User:Dummy index/3rd-tritave temperaments
3edt tempers out (13/9)3 / (3/1) = 2197/2187, the threedie. Most temperaments here are explanation of triple BP.
All "**** III" are placeholder name.
"Threedie family" start from 3.5.7.13
BPS III (b30 & b9, b39 & b9)
Subgroup: 3.5.7.13
Comma list: 245/243, 2197/2187
Sval mapping: [⟨3 5 5 7], ⟨0 -2 1 0]]
3.5.7.11.13
Subgroup: 3.5.7.11.13
Comma list: 245/243, ****, 2197/2187
Sval mapping: [⟨3 5 5 5 7], ⟨0 -2 1 5 0]]
strong extension 3.5.7.11.13 (b39 & b30e)
Subgroup: 3.5.7.11.13
Comma list: 245/243, ****, 2197/2187
Sval mapping: [⟨3 5 5 9 7], ⟨0 -2 1 -8 0]]
weak extension 3.5.7.11.13 (b39 & b60)
Subgroup: 3.5.7.11.13
Comma list: 245/243, ****, 2197/2187
Sval mapping: [⟨3 5 5 7 7], ⟨0 -4 2 -3 0]]
Sirius III (b39 & b6, b39 & b45)
Subgroup: 3.5.7.13
Comma list: 3125/3087, 2197/2187
Sval mapping: [⟨3 3 3 7], ⟨0 3 5 0]]
3.5.7.11.13 (also deneb III)
This tempers out threedie, DPC(3:5:7) and DPC(7/5,13/11).
Subgroup: 3.5.7.11.13
Comma list: 3125/3087, 6655/6561, 2197/2187
Sval mapping: [⟨3 3 3 7 7], ⟨0 3 5 -1 0]]
Canopus III (b39 & b36, b39 & b75)
Subgroup: 3.5.7.13
Comma list: 16875/16807, 2197/2187
Sval mapping: [⟨3 4 5 7], ⟨0 5 4 0]]
3.5.7.11.13 Suhail
b9 & b6
Subgroup: 3.5.7.13
Comma list: 375/343, 2197/2187
Sval mapping: [⟨3 4 5 7], ⟨0 1 1 0]]
"Threedie family" start from 3.7.11.13
Mintaka III (b39 & b66)
Subgroup: 3.7.11.13
Comma list: 1331/1323, 2197/2187
Sval mapping: [⟨3 6 7 7], ⟨0 -3 -2 0]]
3.5.7.11.13 (also procyon III)
This tempers out threedie, DPC(5:7:9) and DPC(9/7,13/11).
Subgroup: 3.5.7.11.13
Comma list: 823543/820125, 1331/1323, 2197/2187
Sval mapping: [⟨3 6 6 7 7], ⟨0 -7 -3 -2 0]]
weak extension 3.5.7.11.13 (b39 & b15, also arcturus III)
Subgroup: 3.5.7.11.13
Comma list: 15625/15309, 1331/1323, 2197/2187
Sval mapping: [⟨3 4 3 5 7], ⟨0 1 6 4 0]]
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