Cloudy comma: Difference between revisions

Line 11:

'''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]].

==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]], and [[Pental family|pentacloud]]. 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

[[Category:7-limit]]

[[Category:Medium comma]]

[[Category:Interval ratio]]

@@ Line 11: / Line 11: @@
 '''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]].
+==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]], and [[Pental family|pentacloud]]. 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>
+Comma: 16807/16384<br><br>
+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>
+'''<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>
+'''<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
 [[Category:7-limit]]
 [[Category:Medium comma]]
 [[Category:Interval ratio]]