Keemic temperaments: Difference between revisions

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 Full [[7-limit]] keemic temperaments discussed elsewhere are:
 * [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]]
+* ''[[Mujannabic]]'' (+25/24) → [[Dicot family #Dicot|Dicot family]]
 * [[Porcupine]] (+64/63) → [[Porcupine family #Septimal porcupine|Porcupine family]]
 * [[Monkey]] (+5120/5103) → [[Tetracot family #Monkey|Tetracot family]]
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 * ''[[Undeka]]'' (+3200/3087) → [[11th-octave temperaments #Undeka|11th-octave temperaments]]
-Discussed below are quasitemp, chromo, barbad, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].
+Discussed below are quasitemp, chromo, barbad, pentadecal, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].
 == Quasitemp ==
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 Badness (Sintel): 1.62
+== Pentadecal ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Pentadecal]].''
+Named by [[Xenllium]] in 2021, pentadecal tempers out the 15-5/3-comma ({{monzo| -11 -15 15 }}) in the 5-limit. This temperament can be described as {{nowrap| 15 & 60 }} temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[keema]], 875/864 in the 7-limit.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 875/864, 16807/16384
+{{Mapping|legend=1| 15 0 11 42 | 0 1 1 0 }}
+: mapping generators: ~21/20, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~21/20 = 80.1141{{c}}, ~3/2 = 700.2213{{c}} (~126/125 = 19.8053{{c}})
+: [[error map]]: {{val| +1.711 +0.977 -2.127 -4.035 }}
+* [[CWE]]: ~21/20 = 80.0000{{c}}, ~3/2 = 701.2357{{c}} (~126/125 = 19.7643{{c}})
+: error map: {{val| 0.000 -0.719 -5.078 -8.826 }}
+{{Optimal ET sequence|legend=1| 15, 45, 60 }}
+[[Badness]] (Sintel): 2.91
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 100/99, 385/384, 1372/1331
+Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}
+Optimal tunings:
+* WE: ~21/20 = 80.0213{{c}}, ~3/2 = 702.9194{{c}} (~56/55 = 17.2721{{c}})
+* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 702.8751{{c}} (~56/55 = 17.1249{{c}})
+{{Optimal ET sequence|legend=0| 15, 45, 60, 75de, 135de }}
+Badness (Sintel): 2.56
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 100/99, 105/104, 144/143, 1372/1331
+Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}
+Optimal tunings:
+* WE: ~21/20 = 80.0207{{c}}, ~3/2 = 701.8966{{c}} (~91/90 = 18.2900{{c}})
+* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.8545{{c}} (~91/90 = 18.1455{{c}})
+{{Optimal ET sequence|legend=0| 15, 45f, 60, 135de, 195cddee }}
+Badness (Sintel): 2.14
+=== Quindecal ===
+Subgroup: 2.3.5.7.11
+Comma list: 121/120, 441/440, 875/864
+Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}
+Optimal tunings:
+* WE: ~21/20 = 80.1322{{c}}, ~3/2 = 701.4751{{c}} (~126/125 = 19.7148{{c}})
+* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.5453{{c}} (~126/125 = 18.4547{{c}})
+{{Optimal ET sequence|legend=0| 15, 45e, 60e }}
+Badness (Sintel): 1.47
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 121/120, 196/195, 352/351, 875/864
+Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}
+Optimal tunings:
+* WE: ~21/20 = 80.1015{{c}}, ~3/2 = 702.5374{{c}} (~126/125 = 18.3763{{c}})
+* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.8504{{c}} (~126/125 = 18.1496{{c}})
+{{Optimal ET sequence|legend=0| 15f, 60e, 135deef }}
+Badness (Sintel): 2.29
 == Hyperkleismic ==