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 [ | 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. | |||
=== Loudspeaker === | === Loudspeaker === | ||
[[Subgroup]]: 2.9.7.11 | [[Subgroup]]: 2.9.7.11 | ||
[[Comma list]]: | [[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]]: ~ | * [[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 |
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]]
- 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