Bug family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus
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: mapping generators: ~2, ~5/3
: mapping generators: ~2, ~5/3


[[Optimal tuning]]s:
[[Optimal tuning]]s:  
* [[CTE]] and [[POTE]]: ~2 = 1200.000, ~5/3 = 939.612
* [[WE]]: ~2 = 1199.665{{c}}, ~5/3 = 939.350{{c}}
: [[error map]]: {{val| 0.000 -22.731 +32.523 }}
: [[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 }}
<!-- * [[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]] (Smith): 0.032801
[[Badness]] (Sintel): 0.769


== Beep ==
== Beep ==
Line 36: Line 40:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/3 = 940.706
* [[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 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 940.706{{c}}
: [[error map]]: {{val| 0.000 -20.543 +35.804 -28.120 }}
: [[error map]]: {{val| 0.000 -20.543 +35.804 -28.120 }}
* [[POTE]]: ~2 = 1200.000, ~5/3 = 936.605
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 936.605{{c}}
: error map: {{val| 0.000 -28.744 +23.502 -32.221 }}
: 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 }}


[[Badness]] (Smith): 0.018638
[[Badness]] (Sintel): 0.472


=== Pentoid ===
=== Pentoid ===
Line 53: Line 61:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/3 = 939.237
* WE: ~2 = 1205.296{{c}}, ~5/3 = 939.817{{c}}
* POTE: ~2 = 1200.000, ~5/3 = 935.688
* 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: {{Optimal ET sequence| 4, 5, 9 }}
{{Optimal ET sequence|legend=0| 4, 5, 9 }}


Badness (Smith): 0.022649
Badness (Sintel): 0.749


==== 13-limit ====
==== 13-limit ====
Line 68: Line 78:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/3 = 939.589
* WE: ~2 = 1205.291{{c}}, ~5/3 = 940.192{{c}}
* POTE: ~2 = 1200.000, ~5/3 = 934.065
* 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 }}


Badness (Smith): 0.021159
Badness (Sintel): 0.874


=== Pento ===
=== Pento ===
Line 83: Line 95:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/3 = 938.078
* WE: ~2 = 1205.575{{c}}, ~5/3 = 938.493{{c}}
* POTE: ~2 = 1200.000, ~5/3 = 934.153
* 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 }}


Badness (Smith): 0.022799
Badness (Sintel): 0.754


== Mite ==
== Mite ==
Line 98: Line 112:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/3 = 952.365
* [[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 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 952.365{{c}}
: [[error map]]: {{val| 0.000 +2.775 +70.781 -54.637 }}
: [[error map]]: {{val| 0.000 +2.775 +70.781 -54.637 }}
* [[POTE]]: ~2 = 1200.000, ~5/3 = 959.288
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 959.288{{c}}
: error map: {{val| 0.000 +16.622 +91.552 -13.095 }}
: 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 }}


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


[[Category:Temperament families]]
[[Category:Temperament families]]

Revision as of 09:12, 20 July 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

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 [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.

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

Bug divides 3/1 in half so it may be viewed as a less accurate version of semaphore (with beep combining the two).

Temperaments discussed elsewhere include ugolino and codex.

Bug

Subgroup: 2.3.5

Comma list: 27/25

Mapping: [⟨1 0 0], ⟨0 -2 -3]]

mapping generators: ~2, ~5/3

Optimal tunings:

  • WE: ~2 = 1199.665 ¢, ~5/3 = 939.350 ¢
error map: ⟨-0.335 -23.255 +31.736]
  • CWE: ~2 = 1200.000 ¢, ~5/3 = 939.481 ¢
error map: ⟨0.000 -22.993 +32.129]

Optimal ET sequence: 4, 5, 9, 14

Badness (Sintel): 0.769

Beep

Main article: Beep
See also: Semaphoresmic clan

Subgroup: 2.3.5.7

Comma list: 21/20, 27/25

Mapping: [⟨1 0 0 2], ⟨0 2 3 1]]

Optimal tunings:

  • WE: ~2 = 1204.399 ¢, ~5/3 = 940.039 ¢
error map: ⟨+4.399 -21.877 +33.803 -19.988]
  • CWE: ~2 = 1200.000 ¢, ~5/3 = 938.111 ¢
error map: ⟨0.000 -25.734 +28.018 -30.715]

Optimal ET sequence: 4, 5, 9

Badness (Sintel): 0.472

Pentoid

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 0 0 2 5], ⟨0 2 3 1 -2]]

Optimal tunings:

  • WE: ~2 = 1205.296 ¢, ~5/3 = 939.817 ¢
  • CWE: ~2 = 1200.000 ¢, ~5/3 = 936.415 ¢

Optimal ET sequence: 4, 5, 9

Badness (Sintel): 0.749

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 0 0 2 5 -1], ⟨0 2 3 1 -2 6]]

Optimal tunings:

  • WE: ~2 = 1205.291 ¢, ~5/3 = 940.192 ¢
  • CWE: ~2 = 1200.000 ¢, ~5/3 = 936.788 ¢

Optimal ET sequence: 4f, 5, 9

Badness (Sintel): 0.874

Pento

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 0 0 2 -2], ⟨0 2 3 1 7]]

Optimal tunings:

  • WE: ~2 = 1205.575 ¢, ~5/3 = 938.493 ¢
  • CWE: ~2 = 1200.000 ¢, ~5/3 = 935.485 ¢

Optimal ET sequence: 4e, 5e, 9

Badness (Sintel): 0.754

Mite

Subgroup: 2.3.5.7

Comma list: 27/25, 28/25

Mapping: [⟨1 0 0 -2], ⟨0 2 3 6]]

Optimal tunings:

  • WE: ~2 = 1187.604 ¢, ~5/3 = 949.379 ¢
error map: ⟨-12.396 -3.196 +61.824 -47.759]
  • CWE: ~2 = 1200.000 ¢, ~5/3 = 955.861 ¢
error map: ⟨0.000 +9.766 +81.268 -33.663]

Optimal ET sequence: 1cdd, 4dd, 5

Badness (Sintel): 1.39

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