Xenharmonic Wiki

Blare comma: Difference between revisions

← Older editNewer edit →
VisualWikitext
Akselai (talk | contribs)
252 edits
Akselai (talk | contribs)
252 edits
the rank 2 temperament is useless for 2.9.7.11. also write monzos in subgroup instead of in full p-limit. also use dirichlet badness (this temp is actually really really bad).
Line 12: Line 12:


== Temperaments ==
== Temperaments ==
=== Loudspeaker ===
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.


=== Rank-3 ===
==== Rank-3 ====
==== Loudspeaker ====
===== Loudspeaker =====
[[Subgroup]]: 2.9.7.11
[[Subgroup]]: 2.9.7.11


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


{{Mapping|legend=2| 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]]: ~{{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 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]
{{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]] (Smith): 7 × 10<sup>-6</sup>
[[Badness]] (Dirichlet): 0.78992


=== Rank-2 ===
=== Blazen ===
==== Microphone ====
Tempering out this interval in the no-fives [[11-limit]] (2.3.7.11 subgroup) leads to the '''blazen family'''.
{{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]].
=== Blare ===
 
Tempering out this interval in the full [[11-limit]] leads to the '''blare family'''.
[[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>
Retrieved from "https://en.xen.wiki/w/Blare_comma"