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| 15, 122d, 137, 152, 608d, 623bd, 775bcd }} | {{Val list|legend=1| 15, 122d, 137, 152, 608d, 623bd, 775bcd }} | ||
[[Badness]]: 0. | [[Badness]]: 0.175840 | ||
=== 11-limit === | === 11-limit === | ||
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Vals: {{Val list| 15, 122d, 137, 152, 608de, 623bde, 775bcde }} | Vals: {{Val list| 15, 122d, 137, 152, 608de, 623bde, 775bcde }} | ||
Badness: 0. | Badness: 0.043743 | ||
== Polypyth == | == Polypyth == | ||
{{see also| High badness temperaments #Leapday }} | |||
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 | ||