Werckismic temperaments
This is a collection of rank-3 temperaments tempering out 441/440, but we can begin by looking at the rank-4 temperament.
Werckismic
Subgroup: 2.3.5.7.11
Mapping: [⟨1 0 0 0 -3], ⟨0 1 0 0 2], ⟨0 0 1 0 -1], ⟨0 0 0 1 2]]
- [[1 0 0 0 0⟩, [1/2 2/3 1/6 -1/3 1/6⟩, [0 0 1 0 0⟩, [1 -2/3 1/3 1/3 1/3⟩, [0 0 0 0 1⟩]
- Eigenmonzos: 2, 5, 11, 9/7
History
Subgroup: 2.3.5.7.11
Comma list: 441/400, 4000/3993
Mapping: [⟨1 2 0 0 1], ⟨0 -6 0 7 2], ⟨0 0 1 1 1]]
Mapping generators: ~2, ~21/20, ~5
- 11-odd-limit
- [[1 0 0 0 0⟩, [4/17 12/17 0 -6/17 6/17⟩, [-27/17 4/17 0 -2/17 19/17⟩, [8/17 -10/17 0 5/17 12/17⟩, [0 0 0 0 1⟩]
- Eigenmonzos: 2, 11, 9/7
Badness: 0.604 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 1001/1000
Mapping: [⟨1 2 0 0 1 2], ⟨0 -6 0 7 2 -9], ⟨0 0 1 1 1 1]]
Mapping generators: ~2, ~21/20, ~5
Minimax tuning:
- 13-odd-limit
- [[1 0 0 0 0 0⟩, [5/4 0 0 -3/8 0 3/8⟩, [0 0 1 0 0 0⟩, [7/8 0 1 7/16 0 -7/16⟩, [5/4 0 1 1/8 0 -1/8⟩, [7/8 0 1 -9/16 0 9/16⟩]
- Eigenmonzos: 2, 5, 13/7
Vals: Template:Val list
Badness: 0.540 × 10-3
Complexity spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7
Varuna
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000
Mapping: [⟨2 0 0 9 12], ⟨0 1 0 -4 -6], ⟨0 0 1 2 3]]
Mapping generators: ~99/70, ~3, ~5
Badness: 0.419 × 10-3