Ragismic family

The ragisma family of temperaments are rank-3 microtemperaments which temper out 4375/4374.

Temperaments not discussed here include ennealimmic.

Ragismic

Comma: 4375/4374

Minimax tuning:

• 7-odd-limit eigenmonzos: 2, 8/7, 5/4
• 9-odd-limit eigenmonzos: 2, 4/3, 7/5

Lattice basis: 10/9 length = 0.789, 6/5 length = 0.921

Angle(10/9, 6/5) = 105.299°

Map to lattice: [⟨0 -1 -1 -3], ⟨0 -1 -2 1]]

Mapping: [⟨1 0 0 1], ⟨0 1 0 7], ⟨0 0 1 -4]]

Mapping generators: 2, ~3, ~5

Projection pair: ~7 = ~4374/625

Scales: Ragismic19

Thor

Comma list: 3025/3024, 4375/4374

Minimax tuning:

• 11-odd-limit eigenmonzos: 2, 11/10, 8/7

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

Mapping generators: ~99/70, ~3, ~5

Badness: 0.0000888

Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11

Donar

Comma list: 3025/3024, 4225/4224, 4375/4374

Minimax tuning:

• 13-odd-limit eigenmonzos: 2, 11/10, 8/7
• 15-odd-limit eigenmonzos: 2, 8/7, 15/11

Lattice basis: 44/39 length = 0.3480, 6/5 length = 0.7828

Angle(44/39, 6/5) = 85.3977°

Map to lattice: [⟨0 2 2 6 4 1], ⟨0 -1 -2 1 1 2]]

Mapping: [⟨2 0 1 -2 2 7], ⟨0 1 0 7 5 3], ⟨0 0 2 -8 -6 -5]]

Mapping generators: ~99/70, ~3, ~220/117

Vals: Template:Val list

Badness: 0.000322

Scales: Donar46

Thunor

Comma list: 1716/1715, 2080/2079, 3025/3024

Minimax tuning:

• 13- and 15-odd-limit eigenmonzos: 2, 16/13, 9/7

Lattice basis: 10/9 length = 0.4234, 6/5 length = 0.8426

Angle(10/9, 6/5) = 84.126°

Map to lattice: [⟨0 -1 -2 -3 -2 -7], ⟨0 -1 -2 1 1 1]]

Mapping: [⟨2 0 0 2 5 -3], ⟨0 1 0 7 5 15], ⟨0 0 1 -4 -3 -8]]

Mapping generators: ~99/70, ~3, ~5

Vals: Template:Val list

Badness: 0.000341

Rym

Comma list: 3025/3024, 4096/4095, 4375/4374

Mapping: [⟨2 0 0 2 5 22], ⟨0 1 0 7 5 -9], ⟨0 0 1 -4 -3 3]]

Mapping generators: ~99/70, ~3, ~5

Vals: Template:Val list

Badness: 0.000549

Vidar

Comma list: 4375/4374, 100663296/100656875

Mapping: [⟨1 0 0 1 5], ⟨0 1 -1 11 1], ⟨0 0 5 -20 -4]]

Mapping generators: 2, ~3, ~55/32

13-limit

Comma list: 4225/4224, 4375/4374, 6656/6655

Mapping: [⟨1 0 0 1 5 6], ⟨0 1 -1 11 1 2], ⟨0 0 5 -20 -4 -7]]

Mapping generators: 2, ~3, ~55/32

Vals: Template:Val list

Bragi

Comma list: 4375/4374, 2097152/2096325

Mapping: [⟨1 0 2 -7 8], ⟨0 1 0 7 -3], ⟨0 0 3 -12 2]]

Mapping generators: 2, ~3, ~320/297

13-limit

Comma list: 2080/2079, 4375/4374, 10985/10976

Mapping: [⟨1 0 2 -7 8 -6], ⟨0 1 0 7 -3 7], ⟨0 0 3 -12 2 -13]]

Mapping generators: 2, ~3, ~14/13

Vals: Template:Val list

Beyla

Comma list: 385/384, 4375/4374

Mapping: [⟨1 0 0 1 6], ⟨0 1 0 7 -6], ⟨0 0 1 -4 3]]

Mapping generators: 2, ~3, ~5

Badness: 0.000721

13-limit

Comma list: 169/168, 325/324, 385/384

Mapping: [⟨1 0 0 1 6 2], ⟨0 1 0 7 -6 4], ⟨0 0 1 -4 3 -2]]

Mapping generators: 2, ~3, ~5

Vals: Template:Val list

Badness: 0.000840

Heimdall

Comma list: 4375/4374, 117649/117612

Mapping: [⟨1 0 0 1 2], ⟨0 2 0 14 37], ⟨0 0 1 -4 -12]]

Mapping generators: 2, ~343/198, ~5