Cloudy comma: Difference between revisions

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 {{Infobox Interval
-| Icon =
 | Ratio = 16807/16384
-| Monzo = -14 0 0 5
-| Cents = 44.12953
 | Name = cloudy comma
-| Color name =
+| Color name = Lz<sup>5</sup>3, Laquinzo comma
-| FJS name = d3<sup>7,7,7,7,7</sup>
+| Comma = yes
-| Sound =
 }}
+'''16807/16384''', the '''cloudy comma''', or systematically the '''5-7-comma''', is a [[medium comma]] in the [[7-limit]] with a size of about 44.1 [[cent]]s. It is the amount by which five [[8/7]]'s fall short of an octave. In the [[2.5.7 subgroup]], it exceeds [[128/125]] by the [[rainy comma]].
-'''16807/16384''', the '''cloudy comma''', is a 7-limit medium comma. It is the amount by which five [[8/7]]s fall short of one octave and exceeds [[128/125]] by [[2100875/2097152]]. For equal divisions ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]].
 == Temperaments ==
-Tempering out the cloudy comma splits the octave into 5 equal parts and maps the harmonic 7 to 4\5. It leads to a number of regular temperaments in the [[cloudy clan]].
+[[Tempering out]] this comma splits the octave into 5 equal parts and maps the [[7/4|harmonic seventh]] to [[5edo|4\5]]. In the full 7-limit, this leads to the rank-3 [[cloudy]] temperament. For [[edo]]s ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]]. Rank-2 temperaments tempering it out include [[blackwood]], [[coblack]], [[cloudtone]], [[sengasec]], [[warlock]], [[pentacloud]], [[decic]], [[pentadecal]], and [[quinkee]].
-Cloudy rank-3 temperament can be described as the 10&amp;15&amp;50 temperament, which tempers out 385/384 and 3087/3025 in the 11-limit; 105/104, 144/143, and 4459/4400 in the 13-limit.
-=== Cloudy (10&amp;15&amp;50) ===
-Subgroup: 2.3.5.7
-[[Comma list]]: 16807/16384
-[[Mapping]]: [{{val| 5 0 0 14 }}, {{val| 0 1 0 0 }}, {{val| 0 0 1 0 }}]
-Mapping generators: ~8/7, ~3, ~5
-[[POTE generator]]s: ~3/2 = 699.467, ~5/4 = 382.669
-{{Val list|legend=1| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}
-=== 11-limit cloudy (10&amp;15&amp;50) ===
-Subgroup: 2.3.5.7.11
-Comma list: 385/384, 3087/3025
-Mapping: [{{val| 5 0 0 14 21 }}, {{val| 0 1 0 0 1 }}, {{val| 0 0 1 0 -1 }}]
-POTE generators: ~3/2 = 699.779, ~5/4 = 386.575
-Vals: {{Val list| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}
-=== 13-limit cloudy (10&amp;15&amp;50) ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 105/104, 144/143, 3087/3025
-Mapping: [{{val| 5 0 0 14 21 -1 }}, {{val| 0 1 0 0 1 1 }}, {{val| 0 0 1 0 -1 1 }}]
-POTE generators: ~3/2 = 698.726, ~5/4 = 384.760
-Vals: {{Val list| 5, 10, 15, 40, 50, 60, 65 }}
-[[Category:7-limit]]
-[[Category:Medium comma]]
-[[Category:Interval]]
 [[Category:Cloudy]]
+[[Category:Commas named for their regular temperament properties]]