35th-octave temperaments

35edo is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either zeta edos like 3395edo, have an exceptionally precise perfect fifth like 665edo, or have high consistency limits like 525edo. In addition, one step of 35edo is close to 50/49 in low limits and 51/50 in the higher limits.

Bromine

Bromine is named after the 35th chemical element.

Subgroup: 2.3.5.7

Comma list: [47 -7 -7 -7⟩, [6 -37 13 8⟩

Mapping: [⟨35 0 -418 653], ⟨0 1 9 -10]]

Mapping generators: ~38263752/37515625 = 1\35, ~3

Optimal tuning (CTE): ~3/2 = 701.973

Optimal ET sequence: 665, 2065, 2730, 3395, 4060, 7455

2.3.5.7.13 subgroup

Subgroup: 2.3.5.7.13

Comma list: 1990656/1990625, 1686616064/1686498489, 44302336000/44295075909

Sval mapping: [⟨35 0 -418 653 1239], ⟨0 1 9 -10 -20]]

Sval mapping generators: ~38263752/37515625 = 1\35, ~3

Optimal tuning (CTE): ~3/2 = 701.973

Supporting ETs: 665, 3395, ...

2.3.5.7.13.17 subgroup

The period is mapped to ~51/50.

Subgroup: 2.3.5.7.13.17

Comma list: 426496/426465, 1990656/1990625, 6251648/6251175, 51200000/51195483

Mapping: [⟨35 0 -418 653 1239], ⟨0 1 9 -10 -20]]

Mapping generators: ~51/50 = 1\35, ~3

Optimal tuning (CTE): ~3/2 = 701.973

Supporting ETs: 665, 3395, ...

Tritonopodismic (rank-3)

Tritonopodismic tempers out tritonopod comma, the comma which sets 7/5 to 17\35, "one leg", and 10/7 to 18\35, the "other leg". Also it sets 50/49 to be equal to 1\35.

Subgroup:2.3.5.7

Comma list: [17 0 35 -35⟩

Mapping: [⟨35 0 0 17], ⟨0 1 0 0], ⟨0 0 1 1]]

Mapping generators: ~50/49 = 1\35, ~3, ~5

Optimal tuning (CTE): ~3/2 = 701.955, ~5/4 = 386.174

Optimal ET sequence: 35, 70, 140, 210, 525, 665

Tritonopod (rank-2)

Subgroup:2.5.7

Comma list: [17 35 -35⟩

Mapping: [⟨35 0 17], ⟨0 1 1]]

Mapping generators: ~50/49, ~5

Optimal tuning (CTE): ~5/4 = 386.174