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| {{Infobox Interval | | {{Infobox Interval |
| | Icon =
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| | Ratio = 16807/16384 | | | Ratio = 16807/16384 |
| | Monzo = -14 0 0 5
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| | Cents = 44.12953
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| | Name = cloudy comma | | | 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]]. |
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| '''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]] 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]]. |
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| ==Cloudy temperaments==
| | [[Category:Cloudy]] |
| Tempering out the cloudy comma leads a number of regular temperaments including [[Marvel temperaments|decic]], [[Starling temperaments|coblack]], [[Archytas clan|blacksmith]], [[Meantone family|cloudtone]], [[Pental family|pental]] (pentacloud), and [[Qintosec family|sengasec]]. Cloudy rank three temperament can be described as the 10&15&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.
| | [[Category:Commas named for their regular temperament properties]] |
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| '''<font style="font-size: 1.2em">7-limit cloudy (10&15&50)</font>'''<br>
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| Comma: 16807/16384<br><br>
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| POTE generators: ~8/7 = 240.000, ~3/2 = 699.467, ~5/4 = 382.669<br><br>
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| Map: [<5 0 0 14|, <0 1 0 0|, <0 0 1 0|]<br><br>
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| EDOs: {{Vals| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}<br><br>
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| '''<font style="font-size: 1.2em">11-limit cloudy (10&15&50)</font>'''<br>
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| Commas: 385/384, 3087/3025<br><br>
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| POTE generators: ~8/7 = 240.000, ~3/2 = 699.779, ~5/4 = 386.575<br><br>
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| Map: [<5 0 0 14 21|, <0 1 0 0 1|, <0 0 1 0 -1|]<br><br>
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| EDOs: {{Vals| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}<br><br>
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| '''<font style="font-size: 1.2em">13-limit cloudy (10&15&50)</font>'''<br>
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| Commas: 105/104, 144/143, 3087/3025<br><br>
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| POTE generators: ~8/7 = 240.000, ~3/2 = 698.726, ~5/4 = 384.760<br><br>
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| Map: [<5 0 0 14 21 -1|, <0 1 0 0 1 1|, <0 0 1 0 -1 1|]<br><br>
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| EDOs: {{Vals| 5, 10, 15, 40, 50, 60, 65 }}
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| [[Category:7-limit]] | |
| [[Category:Medium comma]] | |
| [[Category:Interval ratio]]
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