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Bug family: Difference between revisions

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{{Technical data page}}
{{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 }}. 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 }}.  


Bug has a 7-limit extension, [[#Beep|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 divides [[3/1]] in half so it may be viewed as a less accurate version of [[semaphore and godzilla|semaphore]] (with beep combining the two).
 
Temperaments discussed elsewhere include [[Very low accuracy temperaments #Ugolino|ugolino]] and [[Very low accuracy temperaments #Codex|codex]].


== Bug ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


Line 22: Line 18:
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 939.481{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 939.481{{c}}
: error map: {{val| 0.000 -22.993 +32.129 }}
: error map: {{val| 0.000 -22.993 +32.129 }}
<!-- * [[TE]], [[CTE]] and [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 939.612{{c}}
: [[error map]]: {{val| 0.000 -22.731 +32.523 }} -->


{{Optimal ET sequence|legend=1| 4, 5, 9, 14 }}
{{Optimal ET sequence|legend=1| 4, 5, 9, 14 }}


[[Badness]] (Sintel): 0.769
[[Badness]] (Sintel): 0.769
=== 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.
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 ==
{{Main| Beep }}
{{Main| Beep }}
{{See also| Semaphoresmic clan }}
{{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
[[Subgroup]]: 2.3.5.7
Line 44: Line 47:
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 938.111{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 938.111{{c}}
: error map: {{val| 0.000 -25.734 +28.018 -30.715 }}
: error map: {{val| 0.000 -25.734 +28.018 -30.715 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 940.706{{c}}
: [[error map]]: {{val| 0.000 -20.543 +35.804 -28.120 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 936.605{{c}}
: error map: {{val| 0.000 -28.744 +23.502 -32.221 }} -->


{{Optimal ET sequence|legend=1| 4, 5, 9 }}
{{Optimal ET sequence|legend=1| 4, 5, 9 }}
Line 63: Line 62:
* WE: ~2 = 1205.296{{c}}, ~5/3 = 939.817{{c}}
* WE: ~2 = 1205.296{{c}}, ~5/3 = 939.817{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.415{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.415{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 939.237{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 935.688{{c}} -->


{{Optimal ET sequence|legend=0| 4, 5, 9 }}
{{Optimal ET sequence|legend=0| 4, 5, 9 }}
Line 80: Line 77:
* WE: ~2 = 1205.291{{c}}, ~5/3 = 940.192{{c}}
* WE: ~2 = 1205.291{{c}}, ~5/3 = 940.192{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.788{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.788{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 939.589{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 934.065{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 4f, 5, 9 }}
Optimal ET sequence: {{Optimal ET sequence| 4f, 5, 9 }}
Line 97: Line 92:
* WE: ~2 = 1205.575{{c}}, ~5/3 = 938.493{{c}}
* WE: ~2 = 1205.575{{c}}, ~5/3 = 938.493{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/3 = 935.485{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/3 = 935.485{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 938.078{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 934.153{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 4e, 5e, 9 }}
Optimal ET sequence: {{Optimal ET sequence| 4e, 5e, 9 }}
Line 116: Line 109:
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 955.861{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 955.861{{c}}
: error map: {{val| 0.000 +9.766 +81.268 -33.663 }}
: error map: {{val| 0.000 +9.766 +81.268 -33.663 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 952.365{{c}}
: [[error map]]: {{val| 0.000 +2.775 +70.781 -54.637 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 959.288{{c}}
: error map: {{val| 0.000 +16.622 +91.552 -13.095 }} -->


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