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:
The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]], {{monzo| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
* [[Starling temperaments #Casablanca|Casablanca]] ({126/125, 589824/588245})
* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca|Starling temperaments]]
* [[Gamelismic clan #Miracle|Miracle]] ({225/224, 1029/1024})
* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
* [[Ragismic microtemperaments #Quincy|Quincy]] ({4375/4374, 823543/819200})
* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy|Ragismic microtemperaments]]
* [[31-comma temperaments #Birds|Birds]] ({3136/3125, 823543/819200})
* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds|31st-octave temperaments]]
* [[Varunismic temperaments #Octowerck|Octowerck]] ({321489/320000, 420175/419904})
* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
* [[Hemimage temperaments #Cotoneum|Cotoneum]] ({10976/10935, 823543/819200})
* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum|Garischismic clan]]
* [[Porwell temperaments #Countermiracle|Countermiracle]] ({6144/6125, 50421/50000})
* ''[[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]


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


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


[[Comma list]]: 343/338, 640/637
Comma list: 343/338, 640/637


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


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


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


[[Tp tuning|POL2 generator]]: ~14/13 = 116.094
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094


{{Optimal ET sequence|legend=1| 10, 21, 31}}
{{Optimal ET sequence|legend=1| 10, 21, 31}}
====2.5.7.13.17====
 
==== 2.5.7.13.17 subgroup ====
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


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


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


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


[[Tp tuning|POL2 generator]]: ~14/13 = 115.769
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.769


{{Optimal ET sequence|legend=1| 10, 21, 31}}
{{Optimal ET sequence|legend=1| 10, 21, 31 }}
====2.5.7.13.17.19====
 
==== 2.5.7.13.17.19 subgroup ====
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 }}


{{Optimal ET sequence|legend=1| 10, 21, 31, 52f}}
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Quince clan| ]] <!-- main article -->
[[Category:Quince clan| ]] <!-- main article -->
[[Category:Quince| ]] <!-- key article -->
[[Category:Rank 2]]

Revision as of 07:18, 19 September 2023

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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