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

Mapping: [⟨1 -3 -17 -8], ⟨0 14 59 33]]

Mapping generators: ~2, ~6400/5103

Badness: 0.016736

11-limit

Comma list: 243/242, 441/440, 3584000/3557763

Mapping: [⟨1 -3 -17 -8 -8], ⟨0 14 59 33 35]]

Mapping generators: ~2, ~6400/5103

Badness: 0.052358

13-limit

Comma list: 243/242, 364/363, 441/440, 2200/2197

Mapping: [⟨1 -3 -17 -8 -8 -13], ⟨0 14 59 33 35 51]]

Mapping generators: ~2, ~6400/5103

Badness: 0.026974

17-limit

Comma list: 243/242, 363/363, 441/440, 595/594, 2200/2197

Mapping: [⟨1 -3 -17 -8 -8 -13 9], ⟨0 14 59 33 35 51 -15]]

Mapping generators: ~2, ~64/51

Badness: 0.023205