The Forge: Difference between revisions

Revision as of 02:33, 14 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

Template:Val list

Badness: 0.718 × 10^-3

From here, this temperament has different 11-limit extensions.

@@ Line 19: / Line 19: @@
 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]]: [{{val| 1 -3 -17 -8 }}, {{val| 0 14 59 33 }}]
-Mapping generators: ~2, ~6400/5103
-{{Val list|legend=1| 55c, 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d }}
-[[Badness]]: 0.016736
-==== 11-limit ====
-[[Comma list]]: 243/242, 441/440, 3584000/3557763
-[[Mapping]]: [{{val| 1 -3 -17 -8 -8 }}, {{val| 0 14 59 33 35 }}]
-Mapping generators: ~2, ~6400/5103
-{{Val list|legend=1| 55c, 58, 113, 171 }}
-[[Badness]]: 0.052358
-==== 13-limit ====
-[[Comma list]]: 243/242, 364/363, 441/440, 2200/2197
-[[Mapping]]: [{{val| 1 -3 -17 -8 -8 -13 }}, {{val| 0 14 59 33 35 51 }}]
-Mapping generators: ~2, ~6400/5103
-{{Val list|legend=1| 55cf, 58, 113, 171 }}
-[[Badness]]: 0.026974
-==== 17-limit ====
-[[Comma list]]: 243/242, 363/363, 441/440, 595/594, 2200/2197
-[[Mapping]]: [{{val| 1 -3 -17 -8 -8 -13 9 }}, {{val| 0 14 59 33 35 51 -15 }}]
-Mapping generators: ~2, ~64/51
-{{Val list|legend=1| 58, 113, 171 }}
-[[Badness]]: 0.023205

The Forge: Difference between revisions

Revision as of 02:33, 14 July 2022

Rank-3 temperaments

Forge

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