Bug family: Difference between revisions

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 ==

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.  

[[Subgroup]]: 2.3.5

[[Comma list]]: 27/25

{{Mapping|legend=1| 1 0 0 | 0 -2 -3 }}

: mapping generators: ~2, ~5/3

[[Optimal tuning]]s:

: [[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 }}

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

 

=== 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 ==

 

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

 

 

[[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 }}

 

 

[[Badness]] (Sintel): 0.472

 

=== Pentoid ===

 

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

 

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

 

* WE: ~2 = 1205.296{{c}}, ~5/3 = 939.817{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.415{{c}}

 

{{Optimal ET sequence|legend=0| 4, 5, 9 }}

 

 

 

Comma list: 21/20, 26/25, 27/25, 33/32

 

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

 

Optimal tunings:  

* WE: ~2 = 1205.291{{c}}, ~5/3 = 940.192{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.788{{c}}

 

Optimal ET sequence: {{Optimal ET sequence| 4f, 5, 9 }}

 

Badness (Sintel): 0.874

 

Subgroup: 2.3.5.7.11

 

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

 

 

* WE: ~2 = 1205.575{{c}}, ~5/3 = 938.493{{c}}

* CWE: ~2 = 1200.000{{c}}, ~5/3 = 935.485{{c}}

 

 

Badness (Sintel): 0.754

 

[[Subgroup]]: 2.3.5.7

 

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

 

{{Mapping|legend=1| 1 0 0 -2 | 0 2 3 6 }}

 

[[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 }}

 

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

 

 

[[Category:Bug family]] <!-- Main article -->