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''', 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]].

== 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]].

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.

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

Subgroup: 2.3.5.7

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[[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 }}

{{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

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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

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

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

[[Category:Cloudy]]

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

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

~~[[Category:Interval~~]]

@@ 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]].
 == 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]].
+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
@@ Line 27: / Line 24: @@
 [[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 }}
+{{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
@@ Line 39: / Line 35: @@
 POTE generators: ~3/2 = 699.779, ~5/4 = 386.575
-{{Val list|legend=1| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}
+{{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
@@ Line 51: / Line 46: @@
 POTE generators: ~3/2 = 698.726, ~5/4 = 384.760
-{{Val list|legend=1| 5, 10, 15, 40, 50, 60, 65 }}
+{{Optimal ET sequence|legend=1| 5, 10, 15, 40, 50, 60, 65 }}
-[[Category:7-limit]]
+[[Category:Cloudy]]
-[[Category:Medium comma]]
+[[Category:Commas named for their regular temperament properties]]
-[[Category:Interval]]