Quince clan: Difference between revisions

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The '''quince clan''' tempers out quince, the no-threes comma {{monzo| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
{{Technical data page}}
* [[Starling temperaments #Casablanca|Casablanca]] ({126/125, 589824/588245})
The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]], {{monzo| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
* [[Gamelismic clan #Miracle|Miracle]] ({225/224, 1029/1024})
* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]
* [[Ragismic microtemperaments #Quincy|Quincy]] ({4375/4374, 823543/819200})
* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
* [[31-comma temperaments #Birds|Birds]] ({3136/3125, 823543/819200})
* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy|Ragismic microtemperaments]]
* [[Varunismic temperaments #Octowerck|Octowerck]] ({321489/320000, 420175/419904})
* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds|31st-octave temperaments]]
* [[Hemimage temperaments #Cotoneum|Cotoneum]] ({10976/10935, 823543/819200})
* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
* [[Porwell temperaments #Countermiracle|Countermiracle]] ({6144/6125, 50421/50000})
* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]]
* ''[[Countermiracle]]'' (+6144/6125) → [[Porwell temperaments #Countermiracle|Porwell temperaments]]


== Mercy ==
== 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. 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]].  


Subgroup: 2.5.7
[[Subgroup]]: 2.5.7


[[Comma list]]: 823543/819200
[[Comma list]]: 823543/819200


[[Sval]] [[mapping]]: [{{val| 1 3 3 }}, {{val| 0 -7 -2 }}]
{{Mapping|legend=2| 1 3 3 | 0 -7 -2 }}


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


Gencom mapping: [{{val| 1 0 3 3 }}, {{val| 0 0 -7 -2 }}]
{{Mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}


[[Category:Rank 2]]
: gencom: [2 343/320; 823543/819200]
[[Gencom]]: [2 343/320; 823543/819200]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/320 = 116.291


[[POTE generator]]: ~343/320 = 116.291
{{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}


{{Val list|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
==== 2.5.7.13 subgroup ====
====2.5.7.13====
Subgroup: 2.5.7.13
Subgroup: 2.5.7.13


[[Comma list]]: 343/338, 640/637
Comma list: 343/338, 640/637
 
Sval mapping: {{mapping| 1 3 3 4 | 0 -7 -2 -3 }}


[[Gencom]]: [2 14/13; 343/338 640/637]
Gencom mapping: {{mapping| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}


[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 0 4}}, {{val|0 0 -7 -2 0 -3}}]
: gencom: [2 14/13; 343/338 640/637]


[[Mapping|Sval mapping]]: [{{val|1 3 3 4}}, {{val|0 -7 -2 -3}}]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094


[[Tp tuning|POL2 generator]]: ~14/13 = 116.094
{{Optimal ET sequence|legend=1| 10, 21, 31}}


{{Val list|legend=1| 10, 21, 31}}
==== 2.5.7.13.17 subgroup ====
====2.5.7.13.17====
Subgroup: 2.5.7.13.17
Subgroup: 2.5.7.13.17


[[Comma list]]: 170/169, 224/221, 640/637
Comma list: 170/169, 224/221, 640/637
 
Sval mapping: {{mapping| 1 3 3 4 4 | 0 -7 -2 -3 1 }}


[[Gencom]]: [2 14/13; 170/169 224/221 640/637]
Gencom mapping: {{mapping| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}


[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 0 4 4}}, {{val|0 0 -7 -2 0 -3 1}}]
: gencom: [2 14/13; 170/169 224/221 640/637]


[[Mapping|Sval mapping]]: [{{val|1 3 3 4 4}}, {{val|0 -7 -2 -3 1}}]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.769


[[Tp tuning|POL2 generator]]: ~14/13 = 115.769
{{Optimal ET sequence|legend=1| 10, 21, 31 }}


{{Val list|legend=1| 10, 21, 31}}
==== 2.5.7.13.17.19 subgroup ====
====2.5.7.13.17.19====
Subgroup: 2.5.7.13.17.19
Subgroup: 2.5.7.13.17.19


[[Comma list]]: 170/169, 343/338, 640/637, 16384/16055
Comma list: 170/169, 343/338, 640/637, 16384/16055


[[Gencom]]: [2 14/13; 170/169 343/338 640/637 16384/16055]
Sval mapping: {{mapping| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}


[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 0 4 4 3}}, {{val|0 0 -7 -2 0 -3 1 13}}]
Gencom mapping: {{mapping| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}


[[Mapping|Sval mapping]]: [{{val|1 3 3 4 4 3}}, {{val|0 -7 -2 -3 1 13}}]
: gencom: [2 14/13; 170/169 343/338 640/637 16384/16055]


[[Tp tuning|POL2 generator]]: ~14/13 = 115.716
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.716
 
{{Optimal ET sequence|legend=1| 10, 21, 31, 52f }}


{{Val list|legend=1| 10, 21, 31, 52f}}
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Quince clan| ]] <!-- main article -->
[[Category:Quince clan| ]] <!-- main article -->
[[Category:Quince| ]] <!-- key article -->
[[Category:Rank 2]]

Latest revision as of 00:39, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The quince clan tempers out the quince comma, [-15 0 -2 7⟩ = 823543/819200. Quince temperaments include:

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.

Subgroup: 2.5.7

Comma list: 823543/819200

Subgroup-val mapping: [⟨1 3 3], ⟨0 -7 -2]]

mapping generators: ~2, ~343/320

Gencom mapping: [⟨1 0 3 3], ⟨0 0 -7 -2]]

gencom: [2 343/320; 823543/819200]

Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 116.291

Optimal ET sequence: 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd

2.5.7.13 subgroup

Subgroup: 2.5.7.13

Comma list: 343/338, 640/637

Sval mapping: [⟨1 3 3 4], ⟨0 -7 -2 -3]]

Gencom mapping: [⟨1 0 3 3 0 4], ⟨0 0 -7 -2 0 -3]]

gencom: [2 14/13; 343/338 640/637]

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094

Optimal ET sequence: 10, 21, 31

2.5.7.13.17 subgroup

Subgroup: 2.5.7.13.17

Comma list: 170/169, 224/221, 640/637

Sval mapping: [⟨1 3 3 4 4], ⟨0 -7 -2 -3 1]]

Gencom mapping: [⟨1 0 3 3 0 4 4], ⟨0 0 -7 -2 0 -3 1]]

gencom: [2 14/13; 170/169 224/221 640/637]

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.769

Optimal ET sequence: 10, 21, 31

2.5.7.13.17.19 subgroup

Subgroup: 2.5.7.13.17.19

Comma list: 170/169, 343/338, 640/637, 16384/16055

Sval mapping: [⟨1 3 3 4 4 3], ⟨0 -7 -2 -3 1 13]]

Gencom mapping: [⟨1 0 3 3 0 4 4 3], ⟨0 0 -7 -2 0 -3 1 13]]

gencom: [2 14/13; 170/169 343/338 640/637 16384/16055]

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.716

Optimal ET sequence: 10, 21, 31, 52f

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