Augmented family: Difference between revisions

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Mapping: {{Mapping| 3 1 7 6 8 | 0 3 0 2 2 }}

~~: mapping generators: ~5/4, ~15/11~~

Optimal tunings:

* WE: ~5/4 = 397.~~495~~{{c}}, ~15/11 = 499.~~096~~{{c}} (~12/11 = 101.~~601~~{{c}})

* WE: ~5/4 = 397.4954{{c}}, ~15/11 = 499.0962{{c}} (~15/14 = 101.6008{{c}})

* CWE: ~5/4 = 400.~~000~~{{c}}, ~15/11 = 500.~~775~~{{c}} (~12/11 = 100.~~775~~{{c}})

* CWE: ~5/4 = 400.0000{{c}}, ~15/11 = 500.7745{{c}} (~15/14 = 100.7745{{c}})

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== Subgroup extensions ==

=== 2.3.5.19 subgroup ~~(3 & 12~~) ===

=== Augmented (2.3.5.19 subgroup) ===

Augmented ~~temperament~~ works on the 2.3.5.19 subgroup very well, where the 1/3-octave period stands in for ~5/4, ~19/15, and ~24/19.

Augmented works on the [[2.3.5.19 subgroup]] very well, where the 1/3-octave period stands in for ~5/4, ~19/15, and ~24/19.

[[Subgroup]]: 2.3.5.19

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~~: sval mapping generators: ~5/4, ~3~~

[[Optimal tuning]]s:

* [[WE]]: ~5/4 = 399.~~075~~{{c}}, ~3/2 = 705.~~062~~{{c}} (~19/16 = ~~305~~.~~986~~{{c}})

* [[WE]]: ~5/4 = 399.0754{{c}}, ~3/2 = 705.0615{{c}} (~19/18 = 93.0893{{c}})

* [[CWE]]: ~5/4 = 400.~~000~~{{c}}, ~3/2 = 705.~~107~~{{c}} (~19/16 = ~~305~~.~~107~~{{c}})

* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 705.1072{{c}} (~19/18 = 94.8928{{c}})

[[Badness]] (Sintel): 0.264

@@ Line 653: / Line 653: @@
 Mapping: {{Mapping| 3 1 7 6 8 | 0 3 0 2 2 }}
-: mapping generators: ~5/4, ~15/11
 Optimal tunings:
-* WE: ~5/4 = 397.495{{c}}, ~15/11 = 499.096{{c}} (~12/11 = 101.601{{c}})
+* WE: ~5/4 = 397.4954{{c}}, ~15/11 = 499.0962{{c}} (~15/14 = 101.6008{{c}})
-* CWE: ~5/4 = 400.000{{c}}, ~15/11 = 500.775{{c}} (~12/11 = 100.775{{c}})
+* CWE: ~5/4 = 400.0000{{c}}, ~15/11 = 500.7745{{c}} (~15/14 = 100.7745{{c}})
 {{Optimal ET sequence|legend=0| 3b, 9bde, 12 }}
@@ Line 665: / Line 663: @@
 == Subgroup extensions ==
-=== 2.3.5.19 subgroup (3 & 12) ===
+=== Augmented (2.3.5.19 subgroup) ===
-Augmented temperament works on the 2.3.5.19 subgroup very well, where the 1/3-octave period stands in for ~5/4, ~19/15, and ~24/19.
+Augmented works on the [[2.3.5.19 subgroup]] very well, where the 1/3-octave period stands in for ~5/4, ~19/15, and ~24/19.
 [[Subgroup]]: 2.3.5.19
@@ Line 673: / Line 671: @@
 {{Mapping|legend=2| 3 0 7 8 | 0 1 0 1 }}
-: sval mapping generators: ~5/4, ~3
 [[Optimal tuning]]s:
-* [[WE]]: ~5/4 = 399.075{{c}}, ~3/2 = 705.062{{c}} (~19/16 = 305.986{{c}})
+* [[WE]]: ~5/4 = 399.0754{{c}}, ~3/2 = 705.0615{{c}} (~19/18 = 93.0893{{c}})
-* [[CWE]]: ~5/4 = 400.000{{c}}, ~3/2 = 705.107{{c}} (~19/16 = 305.107{{c}})
+* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 705.1072{{c}} (~19/18 = 94.8928{{c}})
-{{Optimal ET sequence|legend=1| 3, 9, 12, 27, 39 }}
+{{Optimal ET sequence|legend=1| 3, 9, 12, 27, 39, 51c, 90cch }}
 [[Badness]] (Sintel): 0.264