Bug family: Difference between revisions

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+The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or approximately one step of [[9edo|9EDO]]. The monzo for 27/25 is {{monzo|0 3 -2}}, the dual of which is {{multival|2 3 0}}. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&amp;5 temperament, and [[14edo|14EDO]] is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.
-The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or approximately one step of [[9edo|9edo]]. The monzo for 27/25 is |0 3 -2&gt;, the dual of which is &lt;&lt;2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&amp;5 temperament, and [[14edo|14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.
 Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know both the beep tempering and the [[Ragismic_microtemperaments|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.
-=Bug=
+== Bug ==
-Comma: 27/25
+Subgroup: 2.3.5
-[[POTE_tuning|POTE temperament]]: 260.388
+[[Comma]]: 27/25
-Map: [&lt;1 0 0|, &lt;0 2 3|]
+[[Mapping]]: [{{val|1 0 0}}, {{val|0 2 3}}]
-EDOs: 4, 5, 9, 14, 23, 106
+[[POTE generator]]: ~6/5 = 260.388
-Badness: 0.0328
+{{Val list|legend=1| 4, 5, 9, 14, 23c }}
-=Beep=
+[[Badness]]: 0.032801
-Commas: 21/20, 27/25
-[[POTE_tuning|POTE temperament]]: ~6/5 = 263.395
+== Beep ==
+Subgroup: 2.3.5.7
-Map: [&lt;1 0 0 2|, &lt;0 2 3 1|]
+[[Comma list]]: 21/20, 27/25
-Wedgie: &lt;&lt;2 3 1 0 -4 -6||
+[[Mapping]]: [{{val|1 0 0 2}}, {{val|0 2 3 1}}]
-EDOs: 4, 5, 9, 32, 41
+{{Multival|legend=1| 2 3 1 0 -4 -6 }}
-Badness: 0.0186
+[[POTE generator]]: ~6/5 = 263.395
-==Pentoid==
+{{Val list|legend=1| 4, 5, 9, 23cd, 32bcd, 41bcdd }}
-Commas: 21/20, 27/25, 99/98
-[[POTE_tuning|POTE temperament]]: ~6/5 = 264.312
+[[Badness]]: 0.018638
-Map: [&lt;1 0 0 2 5|, &lt;0 2 3 1 -2|]
+=== Pentoid ===
+Subgroup: 2.3.5.7.11
-EDOs: 4, 5, 9, 50, 59
+Comma list: 21/20, 27/25, 33/32
-Badness: 0.0226
+Mapping: [{{val|1 0 0 2 5}}, {{val|0 2 3 1 -2}}]
-==13-limit==
+POTE generator: ~6/5 = 264.312
-Commas: 21/20, 26/25, 27/25, 33/32
+Vals: {{Val list| 4, 5, 9, 32bcde, 41bcdde, 50bbcdde }}
+Badness: 0.022649
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 21/20, 26/25, 27/25, 33/32
+Mapping: [{{val|1 0 0 2 5 -1}}, {{val|0 2 3 1 -2 6}}]
 POTE generator: ~6/5 = 263.935
-Map: [&lt;1 0 0 2 5 -1|, &lt;0 2 3 1 -2 6|]
+Vals: {{Val list| 4f, 5, 9, 32bcde, 41bcddef, 50bbcddeff }}
-EDOs: 5,9, 32bcde, 41bcdef, 50bcdef
+Badness: 0.021159
-Badness: 0.0212
+=== Pento ===
+Subgroup: 2.3.5.7.11
-==Pento==
+Comma list: 21/20, 27/25, 45/44
-Commas: 21/20, 27/25, 45/44
+Mapping: [{{val|1 0 0 2 -2}}, {{val|0 2 3 1 7}}]
 POTE generator: ~6/5 = 265.847
-Map: [&lt;1 0 0 2 -2|, &lt;0 2 3 1 7|]
+Vals: {{Val list| 4e, 5e, 9 }}
+Badness: 0.022799
-EDOs: 9
+== Mite ==
+Subgroup: 2.3.5.7
-Badness: 0.0228
+[[Comma list]]: 27/25, 28/25
-=Mite=
+[[Mapping]]: [{{val|1 0 0 -2}}, {{val|0 2 3 6}}]
-Commas: 27/25, 28/25
-POTE generator: ~6/5 = 240.712
+{{Multival|legend=1| 2 3 6 0 4 6 }}
-Map: [&lt;1 0 0 -2|, &lt;0 2 3 6|]
+[[POTE generator]]: ~6/5 = 240.712
-Wedgie: &lt;&lt;2 3 6 0 4 6||
+{{Val list|legend=1| 4dd, 5 }}
-EDOs: 1cdd, 5
+[[Badness]]: 0.054770
-Badness: 0.0548
+[[Category:Temperament]]
+[[Category:Temperament family]]