Blare comma: Difference between revisions

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== Temperaments ==

=== Loudspeaker ===

Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments.

=== Rank-3 ===

==== Rank-3 ====

==== Loudspeaker ====

===== Loudspeaker =====

[[Subgroup]]: 2.9.7.11

[[Comma list]]: {{monzo| -51 -~~24 0~~ 12 16 }}

[[Comma list]]: {{monzo| -51 -12 12 16 }}

[[Optimal tuning]]s:

* [[CTE]]: ~{{monzo| 13 ~~6 0~~ -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo| 16 ~~8 0~~ -4 -5 }} = 183.772

* [[CTE]]: ~{{monzo| 13 3 -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo| 16 4 -4 -5 }} = 183.772

{{Optimal ET sequence|legend=1| 20, 32}}[+9], {{EDOs|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652}}[-9], {{EDOs|254860}}[-9]

[[Badness]] (~~Smith~~): ~~7 × 10<sup>-6</sup>~~

[[Badness]] (Sintel): 0.78992

=== ~~Rank-2~~ ===

=== Blazen ===

~~==== Microphone ====~~

Tempering out this interval in the no-fives [[11-limit]] (2.3.7.11 subgroup) leads to the '''blazen family'''.

~~{{see also| 44th~~-~~octave temperaments}}~~

~~This temperament additionally tempers~~ out the ~~parismina~~ [1 -~~26 0 2 10⟩, which is even smaller than~~ the blare ~~comma. Surprisingly, this temperament admits an optimal generator very close to [[3/2]]~~.

=== Blare ===

Tempering out this interval in the full [[11-limit]] leads to the '''blare family'''.

[[~~Subgroup]]: 2.9.7.11~~

[[Category:Commas named for their regular temperament properties]]

~~[[Comma list]]: {{monzo| -52 2 0 10 6 }}, {{monzo| 1 -26 0 2 10 }}~~

~~{{Mapping|legend=2| 44 88 175 75 | 0 2 -2 3 }}~~

~~[[Optimal tuning]]s:~~

* [[CTE]]: ~~~64/63 = 1\44 = 27.273, ~{{monzo| 25 0 0 -5 -3 }} = 701.953~~

~~{{Optimal ET sequence|legend=1| 176, 484, 660, 836, 1012, 1848, 4708, 6556, 11264, 17820, 29084, 46904, 75988, 122892}}~~

~~[[Badness~~]] ~~(Smith): 2.466 × 10<sup>-3</sup>~~

@@ Line 12: / Line 12: @@
 == Temperaments ==
+=== Loudspeaker ===
 Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments.
-=== Rank-3 ===
+==== Rank-3 ====
-==== Loudspeaker ====
+===== Loudspeaker =====
 [[Subgroup]]: 2.9.7.11
-[[Comma list]]: {{monzo| -51 -24 0 12 16 }}
+[[Comma list]]: {{monzo| -51 -12 12 16 }}
 {{Mapping|legend=2| 4 12 13 12 | 0 1 1 0 | 0 0 -4 3 }}
 [[Optimal tuning]]s:
-* [[CTE]]: ~{{monzo| 13 6 0 -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo| 16 8 0 -4 -5 }} = 183.772
+* [[CTE]]: ~{{monzo| 13 3 -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo| 16 4 -4 -5 }} = 183.772
 {{Optimal ET sequence|legend=1| 20, 32}}[+9], {{EDOs|52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652}}[-9], {{EDOs|254860}}[-9]
-[[Badness]] (Smith): 7 × 10<sup>-6</sup>
+[[Badness]] (Sintel): 0.78992
-=== Rank-2 ===
+=== Blazen ===
-==== Microphone ====
+Tempering out this interval in the no-fives [[11-limit]] (2.3.7.11 subgroup) leads to the '''blazen family'''.
-{{see also| 44th-octave temperaments}}
-This temperament additionally tempers out the parismina [1 -26 0 2 10⟩, which is even smaller than the blare comma. Surprisingly, this temperament admits an optimal generator very close to [[3/2]].
+=== Blare ===
+Tempering out this interval in the full [[11-limit]] leads to the '''blare family'''.
-[[Subgroup]]: 2.9.7.11
+[[Category:Commas named for their regular temperament properties]]
-[[Comma list]]: {{monzo| -52 2 0 10 6 }}, {{monzo| 1 -26 0 2 10 }}
-{{Mapping|legend=2| 44 88 175 75 | 0 2 -2 3 }}
-[[Optimal tuning]]s:
-* [[CTE]]: ~64/63 = 1\44 = 27.273, ~{{monzo| 25 0 0 -5 -3 }} = 701.953
-{{Optimal ET sequence|legend=1| 176, 484, 660, 836, 1012, 1848, 4708, 6556, 11264, 17820, 29084, 46904, 75988, 122892}}
-[[Badness]] (Smith): 2.466 × 10<sup>-3</sup>