The Forge: Difference between revisions
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'''The Forge''' is a collection of temperaments of | '''The Forge''' is a collection of temperaments of temperaments, 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 mostly rank-3 temperaments provides the foundation for multiple 11-limit and 13-limit temperament families. | ||
== Rank-3 temperaments == | == Rank-3 temperaments == | ||
== Forge == | |||
The parent temperament of this whole collection is a rank-3 temperament. | The parent temperament of this whole collection is a rank-3 temperament. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Mapping generators: ~2, ~3, ~1701/1600 | Mapping generators: ~2, ~3, ~1701/1600 | ||
[[Tuning ranges]]: | |||
{{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 }} | {{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 }} | ||
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[[Badness]]: 0.718 × 10<sup>-3</sup> | [[Badness]]: 0.718 × 10<sup>-3</sup> | ||
=== Eleven limit children === | |||
The next comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 11-limit family member we are looking at. Some of the options are: | |||
* [[243/242]], leading to the 34p & 58 & 113 temperament | |||
* [[441/440]], leading to the 12 & 46 & 113 temperament | |||
* [[6250/6237]], leading to the 12 & 34p & 159 temperament | |||
* [[8019/8000]], leading to the 46 & 58 & 125 temperament | |||
Revision as of 17:50, 14 July 2022
The Forge is a collection of temperaments of temperaments, 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 mostly rank-3 temperaments provides the foundation for multiple 11-limit and 13-limit temperament families.
Rank-3 temperaments
Forge
The parent temperament of this whole collection is a rank-3 temperament.
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
Eleven limit children
The next comma of the normal comma list defines which 11-limit family member we are looking at. Some of the options are: