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[[#Essence|Essence]]
{{Technical data page}}
The '''quince clan''' [[Tempering out|tempers out]] the [[quince comma]], {{monzo| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
* ''[[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]]
* ''[[Countermiracle]]'' (+6144/6125) → [[Porwell temperaments #Countermiracle|Porwell temperaments]]


This tempers out quince, the no-threes comma |-15 0 -2 7> = 823543/819200. Quince temperaments include miracle, quincy, octowerck and birds as well as the ones listed below.
== 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]].  


=Essence=
[[Subgroup]]: 2.5.7
Essence is of interest because of the abundant supply of essentially tempered chords.


Commas: 321489/320000, 823543/820125
[[Comma list]]: 823543/819200


POTE generator: ~243/196 = 372.597
{{Mapping|legend=2| 1 3 3 | 0 -7 -2 }}


Map: [<2 10 27 23|, <0 -11 -36 -28|]
: mapping generators: ~2, ~343/320


Wedgie: <<22 72 56 63 27 -72||
{{Mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}


EDOs: 58, 190, 248, 438d, 686d
: gencom: [2 343/320; 823543/819200]


Badness: 0.1736
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/320 = 116.291


==11-limit==
{{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
Commas: 441/440, 8019/8000, 456533/455625


POTE generator: ~243/196 = 372.599
==== 2.5.7.13 subgroup ====
Subgroup: 2.5.7.13


Map: [<2 10 27 23 33|, <0 -11 -36 -28 -42|]
Comma list: 343/338, 640/637


EDOs: 58, 190, 248, 438d
Sval mapping: {{mapping| 1 3 3 4 | 0 -7 -2 -3 }}


Badness: 0.0464
Gencom mapping: {{mapping| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}


==13-limit==
: gencom: [2 14/13; 343/338 640/637]
Commas: 441/440, 729/728, 847/845, 1001/1000


POTE generator: ~243/196 = 372.602
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094


Map: [<2 10 27 23 33 31|, <0 -11 -36 -28 -42 -38|]
{{Optimal ET sequence|legend=1| 10, 21, 31}}


EDOs: 58, 190, 248, 438d
==== 2.5.7.13.17 subgroup ====
Subgroup: 2.5.7.13.17


Badness: 0.0261
Comma list: 170/169, 224/221, 640/637
 
Sval mapping: {{mapping| 1 3 3 4 4 | 0 -7 -2 -3 1 }}
 
Gencom mapping: {{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|legend=1| 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: {{mapping| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}
 
Gencom mapping: {{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|legend=1| 10, 21, 31, 52f }}
 
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[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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