Cloudy comma: Difference between revisions

16807/16384, the cloudy comma, is a 7-limit medium comma. It is the amount by which five 8/7s 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.

Cloudy temperaments

Tempering out the cloudy comma leads a number of regular temperaments including decic, coblack, blacksmith, cloudtone, pental (pentacloud), and 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.

7-limit cloudy (10&15&50)
Comma: 16807/16384

POTE generators: ~8/7 = 240.000, ~3/2 = 699.467, ~5/4 = 382.669

Map: [<5 0 0 14|, <0 1 0 0|, <0 0 1 0|]

EDOs: 5, 10, 15, 25, 35, 45, 50, 55, 60, 65

11-limit cloudy (10&15&50)
Commas: 385/384, 3087/3025

POTE generators: ~8/7 = 240.000, ~3/2 = 699.779, ~5/4 = 386.575

Map: [<5 0 0 14 21|, <0 1 0 0 1|, <0 0 1 0 -1|]

EDOs: 5, 10, 15, 35, 40, 50, 55, 60, 65

13-limit cloudy (10&15&50)
Commas: 105/104, 144/143, 3087/3025

POTE generators: ~8/7 = 240.000, ~3/2 = 698.726, ~5/4 = 384.760

Map: [<5 0 0 14 21 -1|, <0 1 0 0 1 1|, <0 0 1 0 -1 1|]

EDOs: 5, 10, 15, 40, 50, 60, 65

@@ Line 13: / Line 13: @@
 ==Cloudy temperaments==
-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|pentacloud]], and [[Qintosec family|sengasec]]. Cloudy rank three 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.
+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&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.
 '''<font style="font-size: 1.2em">7-limit cloudy (10&amp;15&amp;50)</font>'''<br>
@@ Line 19: / Line 19: @@
 POTE generators: ~8/7 = 240.000, ~3/2 = 699.467, ~5/4 = 382.669<br><br>
 Map: [&lt;5 0 0 14|, &lt;0 1 0 0|, &lt;0 0 1 0|]<br><br>
-EDOs: 5, 10, 15, 25, 35, 45, 50, 55, 60, 65<br><br>
+EDOs: {{Vals| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}<br><br>
 '''<font style="font-size: 1.2em">11-limit cloudy (10&amp;15&amp;50)</font>'''<br>
 Commas: 385/384, 3087/3025<br><br>
 POTE generators: ~8/7 = 240.000, ~3/2 = 699.779, ~5/4 = 386.575<br><br>
 Map: [&lt;5 0 0 14 21|, &lt;0 1 0 0 1|, &lt;0 0 1 0 -1|]<br><br>
-EDOs: 5, 10, 15, 35, 40, 50, 55, 60, 65<br><br>
+EDOs: {{Vals| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}<br><br>
 '''<font style="font-size: 1.2em">13-limit cloudy (10&amp;15&amp;50)</font>'''<br>
 Commas: 105/104, 144/143, 3087/3025<br><br>
 POTE generators: ~8/7 = 240.000, ~3/2 = 698.726, ~5/4 = 384.760<br><br>
 Map: [&lt;5 0 0 14 21 -1|, &lt;0 1 0 0 1 1|, &lt;0 0 1 0 -1 1|]<br><br>
-EDOs: 5, 10, 15, 40, 50, 60, 65
+EDOs: {{Vals| 5, 10, 15, 40, 50, 60, 65 }}
 [[Category:7-limit]]
 [[Category:Medium comma]]
 [[Category:Interval ratio]]

Cloudy comma: Difference between revisions

Revision as of 02:22, 4 April 2021

Cloudy temperaments

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