|
|
| Line 15: |
Line 15: |
|
| |
|
| Temperaments discussed elsewhere include | | Temperaments discussed elsewhere include |
| * Jubilic ([[50/49]]) → [[Jubilismic clan #Jubilic]] | | * Jubilic ([[50/49]]) → [[Jubilismic clan #Jubilic|Jubilismic clan]] |
| * Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus]] | | * Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus|Hemimean clan]] |
| * Llywelyn a.k.a. shoe ([[4194304/4117715]]) → [[Llywelynsmic clan #Llywelyn a.k.a. shoe]] | | * Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]] |
| | * Llywelyn a.k.a. shoe ([[4194304/4117715]]) → [[Llywelynsmic clan #Llywelyn a.k.a. shoe|Llywelynsmic clan]] |
|
| |
|
| === Rainy === | | === Rainy === |
| Line 177: |
Line 178: |
|
| |
|
| {{Optimal ET sequence|legend=1| 52, 1737, 1789 }}, ... | | {{Optimal ET sequence|legend=1| 52, 1737, 1789 }}, ... |
|
| |
| === 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]].
| |
|
| |
| [[Subgroup]]: 2.5.7
| |
|
| |
| [[Comma list]]: 823543/819200
| |
|
| |
| [[Sval]] [[mapping]]: [{{val| 1 3 3 }}, {{val| 0 -7 -2 }}]
| |
|
| |
| [[Gencom]]: [2 2744/2560; 823543/819200]
| |
|
| |
| [[Gencom]] [[mapping]]: [{{val| 1 0 3 3 }}, {{val| 0 0 -7 -2 }}]
| |
|
| |
| Optimal tuning ([[POTE]]): ~343/320 = 116.291
| |
|
| |
| {{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
| |
|
| |
| ==== 2.5.7.13 ====
| |
| [[Subgroup]]: 2.5.7.13
| |
|
| |
| [[Comma list]]: 343/338, 640/637
| |
|
| |
| [[Sval]] [[mapping]]: [{{val| 1 3 3 4 }}, {{val| 0 -7 -2 -3 }}]
| |
|
| |
| [[Gencom]]: [2 14/13; 343/338 640/637]
| |
|
| |
| [[Gencom]] [[mapping]]: [{{val| 1 0 3 3 4 }}, {{val| 0 0 -7 -2 -3 }}]
| |
|
| |
| Optimal tuning ([[POTE]]): ~14/13 = 116.094
| |
|
| |
| {{Optimal ET sequence|legend=1| 10, 21, 31}}
| |
|
| |
| ==== 2.5.7.13.17 ====
| |
| [[Subgroup]]: 2.5.7.13.17
| |
|
| |
| [[Comma list]]: 170/169, 224/221, 640/637
| |
|
| |
| [[Sval]] [[mapping]]: [{{val| 1 3 3 4 4 }}, {{val| 0 -7 -2 -3 1 }}]
| |
|
| |
| [[Gencom]]: [2 14/13; 170/169 224/221 640/637]
| |
|
| |
| [[Gencom]] [[mapping]]: [{{val| 1 0 3 3 4 4 }}, {{val| 0 0 -7 -2 -3 1 }}]
| |
|
| |
| Optimal tuning ([[POTE]]): ~14/13 = 115.769
| |
|
| |
| {{Optimal ET sequence|legend=1| 10, 21, 31}}
| |
|
| |
| ==== 2.5.7.13.17.19 ====
| |
| [[Subgroup]]: 2.5.7.13.17.19
| |
|
| |
| [[Comma list]]: 170/169, 343/338, 640/637, 16384/16055
| |
|
| |
| [[Sval]] [[mapping]]: [{{val| 1 3 3 4 4 3 }}, {{val| 0 -7 -2 -3 1 13 }}]
| |
|
| |
| [[Gencom]] [[mapping]]: [{{val| 1 0 3 3 4 4 3 }}, {{val| 0 0 -7 -2 -3 1 13 }}]
| |
|
| |
| [[Gencom]]: [2 14/13; 170/169 343/338 640/637 16384/16055]
| |
|
| |
| Optimal tuning ([[POTE]]): ~14/13 = 115.716
| |
|
| |
| {{Optimal ET sequence|legend=1| 10, 21, 31, 52f }}
| |
|
| |
|
| === Pakkanen (rank 3) === | | === Pakkanen (rank 3) === |