The Forge: Difference between revisions
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[[Comma list]]: 1640558367/1638400000 | [[Comma list]]: 1640558367/1638400000 | ||
[[Mapping]]: | [[Mapping]]: [{{val| 1 0 1 8 }}, {{val| 0 1 1 -3 }}, {{val| 0 0 -3 -5 }}] | ||
Mapping generators: ~2, ~3, ~1701/1600 | |||
[[Badness]]: | {{Val list|legend=1| 9c, 12, 34, 46, 58, 104c, 113, 125, 159, 171, 742, 913, 1084, 1255, 2681d, 2864, 3035, 3206, 3377, 4290d, 4461bd }} | ||
[[Badness]]: 0.718 × 10<sup>-3</sup> | |||
From here, this temperament has different 11-limit extensions. | From here, this temperament has different 11-limit extensions. | ||
Revision as of 20:00, 13 July 2022
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