Jubilismic family

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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 of rank-3 temperaments tempers out 50/49 in the full 7-limit. It therefore identifies the two septimal tritones 7/5 and 10/7, an identification familiar from 12edo. While many rank-3 temperaments are planar, a jubilismic temperament divides the octave in two. Related to this is the 2.5.7-subgroup {50/49} temperament jubilic.

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 tunings:

  • WE: ~7/5 = 599.6673 ¢, ~3/2 = 702.5906 ¢, ~5/4 = 380.6287 ¢
error map: -0.665 -0.030 -7.016 +10.139]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.4574 ¢, ~5/4 = 380.0086 ¢
error map: 0.000 +0.502 -6.305 +11.183]

Minimax tuning:

[[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 sequence4, 8d, 10, 12, 22, 34d, 48, 60d

Badness (Sintel): 0.561

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 tunings:

  • WE: ~7/5 = 599.6219 ¢, ~3/2 = 702.9722 ¢, ~5/4 = 380.4574 ¢
error map: -0.756 +0.261 -7.369 +9.741 +0.628]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.9249 ¢, ~5/4 = 379.6796 ¢
error map: 0.000 +0.970 -6.634 +10.854 +2.192]

Optimal ET sequence4, 8d, 10e, 12, 22, 34d, 48

Badness (Sintel): 0.673

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 tunings:

  • WE: ~7/5 = 600.8501 ¢, ~3/2 = 694.6084 ¢, ~5/4 = 371.7918 ¢
error map: +1.700 -5.646 -11.121 +7.216 +13.091]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 694.5001 ¢, ~5/4 = 372.9799 ¢
error map: 0.000 -7.455 -13.334 +4.154 +10.662]

Optimal ET sequence10, 12, 22e, 26

Badness (Sintel): 0.827

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:

  • WE: ~7/5 = 596.3068 ¢, ~3/2 = 709.1930 ¢, ~5/4 = 395.2472 ¢
error map: -7.386 -0.148 -5.839 +7.955 +22.830]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 709.6819 ¢, ~5/4 = 391.4911 ¢
error map: 0.000 +7.727 +5.177 +22.665 +48.682]

Optimal ET sequence8d, 10, 12, 22e, 30dee, 42ddeee

Badness (Sintel): 0.861

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 tunings:

  • WE: ~7/5 = 600.0436 ¢, ~3/2 = 706.7073 ¢, ~5/4 = 376.8582 ¢
error map: +0.087 +4.839 -9.281 +8.250 -7.880]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 706.7334 ¢, ~5/4 = 376.9332 ¢
error map: 0.000 +4.778 -9.381 +8.107 -8.051]

Optimal ET sequence8d, 10, 12e, 14c, 22, 58ce

Badness (Sintel): 0.938