Porwell 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 porwell family of rank-3 regular temperaments tempers out the porwell comma (monzo: [11 1 -3 -2⟩, ratio: 6144/6125).

Porwell

Porwell is catalogued as hewuermity in Graham Breed's temperament finder.

Subgroup: 2.3.5.7

Comma list: 6144/6125

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

mapping generators: ~2, ~3, ~35/32

Optimal tunings:

• WE: ~2 = 1199.7101 ¢, ~3/2 = 702.1785 ¢, ~35/32 = 157.4296 ¢

error map: ⟨-0.290 -0.066 +0.426 +0.415]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1875 ¢, ~35/32 = 157.3944 ¢

error map: ⟨0.000 +0.233 +1.085 +1.170]

Minimax tuning:

• 7- and 9-odd-limit

[[1 0 0 0⟩, [0 1 0 0⟩, [11/5 1/5 2/5 -2/5⟩, [11/5 1/5 -3/5 3/5⟩]

unchanged-interval (eigenmonzo) basis: 2.3.7/5

Optimal ET sequence: 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381

Badness (Sintel): 0.628

Projection pairs: 3 6125/2048 to 2.5.7

Zeus

Main article: Zeus

Zeus tempers out 121/120, 176/175, and 385/384. See Biyatismic clan #Zeus.

Jupiter

Subgroup: 2.3.5.7.11

Comma list: 540/539, 5632/5625

Mapping: [⟨1 0 1 4 -5], ⟨0 1 1 -1 6], ⟨0 0 -2 3 -8]]

Optimal tunings:

• WE: ~2 = 1199.7232 ¢, ~3/2 = 701.9496 ¢, ~35/32 = 157.4667 ¢

error map: ⟨-0.277 -0.282 +0.149 +0.794 +0.369]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9677 ¢, ~35/32 = 157.4315 ¢

error map: ⟨0.000 +0.013 +0.791 +1.501 +1.037]

Optimal ET sequence: 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde

Badness (Sintel): 0.676

Hera

Hera tempers out 8019/8000, the trimitone comma. It was named by Flora Canou in 2021 as a more complex counterpart of zeus.

Subgroup: 2.3.5.7.11

Comma list: 6144/6125, 8019/8000

Mapping: [⟨1 0 1 4 9], ⟨0 1 1 -1 -3], ⟨0 0 -2 3 -6]]

Optimal tunings:

• WE: ~2 = 1199.8410 ¢, ~3/2 = 701.7105 ¢, ~35/32 = 157.1441 ¢

error map: ⟨-0.159 -0.403 +0.791 +0.419 -0.268]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.8035 ¢, ~35/32 = 157.1741 ¢

error map: ⟨0.000 -0.153 +1.140 +0.894 +0.232]

Optimal ET sequence: 46, 53, 84, 99, 130, 183, 313, 359, 542c, 672c

Badness (Sintel): 2.68

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 2080/2079, 4096/4095

Mapping: [⟨1 0 1 4 9 7], ⟨0 1 1 -1 -3 -2], ⟨0 0 -2 3 -6 -1]]

Optimal tunings:

• WE: ~2 = 1199.9170 ¢, ~3/2 = 701.6155 ¢, ~35/32 = 157.1791 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.6672 ¢, ~35/32 = 157.1942 ¢

Optimal ET sequence: 46, 53, 84, 99, 130, 183, 313

Badness (Sintel): 1.21

Semiporwell

Named by Flora Canou in 2021, semiporwell tempers out 9801/9800, the kalisma, as well as 16384/16335, the semiporwellisma.

Subgroup: 2.3.5.7.11

Comma list: 6144/6125, 9801/9800

Mapping: [⟨2 0 0 11 14], ⟨0 1 1 -1 -2], ⟨0 0 2 -3 -1]]

mapping generators: ~99/70, ~3, ~128/99

Optimal tunings:

• WE: ~99/70 = 599.8385 ¢, ~3/2 = 702.2722 ¢, ~128/99 = 442.3712 ¢

error map: ⟨-0.323 -0.006 +0.378 +0.335 +0.152]

• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.4280 ¢, ~128/99 = 442.5202 ¢

error map: ⟨0.000 +0.473 +1.155 +1.185 +1.306]

Optimal ET sequence: 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee

Badness (Sintel): 1.51

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 3584/3575

Mapping: [⟨2 0 0 11 14 15], ⟨0 1 1 -1 -2 -1], ⟨0 0 2 -3 -1 -6]]

Optimal tunings:

• WE: ~99/70 = 599.8357 ¢, ~3/2 = 702.2041 ¢, ~84/65 = 442.4690 ¢
• CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.3576 ¢, ~84/65 = 442.6282 ¢

Optimal ET sequence: 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff

Badness (Sintel): 1.14