Subgroup temperaments: Difference between revisions
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== No-threes subgroup == | == No-threes subgroup == | ||
=== Llywelyn === | === Llywelyn === | ||
Subgroup: 2.5.7 | Subgroup: 2.5.7 | ||
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=== Didacus === | === Didacus === | ||
{{See also| Hemimean clan #Didacus }} | |||
Related temperaments: [[Chromatic pairs #Roulette|roulette]], [[Gamelismic clan #Hemithirds|hemithirds]] | Related temperaments: [[Chromatic pairs #Roulette|roulette]], [[Gamelismic clan #Hemithirds|hemithirds]] | ||
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=== Rainy === | === Rainy === | ||
Three generators make an [[8/7]]; five generators make a [[5/4]]. This is the no-threes version of [[tertiaseptal]]. | Three generators make an [[8/7]]; five generators make a [[5/4]]. This is the no-threes version of [[tertiaseptal]]. | ||
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=== Mercy === | === Mercy === | ||
{{See also| Quince clan #Mercy }} | |||
Two generators make an [[8/7]]; seven generators make an [[8/5]]. Mercy can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]], and is the no-threes or elevens version of [[miracle]]. | Two generators make an [[8/7]]; seven generators make an [[8/5]]. Mercy can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]], and is the no-threes or elevens version of [[miracle]]. | ||
Subgroup: 2.5.7 | Subgroup: 2.5.7 | ||
[[Comma]]: 823543/819200 | [[Comma list]]: 823543/819200 | ||
[[Gencom]]: [2 2744/2560; 823543/819200] | [[Gencom]]: [2 2744/2560; 823543/819200] | ||
[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 }}, {{val|0 0 -7 -2}}] | [[Gencom|Gencom mapping]]: [{{val| 1 0 3 3 }}, {{val| 0 0 -7 -2 }}] | ||
[[ | [[Sval]] [[mapping]]: [{{val| 1 3 3 }}, {{val| 0 -7 -2 }}] | ||
[[Tp tuning|POL2 generator]]: ~ | [[Tp tuning|POL2 generator]]: ~343/320 = 116.291 | ||
{{Val list|legend=1| 10, 21, 31}} | {{Val list|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }} | ||
==== | ==== 2.5.7.13 ==== | ||
Subgroup: 2.5.7.13 | Subgroup: 2.5.7.13 | ||