Bug family: Difference between revisions
KingHyperio (talk | contribs) Tags: Mobile edit Mobile web edit |
Get back to minimal ratio form now all the forms are logged |
||
| Line 1: | Line 1: | ||
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 [[ | 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 [[9edo]]. The monzo for 27/25 is {{monzo| 0 3 -2 }}, the dual of which is {{multival| 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 [[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 [[Ragismic microtemperaments #Ennealimmal|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is. | 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 [[Ragismic microtemperaments #Ennealimmal|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is. | ||
| Line 6: | Line 6: | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
[[Comma]]: 27/25 | [[Comma list]]: 27/25 | ||
[[Mapping]]: [{{val|1 0 0}}, {{val|0 -2 -3}}] | [[Mapping]]: [{{val|1 0 0}}, {{val|0 -2 -3}}] | ||
| Line 19: | Line 19: | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
[[Comma list]]: | [[Comma list]]: 21/20, 27/25 | ||
[[Mapping]]: [{{val|1 0 0 2}}, {{val|0 2 3 1}}] | [[Mapping]]: [{{val|1 0 0 2}}, {{val|0 2 3 1}}] | ||
| Line 85: | Line 85: | ||
[[Badness]]: 0.054770 | [[Badness]]: 0.054770 | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Bug family]] <!-- main article --> | |||
[[Category:Rank 2]] | |||
Revision as of 12:12, 2 October 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 9edo. 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 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
Subgroup: 2.3.5
Comma list: 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: 21/20, 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