Euzenius comma: Difference between revisions

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-The euzenius comma is a 7-limit unnoticeable comma with a ratio of 78125000/78121827, a monzo of [3 -13 10 -2⟩, and a size of 0.070314 cents. It is tempered out in temperaments such as ennealimmal and fortune.
+{{Infobox Interval
+| Ratio = 78125000/78121827
+| Name = euzenius comma
+| Color name = srry<sup>10</sup>-3, Sabiruquinyo comma
+| Comma = yes
+}}
+The '''euzenius comma''' is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] with a [[ratio]] of 78125000/78121827, a [[monzo]] of {{monzo| 3 -13 10 -2 }}, and a size of 0.070314 [[cent]]s. It is the difference between two 6250/5103 intervals and the [[3/2|perfect fifth]]. In terms of commas, it is the difference between a [[2401/2400|breedsma]] and a stack of two [[4375/4374|ragismas]], relating the two smallest 7-limit [[superparticular]] commas.
 == Temperament ==
-Tempering this comma out gives euzenius temperament.
+Tempering out this comma gives the euzenius temperament (→ [[Very high accuracy temperaments #Euzenius or Sabiruquinyo]]). In any tuning of euzenius, the breedsma is split in two, and the perfect fifth as well. [[Ennealimmal]] is an obvious rank-2 temperament where this comma is tempered out, as both the breedsma and the ragisma are tempered out. Another example of rank-2 temperament is given by [[Very high accuracy temperaments #Fortune|fortune]].
-=== Euzenius (3566 & 3125 & 171) ===
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 78125000/78121827
-[[Mapping]]: [⟨1 1 0 -5], ⟨0 2 0 -13], ⟨0 0 1 5]]
-[[POTE generator|POTE generators]]: ~6250/5103 = 350.9788, ~5 = 2786.3104
-[[Val|Vals]]: [[171edo|171]], [[441edo|441]], [[612edo|612]], [[2954edo|2954]], [[3125edo|3125]], [[3566edo|3566]], [[3737edo|3737]], [[6250edo|6250]], [[6520edo|6520]], [[6691edo|6691]]
-[[Badness]]: 0.000205
-Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B3%2C-13%2C10%2C-2%3E&page=2&limit=7
-=== Ennealimmal ===
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 2401/2400, 4375/4374
-[[Mapping]]: [⟨9 1 1 12], ⟨0 2 3 2]]
-[[Wedgie]]: ⟨⟨18 27 18 1 -22 -34]]
-[[POTE generator]]: ~5/3 = 884.3129
-[[Optimal GPV sequence]]: [[27edo|27]], [[45edo|45]], [[72edo|72]], [[99edo|99]], [[171edo|171]], [[441edo|441]], [[612edo|612]]
-[[Badness]]: 0.003610
-=== Fortune ===
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 78125000/78121827, [-52 17 12 -1⟩
-[[Mapping]]: [⟨1 -1 11 63], ⟨0 14 -47 -326]]
-[[POTE generator]]: ~8388608/7381125 = 221.568031
-[[Optimal GPV sequence]]: [[612edo|612]], [[1901edo|1901]], [[2513edo|2513]], [[3125edo|3125]], [[6862edo|6862]], [[9987edo|9987]]
-[[Badness]]: 0.023704
 == See also ==
+* [[Unnoticeable comma]]
-* [[Unnoticeable comma]]
+[[Category:Commas with unknown etymology]]