Bug family

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

Another notable tuning of bug is given by TE, CTE and POTE, all coinciding at 939.612 ¢ with pure octaves since prime 2 is not involved in the comma to begin with.

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