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 = Lz53, Laquinzo comma

~~| FJS name = d3~~~~7,7,7,7,7~~

| Comma = yes

| ~~Sound~~ =

}}

'''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]].

'''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 the [[rainy comma]]. 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~~==

== 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|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~~.

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]].

~~'''7-limit cloudy (~~10&15&50~~)''' ~~

Cloudy rank-3 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.

~~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: {{Vals| 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: {{Vals| 5, 10, 15, 35, 40, 50, 55, 60, 65 }} ~~

~~'''13~~-limit ~~cloudy (10&amp~~;~~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: {{Vals| 5, 10, 15, 40, 50, 60, 65 }}~~

[[~~Category~~:7-limit]]

=== Cloudy (10&15&50) ===

[[Category:~~Medium comma~~]]

Subgroup: 2.3.5.7

[[Category:~~Interval ratio~~]]

[[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

{{Optimal ET sequence|legend=1| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}

=== 11-limit cloudy (10&15&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

{{Optimal ET sequence|legend=1| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}

=== 13-limit cloudy (10&15&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

[[Category:Cloudy]]

[[Category:Commas named for their regular temperament properties]]

@@ Line 1: / Line 1: @@
 {{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''', 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]].
+'''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 the [[rainy comma]]. 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==
+== 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|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.
+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]].
-'''<font style="font-size: 1.2em">7-limit cloudy (10&amp;15&amp;50)</font>'''<br>
+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.
-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: {{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: {{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: {{Vals| 5, 10, 15, 40, 50, 60, 65 }}
-[[Category:7-limit]]
+=== Cloudy (10&amp;15&amp;50) ===
-[[Category:Medium comma]]
+Subgroup: 2.3.5.7
-[[Category:Interval ratio]]
+[[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
+{{Optimal ET sequence|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
+{{Optimal ET sequence|legend=1| 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
+{{Optimal ET sequence|legend=1| 5, 10, 15, 40, 50, 60, 65 }}
+[[Category:Cloudy]]
+[[Category:Commas named for their regular temperament properties]]