Blare comma: Difference between revisions
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Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments. | Tempering out this interval in the 2.9.7.11 subgroup leads to the '''loudspeaker family''' of microtemperaments. | ||
=== Loudspeaker === | === Rank-3 === | ||
==== Loudspeaker ==== | |||
[[Subgroup]]: 2.9.7.11 | [[Subgroup]]: 2.9.7.11 | ||
[[Comma list]]: {{monzo| 51 -24 0 12 16 }} | [[Comma list]]: {{monzo| -51 -24 0 12 16 }} | ||
{{Mapping|legend= | {{Mapping|legend=2| 4 12 13 12 | 0 1 1 0 | 0 0 -4 3 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~{{monzo| 13 6 0 -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo| 16 8 0 -4 -5 }} = 183.772 | * [[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, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652}}[-9], {{EDOs|254860}}[-9] | ||
[[Badness]]: 7 × 10<sup>-6</sup> | [[Badness]] (Smith): 7 × 10<sup>-6</sup> | ||
=== 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]]: {{monzo| -52 2 0 10 6 }}, {{monzo| 1 -26 0 2 10 }} | |||
{{Mapping|legend=2| 44 88 175 75 | 0 2 -2 3 }} | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~64/63 = 1\44 = 27.273, ~{{monzo| 25 0 0 -5 -3 }} = 701.953 | |||
{{Optimal ET sequence|legend=1| 176, 484, 660, 836, 1012, 1848, 4708, 6556, 11264, 17820, 29084, 46904, 75988, 122892}} | |||
[[Badness]] (Smith): 2.466 × 10<sup>-3</sup> | |||
Revision as of 12:50, 24 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.
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]]
- 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
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]]
- 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