Valinorsmic clan
This is a collection of rank-3 temperaments tempering out the valinorsma, 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does).
Discussed elsewhere are:
- Julius or varda, {176/175, 896/891} → Diaschismic rank three family #Julius aka varda
Considered below are manwe, mandos and ulmo, but we can begin with the rank-4 temperament.
Valinorsmic
Subgroup: 2.3.5.7.11
Mapping: [⟨1 0 0 0 -4], ⟨0 1 0 0 0], ⟨0 0 1 0 2], ⟨0 0 0 1 1]]
Manwe
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323
Mapping: [⟨1 0 0 12 8], ⟨0 1 0 3 3], ⟨0 0 1 -6 -4]]
Badness: 0.679 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 1331/1323, 351/350
Mapping: [⟨1 0 0 12 8], ⟨0 1 0 3 3], ⟨0 0 1 -6 -4]]
Vals: Template:Val list
Badness: 1.147 × 10-3
Mandos
Subgroup: 2.3.5.7.11
Comma list: 176/175, 243/242
Mapping: [⟨1 1 0 6 2], ⟨0 2 0 5 5], ⟨0 0 1 -2 0]]
Badness: 0.751 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 243/242
Mapping: [⟨1 1 0 6 2 4], ⟨0 2 0 5 5 -1], ⟨0 0 1 -2 0 0]]
Vals: Template:Val list
Badness: 0.923 × 10-3
Ulmo
Subgroup: 2.3.5.7.11
Comma list: 176/175, 2200/2187
Mapping: [⟨1 0 0 1, -3], ⟨0 1 0 7 7], ⟨0 0 1 -4 -2]]
Badness: 1.23 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 176/175, 325/324
Mapping: [⟨1 0 0 1, -3 2], ⟨0 1 0 7 7 4], ⟨0 0 1 -4 -2 -2]]
Vals: Template:Val list
Badness: 0.932 × 10-3