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

Period: 1\2

Optimal (POTE) generators: ~3/2 = 702.9804, ~5/4 = 380.8399

EDO generators: (2, 1)\4, (6, 3)\10, (7, 4)\12

Scales: jubilismic10, jubilismic12

Technical data

Subgroup: 2.3.5.7

Comma list: 50/49

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⟩]

Eigenmonzos: 2, 3/2, 35/32

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

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

Jubilee

Period: 1\2

Optimal (POTE) generators: ~3/2 = 703.4155, ~5/4 = 380.6973

EDO generators: (5, 3)\8, (7, 4)\12, (8, 4)\14

Scales:

Technical data

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]]

Badness: 0.600 × 10^-3

Festival

Period: 1\2

Optimal (POTE) generators: ~3/2 = 693.6257, ~5/4 = 371.2658

EDO generators: (6, 3)\10, (7, 4)\12, (8, 4)\14

Scales:

Technical data

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]]

Badness: 0.689 × 10^-3

Fiesta

Period: 1\2

Optimal (POTE) generators: ~3/2 = 713.5853, ~5/4 = 397.6952

EDO generators: (5, 3)\8, (6, 3)\10, (7, 4)\12

Scales:

Technical data

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]]

Badness: 0.717 × 10^-3

Jamboree

Period: 1\2

Optimal (POTE) generators: ~3/2 = 706.6559, ~5/4 = 376.8308

EDO generators: (5, 3)\8, (6, 3)\10, (8, 4)\14

Scales:

Technical data

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]]

Badness: 0.781 × 10^-3