2 = 701.946542{{c}}
+* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947581{{c}}
-{{Optimal ET sequence|legend=1| 87, 183, 270, 723, 993, 1263, 2796cd, 4059bccd }}
+{{Optimal ET sequence|legend=0| 1224, 3096e, 4320, 5544 }}
-[[Badness]]: 0.062187
+Badness (Sintel): 2.36
-=== 11-limit ===
+===== 2.3.5.7.11.13.17.31.37 subgroup =====
-Subgroup: 2.3.5.7.11
+Subgroup: 2.3.5.7.11.13.17.31.37
-Comma list: 3025/3024, 5632/5625, 102487/102400
+Comma list: 9801/9800, 10881/10880, 12376/12375, 16576/16575, 57629/57624, 93093/93092, 179712/179707
-Mapping: {{mapping| 3 2 8 16 9 | 0 8 -3 -22 4 }}
+Subgroup-val mapping: {{mapping| 72 0 966 2028 3102 2777 979 -328 3228 | 0 1 -7 -16 -25 -22 -6 6 -25 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~693/640 = 137.771
+Optimal tunings:
+* WE: ~105/104 = 16.666648{{c}}, ~3/2 = 701.946549{{c}}
+* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947386{{c}}
-{{Optimal ET sequence|legend=1| 87, 183, 270, 1263, 1533, 1803c, 2073c }}
+{{Optimal ET sequence|legend=0| 1224, 3096el, 4320, 5544 }}
-Badness: 0.023085
+Badness (Sintel): 1.98
-=== 13-limit ===
+== Slendscape ==
-Subgroup: 2.3.5.7.11.13
+Named by [[Xenllium]] in 2025, slendscape tempers out the [[slendroschisma]] (68719476736/68641485507) in addition to landscape comma, and thereby features a period of 1\15.
-Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095
+[[Subgroup]]: 2.3.5.7
-Mapping: {{mapping| 3 2 8 16 9 8 | 0 8 -3 -22 4 9 }}
+[[Comma list]]: 250047/250000, 12884901888/12867859375
-Optimal tuning (POTE): ~63/50 = 1\3, ~13/12 = 137.777
+{{Mapping|legend=1| 15 0 17 54 | 0 4 3 -2 }}
+: mapping generators: ~8575/8192, ~1152/875
-{{Optimal ET sequence|legend=1| 87, 183, 270 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~8575/8192 = 79.9771{{c}}, ~1152/875 = 475.4832{{c}}
+: [[error map]]: {{val| -0.043 -0.022 +0.087 +0.053 }}
+* [[CWE]]: ~8575/8192 = 80.0000{{c}}, ~1152/875 = 475.4962{{c}}
+: error map: {{val| 0.000 +0.030 +0.175 +0.182 }}
-Badness: 0.015557
+{{Optimal ET sequence|legend=1| 15, 240, 255, 270, 795, 1065, 1335, 2400 }}
-=== 17-limit ===
+[[Badness]] (Sintel): 1.47
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 676/675, 715/714, 1001/1000, 3025/3024, 4096/4095
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Mapping: {{mapping| 3 2 8 16 9 8 4 | 0 8 -3 -22 4 9 24 }}
+Comma list: 3025/3024, 102487/102400, 180224/180075
-Optimal tuning (POTE): ~63/50 = 1\3, ~13/12 = 137.777
+Mapping: {{mapping| 15 0 17 54 40 | 0 4 3 -2 2 }}
-{{Optimal ET sequence|legend=1| 87, 183, 270 }}
+Optimal tunings:
+* WE: ~22/21 = 79.9991{{c}}, ~968/735 = 475.4915{{c}}
+* CWE: ~22/21 = 80.0000{{c}}, ~968/735 = 475.4955{{c}}
-Badness: 0.015557
+{{Optimal ET sequence|legend=0| 15, 240, 255, 270, 795, 1065, 2400e }}
-=== 19-limit ===
+Badness (Sintel): 0.868
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 676/675, 715/714, 1001/1000, 1216/1215, 3025/3024, 4096/4095
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Mapping: {{mapping| 3 2 8 16 9 8 4 0 | 0 8 -3 -22 4 9 24 37 }}
+Comma list: 1716/1715, 3025/3024, 4096/4095, 14641/14625
-Optimal tuning (POTE): ~63/50 = 1\3, ~13/12 = 137.777
+Mapping: {{mapping| 15 0 17 54 40 109 | 0 4 3 -2 2 -9 }}
-{{Optimal ET sequence|legend=1| 87, 183, 270 }}
+Optimal tunings:
+* WE: ~22/21 = 79.9993{{c}}, ~154/117 = 475.4902{{c}}
+* CWE: ~22/21 = 80.0000{{c}}, ~154/117 = 475.4943{{c}}
-Badness: 0.015557
+{{Optimal ET sequence|legend=0| 255, 270, 795, 1065 }}
-== Terture ==
+Badness (Sintel): 0.877
-{{See also| Vulture family }}
+== Avicenna ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 250047/250000, 359661568/358722675
+[[Comma list]]: 250047/250000, 29360128/29296875
-{{Mapping|legend=1| 3 4 3 2 | 0 4 21 34 }}
+{{Mapping|legend=1| 3 2 8 16 | 0 8 -3 -22 }}
+: mapping generators: ~63/50, ~1024/945
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~392/375 = 75.555
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 399.9681{{c}}, ~1024/945 = 137.7570{{c}}
+: [[error map]]: {{val| -0.096 +0.037 +0.160 +0.010 }}
+* [[CWE]]: ~63/50 = 400.0000{{c}}, ~1024/945 = 137.7689{{c}}
+: error map: {{val| 0.000 +0.196 +0.380 +0.259 }}
-{{Optimal ET sequence|legend=1| 111, 159, 270 }}
+{{Optimal ET sequence|legend=1| 87, 183, 270, 723, 993, 1263, 2796cd, 4059bccd }}
-[[Badness]]: 0.087156
+[[Badness]] (Sintel): 1.57
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 3025/3024, 19712/19683, 102487/102400
+Comma list: 3025/3024, 5632/5625, 102487/102400
-Mapping: {{mapping| 3 4 3 2 10 | 0 4 21 34 2 }}
+Mapping: {{mapping| 3 2 8 16 9 | 0 8 -3 -22 4 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~392/375 = 75.550
+Optimal tunings:
+* WE: ~63/50 = 399.9798{{c}}, ~693/640 = 137.7643{{c}}
+* CWE: ~63/50 = 400.0000{{c}}, ~693/640 = 137.7716{{c}}
-{{Optimal ET sequence|legend=1| 111, 159, 270, 1239, 1509, 1779, 2049, 2319 }}
+{{Optimal ET sequence|legend=0| 87, 183, 270, 1263, 1533, 1803c }}
-Badness: 0.029326
+Badness (Sintel): 0.763
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976
+Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095
-Mapping: {{mapping| 3 4 3 2 10 6 | 0 4 21 34 2 27 }}
+Mapping: {{mapping| 3 2 8 16 9 8 | 0 8 -3 -22 4 9 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~117/112 = 75.553
+Optimal tunings:
+* WE: ~63/50 = 399.9921{{c}}, ~13/12 = 137.7743{{c}}
+* CWE: ~63/50 = 400.0000{{c}}, ~13/12 = 137.7770{{c}}
-{{Optimal ET sequence|legend=1| 111, 159, 270 }}
+{{Optimal ET sequence|legend=0| 87, 183, 270 }}
-Badness: 0.018647
+Badness (Sintel): 0.643
 === 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913
+Comma list: 676/675, 715/714, 936/935, 1001/1000, 4096/4095
-Mapping: {{mapping| 3 4 3 2 10 6 10 | 0 4 21 34 2 27 12 }}
+Mapping: {{mapping| 3 2 8 16 9 8 4 | 0 8 -3 -22 4 9 24 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~117/112 = 75.560
+Optimal tunings:
+* WE: ~34/27 = 399.9776{{c}}, ~13/12 = 137.7535{{c}}
+* CWE: ~34/27 = 400.0000{{c}}, ~13/12 = 137.7608{{c}}
-{{Optimal ET sequence|legend=1| 111, 159, 270 }}
+{{Optimal ET sequence|legend=0| 87, 183, 270, 453 }}
-Badness: 0.018705
+Badness (Sintel): 0.869
 === 19-limit ===
 Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615
+Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1729/1728
-Mapping: {{mapping| 3 4 3 2 10 6 10 5 | 0 4 21 34 2 27 12 41 }}
+Mapping: {{mapping| 3 2 8 16 9 8 4 0 | 0 8 -3 -22 4 9 24 37 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~95/91 = 75.560
+Optimal tunings:
+* WE: ~34/27 = 399.9804{{c}}, ~13/12 = 137.7602{{c}}
+* CWE: ~34/27 = 400.0000{{c}}, ~13/12 = 137.7664{{c}}
-{{Optimal ET sequence|legend=1| 111, 159, 270 }}
+{{Optimal ET sequence|legend=0| 87, 183, 270 }}
-Badness: 0.013902
+Badness (Sintel): 0.928
-=== 23-limit ===
+== Zinc ==
-Subgroup: 2.3.5.7.11.13.17.19.23
+{{See also| 10th-octave temperaments #Neon }}
-Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215
+Zinc maybe described as the {{nowrap| 270 & 2190 }} temperament. It was named by [[Eliora]] in 2023 after the 30th element for having a 30th-octave period.
-Mapping: {{mapping| 3 4 3 2 10 6 10 5 13 | 0 4 21 34 2 27 12 41 3 }}
+[[Subgroup]]: 2.3.5.7
-Optimal tuning (POTE): ~63/50 = 1\3, ~24/23 = 75.548
+[[Comma list]]: 250047/250000, {{monzo| -53 -12 2 24 }}
-{{Optimal ET sequence|legend=1| 111, 159, 270 }}
+{{Mapping|legend=1| 30 2 15 66 | 0 5 6 2 }}
+: mapping generators: ~53747712/52521875, ~216/175
-Badness: 0.014915
+[[Optimal tuning]]s:
+* [[WE]]: ~53747712/52521875 = 40.0002{{c}}, ~216/175 = 364.3890{{c}} (~{{monzo| 21 3 1 -10 }} = 4.3869{{c}})
+: [[error map]]: {{val| +0.007 -0.009 +0.024 -0.032 }}
+* [[CWE]]: ~53747712/52521875 = 40.0000{{c}}, ~216/175 = 364.3879{{c}} (~{{monzo| 21 3 1 -10 }} = 4.3879{{c}})
+: error map: {{val| 0.000 -0.015 +0.014 -0.050 }}
-== Akjayland ==
+{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650 }}
-{{See also| 21st-octave temperaments }}
-Akjayland tempers out the [[akjaysma]] in addition to landscape comma, and thereby features a period of 1\21.
+[[Badness]] (Sintel): 1.88
-[[Subgroup]]: 2.3.5.7
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-[[Comma list]]: 250047/250000, {{monzo| 43 -1 -13 -4 }}
+Comma list: 9801/9800, 151263/151250, {{monzo| -27 -6 4 6 3 }}
-{{Mapping|legend=1| 21 1 38 102 | 0 3 1 -4 }}
+Mapping: {{mapping| 30 2 15 66 122 | 0 5 6 2 -2 }}
-: mapping generators: ~1323/1280, ~131072/91875
+Optimal tunings:
+* WE: ~18865/18432 = 40.0005{{c}}, ~216/175 = 364.3881{{c}} (~385/384 = 4.3837{{c}})
+* CWE: ~18865/18432 = 40.0000{{c}}, ~216/175 = 364.3849{{c}} (~385/384 = 4.3849{{c}})
-[[Optimal tuning]] ([[CTE]]): ~1323/1280 = 1\21, ~131072/91875 = 614.9354
+{{Optimal ET sequence|legend=0| 270, 1110, 1380, 1650, 1920, 2190 }}
-{{Optimal ET sequence|legend=1| 84, 273, 357, 441, 966, 1407, 1848, 7833, 9681, 11529, 13377c }}
+Badness (Sintel): 0.727
-[[Badness]]: 0.0309
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-=== Vasca ===
+Comma list: 9801/9800, 10648/10647, 105644/105625, 196625/196608
-Vasca can be described as the 357 & 525 temperament, extended as high as the 23-limit. It tempers out the {{monzo| 95 0 0 0 0 0 0 0 -21 }}, and sets a stack of twenty-one [[23/16]]'s equal with eleven octaves. The name derives from elements vanadium (23) and scandium (21), since this uses the 23rd harmonic, which itself is extremely well represented in 21edo.
-Subgroup: 2.3.5.7.11
+Mapping: {{mapping| 30 2 15 66 122 193 | 0 5 6 2 -2 -9 }}
-Comma list: 3025/3024, 102487/102400, {{monzo| 39 -4 -11 -5 2 }}
+Optimal tunings:
+* WE: ~351/343 = 40.0003{{c}}, ~216/175 = 364.3894{{c}} (~385/384 = 4.3865{{c}})
+* CWE: ~351/343 = 40.0000{{c}}, ~216/175 = 364.3867{{c}} (~385/384 = 4.3867{{c}})
-Mapping: {{mapping| 21 4 39 98 58 | 0 6 2 -8 3 3 }}
+{{Optimal ET sequence|legend=0| 270, 1380, 1650, 1920, 2190, 4650, 6840e, 11490de }}
-: mapping generators: ~1323/1280, ~6615/5632
+Badness (Sintel): 0.640
-Optimal tuning (CTE): ~1323/1280 = 1\21, ~6615/5632 = 278.8998
+==== 2.3.5.7.11.13.19 subgroup (neozinc) ====
+Subgroup: 2.3.5.7.11.13.19
-{{Optimal ET sequence|legend=1| 168, 357, 525, 882, 1407, 2289e }}
+Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 89376/89375
-Badness: 0.0949
+Mapping: {{mapping| 30 2 15 66 122 193 91 | 0 5 6 2 -2 -9 4 }}
-==== 13-limit ====
+Optimal tunings:
-Subgroup: 2.3.5.7.11.13
+* WE: ~175/171 = 40.0002{{c}}, ~216/175 = 364.3885{{c}} (~400/399 = 4.3862{{c}})
+* CWE: ~175/171 = 40.0000{{c}}, ~216/175 = 364.3864{{c}} (~400/399 = 4.3864{{c}})
-Comma list: 3025/3024, 4096/4095, 14641/14625, 85750/85683
+{{Optimal ET sequence|legend=0| 270, 1380, 1650, 1920, 2190, 4650, 6840e }}
-Mapping: {{mapping| 21 4 39 98 58 107 | 0 6 2 -8 3 -6 }}
+Badness (Sintel): 0.477
-Optimal tuning (CTE): ~336/325 = 1\21, ~168/143 = 278.9058
+=== Neodymium ===
+Neodymium (540 & 1920) splits the period into 1/60-octave halves for prime 17.
-{{Optimal ET sequence|legend=1| 168, 357, 525, 882 }}
-Badness: 0.0551
-==== 17-limit ====
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 2601/2600, 3025/3024, 4096/4095, 8624/8619, 14641/14625
+Comma list: 9801/9800, 10648/10647, 31213/31212, 105644/105625, 196625/196608
-Mapping: {{mapping| 21 4 39 98 58 107 120 | 0 6 2 -8 3 -6 -7 }}
+Mapping: {{mapping| 60 4 30 132 244 386 391 | 0 5 6 2 -2 -9 -8 }}
+: mapping generators: ~612/605, ~216/175
-Optimal tuning (CTE): ~336/325 = 1\21, ~168/143 = 278.9036
+Optimal tunings:
+* WE: ~612/605 = 20.0002{{c}}, ~216/175 = 364.3894{{c}}
+* CWE: ~612/605 = 20.0000{{c}}, ~216/175 = 364.3864{{c}}
-{{Optimal ET sequence|legend=1| 168, 357, 525, 882 }}
+{{Optimal ET sequence|legend=0| 540, 1380, 1920, 2460, 4380, 6840e }}
-Badness: 0.0319
+Badness (Sintel): 1.23
 ==== 19-limit ====
 Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 2376/2375, 2601/2600, 2926/2925, 3025/3024, 3213/3211, 4096/4095
+Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 23409/23408, 89376/89375
+Mapping: {{mapping| 60 4 30 132 244 386 391 182 | 0 5 6 2 -2 -9 -8 4 }}
-Mapping: {{mapping| 21 4 39 98 58 107 120 16 | 0 6 2 -8 3 -6 -7 15 }}
+Optimal tunings:
+* WE: ~612/605 = 20.0001{{c}}, ~216/175 = 364.3883{{c}}
+* CWE: ~612/605 = 20.0000{{c}}, ~216/175 = 364.3860{{c}}
-Optimal tuning (CTE): ~336/325 = 1\21, ~168/143 = 278.9036
+{{Optimal ET sequence|legend=0| 540, 1380, 1920, 2460, 4380, 6840e }}
-{{Optimal ET sequence|legend=1| 168h, 357, 525, 882, 1407 }}
+Badness (Sintel): 1.02
-Badness: 0.0270
+== Magnesium ==
+: ''For the 5-limit version, see [[12th-octave temperaments #Magnesium (5-limit)]].
-==== 23-limit ====
+Magnesium is named by [[Eliora]] in 2023 after the 12th element for having a 1/12-octave period; however, it is not an extension of the [[atomic]] – the associated comma is {{monzo| -157 -24 84 }} in the 5-limit, and 7 generator steps together with two [[12edo]] semitones reach the [[3/1|3rd]] [[harmonic]]. It may be described as the {{nowrap| 84 & 612 }} temperament, with a [[ploidacot]] signature of dodecaploid gamma-heptacot.
-Subgroup: 2.3.5.7.11.13.17.19.23
-Comma list: 1496/1495, 2376/2375, 2601/2600, 2646/2645, 2926/2925, 3025/3024, 3213/3211
+[[Subgroup]]: 2.3.5.7
-Mapping: {{mapping| 21 4 39 98 58 107 120 16 95 | 0 -6 -2 8 -3 6 7 -15 0 }}
+[[Comma list]]: 250047/250000, {{monzo| -59 2 18 5 }}
-Optimal tuning (CTE): ~336/325 = 1\21, ~168/143 = 278.8971
+{{Mapping|legend=1| 12 2 23 58 | 0 7 2 -10 }}
+: mapping generators: ~138915/131072, ~3145728/2734375
-{{Optimal ET sequence|legend=1| 168h, 357, 525, 882, 1407 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~138915/131072 = 100.0021{{c}}, ~3145728/2734375 = 243.1333{{c}}
+: [[error map]]: {{val| +0.025 -0.018 +0.000 -0.039 }}
+* [[CWE]]: ~138915/131072 = 100.0000{{c}}, ~3145728/2734375 = 243.1285{{c}}
+: error map: {{val| 0.000 -0.055 -0.057 -0.111 }}
-Badness: 0.0199
+{{Optimal ET sequence|legend=1| 84, 360d, 444, 528, 612, 1920, 2532, 10740cd, 13272bcdd, 15804bcdd, 18336bcddd }}
-== Magnesium ==
+Badness (Sintel): 2.44
-: ''For the 5-limit version, see [[12th-octave temperaments#Magnesium (5-limit)]].
-Magnesium is named after element 12 for being period 12, however, it's not an extension of the [[atomic]] – the associated comma is {{monzo| -157 -24 84 }} in the 5-limit and the 7 generators together with [[12edo]] major second reach the just perfect fifth, [[3/2]].
+== Poe ==
+Named by [[Tristan Bay]] in 2025, poe may be described as the {{nowrap| 60 & 270 }} temperament.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 250047/250000, {{monzo| -59 2 18 5 }}
+[[Comma list]]: 250047/250000, {{monzo| 15 -16 -4 7 }}
+{{Mapping|legend=1| 30 0 -73 -106 | 0 1 3 4 }}
+: mapping generators: ~2240/2187, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~2240/2187 = 39.9982{{c}}, ~3/2 = 702.1533{{c}}
+: [[error map]]: {{val| -0.055 +0.143 +0.115 -0.238 }}
+* [[CWE]]: ~2240/2187 = 40.0000{{c}}, ~3/2 = 702.1656{{c}}
+: error map: {{val| 0.000 +0.211 +0.183 -0.163 }}
+{{Optimal ET sequence|legend=1| 60, 150cd, 210, 270, 1950, 2220, 2490, 2760b, 3030bc, 3300bc }}
+[[Badness]] (Sintel): 2.90
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 9801/9800, 19712/19683, 151263/151250
+Mapping: {{mapping| 30 0 -73 -106 -134 | 0 1 3 4 5 }}
+Optimal tunings:
+* WE: ~45/44 = 39.9976{{c}}, ~3/2 = 702.1955{{c}}
+* CWE: ~45/44 = 40.0000{{c}}, ~3/2 = 702.2129{{c}}
+{{Optimal ET sequence|legend=0| 60e, …, 210e, 270 }}
+Badness (Sintel): 1.31
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-{{Mapping|legend=1| 12 2 23 58 | 0 7 2 -10 }}
+Comma list: 1001/1000, 4225/4224, 4459/4455, 19712/19683
-: mapping generators: ~138915/131072, 3145728/2734375
+Mapping: {{mapping| 30 0 -73 -106 -134 111 | 0 1 3 4 5 0 }}
-Optimal tuning (CTE): ~138915/131072 = 1\12, ~3145728/2734375 = 243.130
+Optimal tunings:
+* WE: ~45/44 = 40.0008{{c}}, ~3/2 = 702.1778{{c}}
+* CWE: ~45/44 = 40.0000{{c}}, ~3/2 = 702.1699{{c}}
-{{Optimal ET sequence|legend=1| 84, 360d, 444, 528, 612, 1920, 2532, 10740cd, 13272bcdd, 15804bcdd, 18336bcddd }}
+{{Optimal ET sequence|legend=0| 60e, 210e, 270, 1410ef, 1680ef }}
-Badness: 0.0964
+Badness (Sintel): 1.19
 == Chromium ==
-: ''For the 5-limit version, see [[12th-octave temperaments#Magnesium (5-limit)]].
+: ''For the 5-limit version, see [[24th-octave temperaments #Chromium (5-limit)]].
-[[Chromium]] is defined by associating the porcupine comma [[256/243]] to the 24th of an octave. Named after the 24th element for being period 24.
+[[Chromium]] is defined by associating the porcupine comma [[250/243]] to the 24th of an octave, and may be described as the {{nowrap| 72 & 624 }} temperament. It was named by [[Eliora]] in 2022 after the 24th element for having a 24th-octave period.
 [[Subgroup]]: 2.3.5.7
@@ Line 505: / Line 694: @@
 {{Mapping|legend=1| 24 1 -6 18 | 0 3 5 4 }}
 : mapping generators: ~250/243, ~10/7
-[[Optimal tuning]] ([[CTE]]): ~250/243 = 1\24, ~10/7 = 617.2710
+[[Optimal tuning]]s:
+* [[WE]]: ~250/243 = 49.9992{{c}}, ~10/7 = 617.2714{{c}}
+: [[error map]]: {{val| -0.019 -0.142 +0.048 +0.246 }}
+* [[CWE]]: ~250/243 = 50.0000{{c}}, ~10/7 = 617.2762{{c}}
+: error map: {{val| 0.000 -0.126 +0.067 +0.279 }}
 {{Optimal ET sequence|legend=1| 72, …, 480, 552, 624, 1320, 1944d, 3264d }}
-[[Badness]]: 0.139
+[[Badness]] (Sintel): 3.52
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 9801/9800, 46656/46585, 250047/250000
+Comma list: 9801/9800, 46656/46585, 151263/151250
 Mapping: {{mapping| 24 1 -6 18 46 | 0 3 5 4 3 }}
-Optimal tuning (CTE): ~250/243 = 1\24, ~10/7 = 617.2597
+Optimal tunings:
+* WE: ~250/243 = 49.9972{{c}}, ~10/7 = 617.2639{{c}}
+* CWE: ~250/243 = 50.0000{{c}}, ~10/7 = 617.2823{{c}}
-{{Optimal ET sequence|legend=1| 72, …, 480, 552, 624 }}
+{{Optimal ET sequence|legend=0| 72, …, 480, 552, 624 }}
-Badness: 0.0398
+Badness (Sintel): 1.32
 === 13-limit ===
@@ Line 534: / Line 728: @@
 Mapping: {{mapping| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 }}
-Optimal tuning (CTE): ~250/243 = 1\24, ~10/7 = 617.2869
+Optimal tunings:
+* WE: ~250/243 = 49.9958{{c}}, ~10/7 = 617.2824{{c}}
+* CWE: ~250/243 = 50.0000{{c}}, ~10/7 = 617.3161{{c}}
-{{Optimal ET sequence|legend=1| 72, …, 480f, 552, 624, 1176de, 1800cdee }}
+{{Optimal ET sequence|legend=0| 72, …, 480f, 552, 624, 1176de, 1800cdee }}
-Badness: 0.0293
+Badness (Sintel): 1.21
 === 17-limit ===
@@ Line 547: / Line 743: @@
 Mapping: {{mapping| 24 1 -6 18 46 -47 -13 | 0 3 5 4 3 11 9 }}
-Optimal tuning (CTE): ~35/34 = 1\24, ~10/7 = 617.2732
+Optimal tunings:
+* WE: ~35/34 = 49.9959{{c}}, ~10/7 = 617.2685{{c}}
-{{Optimal ET sequence|legend=1| 72, …, 480fgg, 552g, 624 }}
+* CWE: ~35/34 = 50.0000{{c}}, ~10/7 = 617.3015{{c}}
-Badness: 0.0209
-== Zinc ==
-{{See also|30th-octave temperaments#Zinc}}
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 250047/250000, {{monzo| -45 -24 14 18 }}
-{{Mapping|legend=1| 30 2 15 66 | 0 5 6 2 }}
-[[Optimal tuning]] ([[CTE]]): ~53747712/52521875 = 1\30, ~216/175 = 364.389
-{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650 }}
-[[Badness]]: 0.0742
-=== 11-limit===
-Subgroup: 2.3.5.7.11
-Comma list: 9801/9800, 250047/250000, 97869261875/97844723712
-Mapping: {{mapping| 30 2 15 66 122 | 0 5 6 2 -2 }}
-Optimal tuning (CTE): ~18865/18432 = 1\30, ~216/175 = 364.389
-{{Optimal ET sequence|legend=1| 270, 1110, 1380, 1650, 1920, 2190 }}
-Badness: 0.0220
-===13-limit===
-Subgroup: 2.3.5.7.11
-Comma list: 9801/9800, 123201/123200, 250047/250000, 1990656/1990625
-Mapping: {{mapping| 30 2 15 66 122 193 | 0 5 6 2 -2 -9 }}
-Optimal tuning (CTE): ~351/343 = 1\30, ~216/175 = 364.389
+{{Optimal ET sequence|legend=0| 72, …, 480fgg, 552g, 624 }}
-{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650, 6840e, 11490de }}
+Badness (Sintel): 1.06
-Badness: 0.0150
 [[Category:Temperament collections]]
 [[Category:Landscape microtemperaments| ]] <!-- main article -->
-[[Category:Landscape| ]] <!-- key article -->
 [[Category:Rank 2]]
-[[Category:Microtemperaments]]

Landscape microtemperaments: Difference between revisions