The Forge: Difference between revisions
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'''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 {{monzo|-19 14 -5 3}}. This collection of temperaments provides the foundation for multiple 11-limit and 13-limit temperament families. | '''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 {{monzo|-19 14 -5 3}}. This collection of temperaments provides the foundation for multiple 11-limit and 13-limit temperament families. | ||
= Rank-3 temperaments = | == Rank-3 temperaments == | ||
The parent temperament of this whole collection is a rank-3 temperament. | The parent temperament of this whole collection is a rank-3 temperament. | ||
== Forge == | === Forge === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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From here, this temperament has different 11-limit extensions. | From here, this temperament has different 11-limit extensions. | ||
= Rank-2 temperaments = | == 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. | 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 == | === Forger === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Badness]]: 0.016736 | [[Badness]]: 0.016736 | ||
=== 11-limit === | ==== 11-limit ==== | ||
[[Comma list]]: 243/242, 441/440, 3584000/3557763 | [[Comma list]]: 243/242, 441/440, 3584000/3557763 | ||
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[[Badness]]: 0.052358 | [[Badness]]: 0.052358 | ||
=== 13-limit === | ==== 13-limit ==== | ||
[[Comma list]]: 243/242, 364/363, 441/440, 2200/2197 | [[Comma list]]: 243/242, 364/363, 441/440, 2200/2197 | ||
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[[Badness]]: 0.026974 | [[Badness]]: 0.026974 | ||
=== 17-limit === | ==== 17-limit ==== | ||
[[Comma list]]: 243/242, 363/363, 441/440, 595/594, 2200/2197 | [[Comma list]]: 243/242, 363/363, 441/440, 595/594, 2200/2197 | ||
Revision as of 21:26, 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
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