Bug family: Difference between revisions
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Mapping: [{{val|1 0 0 2 5}}, {{val|0 2 3 1 -2}}] | Mapping: [{{val|1 0 0 2 5}}, {{val|0 2 3 1 -2}}] | ||
POTE generator: ~ | POTE generator: ~5/3 = 935.688 | ||
Vals: {{Val list| 4, 5, 9, 32bcde, 41bcdde, 50bbcdde }} | Vals: {{Val list| 4, 5, 9, 32bcde, 41bcdde, 50bbcdde }} | ||
| Line 51: | Line 51: | ||
Mapping: [{{val|1 0 0 2 5 -1}}, {{val|0 2 3 1 -2 6}}] | Mapping: [{{val|1 0 0 2 5 -1}}, {{val|0 2 3 1 -2 6}}] | ||
POTE generator: ~ | POTE generator: ~5/3 = 934.065 | ||
Vals: {{Val list| 4f, 5, 9, 32bcde, 41bcddef, 50bbcddeff }} | Vals: {{Val list| 4f, 5, 9, 32bcde, 41bcddef, 50bbcddeff }} | ||
| Line 64: | Line 64: | ||
Mapping: [{{val|1 0 0 2 -2}}, {{val|0 2 3 1 7}}] | Mapping: [{{val|1 0 0 2 -2}}, {{val|0 2 3 1 7}}] | ||
POTE generator: ~ | POTE generator: ~5/3 = 934.153 | ||
Vals: {{Val list| 4e, 5e, 9 }} | Vals: {{Val list| 4e, 5e, 9 }} | ||
Revision as of 18:11, 31 July 2021
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, or approximately one step of 9 EDO. The monzo for 27/25 is [0 3 -2⟩, the dual of which is ⟨⟨ 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.
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
Subgroup: 2.3.5
Comma: 27/25
Mapping: [⟨1 0 0], ⟨0 -2 -3]]
POTE generator: ~5/3 = 939.612
Badness: 0.032801
Beep
Subgroup: 2.3.5.7
Comma list: 36/35, 27/25
Mapping: [⟨1 0 0 2], ⟨0 2 3 1]]
Wedgie: ⟨⟨ 2 3 1 0 -4 -6 ]]
POTE generator: ~5/3 = 936.605
Badness: 0.018638
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]]
POTE generator: ~5/3 = 935.688
Vals: Template:Val list
Badness: 0.022649
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]]
POTE generator: ~5/3 = 934.065
Vals: Template:Val list
Badness: 0.021159
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]]
POTE generator: ~5/3 = 934.153
Vals: Template:Val list
Badness: 0.022799
Mite
Subgroup: 2.3.5.7
Comma list: 27/25, 28/25
Mapping: [⟨1 0 0 -2], ⟨0 2 3 6]]
Wedgie: ⟨⟨ 2 3 6 0 4 6 ]]
POTE generator: ~5/3 = 959.288
Badness: 0.054770