Jubilismic family

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

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⟩]

unchanged-interval (eigenmonzo) 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