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]-[/math]
Special properties	reduced
Tenney height (log2 nd)	178.078
Weil height (log2 max(n, d))	178.078
Wilson height (sopfr(nd))	434
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19987 bits
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.

Temperaments

Loudspeaker

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

Rank-3

Loudspeaker

Subgroup: 2.9.7.11

Comma list: [-51 -12 12 16⟩

Sval mapping: [⟨4 12 13 12], ⟨0 1 1 0], ⟨0 0 -4 3]]

Optimal tunings:

• CTE: ~[13 3 -3 -4⟩ = 1\4 = 300.000, ~9/8 = 203.912, ~[16 4 -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, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652[-9], 254860[-9]

Badness (Dirichlet): 0.78992

Blazen

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

Blare

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