Blare comma
| Factorization | 2-51 × 3-24 × 712 × 1116 |
| Monzo | [-51 -24 0 12 16⟩ |
| Size in cents | 0.077934696¢ |
| 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{n\cdot d}[/math]) |
~2.39751 bits |
| 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
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]]
- 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.