Swetismic temperaments

These are rank-3 temperaments tempering out 540/539, but we can begin by looking at the rank-4 temperament.

Swetismic

Comma list: 540/539

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

Generators: ~2, ~3, ~5, ~7

Hades

Comma list: 540/539, 4000/3993

Mapping: [⟨2 1 0 2 3], ⟨0 3 0 5 -1], ⟨0 0 1 0 1]]

Mapping generators: ~99/70, ~9/7, ~5

Badness: 0.361 × 10^-3

13-limit

Comma list: 540/539, 729/728, 1575/1573

Mapping: [⟨2 1 0 2 3 -2], ⟨0 3 0 5 -1 13], ⟨0 0 1 0 1 0]]

Mapping generators: ~99/70, ~9/7, ~5

Vals: Template:Val list

Badness: 0.535 × 10^-3

Cerberus

Comma list: 351/350, 364/363, 540/539

Mapping: [⟨2 1 0 2 3 1], ⟨0 3 0 5 -1 -4], ⟨0 0 1 0 1 2]]

Mapping generators: ~55/39, ~9/7, ~5

Vals: Template:Val list

Badness: 0.766 × 10^-3

Minos

Comma list: 540/539, 12005/11979

Mapping: [⟨1 0 2 1 2], ⟨0 2 4 3 4], ⟨0 0 -5 -1 -3]]

Mapping generators: ~2, ~121/70, ~49/33

Badness: 0.886 × 10^-3

13-limit

Comma list: 364/363, 540/539, 676/675

Mapping: [⟨1 0 2 1 2 1], ⟨0 2 4 3 4 7], ⟨0 0 -5 -1 -3 -5]]

Mapping generators: ~2, ~26/15, ~49/33

Vals: Template:Val list

Badness: 0.724 × 10^-3

Persephone

Comma list: 540/539, 88209/87500

Mapping: [⟨1 0 4 -2 10], ⟨0 1 4 0 7], ⟨0 0 -5 3 -11]]

Badness: 2.015 × 10^-3

13-limit

Comma list: 351/350, 540/539, 847/845

Mapping: [⟨1 0 4 -2 10 7], ⟨0 1 4 0 7 5], ⟨0 0 -5 3 -11 -7]]

Vals: Template:Val list

Badness: 0.997 × 10^-3

Hypnos

Comma list: 540/539, 72171/71680

Mapping: [⟨1 0 0 -3 8], ⟨0 3 0 11 -13], ⟨0 0 1 0 1]]

Badness: 1.629 × 10^-3

13-limit

Comma list: 169/168, 540/539, 729/728

Mapping: [⟨1 0 0 -3 8 0], ⟨0 3 0 11 -13 7], ⟨0 0 1 0 1 0]]

Vals: Template:Val list

Badness: 1.439 × 10^-3