Blare comma: Difference between revisions

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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 ===
=== Loudspeaker ===
[[Subgroup]]: 2.9.7.11
[[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 }}
{{Mapping|legend=1| 4 12 13 12 | 0 1 1 0 | 0 0 -4 3 }}


[[Optimal tuning]]s:
[[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}}
{{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>
[[Badness]]: 7 × 10<sup>-6</sup>

Revision as of 15:30, 22 April 2024

Interval information
Factorization 2-51 × 3-24 × 712 × 1116
Monzo [-51 -24 0 12 16
Size in cents 0.0779347¢
Name blare comma
Color name Laquadquadlo-aquadtrizo comma
FJS name [math]\displaystyle{ - }[/math]
Special properties reduced
Tenney norm (log2 nd) 178.078
Weil norm (log2 max(n, d)) 178.078
Wilson norm (sopfr(nd)) 434
Comma size unnoticeable
Open this interval in xen-calc

The blare comma is an unnoticeable 11-limit comma in the 2.9.7.11 subgroup, with a size of only 0.078 cents. 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 2.9.7.11 subgroup temperaments, "blare" being a word used to describe the loud and piercing noise of machines.

Temperaments

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

Loudspeaker

Subgroup: 2.9.7.11

Comma list: [51 -24 0 12 16

Mapping[4 12 13 12], 0 1 1 0], 0 0 -4 3]]

Optimal tunings:

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

Optimal ET sequence20, 32[+9], 52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012

Badness: 7 × 10-6