Ptolemismic temperaments

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

Temperaments discussed elsewhere include:

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

Vals7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e *

* optimal patent val: 104

Badness: 0.0225 × 10-6

No-7 ptolemismic

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

Vals7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e

Badness: 0.0226 × 10-3