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.
+{{Technical data page}}
+'''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 ==
-The parent temperament of this whole collection is a rank-3 temperament.
-= 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 ==
+=== Forge ===
+The parent temperament of this whole collection is a rank-3 temperament.
 Subgroup: 2.3.5.7
-[[Comma list]]: 2401/2400, 14348907/14336000
+[[Comma list]]: 1640558367/1638400000
-[[Mapping]]:
-{{Val list|legend=1| }}
-[[Badness]]:
-[[Complexity spectrum]]:
-=== 11-limit ===
-[[Comma list]]:
-[[Mapping]]:
-{{Val list|legend=1| }}
-[[Badness]]:
-[[Complexity spectrum]]:
+[[Mapping]]: [{{val| 1 0 1 8 }}, {{val| 0 1 1 -3 }}, {{val| 0 0 -3 -5 }}]
-=== 13-limit ===
+Mapping generators: ~2, ~3, ~1701/1600
-[[Comma list]]:
+[[Tuning ranges]]:
-[[Mapping]]:
+{{Optimal ET sequence|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| }}
+[[Badness]]: 0.718 × 10<sup>-3</sup>
-[[Badness]]:
+==== Eleven limit children ====
+The next comma of the [[Normal lists #Normal interOptimal ET sequence|normal comma list]] defines which 11-limit family member we are looking at.  Some of the options are:
-[[Complexity spectrum]]:
+* [[385/384]], leading to the 113 & 125 & 159 temperament
+* [[441/440]], leading to the 12 & 46 & 113 temperament
+* [[2835/2816]], leading to the 12 & 34p & 113 temperament
+* [[6250/6237]], leading to the 12 & 34p & 159 temperament- named "Ring"
+* [[8019/8000]], leading to the 46 & 58 & 125 temperament- named "Trimmer"
+[[Category:Temperament collections]]