Quince clan: Difference between revisions

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The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]], {{monzo| -15 0 -2 7 }} ~~= 823543/819200. Quince temperaments include:~~

The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]] ({{monzo|legend=1| -15 0 -2 7 }}, [[ratio]]: 823543/819200).

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

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

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

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

* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]

* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]]

== 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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~~: mapping generators: ~2, ~343/320~~

: mapping generators: ~2, ~343/320

[[Optimal tuning]]s:

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[[Badness]] (Sintel): 0.428

=== Overview to extensions ===

Temperaments discussed elsewhere are:

* ''[[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]]

* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]

* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]]

Discussed below is countermiracle.

== 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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[[Category:Temperament clans]]

[[Category:Quince clan| ]]

~~[[Category:Quince| ]] ~~

[[Category:Rank 2]]

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 {{Technical data page}}
-The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]], {{monzo| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
+The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]] ({{monzo|legend=1| -15 0 -2 7 }}, [[ratio]]: 823543/819200).
-* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]
-* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
-* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy|Ragismic microtemperaments]]
-* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds|31st-octave temperaments]]
-* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
-* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]]
 == 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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 {{Mapping|legend=2| 1 3 3 | 0 -7 -2 }}
-: mapping generators: ~2, ~343/320
 {{Mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}
+: mapping generators: ~2, ~343/320
 [[Optimal tuning]]s:
@@ Line 29: / Line 23: @@
 [[Badness]] (Sintel): 0.428
+=== Overview to extensions ===
+Temperaments discussed elsewhere are:
+* ''[[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]]
+* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
+* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]]
+Discussed below is countermiracle.
 == 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
@@ Line 204: / Line 210: @@
 == 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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 [[Category:Temperament clans]]
 [[Category:Quince clan| ]] <!-- main article -->
-[[Category:Quince| ]] <!-- key article -->
 [[Category:Rank 2]]