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__FORCETOC__
The '''breed family''' of temperaments are rank-3 microtemperaments which temper out [[2401/2400]]. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[optimal patent val]] 2749et will certainly do the trick.  
Breed is a 7-limit microtemperament which tempers out 2401/2400. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[Optimal_patent_val|optimal patent val]] 2749et will certainly do the trick.


=Vital statistics=
= Breed =
[[Comma|Comma]] c = 2401/2400
[[Comma]] c = 2401/2400


7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat
7- and 9-limit minimax tuning: 3 and 5 just, 7 1/4c flat


[[Eigenmonzo|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
Line 17: Line 16:
Map [<1 1 1 2|, <0 2 1 1|, <0 0 2 1|]
Map [<1 1 1 2|, <0 2 1 1|, <0 0 2 1|]


[[generator|Generators]]: 2, 49/40, 10/7
[[Generator]]s: 2, 49/40, 10/7


[[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]]
[[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]]
Line 23: Line 22:
Badness: 0.0000153
Badness: 0.0000153


[[Projection_pair|Projection pair]]: 3 2401/800 to 2.5.7
[[Projection pair]]: 3 2401/800 to 2.5.7


Scales: [[breed11|breed11]]
Scales: [[breed11]]


=Jove, aka Wonder=
= Jove, aka Wonder =
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.


11-limit
[[Comma]]s: 243/242, 441/440


[[Comma|Commas]]: 243/242, 441/440
[[Minimax tuning]]
 
[[Minimax_tuning|Minimax tuning]]


[|1 0 0 0 0>, |1/5 0 0 0 2/5>,  
[|1 0 0 0 0>, |1/5 0 0 0 2/5>,  
Line 40: Line 37:
|0 0 0 0 1>]
|0 0 0 0 1>]


[[Eigenmonzo|Eigenmonzos]]: 2, 7/5, 11/8
[[Eigenmonzo]]s: 2, 7/5, 11/8


Map: [<1 1 1 2 2|, <0 2 1 1 5|, <0 0 2 1 0|]
Map: [<1 1 1 2 2|, <0 2 1 1 5|, <0 0 2 1 0|]
Line 50: Line 47:
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|jove41]] by Chris Vaisvil
* [http://micro.soonlabel.com/hobbit_scales/20120418-jove41.mp3 By Jove!] in [[jove41]] by Chris Vaisvil


==Jovial==
== Jovial ==
[[Comma|Commas]]: 243/242, 441/440, 364/363
[[Comma]]s: 243/242, 441/440, 364/363


13-limit minimax
13-limit minimax
Line 62: Line 59:
|34/11 -46/11 4/11 0 0 19/11>]
|34/11 -46/11 4/11 0 0 19/11>]


[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/9
[[Eigenmonzo]]s: 2, 10/9, 13/9


15-limit minimax
15-limit minimax
Line 72: Line 69:
|11/2 -11/8 7/4 -25/8 0 11/8>]
|11/2 -11/8 7/4 -25/8 0 11/8>]


[[Eigenmonzo|Eigenmonzos]]: 2, 15/13, 7/5
[[Eigenmonzo]]s: 2, 15/13, 7/5


Map: [<1 1 1 2 2 1|, <0 2 1 1 5 11|, <0 2 1 1 0 -1|]
Map: [<1 1 1 2 2 1|, <0 2 1 1 5 11|, <0 2 1 1 0 -1|]
Line 80: Line 77:
Badness: 0.000624
Badness: 0.000624


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


Line 100: Line 97:
Badness: 0.000741
Badness: 0.000741


==Jofur==
== Jofur ==
Commas: 243/242, 441/440, 144/143
Commas: 243/242, 441/440, 144/143


Line 109: Line 106:
Badness: 0.000749
Badness: 0.000749


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


Line 118: Line 115:
Badness: 0.000542
Badness: 0.000542


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


11-limit minimax
11-limit minimax
Line 129: Line 124:
|9/5 4/5 0 2/5 -2/5>, |9/5 4/5 0 -3/5 3/5>]
|9/5 4/5 0 2/5 -2/5>, |9/5 4/5 0 -3/5 3/5>]


[[Eigenmonzo|Eigenmonzos]]: 2, 14/11, 4/3
[[Eigenmonzo]]s: 2, 14/11, 4/3


Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -3 2|]
Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -3 2|]
Line 139: Line 134:
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
Commas: 2401/2400, 3025/3024, 4096/4095


Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -2 3|]
Map: [<1 1 3 3 2|, <0 2 3 2 1|, <0 0 -4 -2 3|]


[[generator|Generators]]: 2, 49/40, 55/42
[[Generator]]s: 2, 49/40, 55/42


[[EDO|Edos]]: 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615
[[EDO|Edos]]: 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615
Line 152: Line 147:
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 1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3


=Baldur=
= Baldur =
[[Comma|Commas]]: 2401/2400, 9801/9800
[[Comma]]s: 2401/2400, 9801/9800


11-limit minimax
11-limit minimax
Line 161: Line 156:
|23/16 0 5/8 -7/8 7/8>]
|23/16 0 5/8 -7/8 7/8>]


[[Eigenmonzo|Eigenmonzos]]: 5/4, 14/11
[[Eigenmonzo]]s: 5/4, 14/11


Map: [<2 0 1 3 7|, <0 2 1 1 -2|, <0 0 2 1 3|]
Map: [<2 0 1 3 7|, <0 2 1 1 -2|, <0 0 2 1 3|]


[[generator|Generators]]: 99/70, 343/198, 10/7
[[Generator]]s: 99/70, 343/198, 10/7


EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de
EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de
Line 173: Line 168:
Projection pairs: 2 9801/4900 3 117649/39204 7 9801/1400 11  913517247483640899/83082326424002500 to 5.7/2.99/4
Projection pairs: 2 9801/4900 3 117649/39204 7 9801/1400 11  913517247483640899/83082326424002500 to 5.7/2.99/4


==Greenland==
== Greenland ==
Commas: 676/675, 1001/1000, 1716/1715
Commas: 676/675, 1001/1000, 1716/1715


Line 182: Line 177:
Badness: 0.000433
Badness: 0.000433


[[Spectrum_of_a_temperament|Spectrum]]: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9
[[Spectrum of a temperament|Spectrum]]: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9


Projection pairs: 2 19600/9801 3 676/225 5 10400/2079 7 20384000/2910897 11 19208000000000000/1750211597736459 13 5026736/385875 to 10/7.200/99.26/15
Projection pairs: 2 19600/9801 3 676/225 5 10400/2079 7 20384000/2910897 11 19208000000000000/1750211597736459 13 5026736/385875 to 10/7.200/99.26/15


=Agni=
= Agni =
[[Comma|Commas]]: 385/384, 1375/1372
[[Comma]]s: 385/384, 1375/1372


11-limit minimax
11-limit minimax
Line 196: Line 191:
|23/10 3/10 -3/5 0 3/5>]
|23/10 3/10 -3/5 0 3/5>]


[[Eigenmonzo|Eigenmonzos]]: 2, 4/3, 11/10
[[Eigenmonzo]]s: 2, 4/3, 11/10


Lattice basis: 49/40 length 0.756, 10/7 length 0.819
Lattice basis: 49/40 length 0.756, 10/7 length 0.819
Line 206: Line 201:
Map: [<1 1 1 2 5|, <0 2 1 1 0|, <0 0 2 1 -3|]
Map: [<1 1 1 2 5|, <0 2 1 1 0|, <0 0 2 1 -3|]


[[generator|Generators]]: 2, 49/40, 10/7
[[Generator]]s: 2, 49/40, 10/7


[[EDO|Edos]]: 27, 31, 41, 68, 72, 140, 171e, 181, [[212edo|212]], [[284edo|284]], [[496edo|496ce]], [[527edo|527ce]]
[[EDO|Edos]]: 27, 31, 41, 68, 72, 140, 171e, 181, [[212edo|212]], [[284edo|284]], [[496edo|496ce]], [[527edo|527ce]]
Line 212: Line 207:
Badness: 0.000494
Badness: 0.000494


==13-limit==
== 13-limit ==
Commas: 385/384, 1375/1372, 625/624
Commas: 385/384, 1375/1372, 625/624


Line 221: Line 216:
Badness: 0.000923
Badness: 0.000923


=Vili=
= Vili =
Commas: 2401/2400, 391314/390625
Commas: 2401/2400, 391314/390625


Line 230: Line 225:
Badness: 0.00126
Badness: 0.00126


==13-limit==
== 13-limit ==
Commas: 2401/2400, 10985/10976, 1001/1000
Commas: 2401/2400, 10985/10976, 1001/1000


Line 239: Line 234:
Badness: 0.000738
Badness: 0.000738


=Zisa=
= Zisa =
Commas: 2401/2400, 5632/5625
Commas: 2401/2400, 5632/5625


Line 248: Line 243:
Badness: 0.000640
Badness: 0.000640


==13-limit==
== 13-limit ==
Commas: 2401/2400, 5632/5625, 4096/4095
Commas: 2401/2400, 5632/5625, 4096/4095


Line 257: Line 252:
Badness: 0.000830
Badness: 0.000830


=Frigg=
= Frigg =
Commas: 2401/2400, 644204/643125
Commas: 2401/2400, 644204/643125


Line 266: Line 261:
Badness: 0.00179
Badness: 0.00179


==13-limit==
== 13-limit ==
Commas: 2401/2400, 10648/10647, 1001/1000
Commas: 1001/1000, 2401/2400, 10648/10647


Map: [<1 1 3 3 4 5|, <0 2 3 2 4 3|, <0 0 -10 -5 -11 -14|]
Map: [<1 1 3 3 4 5|, <0 2 3 2 4 3|, <0 0 -10 -5 -11 -14|]
Line 275: Line 270:
Badness: 0.000934
Badness: 0.000934


=Ennealimmic=
= Ennealimmic =
Commas: 2401/2400, 4375/4374
Commas: 2401/2400, 4375/4374


Line 286: Line 281:
Badness: 0.000275
Badness: 0.000275


==13-limit==
== 13-limit ==
Commas: 2080/2079, 2401/2400, 4375/4374
Commas: 2080/2079, 2401/2400, 4375/4374


Line 297: Line 292:
[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Planar temperament]]
[[Category:Breed]]
[[Category:Breed]]
[[Category:Rank 3]]
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