Semiporwellismic clan

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 semiporwellismic clan of rank-3 temperaments tempers out the semiporwellisma (monzo: [14 -3 -1 0 -2⟩, ratio: 16384/16335).

For the rank-4 temperament, see Catalog of rank-4 temperaments #Semiporwellismic (16384/16335).

Semiporwellic

Subgroup: 2.3.5.11

Comma list: 16384/16335

Subgroup-val mapping: [⟨1 0 0 0 7], ⟨0 1 1 0 -2], ⟨0 0 2 0 -1]]

mapping generators: ~2, ~3, ~128/99

Optimal tunings:

• WE: ~2 = 1199.7329 ¢, ~3/2 = 702.3657 ¢, ~128/99 = 442.1589 ¢

error map: ⟨-0.267 +0.144 +0.103 +0.456]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.5107 ¢, ~128/99 = 442.2243 ¢

error map: ⟨0.000 +0.556 +0.646 +1.436]

Optimal ET sequence: 19, 22, 41, 46, 65, 87, 152, 369, 521e, 1194bcee, 1305bcee, 1457bceee, 1609bcceee, 1674bcceee, 1826bcceeee

Badness (Sintel): 0.761

Overview to extensions

Temperaments discussed elsewhere are:

• Sensamagic (+385/384 or 896/891) → Sensamagic family
• Kapo (+3025/3024 or 5120/5103) → Aberschismic family
• Semiporwell (+6144/6125 or 9801/9800) → Porwell family

Considered below is the add-31 subgroup temperament of semiporwellic.

Subgroup extensions

Semiporwellic (2.3.5.11.31)

Subgroup: 2.3.5.11.31

Comma list: 496/495, 961/960

Subgroup-val mapping: [⟨1 0 0 0 7], ⟨0 1 1 0 -2], ⟨0 0 2 0 -1]]

Optimal tunings:

• WE: ~2 = 1199.7927 ¢, ~3/2 = 702.4205 ¢, ~31/24 = 442.1885 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.5302 ¢, ~31/24 = 442.2374 ¢

Optimal ET sequence: 19, 22, 41, 46, 65, 87, 152, 369, 521e

Badness (Sintel): 0.201