Bug family: Difference between revisions

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The 5-limit parent of the '''bug family''' is bug, a temperament of sorts (that is, an [[exotemperament]]) which tempers out [[27/25]], the large limma, or approximately one step of [[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&5 temperament, and [[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 (that is, an [[exotemperament]]) which tempers out [[27/25]], the large limma, approximately one step of [[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 & 5 temperament, and [[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|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.

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|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.

Temperaments discussed elsewhere include [[Very low accuracy temperaments #Ugolino|ugolino]].

== Bug ==

Subgroup: 2.3.5

[[Subgroup]]: 2.3.5

[[Comma list]]: 27/25

~~[[Mapping]]: [~~{{~~val~~|1 0 0~~}}, {{val~~|0 -2 -3}}]

[[POTE ~~generator~~]]: ~5/3 = 939.612

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/3 = 939.612

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== Beep ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 21/20, 27/25

~~[[Mapping]]: [~~{{~~val~~|1 0 0 2~~}}, {{val~~|0 2 3 1}}]

[[POTE ~~generator~~]]: ~5/3 = 936.605

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/3 = 936.605

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Comma list: 21/20, 27/25, 33/32

Mapping: [{{~~val~~|1 0 0 2 5~~}}, {{val~~|0 2 3 1 -2}}]

Mapping: {{mapping| 1 0 0 2 5 | 0 2 3 1 -2 }}

POTE ~~generator~~: ~5/3 = 935.688

Optimal tuning (POTE): ~2 = 1\1, ~5/3 = 935.688

{{Optimal ET sequence|legend=1| 4, 5, 9, 32bcde, 41bcdde, 50bbcdde }}

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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}}]

Mapping: {{mapping| 1 0 0 2 5 -1 | 0 2 3 1 -2 6 }}

POTE ~~generator~~: ~5/3 = 934.065

Optimal tuning (POTE): ~2 = 1\1, ~5/3 = 934.065

{{Optimal ET sequence|legend=1| 4f, 5, 9, 32bcde, 41bcddef, 50bbcddeff }}

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Comma list: 21/20, 27/25, 45/44

Mapping: [{{~~val~~|1 0 0 2 -2~~}}, {{val~~|0 2 3 1 7}}]

Mapping: {{mapping| 1 0 0 2 -2 | 0 2 3 1 7 }}

POTE ~~generator~~: ~5/3 = 934.153

Optimal tuning (POTE): ~2 = 1\1, ~5/3 = 934.153

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== Mite ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 27/25, 28/25

~~[[Mapping]]: [~~{{~~val~~|1 0 0 -2~~}}, {{val~~|0 2 3 6}}]

[[POTE ~~generator~~]]: ~5/3 = 959.288

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/3 = 959.288

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-The 5-limit parent of the '''bug family''' is bug, a temperament of sorts (that is, an [[exotemperament]]) which tempers out [[27/25]], the large limma, or approximately one step of [[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]] 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 (that is, an [[exotemperament]]) which tempers out [[27/25]], the large limma, approximately one step of [[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]] 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|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.
+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|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.
 Temperaments discussed elsewhere include [[Very low accuracy temperaments #Ugolino|ugolino]].
 == Bug ==
-Subgroup: 2.3.5
+[[Subgroup]]: 2.3.5
 [[Comma list]]: 27/25
-[[Mapping]]: [{{val|1 0 0}}, {{val|0 -2 -3}}]
+{{Mapping|legend=1| 1 0 0 | 0 -2 -3 }}
-[[POTE generator]]: ~5/3 = 939.612
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/3 = 939.612
 {{Optimal ET sequence|legend=1| 4, 5, 9, 14, 23c }}
@@ Line 19: / Line 19: @@
 == Beep ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 21/20, 27/25
-[[Mapping]]: [{{val|1 0 0 2}}, {{val|0 2 3 1}}]
+{{Mapping|legend=1| 1 0 0 2 | 0 2 3 1 }}
 {{Multival|legend=1| 2 3 1 0 -4 -6 }}
-[[POTE generator]]: ~5/3 = 936.605
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/3 = 936.605
 {{Optimal ET sequence|legend=1| 4, 5, 9, 23cd, 32bcd, 41bcdd }}
@@ Line 38: / Line 38: @@
 Comma list: 21/20, 27/25, 33/32
-Mapping: [{{val|1 0 0 2 5}}, {{val|0 2 3 1 -2}}]
+Mapping: {{mapping| 1 0 0 2 5 | 0 2 3 1 -2 }}
-POTE generator: ~5/3 = 935.688
+Optimal tuning (POTE): ~2 = 1\1, ~5/3 = 935.688
 {{Optimal ET sequence|legend=1| 4, 5, 9, 32bcde, 41bcdde, 50bbcdde }}
@@ Line 51: / Line 51: @@
 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}}]
+Mapping: {{mapping| 1 0 0 2 5 -1 | 0 2 3 1 -2 6 }}
-POTE generator: ~5/3 = 934.065
+Optimal tuning (POTE): ~2 = 1\1, ~5/3 = 934.065
 {{Optimal ET sequence|legend=1| 4f, 5, 9, 32bcde, 41bcddef, 50bbcddeff }}
@@ Line 64: / Line 64: @@
 Comma list: 21/20, 27/25, 45/44
-Mapping: [{{val|1 0 0 2 -2}}, {{val|0 2 3 1 7}}]
+Mapping: {{mapping| 1 0 0 2 -2 | 0 2 3 1 7 }}
-POTE generator: ~5/3 = 934.153
+Optimal tuning (POTE): ~2 = 1\1, ~5/3 = 934.153
 {{Optimal ET sequence|legend=1| 4e, 5e, 9 }}
@@ Line 73: / Line 73: @@
 == Mite ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 27/25, 28/25
-[[Mapping]]: [{{val|1 0 0 -2}}, {{val|0 2 3 6}}]
+{{Mapping|legend=1| 1 0 0 -2 | 0 2 3 6 }}
 {{Multival|legend=1| 2 3 6 0 4 6 }}
-[[POTE generator]]: ~5/3 = 959.288
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/3 = 959.288
 {{Optimal ET sequence|legend=1| 4dd, 5 }}