User:Dummy index/3rd-tritave temperaments

3edt tempers out (13/9)³ / (3/1) = 2197/2187, the threedie.

All "**** III" are placeholder name.

"Threedie family" start from 3.5.7.13

BPS III (b30 & b9, b39 & b9)

Proposed names: User:Recentlymaterialized/Miscellaneous rank-2 temperaments #Tripierce (b30 & b39)

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

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

Main article: No-twos subgroup temperaments § 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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