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 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 ==

~~The parent temperament of this whole collection is a rank-3 temperament.~~

=== Forge ===

The parent temperament of this whole collection is a rank-3 temperament.

Subgroup: 2.3.5.7

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Mapping generators: ~2, ~3, ~1701/1600

{{~~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 }}

[[Tuning ranges]]:

{{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 }}

[[Badness]]: 0.718 × 10<sup>-3</sup>

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

==== 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:

* [[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]]

@@ Line 1: / Line 1: @@
-'''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 ==
-The parent temperament of this whole collection is a rank-3 temperament.
 === Forge ===
+The parent temperament of this whole collection is a rank-3 temperament.
 Subgroup: 2.3.5.7
@@ Line 14: / Line 16: @@
 Mapping generators: ~2, ~3, ~1701/1600
-{{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 }}
+[[Tuning ranges]]:
+{{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 }}
 [[Badness]]: 0.718 × 10<sup>-3</sup>
-From here, this temperament has different 11-limit extensions.
+==== 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:
+* [[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]]