Semiporwellismic clan

The semiporwellismic clan of rank-3 temperaments tempers out the semiporwellisma, 16384/16335 = [14 -3 -1 0 -2⟩.

Temperaments discussed elsewhere are:

• Sensamagic, {385/384, 896/891} → Sensamagic family
• Kapo, {3025/3024, 5120/5103} → Hemifamity family
• Semiporwell, {6144/6125, 9801/9800} → Porwell family

Considered below is the no-7 subgroup temperament, but we can begin by looking at the rank-4 temperament.

Semiporwellismic

Subgroup: 2.3.5.7.11

Comma list: 16384/16335

Mapping: [⟨1 0 0 0 7], ⟨0 1 1 0 -2], ⟨0 0 2 0 -1], ⟨0 0 0 1 0]]

Mapping generators: ~2, ~3, ~128/99, ~7

Optimal GPV sequence: 19, 22, 41, 65d, 68, 84, 87, 111, 130, 152, 239, 282, 328, 369, 521e, 1370bcdeee, 1411bcdeee, 1609bccdeee

Badness: 0.219 × 10^-6

No-7 semiporwellismic

Subgroup: 2.3.5.11

Comma list: 16384/16335

Sval mapping: [⟨1 0 0 0 7], ⟨0 1 1 0 -2], ⟨0 0 2 0 -1]]

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

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

Badness: 0.0922 × 10^-3