Semicomma family: Difference between revisions
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The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65536/65625 leads to orwell, but we could also add | The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at. Adding 65536/65625 leads to orwell, but we could also add | ||
* 1029/1024, leading to the 31&159 temperament (triwell) with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or | * 1029/1024, leading to the 31&159 temperament (triwell) with wedgie {{multival| 21 -9 -7 -63 -70 9 }}, or | ||
* 2401/2400, giving the 31&243 temperament with wedgie {{multival| 28 -12 1 -84 -77 36 }}, or | * 2401/2400, giving the 31&243 temperament (quadrawell) with wedgie {{multival| 28 -12 1 -84 -77 36 }}, or | ||
* 4375/4374, giving the 53&243 temperament (sabric) with wedgie {{multival| 7 -3 61 -21 77 150 }}. | * 4375/4374, giving the 53&243 temperament (sabric) with wedgie {{multival| 7 -3 61 -21 77 150 }}. | ||
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Badness: 0.029807 | Badness: 0.029807 | ||
= Quadrawell = | |||
The ''quadrawell'' temperament (31&212, named by [[User:Xenllium|Xenllium]]) has an [[8/7]] generator of about 232 cents, twelve of which give the fifth harmonic. | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 2401/2400, 2109375/2097152 | |||
[[Mapping]]: [{{val| 1 7 0 3 }}, {{val| 0 -28 12 -1 }}] | |||
{{Multival|legend=1| 28 -12 1 -84 -77 36 }} | |||
[[POTE generator]]: ~8/7 = 232.094 | |||
{{Val list|legend=1| 31, 119, 150, 181, 212, 243, 698cd, 941cd }} | |||
[[Badness]]: 0.075754 | |||
== 11-limit == | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 385/384, 1375/1372, 14641/14580 | |||
Map: [{{val| 1 7 0 3 11 }}, {{val| 0 -28 12 -1 -39}}] | |||
POTE generator: ~8/7 = 232.083 | |||
Vals: {{Val list| 31, 119, 150, 181, 212, 455ee, 667cdee }} | |||
Badness: 0.036493 | |||
= Sabric = | = Sabric = | ||
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[[Mapping]]: [{{val| 1 0 3 -11 }}, {{val| 0 7 -3 61 }}] | [[Mapping]]: [{{val| 1 0 3 -11 }}, {{val| 0 7 -3 61 }}] | ||
{{ | {{Multival|legend=1| 7 -3 61 -21 77 150 }} | ||
[[POTE generator]]: ~75/64 = 271.607 | [[POTE generator]]: ~75/64 = 271.607 | ||