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= Breed =
= Breed =
[[Comma]] c = 2401/2400
[[Comma]]: 2401/2400


7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat
[[Minimax tuning]]:
* 7- and 9-odd-limit minimax eigenmonzos: 2, 6/5, 5/4


[[Eigenmonzo]]s: 2, 6/5, 5/4
Lattice basis: 49/40 length = 0.7858, 8/7 length = 1.1241


Lattice basis: 49/40 length 0.7858 8/7 length 1.1241
Angle(49/40, 8/7) = 107.367°


Angle(49/40, 8/7) = 107.367 degrees
Map to lattice: [{{val|0 2 -1 0}}, {{val|0 0 -2 -1}}]


Map to lattice: [<0 2 -1 0|, <0 0 -2 -1|]
[[Mapping]]: [{{val|1 1 1 2}}, {{val|0 2 1 1}}, {{val|0 0 2 1}}]


Map [<1 1 1 2|, <0 2 1 1|, <0 0 2 1|]
Mapping generators: 2, ~49/40, ~10/7


[[Generator]]s: 2, 49/40, 10/7
{{Val list|legend=1| 31, 41, 58, 68, 72, 171, 441, 612, 2308, 2578, 2749, 3361d }}


[[EDO|EDOs]]: [[31edo|31]], [[41edo|41]], [[58edo|58]], [[68edo|68]], [[72edo|72]], [[171edo|171]], [[441edo|441]], [[612edo|612]], [[2308edo|2308]], [[2578edo|2578]], [[2749edo|2749]], [[3361edo|3361d]]
[[Badness]]: 0.0000153


Badness: 0.0000153
[[Projection pair]]: 3 = ~2401/800 to 2.5.7
 
[[Projection pair]]: 3 2401/800 to 2.5.7


Scales: [[breed11]]
Scales: [[breed11]]
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Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated as a name due to conflict with another temperament also given that name. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72, 130, 171 and 202 are good edos for jove.
Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated as a name due to conflict with another temperament also given that name. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72, 130, 171 and 202 are good edos for jove.


[[Comma]]s: 243/242, 441/440
[[Comma list]]: 243/242, 441/440


[[Minimax tuning]]
[[Minimax tuning]]:
* 11-odd-limit eigenmonzos: 2, 7/5, 11/8


[|1 0 0 0 0>, |1/5 0 0 0 2/5>,  
[[Mapping]]: [{{val|1 1 1 2 2}}, {{val|0 2 1 1 5}}, {{val|0 0 2 1 0}}]
|13/5 0 2 -2 1/5>, |13/5 0 1 -1 1/5>,  
|0 0 0 0 1>]


[[Eigenmonzo]]s: 2, 7/5, 11/8
Mapping generators: 2, ~11/9, ~10/7


Map: [<1 1 1 2 2|, <0 2 1 1 5|, <0 0 2 1 0|]
{{Val list|legend=1| 31, 41, 58, 72, 130, 161, 171, 202 }}


EDOs: 31, 41, 58, 72, 130, 161, 171, 202
[[Badness]]: 0.000241


Badness: 0.000241
Projection pairs: ~3 = ~242/81, ~5 = ~2200/441, ~7 = ~440/63, ~11 = ~644204/59049 to 2.7/5.11/9
 
Projection pairs: 3 242/81 5 2200/441 7 440/63 11 644204/59049 to 2.7/5.11/9


* [http://micro.soonlabel.com/hobbit_scales/20120418-jove41.mp3 By Jove!] in [[jove41]] by Chris Vaisvil
* [http://micro.soonlabel.com/hobbit_scales/20120418-jove41.mp3 By Jove!] in [[jove41]] by Chris Vaisvil


== Jovial ==
== Jovial ==
[[Comma]]s: 243/242, 441/440, 364/363
Comma list: 243/242, 364/363, 441/440
 
13-limit minimax
 
[|1 0 0 0 0 0>, |17/11 -12/11 2/11 0 0 4/11>, |34/11 -46/11 15/11 0 0 8/11>,
|35/11 -26/11 8/11 0 0 5/11>,
|37/11 -30/11 5/11 0 0 10/11>,
|34/11 -46/11 4/11 0 0 19/11>]


[[Eigenmonzo]]s: 2, 10/9, 13/9
Minimax tuning:
* 13-odd-limit eigenmonzos: 2, 10/9, 13/10
* 15-odd-limit eigenmonzos: 2, 15/13, 7/5


15-limit minimax
Mapping: [{{val|1 1 1 2 2 1}}, {{val|0 2 1 1 5 11}}, {{val|0 0 2 1 0 -1}}]


[|1 0 0 0 0 0>, |2 -1/4 1/2 -3/4 0 1/4>,
Mapping generators: 2, ~11/9, ~10/7
|7/2 -1/8 9/4 -19/8 0 1/8>,  
|7/2 -1/8 5/4 -11/8 0 1/8>,
|9/2 -5/8 5/4 -15/8 0 5/8>,
|11/2 -11/8 7/4 -25/8 0 11/8>]


[[Eigenmonzo]]s: 2, 15/13, 7/5
Vals: {{Val list| 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e }}
 
Map: [<1 1 1 2 2 1|, <0 2 1 1 5 11|, <0 2 1 1 0 -1|]
 
EDOs: 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e


Badness: 0.000624
Badness: 0.000624


=== 17-limit ===
=== 17-limit ===
Commas: 243/242, 441/440, 364/363, 595/594
Comma list: 243/242, 364/363, 441/440, 595/594


17-limit minimax
Minimax tuning:
* 17-odd-limit eigenmonzos: 2, 18/17, 6/5


[|1 0 0 0 0 0 0>, |3/7 -2 6/7 0 0 0 4/7>,  
Mapping: [{{val|1 1 1 2 2 1 3}}, {{val|0 2 1 1 5 11 9}}, {{val|0 0 2 1 0 -1 -3}}]
|3/7 -3 13/7 0 0 0 4/7>, |11/7 -2 8/7 0 0 0 3/7>,  
|4/7 -5 15/7 0 0 0 10/7>, |-2 -10 4 0 0 0 3>,
|6/7 -6 12/7 0 0 0 15/7>]


[[Eigenmonzo|Eigenmonzos]]: 2, 18/17, 6/5
Mapping generators: 2, ~11/9, ~10/7


Map: [<1 1 1 2 2 1 3|, <0 2 1 1 5 11 9|, <0 0 2 1 0 -1 -3|]
Vals: {{Val list| 41, 58, 72, 130, 171, 243, 274, 346, 373eg, 414e, 540eg, 787eg }}
 
[[generator|Generators]]: 2, 11/9, 10/7
 
[[EDO|Edos]]: 41, 58, [[72edo|72]], [[130edo|130]], [[171edo|171]], [[243edo|243]], [[274edo|274]], [[346edo|346]], [[373edo|373eg]], [[414edo|414e]], [[544edo|540eg]], [[787edo|787eg]]


Badness: 0.000741
Badness: 0.000741


== Jofur ==
== Jofur ==
Commas: 243/242, 441/440, 144/143
Comma list: 144/143, 196/195, 243/242


Map: [<1 1 1 2 2 4|, <0 2 1 1 5 -1|, <0 0 2 1 0 0|]
Map: [{{val|1 1 1 2 2 4}}, {{val|0 2 1 1 5 -1}}, {{val|0 0 2 1 0 0}}]


EDOs: 31, 41, 58, 89f, 99ef, 157ef
Mapping generators: 2, ~11/9, ~10/7
 
Vals: {{Val list| 31, 41, 58, 89f, 99ef, 157ef }}


Badness: 0.000749
Badness: 0.000749


== Jovis ==
== Jovis ==
Commas: 243/242, 351/350, 441/440
Comma list: 243/242, 351/350, 441/440


Map: [<1 1 1 2 2 2|, <0 2 1 1 5 -3|, <0 0 2 1 0 5|]
Map: [{{val|1 1 1 2 2 2}}, {{val|0 2 1 1 5 -3}}, {{val|0 0 2 1 0 5}}]


EDOs: 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef
Mapping generators: 2, ~11/9, ~10/7
 
Vals: {{Val list| 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef }}


Badness: 0.000542
Badness: 0.000542


= Freya =
= Freya =
[[Comma]]s: 2401/2400, 3025/3024
[[Comma list]]: 2401/2400, 3025/3024
 
11-limit minimax


[|1 0 0 0 0>, |0 1 0 0 0>,
[[Minimax tuning]]:
|11/10 11/10 0 4/5 -4/5>,
* 11-odd-limit eigenmonzos: 2, 14/11, 4/3
|9/5 4/5 0 2/5 -2/5>, |9/5 4/5 0 -3/5 3/5>]


[[Eigenmonzo]]s: 2, 14/11, 4/3
[[Mapping]]: [{{val|1 1 3 3 2}}, {{val|0 2 3 2 1}}, {{val|0 0 -4 -2 3}}]


Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -3 2|]
Mapping generators: 2, ~49/40, ~55/42


EDOs: 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde
{{Val list|legend=1| 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde }}


Badness: 0.000170
[[Badness]]: 0.000170


Projection pairs: 3 2401/800 5 22880495169/4575312500 7 1058841/151250 11 33275/3024 to 2.49/5.77/3
Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3


== 13-limit ==
== 13-limit ==
Commas: 2401/2400, 3025/3024, 4096/4095
Comma list: 2401/2400, 3025/3024, 4096/4095


Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -2 3|]
Mapping: [{{val|1 1 3 3 2 4}}, {{val|0 2 3 2 1 -9}}, {{val|0 0 -4 -2 3 6}}]


[[Generator]]s: 2, 49/40, 55/42
Mapping generators: 2, ~49/40, ~55/42


[[EDO|Edos]]: 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615
Vals: {{Val list| 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }}


Badness: 0.000855
Badness: 0.000855


Projection pairs: 3 2401/800 5 22880495169/4575312500 7 1058841/151250 11 33275/3024 1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3
Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024, ~13 = ~1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3


= Baldur =
= Baldur =
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