Diaschismic rank three family

From Xenharmonic Wiki
(Redirected from Julius)
Jump to navigation Jump to search

These are the rank-3 temperaments tempering out the diaschisma, 2048/2025. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

Julius aka varda

Subgroup: 2.3.5.7.11

Comma list: 176/175, 896/891

Mapping: [2 0 11 0 14], 0 1 -2 0 -4], 0 0 0 1 1]]

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

Lattice basis:

3/2, 9/7
Angle (3/2, 9/7) = 82.289 degrees

Minimax tuning:

[[1 0 0 0 0, [11/8 1/2 -1/4 0 0, [11/4 -1 1/2 0 0, [-1/8 3/2 -5/4 0 1, [11/8 -1/2 -1/4 0 1]
Eigenmonzos (unchanged intervals): 2, 12/11, 10/9

Vals12, 22, 34d, 46, 58, 68, 80, 126, 184c, 206cd, 264bccde

Badness: 0.728 × 10-3

Julius[22] hobbit transversal:

28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2

Julius[24] hobbit transversal

28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2

Varda

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 352/351, 364/363

Mapping: [2 0 11 0 14 24], 0 1 -2 0 -4 -7], 0 0 0 1 1 1]]

Vals: 22, 46, 58, 80, 138cde, 242cde, 322bcde

Badness: 0.970 × 10-3

Julius

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 325/324, 896/891

Mapping: [2 0 11 0 14 -18], 0 1 -2 0 -4 8], 0 0 0 1 1 0]]

Vals: 12f, 22f, 34d, 46, 68, 80, 148d, 228bcd

Badness: 1.78 × 10-3

Augustus

Subgroup: 2.3.5.7.11

Comma list: 385/384, 1232/1215

Mapping: [2 0 11 0 3], 0 1 -2 0 3], 0 0 0 1 -1]]

Minimax tuning:

[|1 0 0 0 0 }}, |11/8 1/2 -1/4 0 0 }}, |11/4 -1 1/2 0 0 }}, |45/16 3/4 -3/8 1/2 -1/2 }}, |45/16 3/4 -3/8 -1/2 1/2 }}]
Eigenmonzos (unchanged intervals): 2, 10/9, 14/11

Vals10, 12e, 22, 46, 68, 114, 170b

Badness: 1.58 × 10-3

Tiberius

Subgroup: 2.3.5.7.11

Comma list: 441/440, 2048/2025

Mapping: [2 0 11 0 -17], 0 1 -2 0 4], 0 0 0 1 2]]

Minimax tuning:

[[1 0 0 0 0, [11/8 1/2 -1/4 0 0, [11/4 -1 1/2 0 0, [0 0 0 1 0, [-3 2 -1 2 0]
Eigenmonzos (unchanged intervals): 2, 9/5, 7

Vals46, 58, 104c, 160, 162ce, 172ce, 218ce

Badness: 1.71 × 10-3

Claudius

Subgroup: 2.3.5.7.11

Comma list: 540/539, 2048/2025

Mapping: [2 0 11 0 15], 0 1 -2 0 1], 0 0 0 1 -2]]

Minimax tuning:

[[1 0 0 0 0, [9/7 0 -3/7 2/7 1/7, [41/14 0 6/7 -4/7 -2/7, [41/14 0 -1/7 3/7 -2/7, [41/14 0 -1/7 -4/7 5/7]
Eigenmonzos (unchanged intervals): 2, 7/5, 11/5

Vals22, 46e, 48c, 58, 80, 138cde, 218cde, 286bcddeee, 366bccdddeee

Badness: 1.97 × 10-3