Breedsmic temperaments: Difference between revisions

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 = Septidiasemi =
-Commas: 2401/2400, 2152828125/2147483648
+Aside from 2401/2400, septidiasemi tempers out 2152828125/2147483648 in the 7-limit. It is so named because the generator is a "septimal diatonic semitone" (0.15 cents flat of [[15/14]]). It is an excellent tuning for 2.3.5.7.13 and 2.3.5.7.13.17 subgroups rather than full 13- and 17-limit.
-POTE generator: ~15/14 = 119.297
+Subgroup: 2.3.5.7
+[[Comma list]]: 2401/2400, 2152828125/2147483648
+[[Mapping]]: [{{val|1 -1 6 4}}, {{val|0 26 -37 -12}}]
+{{Multival|legend=1|26 -37 -12 -119 -92 76}}
+[[POTE generator]]: ~15/14 = 119.297
+{{Val list|legend=1| 10, 151, 161, 171, 3581bcdd, 3752bcdd, 3923bcdd, 4094bcdd, 4265bccdd, 4436bccdd, 4607bccdd }}
+[[Badness]]: 0.044115
+== Sedia ==
+The ''sedia'' temperament (10&amp;161, named by [[User:Xenllium|Xenllium]]) is an 11-limit extension of the septidiasemi, which tempers out 243/242 and 441/440.
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 441/440, 939524096/935859375
-Map: [&lt;1 -1 6 4|, &lt;0 26 -37 -12|]
+Mapping: [{{val|1 -1 6 4 -3}}, {{val|0 26 -37 -12 65}}]
-Wedgie: &lt;&lt;26 -37 -12 -119 -92 76||
+POTE generator: ~15/14 = 119.279
-EDOs: 10, 151, 161, 171, 3581bcd, 3752bcd, 3923bcd, 4094bcd, 4265bcd, 4436bcd, 4607bcd
+Vals: {{Val list| 10, 151, 161, 171, 332 }}
-Badness: 0.0441
+Badness: 0.090687
-=Maviloid=
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 441/440, 2200/2197, 3584/3575
+Mapping: [{{val|1 -1 6 4 -3 4}}, {{val|0 26 -37 -12 65 -3}}]
+POTE generator: ~15/14 = 119.281
+Vals: {{Val list| 10, 151, 161, 171, 332, 835eeff }}
+Badness: 0.045773
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575
+Mapping: [{{val|1 -1 6 4 -3 4 2}}, {{val|0 26 -37 -12 65 -3 21}}]
+POTE generator: ~15/14 = 119.281
+Vals: {{Val list| 10, 151, 161, 171, 332, 503ef, 835eeff }}
+Badness: 0.027322
+= Maviloid =
 {{see also| Ragismic microtemperaments #Parakleismic }}
-Commas: 2401/2400, 1224440064/1220703125
+[[Comma list]]: 2401/2400, 1224440064/1220703125
-POTE generator: ~1296/875 = 678.810
+[[Mapping]]: [{{val|1 31 34 26}}, {{val|0 -52 -56 -41}}]
-Map: [&lt;1 31 34 26|, &lt;0 -52 -56 -41|]
+{{Multival|legend=1|52 56 41 -32 -81 -62}}
-Wedgie: &lt;&lt;52 56 41 -32 -81 -62||
+[[POTE generator]]: ~1296/875 = 678.810
-EDOs: 76, 99, 274, 373, 472, 571, 1043, 1614
+{{Val list|legend=1| 76, 99, 274, 373, 472, 571, 1043, 1614 }}
-Badness: 0.0576
+[[Badness]]: 0.057632
-=Subneutral=
+= Subneutral =
-Commas: 2401/2400, 274877906944/274658203125
+[[Comma list]]: 2401/2400, 274877906944/274658203125
-POTE generator: ~57344/46875 = 348.301
+[[Mapping]]: [{{val|1 19 0 6}}, {{val|0 -60 8 -11}}]
-Map: [&lt;1 19 0 6}, &lt;0 -60 8 -11|]
+{{Multival|legend=1|60 -8 11 -152 -151 48}}
-Wedgie: &lt;&lt;60 -8 11 -152 -151 48||
+[[POTE generator]]: ~57344/46875 = 348.301
-EDOs: 31, 348, 379, 410, 441, 1354, 1795, 2236
+{{Val list|legend=1| 31, 348, 379, 410, 441, 1354, 1795, 2236 }}
-Badness: 0.0458
+[[Badness]]: 0.045792
 =Osiris=
@@ Line 615: / Line 660: @@
 EDOs: 157, 171, 1012, 1183, 1354, 1525, 1696, 6955d
-Badness: 0.0283
+Badness: 0.028307
 =Gorgik=
@@ Line 774: / Line 819: @@
 [[Mapping]]: [{{val|1 -13 -4 -4}}, {{val|0 30 13 14}}]
+{{Multival|legend=1|30 13 14 -49 -62 -4}}
 [[POTE generator]]: ~7/5 = 583.385