Xenharmonic Wiki

Blare comma: Difference between revisions

← Older edit
VisualWikitext
Akselai (talk | contribs)
252 edits
mNo edit summary
m Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "
 
(4 intermediate revisions by 3 users not shown)
Line 7: Line 7:
}}
}}


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 [https://en.xen.wiki/w/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.
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.
 
== Related temperaments ==


== Temperaments ==
=== Loudspeaker ===
=== 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
[[Subgroup]]: 2.9.7.11


[[Comma list]]: [51 -24 0 12 16⟩
[[Comma list]]: {{monzo| -51 -12 12 16 }}


{{Mapping|legend=1| 4 12 13 12 | 0 1 1 0 | 0 0 -4 3 }}
{{Mapping|legend=2| 4 12 13 12 | 0 1 1 0 | 0 0 -4 3 }}


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~[13 6 0 -3 -4⟩ = 1\4 = 300.000, ~9/8 = 203.912, ~[16 8 0 -4 -5⟩ = 183.772
* [[CTE]]: ~{{monzo| 13 3 -3 -4 }} = 1\4 = 300.000, ~9/8 = 203.912, ~{{monzo| 16 4 -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, 1848, 4708, 6556, 11264, 17820, 18708, 21568, 29972, 34680, 41256, 71208, 183652}}[-9], {{EDOs|254860}}[-9]
 
[[Badness]] (Sintel): 0.78992
 
=== Blazen ===
Tempering out this interval in the no-fives [[11-limit]] (2.3.7.11 subgroup) leads to the '''blazen family'''.


{{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}}
=== Blare ===
Tempering out this interval in the full [[11-limit]] leads to the '''blare family'''.


[[Badness]]: 7 × 10<sup>-6</sup>
[[Category:Commas named for their regular temperament properties]]
Retrieved from "https://en.xen.wiki/w/Blare_comma"