Porwell temperaments: Difference between revisions
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== Hendecatonic == | == Hendecatonic == | ||
The hendecatonic temperament has a period of 1/11 octave, which represents [[16/15]] and four times of which represents [[9/7]]. | The hendecatonic temperament has a period of 1/11 octave, which represents [[16/15]] and four times of which represents [[9/7]]. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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{{Val list|legend=1| 16, 37, 53, 196d }} | {{Val list|legend=1| 16, 37, 53, 196d }} | ||
[[Badness]]: 0. | [[Badness]]: 0.107023 | ||
=== 11-limit === | === 11-limit === | ||
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Vals: {{Val list| 16, 37, 53 }} | Vals: {{Val list| 16, 37, 53 }} | ||
Badness: 0. | Badness: 0.059838 | ||
=== 13-limit === | === 13-limit === | ||
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Vals: {{Val list| 16, 37, 53 }} | Vals: {{Val list| 16, 37, 53 }} | ||
Badness: 0. | Badness: 0.032564 | ||
== Nessafof == | == Nessafof == | ||
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Badness: 0.033038 | Badness: 0.033038 | ||
== Aufo == | |||
{{see also| High badness temperaments #Aufo }} | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 6144/6125, 177147/175616 | |||
[[Mapping]]: [{{Val|1 6 -7 19}}, {{Val|0 -9 19 -33}}] | |||
{{Multival|legend=1|9 -19 33 -51 27 130}} | |||
[[POTE generator]]: ~45/32 = 588.782 | |||
{{Val list|legend=1| 53, 161, 214 }} | |||
[[Badness]]: 0.121428 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 121/120, 176/175, 177147/175616 | |||
Mapping: [{{Val|1 6 -7 19 1}}, {{Val|0 -9 19 -33 5}}] | |||
POTE generator: ~45/32 = 588.811 | |||
Vals: {{Val list| 53, 108e, 161e }} | |||
Badness: 0.088631 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 121/120, 176/175, 351/350, 58806/57967 | |||
Mapping: [{{Val|1 6 -7 19 1 -12}}, {{Val|0 -9 19 -33 5 32}}] | |||
POTE generator: ~45/32 = 588.788 | |||
Vals: {{Val list| 53, 108e, 161e, 214ee }} | |||
Badness: 0.058507 | |||
== Whoops == | == Whoops == | ||
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== Polypyth == | == Polypyth == | ||
Polypyth (46&121) tempers out the same 5-limit comma as the [[Hemifamity temperaments #Leapday|leapday temperament]] (29&46), but with the porwell (6144/6125) rather than the hemifamity (5120/5103) tempered out. | Polypyth (46&121) tempers out the same 5-limit comma as the [[Hemifamity temperaments #Leapday|leapday temperament]] (29&46), but with the porwell (6144/6125) rather than the hemifamity (5120/5103) tempered out. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Icositritonic == | == Icositritonic == | ||
The ''icositritonic'' temperament (46&161) has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]]. | The ''icositritonic'' temperament (46&161) has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]]. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Countermiracle == | == Countermiracle == | ||
The ''countermiracle'' temperament (31&145) tempers out the trimyna, 50421/50000 and the [[Quince clan|quince comma]], 823543/819200. | The ''countermiracle'' temperament (31&145) tempers out the trimyna, 50421/50000 and the [[Quince clan|quince comma]], 823543/819200. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||