|
|
| Line 20: |
Line 20: |
|
| |
|
| [[Badness]]: 0.014884 | | [[Badness]]: 0.014884 |
| | |
| | === Overview to extensions === |
| | Strong extensions of father to include an approximation of harmonic 7 are septimal father (5 & 8d), mother (2 & 3), and pater (3 & 5d), all considered below. |
| | |
| | Temperaments discussed elsewhere include: |
| | * ''[[Baba]]'' → [[Slendro clan #Baba|Slendro clan]] |
| | * ''[[Walid]]'' → [[Jubilismic clan #Walid|Jubilismic clan]] |
|
| |
|
| == Septimal father == | | == Septimal father == |
| Line 112: |
Line 119: |
|
| |
|
| Badness: 0.035487 | | Badness: 0.035487 |
|
| |
| == Baba ==
| |
| [[Subgroup]]: 2.3.5.7
| |
|
| |
| [[Comma list]]: 16/15, 49/45
| |
|
| |
| {{Mapping|legend=1| 1 0 4 2 | 0 2 -2 1 }}
| |
|
| |
| : mapping generators: ~2, ~7/4
| |
|
| |
| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 973.296
| |
|
| |
| {{Multival|legend=1| 2 -2 1 -8 -4 8 }}
| |
|
| |
| {{Optimal ET sequence|legend=1| 5, 11b, 16bc }}
| |
|
| |
| [[Badness]]: 0.044321
| |
|
| |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
|
| |
| Comma list: 16/15, 22/21, 49/45
| |
|
| |
| Mapping: {{mapping| 1 0 4 2 1 | 0 2 -2 1 3 }}
| |
|
| |
| Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 978.164
| |
|
| |
| {{Optimal ET sequence|legend=1| 5, 11b, 16bc, 27bbcc }}
| |
|
| |
| Badness: 0.036538
| |
|
| |
| == Walid ==
| |
| [[Subgroup]]: 2.3.5.7
| |
|
| |
| [[Comma list]]: 16/15, 50/49
| |
|
| |
| {{Mapping|legend=1| 2 0 8 9 | 0 1 -1 -1 }}
| |
|
| |
| : mapping generators: ~7/5, ~3
| |
|
| |
| {{Multival|legend=1| 2 -2 -2 -8 -9 1 }}
| |
|
| |
| [[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 749.415
| |
|
| |
| {{Optimal ET sequence|legend=1| 2, 6, 8d }}
| |
|
| |
| [[Badness]]: 0.048978
| |
|
| |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
|
| |
| Comma list: 16/15, 22/21, 50/49
| |
|
| |
| Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}
| |
|
| |
| Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 749.756
| |
|
| |
| {{Optimal ET sequence|legend=1| 2, 6, 8d }}
| |
|
| |
| Badness: 0.029193
| |
|
| |
|
| == Ternary == | | == Ternary == |