Ptolemismic clan

This page discusses some rank-3 temperaments tempering out the ptolemisma, 100/99. But we can start with the rank-4 temperament.

Ptolemismic

Subgroup: 2.3.5.7.11

Comma list: 100/99

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

POTE generators: ~3/2 = 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803

Template:Val list *

* optimal patent val: 104

Badness: 0.0225 × 10^-6

Ptolemy

Subgroup: 2.3.5.11

Comma list: 100/99

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

POTE generators: ~3/2 = 704.9532, ~5/4 = 384.0675

Badness: 0.0226 × 10^-3