Father 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 father family is a family of rank-2 temperaments which temper out the classic diatonic semitone, 16/15. This equates 4/3 with 5/4 and 8/5 with 3/2, so the generator is a "fourth-third" (or "fifth-sixth"), hence the name father. In a sense, what father is all about is using semisixths or subfourths and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", father is close to the edge of what can be sensibly called a temperament at all. In other words, it is an exotemperament.

Father

Main article: Father

Subgroup: 2.3.5

Comma list: 16/15

Mapping: [⟨1 0 4], ⟨0 1 -1]]

mapping generators: ~2, ~3

Optimal tunings:

• WE: ~2 = 1180.875 ¢, ~3/2 = 732.129 ¢

error map: ⟨-19.125 +11.048 +24.181]

• CWE: ~2 = 1200.000 ¢, ~3/2 = 742.290 ¢

error map: ⟨0.000 +40.335 +71.396]

Minimax tuning:

• 5-odd-limit: ~3/2 = [1 1/2 -1/2⟩

unchanged-interval (eigenmonzo) basis: 2.5/3

Optimal ET sequence: 1, 2, 3, 5, 8, 13c, 21bcc

Badness (Sintel): 0.349

Overview to extensions

Strong extensions of father to include an approximation of harmonic 7 are septimal father (5 & 8d), mother (2 & 3), and pater (3 & 5d), all considered below.

Temperaments discussed elsewhere include:

• Baba → Semaphoresmic clan
• Walid → Jubilismic clan

Septimal father

Main article: Father

See also: Trienstonic clan

Septimal father tempers out 28/27, making it a strong extension of trienstonian.

Subgroup: 2.3.5.7

Comma list: 16/15, 28/27

Mapping: [⟨1 0 4 -2], ⟨0 1 -1 3]]

Optimal tunings:

• WE: ~2 = 1180.634 ¢, ~3/2 = 730.027 ¢

error map: ⟨-19.366 +8.706 +25.561 +1.890]

• CWE: ~2 = 1200.000 ¢, ~3/2 = 738.443 ¢

error map: ⟨0.000 +36.488 +75.244 +46.502]

Minimax tuning:

• 7-odd-limit: ~3/2 = [1/2 0 -1/4 1/4⟩

unchanged-interval (eigenmonzo) basis: 2.7/5

• 9-odd-limit: ~3/2 = [1 -2 0 1⟩ = 14/9

unchanged-interval (eigenmonzo) basis: 2.9/7

Optimal ET sequence: 2d, 3d, 5, 8d, 13cd, 21bccdd

Badness (Sintel): 0.539

11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 28/27

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

Optimal tunings:

• WE: ~2 = 1180.894 ¢, ~3/2 = 735.260 ¢
• CWE: ~2 = 1200.000 ¢, ~3/2 = 743.387 ¢

Optimal ET sequence: 2de, 3de, 5, 8d

Badness (Sintel): 0.681

Mother

Subgroup: 2.3.5.7

Comma list: 16/15, 21/20

Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]

Optimal tunings:

• WE: ~2 = 1186.985 ¢, ~3/2 = 713.743 ¢

error map: ⟨-13.015 -1.228 +60.898 -48.372]

• CWE: ~2 = 1200.000 ¢, ~3/2 = 722.866 ¢

error map: ⟨0.000 +20.911 +90.820 -14.559]

Optimal ET sequence: 2, 3, 5

Badness (Sintel): 0.611

11-limit

Subgroup: 2.3.5.7.11

Comma list: 11/10, 16/15, 21/20

Mapping: [⟨1 0 4 6 5], ⟨0 1 -1 -2 -1]]

Optimal tunings:

• WE: ~2 = 1192.016 ¢, ~3/2 = 712.592 ¢
• CWE: ~2 = 1200.000 ¢, ~3/2 = 743.387 ¢

Optimal ET sequence: 2, 3, 5

Badness (Sintel): 0.726

Pater

Subgroup: 2.3.5.7

Comma list: 16/15, 126/125

Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]

Optimal tunings:

• WE: ~2 = 1179.316 ¢, ~3/2 = 740.132 ¢

error map: ⟨-20.684 +17.493 +11.503 +6.412]

• CWE: ~2 = 1200.000 ¢, ~3/2 = 755.156 ¢

error map: ⟨0.000 +53.201 +58.530 +55.392]

Optimal ET sequence: 3, 5d, 8d, 27bbccdd

Badness (Sintel): 1.34

11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 100/99

Mapping: [⟨1 0 4 11 10], ⟨0 1 -1 -5 -4]]

Optimal tunings:

• WE: ~2 = 1180.290 ¢, ~3/2 = 739.054 ¢
• CWE: ~2 = 1200.000 ¢, ~3/2 = 753.774 ¢

Optimal ET sequence: 3, 5de, 8d

Badness (Sintel): 1.17