Porwell family
The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.
Hewuermity
Subgroup: 2.3.5.7
Mapping: [⟨1 0 1 4], ⟨0 1 1 -1], ⟨0 0 -2 3]]
Mapping generators: ~2, ~3, ~35/32
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [11/5 1/5 2/5 -2/5⟩, [11/5 1/5 -3/5 3/5⟩]
- Eigenmonzos: 4/3, 7/5
Badness: 0.142 × 10-3
Projection pairs: 3 6125/2048 to 2.5.7
Zeus
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175
Mapping: [⟨1 0 1 4 2], ⟨0 1 1 -1 1], ⟨0 0 -2 3 1]]
Mapping generators: 2, 3, 11/10
Map to lattice: [⟨0 1 -1 2 0], ⟨0 1 1 -1 1]]
Lattice basis:
- 11/10, 11/8
- Angle (11/10, 11/8) = 87.464 degrees
- [[1 0 0 0 0⟩, [11/9 10/9 -1/3 -2/9 0⟩, [22/9 2/9 1/3 -4/9 0⟩, [22/9 2/9 -2/3 5/9 0⟩, [10/3 2/3 0 -1/3 0⟩]
- Eigenmonzos: 2, 9/7, 7/5
Badness: 0.400 × 10-3
Projection pairs: 5 600/121 7 2662/375 11 120/11 to 2.3.11/5
Zeus11[22] hobbit transversal
- 33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3,
- 11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4,
- 11/6, 15/8, 64/33, 2
Zeus11[24] hobbit transversal
- 33/32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,
- 11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9,
- 11/6, 15/8, 64/33, 2
Scales:
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 351/350
Mapping: [⟨1 0 1 4 2 7], ⟨0 1 1 -1 1 -2], ⟨0 0 -2 3 -1 -1]]
Mapping generators: ~2, ~3, ~11/10
Map to lattice: [⟨0 1 -1 2 0 -3], ⟨0 1 1 -1 1 -2]]
Lattice basis:
- 11/10 length = 0.7898, 11/8 length = 1.002
- Angle (11/10, 11/8) = 106.7439 degrees
Minimax tuning:
- 13-odd-limit
- [[1 0 0 0 0 0⟩, [11/9 10/9 -1/3 -2/9 0 0⟩, [22/9 2/9 1/3 -4/9 0 0⟩, [22/9 2/9 -2/3 5/9 0 0⟩, [10/3 2/3 0 -1/3 0 0⟩, [14/3 -8/3 1 1/3 0 0⟩]
- Eigenmonzos: 2, 9/7, 7/5
- 15-odd-limit
- [[1 0 0 0 0 0⟩, [0 1 0 0 0 0⟩, [11/5 1/5 2/5 -2/5 0 0⟩, [11/5 1/5 -3/5 3/5 0 0⟩, [13/5 3/5 1/5 -1/5 0 0⟩, [38/5 -12/5 1/5 -1/5 0 0⟩]
- Eigenmonzos: 2, 4/3, 7/5
Vals: Template:Val list
Badness: 0.934 × 10-3
Projection pairs: 5 600/121 7 2662/375 11 120/11 13 1280/99 to 2.3.11/5
Zeus13[22] hobbit transversal
- 260/243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2
Tinia
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 121/120, 176/175
Mapping: [⟨1 0 1 4 2 2], ⟨0 1 1 -1 1 1], ⟨0 0 -2 3 -1 -1]]
Vals: Template:Val list
Badness: 0.808 × 10-3
Jupiter
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5632/5625
Mapping: [⟨1 0 1 4 -5], ⟨0 1 1 -1 6], ⟨0 0 2 -3 8]]
Badness: 0.562 × 10-3