Meantone family: Difference between revisions

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 POTE generator: ~3/2 = 699.001
-Vals: {{Val list| 12, 14ce }}
+Vals: {{Val list| 2cd, 10cd, 12 }}
 Badness: 0.043062
-== [[Teff]] ==
+=== Teff ===
-Teff (developed by Mason Green) is to Injera what Mohajira is to Meantone; it splits the generator in half in order to accommodate higher limit intervals, creating a half-octave quarter-tone temperament.
+{{Main| Teff }}
-Subgroup: 2.3.5.7.11.13
+Teff (found by Mason Green) is to injera what mohajira is to meantone; it splits the generator in half in order to accommodate higher limit intervals, creating a half-octave quarter-tone temperament.
+Subgroup: 2.3.5.7.11
+[[Comma list]]: 50/49, 81/80, 864/847
-[[Comma list]]: 50/49, 78/77, 81/80, 144/143
+[[Mapping]]: [{{val| 2 1 -4 -3 8 }}, {{val| 0 2 8 8 -1 }}]
-[[Mapping]]: [{{val| 2 3 4 5 7 7}}, {{val| 0 2 8 8 -1 5}}]
+Mapping generators: ~7/5, ~16/11
-Mapping generators: ~7/5, ~11/8''?''
+[[POTE generator]]: ~11/8 = 552.5303
-{{Multival|legend=1|? ? ? ? ? ?}}
+{{Val list|legend=1| 24d, 26, 50d }}
-[[POTE generator]]: ~11/8 = 552.5324''?''
+[[Badness]]: 0.0707
-[[Tuning ranges]]:
+==== 13-limit ====
-* ???
+Subgroup: 2.3.5.7.11.13
-{{Val list|legend=1|24d, 26, 50d, 76d}}
+[[Comma list]]: 50/49, 78/77, 81/80, 144/143
-[[Badness]]: ?????
+[[Mapping]]: [{{val| 2 1 -4 -3 8 2 }}, {{val| 0 2 8 8 -1 5 }}]
-==== 17-limit ====
+[[POTE generator]]: ~11/8 = 552.5324
-Subgroup: 2.3.5.7.11.13.17
-[[Comma list]]: 50/49, 78/77, 81/80, 144/143, 289/288
+{{Val list|legend=1| 24d, 26, 50d }}
-[[Mapping]]: [{{val| 2 3 4 5 7 7 8}}, {{val| 0 2 8 8 -1 5 2}}]
+[[Badness]]: 0.0400
-Mapping generators: ~7/5, ~11/8''?''
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
-{{Multival|legend=1|? ? ? ? ? ?}}
+[[Comma list]]: 50/49, 78/77, 81/80, 85/84, 144/143
-[[POTE generator]]: ~11/8 = 552.6558''?''
+[[Mapping]]: [{{val| 2 1 -4 -3 8 2 6 }}, {{val| 0 2 8 8 -1 5 2 }}]
-[[Tuning ranges]]:
+[[POTE generator]]: ~11/8 = 552.6558
-* ???
-{{Val list|legend=1|24d, 26, 50d, 76dg}}
+{{Val list|legend=1| 24d, 26 }}
-[[Badness]]: ?????
+[[Badness]]: 0.0295
 ==== 19-limit ====
 Subgroup: 2.3.5.7.11.13.17.19
-[[Comma list]]: 50/49, 57/56 78/77, 81/80, 144/143, 289/288
+[[Comma list]]: 50/49, 57/56, 78/77, 81/80, 85/84, 144/143
-[[Mapping]]: [{{val| 2 3 4 5 7 7 8 8}}, {{val| 0 2 8 8 -1 5 2 6}}]
+[[Mapping]]: [{{val| 2 1 -4 -3 8 2 6 2 }}, {{val| 0 2 8 8 -1 5 2 6 }}]
-Mapping generators: ~7/5, ~11/8''?''
+[[POTE generator]]: ~11/8 = 552.6382
-{{Multival|legend=1|? ? ? ? ? ?}}
+{{Val list|legend=1| 24d, 26 }}
-[[POTE generator]]: ~11/8 = 552.6382''?''
+[[Badness]]: 0.0231
-[[Tuning ranges]]:
+== Pombe ==
-* ???
+Pombe (named after the African millet beer) is a variant of [[#teff]] by Kaiveran Lugheidh that eschews the tempering of 50/49 to attain more accuracy in the 7-limit. Oddly, the 7th harmonic has a lesser generator distance than in teff (-5 vs +8), but this combined with the fact that other harmonics are in the opposite direction means that the 7-limit diamond is more complex overall.
-{{Val list|legend=1|24d, 26, 50d, 76dg}}<nowiki/>h
+Subgroup: 2.3.5.7.11.13
-[[Badness]]: ?????
+[[Comma list]]: 81/80, 300125/294912
-=== Pombe ===
+[[Mapping]]: [{{val| 2 1 -4 11 }}, {{val| 0 2 8 -5 }}]
-Pombe (named after the African millet beer) is a variant of Teff by Kaiveran Lugheidh that eschews the tempering of 50/49 to attain more accuracy in the 7-limit. Oddly, the 7th harmonic has a lesser generator distance than in Teff (-5 vs +8), but this combined with the fact that other harmonics are in the opposite direction means that the 7-limit diamond is more complex overall.
-Subgroup: 2.3.5.7.11.13
+Mapping generators: ~735/512, ~35/24
+{{Multival|legend=1| 4 16 -10 16 -27 -68 }}
+[[POTE generator]]: ~48/35 = 552.2206
-[[Comma list]]: 81/80, 105/104, 144/143, 245/242
+{{Val list|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }}
-[[Mapping]]: [{{val| 2 3 4 5 7 7}}, {{val| 0 2 8 -5 -1 5}}]
+[[Badness]]: 0.1161
-Mapping generators: ~''???'', ~11/8''?''
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-{{Multival|legend=1|? ? ? ? ? ?}}
+Comma list: 81/80, 245/242, 385/384
-[[POTE generator]]: ~11/8 = 552.1498''?''
+Mapping: [{{val| 2 1 -4 11 8 }}, {{val| 0 2 8 -5 -1 }}]
-[[Tuning ranges]]:
+POTE generator: ~11/8 = 552.0929
-* ???
-{{Val list|legend=1|24, 26, 50, 76}}
+Vals: {{Val list| 24, 26, 50 }}
-[[Badness]]: ?????
+Badness: 0.0521
-==== 17-limit ====
+=== 13-limit ===
-Subgroup: 2.3.5.7.11.13.17
+Subgroup: 2.3.5.7.11.13
-[[Comma list]]: 81/80, 105/104, 144/143, 273/272, 288/289
+Comma list: 81/80, 105/104, 144/143, 245/242
-[[Mapping]]: [{{val| 2 3 4 5 7 7 8}}, {{val| 0 2 8 -5 -1 5 2}}]
+Mapping: [{{val| 2 1 -4 11 8 2 }}, {{val| 0 2 8 -5 -1 5 }}]
-Mapping generators: ~17/12''?'', ~11/8''?''
+POTE generator: ~11/8 = 552.1498
-{{Multival|legend=1|? ? ? ? ? ?}}
+Vals: {{Val list| 24, 26, 50 }}
-[[POTE generator]]: ~11/8 = 552.1579''?''
+Badness: 0.0310
-[[Tuning ranges]]:
+=== 17-limit ===
-* ???
+Subgroup: 2.3.5.7.11.13.17
-{{Val list|legend=1|24, 26, 50, 76g}}
+Comma list: 81/80, 105/104, 144/143, 245/242, 273/272
-[[Badness]]: ?????
+Mapping: [{{val| 2 1 -4 11 8 2 6 }}, {{val| 0 2 8 -5 -1 5 2 }}]
-==== 19-limit ====
+POTE generator: ~11/8 = 552.1579
-Subgroup: 2.3.5.7.11.13.17.19
-[[Comma list]]: 81/80, 105/104, 133/132, 144/143, 273/272, 288/289
+Vals: {{Val list| 24, 26, 50 }}
-[[Mapping]]: [{{val| 2 3 4 5 7 7 8 8}}, {{val| 0 2 8 -5 -1 5 2 6}}]
+Badness: 0.0213
-Mapping generators: ~17/12''?'', ~11/8''?''
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
-{{Multival|legend=1|? ? ? ? ? ?}}
+Comma list: 81/80, 105/104, 133/132, 144/143, 171/170, 210/209
-[[POTE generator]]: ~11/8 = 552.1196''?''
+Mapping: [{{val| 2 1 -4 11 8 2 6 2 }}, {{val| 0 2 8 -5 -1 5 2 6 }}]
-[[Tuning ranges]]:
+POTE generator: ~11/8 = 552.1196
-* ???
-{{Val list|legend=1|24, 26, 50, 76g}}<nowiki/>h
+Vals: {{Val list| 24, 26, 50 }}
-[[Badness]]: ?????
+Badness: 0.0165
 == Mohaha ==