Blare comma: Difference between revisions

Line 7:

}}

The '''blare comma''' is an [[unnoticeable comma|unnoticeable]] [[11-limit]] comma in the 2.9.7.11 subgroup, with a size of only 0.078 [[cent]]s. It is the interval in which twelve [[9/7]] septimal major thirds plus three octaves fall short by sixteen [[11/8]] undecimal major fourths.

The '''blare comma''' is an [[unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]] in the 2.9.7.11 [[subgroup]], with a size of only 0.078 [[cent]]s. It is the interval in which twelve [[9/7]] septimal major thirds plus three octaves fall short by sixteen [[11/8]] undecimal major fourths.

It is named in analogy with the industrial theme of [~~https://en.xen.wiki/w/Subgroup_temperaments~~#2.9.7.~~11_subgroup~~ 2.9.7.11 subgroup temperaments], "blare" being a word used to describe the loud and piercing noise of machines.

It is named in analogy with the industrial theme of [[Subgroup temperaments #2.9.7.11 subgroup|2.9.7.11 subgroup temperaments]], "blare" being a word used to describe the loud and piercing noise of machines.

Tempering out this interval leads to the loudspeaker family of microtemperaments.

== Temperaments ==

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

~~== Related temperaments ==~~

=== Loudspeaker ===

[[Subgroup]]: 2.9.7.11

[[Comma list]]: [51 -24 0 12 ~~16⟩~~

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

[[Optimal tuning]]s:

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

* [[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}}

[[Badness]]: 7 × 10<sup>-6</sup>

@@ Line 7: / Line 7: @@
 }}
-The '''blare comma''' is an [[unnoticeable comma|unnoticeable]] [[11-limit]] comma in the 2.9.7.11 subgroup, with a size of only 0.078 [[cent]]s. It is the interval in which twelve [[9/7]] septimal major thirds plus three octaves fall short by sixteen [[11/8]] undecimal major fourths.
+The '''blare comma''' is an [[unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]] in the 2.9.7.11 [[subgroup]], with a size of only 0.078 [[cent]]s. It is the interval in which twelve [[9/7]] septimal major thirds plus three octaves fall short by sixteen [[11/8]] undecimal major fourths.
-It is named in analogy with the industrial theme of [https://en.xen.wiki/w/Subgroup_temperaments#2.9.7.11_subgroup 2.9.7.11 subgroup temperaments], "blare" being a word used to describe the loud and piercing noise of machines.
+It is named in analogy with the industrial theme of [[Subgroup temperaments #2.9.7.11 subgroup|2.9.7.11 subgroup temperaments]], "blare" being a word used to describe the loud and piercing noise of machines.
-Tempering out this interval leads to the loudspeaker family of microtemperaments.
+== Temperaments ==
+Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments.
-== Related temperaments ==
 === Loudspeaker ===
 [[Subgroup]]: 2.9.7.11
-[[Comma list]]: [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 }}
 [[Optimal tuning]]s:
-* [[CTE]]: ~[13 6 0 -3 -4⟩ = 1\4 = 300.000, ~9/8 = 203.912, ~[16 8 0 -4 -5⟩ = 183.772
+* [[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}}
 [[Badness]]: 7 × 10<sup>-6</sup>