Quince clan: Difference between revisions

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== Mercy ==

Mercy is the no-3 version ~~of miracle. It can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup~~ of [[~~31edo~~]]. Two generators make an [[8/7]]; five generators make a [[7/5]].

Mercy is the no-3 version of [[miracle]]. Two generators make [[~]][[8/7]], five generators make ~[[7/5]], and seven make ~[[8/5]]. The [[ploidacot]] for this temperament is omega-heptaseph.

[[Subgroup]]: 2.5.7

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* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]

* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]

* ''[[Slendi]]'' (+4000/3969) → [[Octagar temperaments #Slendi|Octagar temperaments]]

* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy|Ragismic microtemperaments]]

* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds|31st-octave temperaments]]

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== Countermiracle ==

The ''countermiracle'' temperament ({{nowrap| 31 & 145 }}~~) tempers out~~ the ~~trimyna, 50421~~/~~50000 and~~ the [[~~quince comma~~]]~~, 823543/819200~~.

The countermiracle temperament tempers out the porwell comma ([[6144/6125]]), the trimyna comma ([[50421/50000]]) and the quince comma ([[823543/819200]]). It can be described as the {{nowrap| 31 & 145 }} temperament, and finds the [[3/2|perfect fifth]] -25 generators away (normalized for 2.5.7) as opposed to miracle's +6 generators. It has the [[ploidacot]] signature of 22-sheared 25-cot.

~~{{Todo|inline=1|expand|comment=Explain relationship to~~ miracle~~. There's clearly ''some'' relationship~~, ~~since the extensions are named~~ the ~~same way~~, but the ~~nature of that relationship isn't obvious from looking at this page~~.}}

Like miracle, it is naturally an 11-limit temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]].

[[Subgroup]]: 2.3.5.7

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== Subgroup extensions ==

=== Mercy (2.5.7.13) ===

This extension may be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]].

Subgroup: 2.5.7.13

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 == Mercy ==
-Mercy is the no-3 version of miracle. It can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]]. Two generators make an [[8/7]]; five generators make a [[7/5]].
+Mercy is the no-3 version of [[miracle]]. Two generators make [[~]][[8/7]], five generators make ~[[7/5]], and seven make ~[[8/5]]. The [[ploidacot]] for this temperament is omega-heptaseph.
 [[Subgroup]]: 2.5.7
@@ Line 28: / Line 28: @@
 * ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]
 * [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
+* ''[[Slendi]]'' (+4000/3969) → [[Octagar temperaments #Slendi|Octagar temperaments]]
 * ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy|Ragismic microtemperaments]]
 * ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds|31st-octave temperaments]]
@@ Line 36: / Line 37: @@
 == Countermiracle ==
-The ''countermiracle'' temperament ({{nowrap| 31 & 145 }}) tempers out the trimyna, 50421/50000 and the [[quince comma]], 823543/819200.
+The countermiracle temperament tempers out the porwell comma ([[6144/6125]]), the trimyna comma ([[50421/50000]]) and the quince comma ([[823543/819200]]). It can be described as the {{nowrap| 31 & 145 }} temperament, and finds the [[3/2|perfect fifth]] -25 generators away (normalized for 2.5.7) as opposed to miracle's +6 generators. It has the [[ploidacot]] signature of 22-sheared 25-cot.
-{{Todo|inline=1|expand|comment=Explain relationship to miracle. There's clearly ''some'' relationship, since the extensions are named the same way, but the nature of that relationship isn't obvious from looking at this page.}}
+Like miracle, it is naturally an 11-limit temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]].
 [[Subgroup]]: 2.3.5.7
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 == Subgroup extensions ==
 === Mercy (2.5.7.13) ===
+This extension may be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]].
 Subgroup: 2.5.7.13