Landscape family

The landscape family of rank-3 temperaments tempers out the landscape comma, 250047/250000.

Landscape

Subgroup: 2.3.5.7

Comma list: 250047/250000

Mapping: [⟨3 0 0 4], ⟨0 1 0 -2], ⟨0 0 1 2]]

mapping generators: ~63/50, ~3, ~5

Minimax tuning:

• 7-odd-limit

[[9 0 0 0⟩, [4 3 6 -3⟩, [0 0 9 0⟩, [4 -6 6 6⟩]/9

eigenmonzo (unchanged-interval) basis: 2.5.7/3

• 9-odd-limit

[[12 0 0 0⟩, [4 6 6 -3⟩, [0 0 12 0⟩, [8 -12 12 6⟩]/12

eigenmonzo (unchanged-interval) basis: 2.5.9/7

Optimal ET sequence: 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555

Badness: 0.02130 × 10^-3

House

House tempers out the quartisma alongside the landscape comma.

Subgroup: 2.3.5.7.11

Comma list: 250047/250000, 117440512/117406179

Mapping: [⟨3 0 2 8 16], ⟨0 1 4 6 0], ⟨0 0 -5 -10 2]]

mapping generators: ~63/50, ~3, ~9801/5120

Optimal tuning (CTE) ~63/50 = 1\3, ~3/2 = 701.9592, ~9801/5120 = 1124.2969

Optimal ET sequence: 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee

Badness: 1.92 × 10^-3

Odin

See also: Kalismic temperaments #Odin

Tyr

See also: Lehmerismic temperaments #Tyr