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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 [[9 EDO]]. 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 [[14 EDO]] 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.
{{Technical data page}}
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 }}.  


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 ==
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 {{nowrap| 4 & 5 }} temperament, and its [[ploidacot]] is alpha-dicot. [[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. Another notable tuning of bug is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 939.612{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.  


== Bug ==
[[Subgroup]]: 2.3.5
Subgroup: 2.3.5
 
[[Comma list]]: 27/25
 
{{Mapping|legend=1| 1 0 0 | 0 -2 -3 }}
 
: mapping generators: ~2, ~5/3


[[Comma]]: 27/25
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.665{{c}}, ~5/3 = 939.350{{c}}
: [[error map]]: {{val| -0.335 -23.255 +31.736 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 939.481{{c}}
: error map: {{val| 0.000 -22.993 +32.129 }}


[[Mapping]]: [{{val|1 0 0}}, {{val|0 2 3}}]
{{Optimal ET sequence|legend=1| 4, 5, 9, 14 }}


[[POTE generator]]: ~6/5 = 260.388
[[Badness]] (Sintel): 0.769


{{Val list|legend=1| 4, 5, 9, 14, 23c }}
=== Overview to extensions ===
Bug has an obvious 7-limit extension, [[#Beep|beep]], via the normal comma list {27/25, 36/35} which can also be obtained by adding [[21/20]]. There is an alternative, [[#Mite|mite]], which adds [[28/25]] instead.


[[Badness]]: 0.032801
Temperaments discussed elsewhere include [[Very low accuracy temperaments #Ugolino|ugolino]] and [[Very low accuracy temperaments #Codex|codex]]. Considered below are beep and mite.  


== Beep ==
== Beep ==
Subgroup: 2.3.5.7
{{Main| Beep }}
{{See also| Semaphoresmic clan }}
 
As bug divides [[3/1]] in half for 5/3~9/5, it only makes sense to also equate this interval with 7/4~12/7, joining the temperament with [[semaphore and godzilla|semaphore]].
 
Beep has the curious property that if we know both the beep tempering and the [[ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 21/20, 27/25
[[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 }}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1204.399{{c}}, ~5/3 = 940.039{{c}}
: [[error map]]: {{val| +4.399 -21.877 +33.803 -19.988 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 938.111{{c}}
: error map: {{val| 0.000 -25.734 +28.018 -30.715 }}


[[POTE generator]]: ~6/5 = 263.395
{{Optimal ET sequence|legend=1| 4, 5, 9 }}


{{Val list|legend=1| 4, 5, 9, 23cd, 32bcd, 41bcdd }}
[[Badness]] (Sintel): 0.472
 
[[Badness]]: 0.018638


=== Pentoid ===
=== Pentoid ===
Line 36: Line 57:
Comma list: 21/20, 27/25, 33/32
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: ~6/5 = 264.312
Optimal tunings:  
* WE: ~2 = 1205.296{{c}}, ~5/3 = 939.817{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.415{{c}}


Vals: {{Val list| 4, 5, 9, 32bcde, 41bcdde, 50bbcdde }}
{{Optimal ET sequence|legend=0| 4, 5, 9 }}


Badness: 0.022649
Badness (Sintel): 0.749


==== 13-limit ====
==== 13-limit ====
Line 49: Line 72:
Comma list: 21/20, 26/25, 27/25, 33/32
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: ~6/5 = 263.935
Optimal tunings:  
* WE: ~2 = 1205.291{{c}}, ~5/3 = 940.192{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.788{{c}}


Vals: {{Val list| 4f, 5, 9, 32bcde, 41bcddef, 50bbcddeff }}
Optimal ET sequence: {{Optimal ET sequence| 4f, 5, 9 }}


Badness: 0.021159
Badness (Sintel): 0.874


=== Pento ===
=== Pento ===
Line 62: Line 87:
Comma list: 21/20, 27/25, 45/44
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: ~6/5 = 265.847
Optimal tunings:  
* WE: ~2 = 1205.575{{c}}, ~5/3 = 938.493{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/3 = 935.485{{c}}


Vals: {{Val list| 4e, 5e, 9 }}
Optimal ET sequence: {{Optimal ET sequence| 4e, 5e, 9 }}


Badness: 0.022799
Badness (Sintel): 0.754


== Mite ==
== Mite ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 27/25, 28/25
[[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]]: ~6/5 = 240.712
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1187.604{{c}}, ~5/3 = 949.379{{c}}
: [[error map]]: {{val| -12.396 -3.196 +61.824 -47.759 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 955.861{{c}}
: error map: {{val| 0.000 +9.766 +81.268 -33.663 }}


{{Val list|legend=1| 4dd, 5 }}
{{Optimal ET sequence|legend=1| 1cdd, 4dd, 5 }}


[[Badness]]: 0.054770
[[Badness]] (Sintel): 1.39


[[Category:Temperament]]
[[Category:Temperament families]]
[[Category:Temperament family]]
[[Category:Pages with mostly numerical content]]
[[Category:Bug family]] <!-- Main article -->
[[Category:Rank 2]]
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