Blare comma: Difference between revisions

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

=== Loudspeaker ===

=== Rank-3 ===

==== Loudspeaker ====

[[Subgroup]]: 2.9.7.11

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

[[Comma list]]: {{monzo| -51 -24 0 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

{{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}}

{{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]]: 7 × 10-6

[[Badness]] (Smith): 7 × 10-6

=== Rank-2 ===

==== Microphone ====

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]].

[[Subgroup]]: 2.9.7.11

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

[[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 × 10-3

@@ Line 14: / Line 14: @@
 Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments.
-=== Loudspeaker ===
+=== Rank-3 ===
+==== Loudspeaker ====
 [[Subgroup]]: 2.9.7.11
-[[Comma list]]: {{monzo| 51 -24 0 12 16 }}
+[[Comma list]]: {{monzo| -51 -24 0 12 16 }}
-{{Mapping|legend=1| 4 12 13 12 | 0 1 1 0 | 0 0 -4 3 }}
+{{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
-{{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}}
+{{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]]: 7 × 10<sup>-6</sup>
+[[Badness]] (Smith): 7 × 10<sup>-6</sup>
+=== Rank-2 ===
+==== Microphone ====
+{{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]].
+[[Subgroup]]: 2.9.7.11
+[[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>