Maja family

The maja family of rank-2 temperaments tempers out the maja comma, [-3 -23 17⟩ = 762939453125/753145430616.

Maja

Subgroup: 2.3.5

Comma list: 762939453125/753145430616

Mapping: [⟨1 8 11], ⟨0 -17 -23]]

Optimal tuning (POTE): ~2 = 1\1, ~125/81 = 747.198

Optimal ET sequence: 8, 45, 53, 432, 485, 538, 591, 644, 697, 750, 803c

Badness: 0.361013

Septimal maja

Subgroup: 2.3.5.7

Comma list: 2430/2401, 3125/3087

Mapping: [⟨1 8 11 13], ⟨0 -17 -23 -27]]

Wedgie: ⟨⟨17 23 27 -3 -5 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~125/81 = 747.145

Optimal ET sequence: 8d, 45, 53

Badness: 0.089454

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 121/120, 3125/3087

Mapping: [⟨1 8 11 13 11], ⟨0 -17 -23 -27 -20]]

Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.100

Optimal ET sequence: 8d, 45e, 53

Badness: 0.049991

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 121/120, 169/168, 275/273

Mapping: [⟨1 8 11 13 11 12], ⟨0 -17 -23 -27 -20 -22]]

Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.095

Optimal ET sequence: 8d, 45ef, 53

Badness: 0.027532

Majo

Subgroup: 2.3.5.7

Comma list: 6144/6125, 1250000/1240029

Mapping: [⟨1 8 11 -7], ⟨0 -17 -23 26]]

Wedgie: ⟨⟨17 23 -26 -3 -89 -125]]

Optimal tuning (POTE): ~2 = 1\1, ~125/81 = 747.264

Optimal ET sequence: 53, 167, 220, 493bd, 713bdd

Badness: 0.140489

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2200/2187, 3388/3375, 6144/6125

Mapping: [⟨1 8 11 -7 31], ⟨0 -17 -23 26 -73]]

Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.287

Optimal ET sequence: 53, 114e, 167, 220, 387bd

Badness: 0.081931

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 1001/1000, 2704/2695

Mapping: [⟨1 8 11 -7 31 12], ⟨0 -17 -23 26 -73 -22]]

Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.286

Optimal ET sequence: 53, 114e, 167, 220, 387bd

Badness: 0.043128