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-subgroup {49/48} temperament semaphore, and the 7-limit {49/48, 81/80} temperament godzilla.

Semaphoresmic a.k.a. semiphore

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:

• WE: ~2 = 1202.8324 ¢, ~7/4 = 951.8567 ¢, ~5/4 = 380.5997 ¢

error map: ⟨+2.832 +1.758 -0.049 -11.304]

• 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, 48d, 53d, 67cdd, 86cdd

Badness (Sintel): 0.510

2.3.5.7.13 subgroup

Subgroup: 2.3.5.7.13

Comma list: 49/48, 91/90

Sval mapping: [⟨1 0 0 2 -1], ⟨0 2 0 1 3], ⟨0 0 1 0 1]]

Optimal tunings:

• WE: ~2 = 1202.7771 ¢, ~7/4 = 951.9629 ¢, ~5/4 = 381.0131 ¢
• CWE: ~2 = 1200.0000 ¢, ~7/4 = 950.6703 ¢, ~5/4 = 382.2972 ¢

Optimal ET sequence: 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd

Badness (Sintel): 0.380

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:

• WE: ~2 = 1200.0412 ¢, ~7/4 = 951.7616 ¢, ~5/4 = 390.6621 ¢

error map: ⟨+0.041 +1.568 +4.431 -16.982 +9.905]

• 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:

• WE: ~2 = 1200.0790 ¢, ~7/4 = 951.3067 ¢, ~5/4 = 389.6213 ¢
• 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:

• WE: ~2 = 1203.4810 ¢, ~15/14 = 125.9724 ¢, ~11/8 = 540.7985 ¢

error map: ⟨+3.481 +1.118 -1.435 -10.328 -0.076]

• 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:

• WE: ~2 = 1203.6981 ¢, ~14/13 = 125.9545 ¢, ~11/8 = 540.1440 ¢
• 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