Breed family: Difference between revisions

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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]]

Revision as of 05:10, 6 January 2021

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

Comma c = 2401/2400

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

Eigenmonzos: 2, 6/5, 5/4

Lattice basis: 49/40 length 0.7858 8/7 length 1.1241

Angle(49/40, 8/7) = 107.367 degrees

Map to lattice: [<0 2 -1 0|, <0 0 -2 -1|]

Map [<1 1 1 2|, <0 2 1 1|, <0 0 2 1|]

Generators: 2, 49/40, 10/7

EDOs: 31, 41, 58, 68, 72, 171, 441, 612, 2308, 2578, 2749, 3361d

Badness: 0.0000153

Projection pair: 3 2401/800 to 2.5.7

Scales: breed11

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.

Commas: 243/242, 441/440

Minimax tuning

[|1 0 0 0 0>, |1/5 0 0 0 2/5>, |13/5 0 2 -2 1/5>, |13/5 0 1 -1 1/5>, |0 0 0 0 1>]

Eigenmonzos: 2, 7/5, 11/8

Map: [<1 1 1 2 2|, <0 2 1 1 5|, <0 0 2 1 0|]

EDOs: 31, 41, 58, 72, 130, 161, 171, 202

Badness: 0.000241

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

Jovial

Commas: 243/242, 441/440, 364/363

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>]

Eigenmonzos: 2, 10/9, 13/9

15-limit minimax

[|1 0 0 0 0 0>, |2 -1/4 1/2 -3/4 0 1/4>, |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>]

Eigenmonzos: 2, 15/13, 7/5

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

17-limit

Commas: 243/242, 441/440, 364/363, 595/594

17-limit minimax

[|1 0 0 0 0 0 0>, |3/7 -2 6/7 0 0 0 4/7>, |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>]

Eigenmonzos: 2, 18/17, 6/5

Map: [<1 1 1 2 2 1 3|, <0 2 1 1 5 11 9|, <0 0 2 1 0 -1 -3|]

Generators: 2, 11/9, 10/7

Edos: 41, 58, 72, 130, 171, 243, 274, 346, 373eg, 414e, 540eg, 787eg

Badness: 0.000741

Jofur

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

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

EDOs: 31, 41, 58, 89f, 99ef, 157ef

Badness: 0.000749

Jovis

Commas: 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|]

EDOs: 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef

Badness: 0.000542

Freya

Commas: 2401/2400, 3025/3024

11-limit minimax

[|1 0 0 0 0>, |0 1 0 0 0>, |11/10 11/10 0 4/5 -4/5>, |9/5 4/5 0 2/5 -2/5>, |9/5 4/5 0 -3/5 3/5>]

Eigenmonzos: 2, 14/11, 4/3

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

EDOs: 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde

Badness: 0.000170

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

13-limit

Commas: 2401/2400, 3025/3024, 4096/4095

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

Generators: 2, 49/40, 55/42

Edos: 31, 41, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615

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

Baldur

Commas: 2401/2400, 9801/9800

11-limit minimax

[|1 0 0 0 0>, |3/4 0 1/2 1/2 -1/2>, |0 0 1 0 0>, |23/16 0 5/8 1/8 -1/8>, |23/16 0 5/8 -7/8 7/8>]

Eigenmonzos: 5/4, 14/11

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

Generators: 99/70, 343/198, 10/7

EDOs: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de

Badness: 0.000166

Projection pairs: 2 9801/4900 3 117649/39204 7 9801/1400 11 913517247483640899/83082326424002500 to 5.7/2.99/4

Greenland

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

Map: [<2 0 1 3 7 -1|, <0 2 1 1 -2 4|, <0 0 2 1 3 2|]

Edos: 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf

Badness: 0.000433

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

Agni

Commas: 385/384, 1375/1372

11-limit minimax

[|1 0 0 0 0>, |0 1 0 0 0>, |23/10 3/10 2/5 0 -2/5>, |12/5 2/5 1/5 0 -1/5>, |23/10 3/10 -3/5 0 3/5>]

Eigenmonzos: 2, 4/3, 11/10

Lattice basis: 49/40 length 0.756, 10/7 length 0.819

Angle(49/40, 10/7) = 106.460 degrees

Map to lattice: [<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|]

Generators: 2, 49/40, 10/7

Edos: 27, 31, 41, 68, 72, 140, 171e, 181, 212, 284, 496ce, 527ce

Badness: 0.000494

13-limit

Commas: 385/384, 1375/1372, 625/624

Map: [<1 1 1 2 5 -1|, <0 2 1 1 0 2|, <0 0 2 1 -3 8|]

EDOs: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455ef

Badness: 0.000923

Vili

Commas: 2401/2400, 391314/390625

Map: [<1 1 5 4 10|, <0 2 3 2 6|, <0 0 -6 -3 -14|]

EDOs: 37, 93, 103, 130, 233, 270, 643, 670, 913, 1043, 1313, 1583

Badness: 0.00126

13-limit

Commas: 2401/2400, 10985/10976, 1001/1000

Map: [<1 1 5 4 10 4|, <0 2 3 2 6 1|, <0 0 -6 -3 -14 -1|]

EDOs: 37, 93, 103, 130, 233, 270, 643, 773, 913f, 1956ef

Badness: 0.000738

Zisa

Commas: 2401/2400, 5632/5625

Map: [<1 1 1 2 -3|, <0 2 1 1 8|, <0 0 2 1 8|]

EDOs: 21, 31, 109, 130, 239, 270, 670, 940, 1210, 2150c

Badness: 0.000640

13-limit

Commas: 2401/2400, 5632/5625, 4096/4095

Map: [<1 1 1 2 -3 7|, <0 2 1 1 8 -6|, <0 0 2 1 8 -3|]

EDOs: 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241

Badness: 0.000830

Frigg

Commas: 2401/2400, 644204/643125

Map: [<1 1 3 3 4|, <0 2 3 2 4|, <0 0 -10 -5 -11|]

EDOs: 51, 58, 103, 161, 212, 270, 643, 913

Badness: 0.00179

13-limit

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|]

EDOs: 58, 103, 161, 212, 270, 643, 1241, 2082ce, 3053ce, 3323cef

Badness: 0.000934

Ennealimmic

Commas: 2401/2400, 4375/4374

Map: [<9 1 1 12 0|, <0 2 3 2 0|, <0 0 0 0 1|]

Generators: 27/25, 5/3, 11

EDOs: 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d

Badness: 0.000275

13-limit

Commas: 2080/2079, 2401/2400, 4375/4374

Map: [<9 1 1 12 0 -31|, <0 2 3 2 0 5|, <0 0 0 0 1 1|]

EDOs: 27, 72, 171, 198, 270, 639, 711, 981, 1692e, 2673e

Badness: 0.000755

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