Pythagorean family: Difference between revisions
Bold lemma; +dis-confusion reminder |
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In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]]. For this [[72edo]] can be recommended as a tuning. | In terms of the normal comma list, we may add 8019/8000 to get to the 11-limit version of compton, which also adds [[441/440]]. For this [[72edo]] can be recommended as a tuning. | ||
== 7-limit (aka Waage) == | |||
Comma list: 225/224, 250047/250000 | Comma list: 225/224, 250047/250000 | ||
[[POTE generator]]: ~5/4 = 383. | [[POTE generator]]: ~5/4 = 383.7752 | ||
Mapping: [{{val| 12 19 0 -22 }}, {{val| 0 0 1 2 }}] | Mapping: [{{val| 12 19 0 -22 }}, {{val| 0 0 1 2 }}] | ||
{{Val list|legend=1| 12, 60, 72, 228, 300c, 372bc, 444bc }} | {{Val list|legend=1| 12, 60, 72, 228, 300c, 372bc, 444bc }} | ||
Badness: 0.035686 | |||
== 11-limit == | == 11-limit == | ||
Comma list: 225/224, 441/440, 4375/4356 | Comma list: 225/224, 441/440, 4375/4356 | ||
[[POTE generator]]: ~5/4 = 383. | [[POTE generator]]: ~5/4 = 383.2660 | ||
Mapping: [{{val|12 19 0 -22 -42 }}, {{val| 0 0 1 2 3 }}] | Mapping: [{{val|12 19 0 -22 -42 }}, {{val| 0 0 1 2 3 }}] | ||
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{{Val list|legend=1| 12, 60e, 72 }} | {{Val list|legend=1| 12, 60e, 72 }} | ||
Badness: 0.022235 | |||
POTE generator: ~5/4 = 383. | == 13-limit == | ||
Comma list: 225/224, 351/350, 364/363, 441/440 | |||
POTE generator: ~5/4 = 383.9628 | |||
Mapping: [{{val| 12 19 0 -22 -42 -67 }}, {{val| 0 0 1 2 3 4 }}] | Mapping: [{{val| 12 19 0 -22 -42 -67 }}, {{val| 0 0 1 2 3 4 }}] | ||
{{Val list|legend=1| 72, 228f, 300cf }} | {{Val list|legend=1| 12f, 72, 84, 156, 228f, 300cf }} | ||
Badness: 0.021852 | |||
== 17-limit == | |||
Comma list: 221/220, 225/224, 289/288, 351/350, 441/440 | |||
POTE generator: ~5/4 = 383.7500 | |||
Mapping: [{{val| 12 19 0 -22 -42 -67 49 }}, {{val| 0 0 1 2 3 4 0 }}] | |||
{{Val list|legend=1| 12f, 72, 84, 156g, 228fg }} | |||
Badness: 0. | Badness: 0.017131 | ||
== Comptone == | |||
Comma list: 225/224, 441/440 | Comma list: 225/224, 325/324, 441/440, 1001/1000 | ||
POTE generator: ~5/4 = 382. | POTE generator: ~5/4 = 382.6116 | ||
Mapping: [{{val| 12 19 0 -22 -42 100 }}, {{val| 0 0 1 2 3 -2 }}] | Mapping: [{{val| 12 19 0 -22 -42 100 }}, {{val| 0 0 1 2 3 -2 }}] | ||
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{{Val list|legend=1| 12, 60e, 72, 204cdef, 276cdef }} | {{Val list|legend=1| 12, 60e, 72, 204cdef, 276cdef }} | ||
Badness: 0. | Badness: 0.025144 | ||
=== 17-limit === | |||
Comma list: 225/224, 273/272, 289/288, 325/324, 441/440 | |||
POTE generator: ~5/4 = 382.5968 | |||
Mapping: [{{val| 12 19 0 -22 -42 100 49 }}, {{val| 0 0 1 2 3 -2 0 }}] | |||
{{Val list|legend=1| 12, 60e, 72, 132deg, 204cdefg }} | |||
Badness: 0.016361 | |||
= Catler = | = Catler = | ||