Blare comma

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.

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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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.

Rank-3

Loudspeaker

Subgroup: 2.9.7.11

Comma list: [-51 -24 0 12 16⟩

Subgroup-val 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, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652[-9], 254860[-9]

Badness (Smith): 7 × 10^-6

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: [-52 2 0 10 6⟩, [1 -26 0 2 10⟩

Subgroup-val mapping: [⟨44 88 175 75], ⟨0 2 -2 3]]

Optimal tunings:

• CTE: ~64/63 = 1\44 = 27.273, ~[25 0 0 -5 -3⟩ = 701.953

Optimal ET sequence: 176, 484, 660, 836, 1012, 1848, 4708, 6556, 11264, 17820, 29084, 46904, 75988, 122892

Badness (Smith): 2.466 × 10^-3