Jubilismic family

The jubilismic family contains temperaments that temper out the jubilisma (50/49) (also called tritonic diesis, or septimal sixth-tone). It therefore identifies the two septimal tritones 7/5 and 10/7, an identification familiar from 12edo. While most rank-three temperaments are planar, a jubilismic temperament divides the octave in two.

Jubilismic

Subgroup: 2.3.5.7

Comma list: 50/49

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

mapping generators: ~7/5, ~3, ~5

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 702.9804, ~5/4 = 380.8399

Minimax tuning:

• 7- and 9-odd-limit

[[1 0 0 0⟩, [0 1 0 0⟩, [-1/4 0 1/2 1/2⟩, [1/4 0 1/2 1/2⟩]

eigenmonzo (unchanged-interval) basis: 2.3.35

Optimal ET sequence: 4, 8d, 10, 12, 22, 34d, 48

Scales: jubilismic10, jubilismic12

Jubilee

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98

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

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 703.4155, ~5/4 = 380.6973

Optimal ET sequence: 4, 8d, 10e, 12, 22, 34d, 48

Badness: 0.600 × 10^-3

Festival

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49

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

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 693.6257, ~5/4 = 371.2658

Optimal ET sequence: 10, 12, 22e, 26

Badness: 0.689 × 10^-3

Fiesta

Subgroup: 2.3.5.7.11

Comma list: 50/49, 56/55

Mapping: [⟨2 0 0 1 7], ⟨0 1 0 0 0], ⟨0 0 1 1 0]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 713.5853, ~5/4 = 397.6952

Optimal ET sequence: 8d, 10, 12, 22e

Badness: 0.717 × 10^-3

Jamboree

Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54

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

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.6559, ~5/4 = 376.8308

Optimal ET sequence: 8d, 10, 12e, 14c, 22

Badness: 0.781 × 10^-3