Blare comma

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
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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.

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

Related temperaments

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 sequence: 20, 32[+9], 52, 72, 124, 300, 424, 516, 536, 588, 640, 660, 712, 764, 836, 888, 960, 1012

Badness: 7 × 10^-6