The Forge
The Forge is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the forge comma – the unnoticeable comma with the ratio 1640558367/1638400000, and a monzo of [-19 14 -5 3⟩. This collection of temperaments provides the foundation for multiple 11-limit and 13-limit temperament families.
Rank-3 temperaments
The parent temperament of this whole collection is a rank-3 temperament.
Forge
Subgroup: 2.3.5.7
Comma list: 1640558367/1638400000
Mapping: [⟨1 0 1 8], ⟨0 1 1 -3], ⟨0 0 -3 -5]]
Mapping generators: ~2, ~3, ~1701/1600
Badness: 0.718 × 10-3
From here, this temperament has different 11-limit extensions.
Rank-2 temperaments
Many of the rank-2 temperaments that temper out the Forge comma are controrted, considered below is the only one found so far that isn't.
Forger
Subgroup: 2.3.5.7
Comma list: 2401/2400, 14348907/14336000