Semaphoresmic 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 semaphoresmic family of rank-3 temperaments tempers out 49/48 in the full 7-limit, and thereby identifies the septimal minor third, 7/6, and the septimal whole tone, 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament semaphore, and the 2.3.5.7 49/48 and 81/80 temperament godzilla.

Semiphore

This temperament is also known as semaphoresmic.

Subgroup: 2.3.5.7

Comma list: 49/48

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

mapping generators: ~2, ~7/4, ~5

Lattice basis:

7/6 length = 0.7627, 5/4 length = 2.322

Angle (7/6, 5/4) = 90 degrees

Optimal tunings:

• CTE: ~2 = 1200.0000, ~7/4 = 952.2948, ~5/4 = 386.3137

error map: ⟨0.000 +2.635 0.000 -16.531]

• CWE: ~2 = 1200.0000, ~7/4 = 950.6890, ~5/4 = 382.3522

error map: ⟨0.000 -0.577 -3.962 -18.137]

Optimal ET sequence: 4, 5, 9, 10, 14c, 15, 19

Badness (Sintel): 0.510

Selenium

Subgroup: 2.3.5.7.11

Comma list: 49/48, 56/55

Mapping: [⟨1 0 2 2 5], ⟨0 2 0 1 1], ⟨0 0 1 0 -1]]

Optimal tunings:

• CTE: ~2 = 1200.0000, ~7/4 = 951.8194, ~5/4 = 390.7202

error map: ⟨0.000 +1.684 +4.407 -17.007 +9.781]

• CWE: ~2 = 1200.0000, ~7/4 = 951.7409, ~5/4 = 390.6582

error map: ⟨0.000 +1.527 +4.344 -17.085 +9.765]

Optimal ET sequence: 4, 5, 9, 10, 15, 19, 24, 34

Badness (Sintel): 0.800

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 56/55, 91/90

Mapping: [⟨1 0 2 2 5 -1], ⟨0 2 0 1 1 3], ⟨0 0 1 0 -1 1]]

Optimal tunings:

• CTE: ~2 = 1200.0000, ~7/4 = 951.3729, ~5/4 = 389.6907
• CWE: ~2 = 1200.0000, ~7/4 = 951.2662, ~5/4 = 389.6120

Optimal ET sequence: 5, 9, 10, 15, 19, 24, 34

Badness (Sintel): 0.736

Negric

Subgroup: 2.3.5.7.11

Comma list: 49/48, 225/224

Mapping: [⟨1 2 2 3 0], ⟨0 -4 3 -2 0], ⟨0 0 0 0 1]]

Optimal tunings:

• CTE: ~2 = 1200.0000, ~15/14 = 124.8134, ~11/8 = 551.3179

error map: ⟨0.000 -1.209 -11.874 -18.453 0.000]

• CWE: ~2 = 1200.0000, ~15/14 = 125.4347, ~11/8 = 541.8688

error map: ⟨0.000 -3.694 -10.009 -19.695 -9.449]

Optimal ET sequence: 9, 10, 19, 29, 38d, 67cdde, 105cdddee

Badness (Sintel): 1.31

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 65/64, 91/90

Mapping: [⟨1 2 2 3 0 4], ⟨0 -4 3 -2 0 -3], ⟨0 0 0 0 1 0]]

Optimal tunings:

• CTE: ~2 = 1200.0000, ~14/13 = 124.4571, ~11/8 = 551.3179
• CWE: ~2 = 1200.0000, ~14/13 = 125.3543, ~11/8 = 540.9490

Optimal ET sequence: 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff

Badness (Sintel): 0.755