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== Breed  ==
== Breed  ==
[[Comma]]: 2401/2400
Subgroup: 2.3.5.7


[[Minimax tuning]]:
[[Comma list]]: 2401/2400
* 7- and 9-odd-limit minimax eigenmonzos: 2, 6/5, 5/4


Lattice basis: 49/40 length = 0.7858, 8/7 length = 1.1241
[[Mapping]]: [{{val| 1 1 1 2 }}, {{val| 0 2 1 1 }}, {{val| 0 0 2 1 }}]


Angle(49/40, 8/7) = 107.367°
Mapping generators: ~2, ~49/40, ~10/7


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


[[Mapping]]: [{{val|1 1 1 2}}, {{val|0 2 1 1}}, {{val|0 0 2 1}}]
Lattice basis:  
: 49/40 length = 0.7858, 8/7 length = 1.1241
: Angle (49/40, 8/7) = 107.367°


Mapping generators: 2, ~49/40, ~10/7
[[Minimax tuning]]:
* 7- and [[9-odd-limit]] eigenmonzos: 2, 6/5, 5/4


{{Val list|legend=1| 31, 41, 58, 68, 72, 171, 441, 612, 2308, 2578, 2749, 3361d }}
{{Val list|legend=1| 31, 41, 58, 68, 72, 171, 441, 612, 2308, 2578, 2749, 3361d }}


[[Badness]]: 0.0000153
[[Badness]]: 0.0153 × 10<sup>-3</sup>


[[Projection pair]]: 3 = ~2401/800 to 2.5.7
[[Projection pair]]: 3 = ~2401/800 to 2.5.7
Line 25: Line 27:
Scales: [[breed11]]
Scales: [[breed11]]


== Jove, aka Wonder  ==
== 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.
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.
Subgroup: 2.3.5.7.11


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


[[Minimax tuning]]:
[[Mapping]]: [{{val| 1 1 1 2 2 }}, {{val| 0 2 1 1 5 }}, {{val| 0 0 2 1 0 }}]
* 11-odd-limit eigenmonzos: 2, 7/5, 11/8


[[Mapping]]: [{{val|1 1 1 2 2}}, {{val|0 2 1 1 5}}, {{val|0 0 2 1 0}}]
Mapping generators: ~2, ~11/9, ~10/7


Mapping generators: 2, ~11/9, ~10/7
[[Minimax tuning]]:
* [[11-odd-limit]] eigenmonzos: 2, 7/5, 11/8


{{Val list|legend=1| 31, 41, 58, 72, 130, 161, 171, 202 }}
{{Val list|legend=1| 31, 41, 58, 72, 130, 161, 171, 202 }}


[[Badness]]: 0.000241
[[Badness]]: 0.241 × 10<sup>-3</sup>


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


; Music
* [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 ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 243/242, 364/363, 441/440
Comma list: 243/242, 364/363, 441/440


Line 52: Line 59:
* 15-odd-limit eigenmonzos: 2, 15/13, 7/5
* 15-odd-limit eigenmonzos: 2, 15/13, 7/5


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


Mapping generators: 2, ~11/9, ~10/7
Mapping generators: ~2, ~11/9, ~10/7


Vals: {{Val list| 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e }}
Vals: {{Val list| 41, 58, 72, 89, 113, 130, 243, 301e, 373e, 503e, 674e }}


Badness: 0.000624
Badness: 0.624 × 10<sup>-3</sup>
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


==== 17-limit  ====
Comma list: 243/242, 364/363, 441/440, 595/594
Comma list: 243/242, 364/363, 441/440, 595/594
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 }}]
Mapping generators: ~2, ~11/9, ~10/7


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


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}}]
Vals: {{Val list| 41, 58, 72, 130, 171, 243, 274, 346, 373eg, 414e, 540eg, 787eg }}
 
Mapping generators: 2, ~11/9, ~10/7


Vals: {{Val list| 41, 58, 72, 130, 171, 243, 274, 346, 373eg, 414e, 540eg, 787eg }}
Badness: 0.741 × 10<sup>-3</sup>


Badness: 0.000741
=== Jofur ===
Subgroup: 2.3.5.7.11.13


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


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


Mapping generators: 2, ~11/9, ~10/7
Mapping generators: ~2, ~11/9, ~10/7


Vals: {{Val list| 31, 41, 58, 89f, 99ef, 157ef }}
Vals: {{Val list| 31, 41, 58, 89f, 99ef, 157ef }}


Badness: 0.000749
Badness: 0.749 × 10<sup>-3</sup>
 
=== Jovis ===
Subgroup: 2.3.5.7.11.13


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


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


Mapping generators: 2, ~11/9, ~10/7
Mapping generators: ~2, ~11/9, ~10/7


Vals: {{Val list| 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef }}
Vals: {{Val list| 31, 58, 72, 103, 130, 233, 363, 798bf, 928bef }}


Badness: 0.000542
Badness: 0.542 × 10<sup>-3</sup>
 
== Freya ==
Subgroup: 2.3.5.7.11


== Freya  ==
[[Comma list]]: 2401/2400, 3025/3024
[[Comma list]]: 2401/2400, 3025/3024
[[Mapping]]: [{{val| 1 1 3 3 2 }}, {{val| 0 2 3 2 1 }}, {{val| 0 0 -4 -2 3 }}]
Mapping generators: ~2, ~49/40, ~55/42


[[Minimax tuning]]:
[[Minimax tuning]]:
* 11-odd-limit eigenmonzos: 2, 14/11, 4/3
* 11-odd-limit eigenmonzos: 2, 14/11, 4/3


[[Mapping]]: [{{val|1 1 3 3 2}}, {{val|0 2 3 2 1}}, {{val|0 0 -4 -2 3}}]
{{Val list|legend=1| 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde }}


Mapping generators: 2, ~49/40, ~55/42
[[Badness]]: 0.170 × 10<sup>-3</sup>


{{Val list|legend=1| 31, 41, 72, 167, 188, 198, 229, 239, 270, 342, 612, 954, 1566, 3443de, 4055de, 4397cde }}
[[Projection pair]]s: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3


[[Badness]]: 0.000170
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3
=== 13-limit  ===
Comma list: 2401/2400, 3025/3024, 4096/4095
Comma list: 2401/2400, 3025/3024, 4096/4095


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


Mapping generators: 2, ~49/40, ~55/42
Mapping generators: ~2, ~49/40, ~55/42


Vals: {{Val list| 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: 0.855 × 10<sup>-3</sup>


Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024, ~13 = ~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 ==
[[Comma]]s: 2401/2400, 9801/9800
Subgroup: 2.3.5.7.11


11-limit minimax
[[Comma list]]: 2401/2400, 9801/9800


[|1 0 0 0 0&gt;, |3/4 0 1/2 1/2 -1/2&gt;,  
[[Mapping]]: [{{val| 2 0 1 3 7 }}, {{val| 0 2 1 1 -2 }}, {{val| 0 0 2 1 3 }}]
|0 0 1 0 0&gt;, |23/16 0 5/8 1/8 -1/8&gt;,
|23/16 0 5/8 -7/8 7/8&gt;]


[[Eigenmonzo]]s: 5/4, 14/11
[[Mapping generator]]s: ~99/70, ~343/198, ~10/7


Map: [&lt;2 0 1 3 7|, &lt;0 2 1 1 -2|, &lt;0 0 2 1 3|]
[[Minimax tuning]]:  
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/4 0 1/2 1/2 -1/2 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 23/16 0 5/8 1/8 -1/8 }}, {{monzo| 23/16 0 5/8 -7/8 7/8 }}]
: [[Eigenmonzo]]s: 5/4, 14/11


[[Generator]]s: 99/70, 343/198, 10/7
{{Val list|legend=1| 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
[[Badness]]: 0.166 × 10<sup>-3</sup>


Badness: 0.000166
[[Projection pair]]s: 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 ===
Subgroup: 2.3.5.7.11.13


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


Map: [&lt;2 0 1 3 7 -1|, &lt;0 2 1 1 -2 4|, &lt;0 0 2 1 3 2|]
Mapping: [{{val| 2 0 1 3 7 -1 }}, {{val| 0 2 1 1 -2 4 }}, {{val| 0 0 2 1 3 2 }}]


[[EDO|Edos]]: 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf
Vals: {{Val list| 58, 72, 130, 198, 270, 940, 1210f, 1480cf, 1750cf }}


Badness: 0.000433
Badness: 0.433 × 10<sup>-3</sup>


[[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
Complexity 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]]s: 385/384, 1375/1372
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 385/384, 1375/1372
 
[[Mapping]]: [{{val| 1 1 1 2 5 }}, {{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}]
 
Mapping generators: ~2, ~49/40, ~10/7
 
Map to lattice: [{{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}]
 
Lattice basis:
: 49/40 length = 0.756, 10/7 length = 0.819
: Angle (49/40, 10/7) = 106.460 degrees
 
[[Minimax tuning]]:
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 23/10 3/10 2/5 0 -2/5 }}, {{monzo| 12/5 2/5 1/5 0 -1/5 }}, {{monzo| 23/10 3/10 -3/5 0 3/5 }}]
: [[Eigenmonzo]]s: 2, 4/3, 11/10
 
{{Val list|legend=1| 27, 31, 41, 68, 72, 140, 171e, 181, 212, 284, 496ce, 527ce }}


11-limit minimax
[[Badness]]: 0.494 × 10<sup>-3</sup>


[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;,
=== 13-limit ===
|23/10 3/10 2/5 0 -2/5&gt;,
Subgroup: 2.3.5.7.11.13
|12/5 2/5 1/5 0 -1/5&gt;,
|23/10 3/10 -3/5 0 3/5&gt;]


[[Eigenmonzo]]s: 2, 4/3, 11/10
Comma list: 385/384, 625/624, 1375/1372


Lattice basis: 49/40 length 0.756, 10/7 length 0.819
Mapping: [{{val| 1 1 1 2 5 -1 }}, {{val| 0 2 1 1 0 2 }}, {{val| 0 0 2 1 -3 8 }}]


Angle(49/40, 10/7) = 106.460 degrees
Vals: {{Val list| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455ef }}


Map to lattice: [&lt;0 2 1 1 0|, &lt;0 0 2 1 -3|]
Badness: 0.923 × 10<sup>-3</sup>


Map: [&lt;1 1 1 2 5|, &lt;0 2 1 1 0|, &lt;0 0 2 1 -3|]
== Vili ==
Subgroup: 2.3.5.7.11


[[Generator]]s: 2, 49/40, 10/7
[[Comma list]]: 2401/2400, 391314/390625


[[EDO|Edos]]: 27, 31, 41, 68, 72, 140, 171e, 181, [[212edo|212]], [[284edo|284]], [[496edo|496ce]], [[527edo|527ce]]
[[Mapping]]: [{{val| 1 1 5 4 10 }}, {{val| 0 2 3 2 6 }}, {{val| 0 0 -6 -3 -14 }}]


Badness: 0.000494
{{Val list|legend=1| 37, 93, 103, 130, 233, 270, 643, 670, 913, 1043, 1313, 1583 }}


=== 13-limit  ===
[[Badness]]: 1.26 × 10<sup>-3</sup>
Commas: 385/384, 1375/1372, 625/624


Map: [&lt;1 1 1 2 5 -1|, &lt;0 2 1 1 0 2|, &lt;0 0 2 1 -3 8|]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455ef
Comma list: 1001/1000, 2401/2400, 10985/10976


Badness: 0.000923
Mapping: [{{val| 1 1 5 4 10 4 }}, {{val| 0 2 3 2 6 1 }}, {{val| 0 0 -6 -3 -14 -1 }}]


== Vili  ==
Vals: {{Val list| 37, 93, 103, 130, 233, 270, 643, 773, 913f, 1956ef }}
Commas: 2401/2400, 391314/390625


Map: [&lt;1 1 5 4 10|, &lt;0 2 3 2 6|, &lt;0 0 -6 -3 -14|]
Badness: 0.738 × 10<sup>-3</sup>


EDOs: 37, 93, 103, 130, 233, 270, 643, 670, 913, 1043, 1313, 1583
== Zisa ==
Subgroup: 2.3.5.7.11


Badness: 0.00126
[[Comma list]]: 2401/2400, 5632/5625


=== 13-limit  ===
[[Mapping]]: [{{val| 1 1 1 2 -3 }}, {{val| 0 2 1 1 8 }}, {{val| 0 0 2 1 8 }}]
Commas: 2401/2400, 10985/10976, 1001/1000


Map: [&lt;1 1 5 4 10 4|, &lt;0 2 3 2 6 1|, &lt;0 0 -6 -3 -14 -1|]
{{Val list|legend=1| 21, 31, 109, 130, 239, 270, 670, 940, 1210, 2150c }}


EDOs: 37, 93, 103, 130, 233, 270, 643, 773, 913f, 1956ef
[[Badness]]: 0.640 × 10<sup>-3</sup>


Badness: 0.000738
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== Zisa  ==
Comma list: 2401/2400, 4096/4095, 5632/5625
Commas: 2401/2400, 5632/5625


Map: [&lt;1 1 1 2 -3|, &lt;0 2 1 1 8|, &lt;0 0 2 1 8|]
Mapping: [{{val| 1 1 1 2 -3 7 }}, {{val| 0 2 1 1 8 -6 }}, {{val| 0 0 2 1 8 -3 }}]


EDOs: 21, 31, 109, 130, 239, 270, 670, 940, 1210, 2150c
Vals: {{Val list| 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }}


Badness: 0.000640
Badness: 0.830 × 10<sup>-3</sup>


=== 13-limit  ===
== Frigg ==
Commas: 2401/2400, 5632/5625, 4096/4095
Subgroup: 2.3.5.7.11


Map: [&lt;1 1 1 2 -3 7|, &lt;0 2 1 1 8 -6|, &lt;0 0 2 1 8 -3|]
[[Comma list]]: 2401/2400, 644204/643125


EDOs: 21, 31, 109, 130, 239, 270, 571, 701, 841, 971, 1241
[[Mapping]]: [{{val| 1 1 3 3 4 }}, {{val| 0 2 3 2 4 }}, {{val| 0 0 -10 -5 -11 }}]


Badness: 0.000830
{{Val list|legend=1| 51, 58, 103, 161, 212, 270, 643, 913 }}


== Frigg  ==
[[Badness]]: 1.79 × 10<sup>-3</sup>
Commas: 2401/2400, 644204/643125


Map: [&lt;1 1 3 3 4|, &lt;0 2 3 2 4|, &lt;0 0 -10 -5 -11|]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: 51, 58, 103, 161, 212, 270, 643, 913
Comma list: 1001/1000, 2401/2400, 10648/10647


Badness: 0.00179
Mapping: [{{val| 1 1 3 3 4 5 }}, {{val| 0 2 3 2 4 3 }}, {{val| 0 0 -10 -5 -11 -14 }}]


=== 13-limit  ===
Vals: {{Val list| 58, 103, 161, 212, 270, 643, 1241, 2082ce, 3053ce, 3323cef }}
Commas: 1001/1000, 2401/2400, 10648/10647


Map: [&lt;1 1 3 3 4 5|, &lt;0 2 3 2 4 3|, &lt;0 0 -10 -5 -11 -14|]
Badness: 0.934 × 10<sup>-3</sup>


EDOs: 58, 103, 161, 212, 270, 643, 1241, 2082ce, 3053ce, 3323cef
== Ennealimmic ==
Subgroup: 2.3.5.7.11


Badness: 0.000934
[[Comma list]]: 2401/2400, 4375/4374


== Ennealimmic  ==
[[Mapping]]: [{{val| 9 1 1 12 0 }}, {{val| 0 2 3 2 0 }}, {{val| 0 0 0 0 1 }}]
Commas: 2401/2400, 4375/4374


Map: [&lt;9 1 1 12 0|, &lt;0 2 3 2 0|, &lt;0 0 0 0 1|]
Mapping generators: 27/25, 5/3, 11


Generators: 27/25, 5/3, 11
{{Val list|legend=1| 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d }}


EDOs: 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 4896d
[[Badness]]: 0.275 × 10<sup>-3</sup>


Badness: 0.000275
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


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


Map: [&lt;9 1 1 12 0 -31|, &lt;0 2 3 2 0 5|, &lt;0 0 0 0 1 1|]
Mapping: [{{val| 9 1 1 12 0 -31 }}, {{val| 0 2 3 2 0 5 }}, {{val| 0 0 0 0 1 1 }}]


EDOs: 27, 72, 171, 198, 270, 639, 711, 981, 1692e, 2673e
Vals: {{Val list| 27, 72, 171, 198, 270, 639, 711, 981, 1692e, 2673e }}


Badness: 0.000755
Badness: 0.755 × 10<sup>-3</sup>


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Breed]]
[[Category:Breed]]
[[Category:Rank 3]]
[[Category:Rank 3]]

Revision as of 06:11, 6 June 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

Subgroup: 2.3.5.7

Comma list: 2401/2400

Mapping: [⟨1 1 1 2], ⟨0 2 1 1], ⟨0 0 2 1]]

Mapping generators: ~2, ~49/40, ~10/7

Map to lattice: [⟨0 2 -1 0], ⟨0 0 -2 -1]]

Lattice basis:

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

Minimax tuning:

Template:Val list

Badness: 0.0153 × 10-3

Projection pair: 3 = ~2401/800 to 2.5.7

Scales: breed11

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.

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440

Mapping: [⟨1 1 1 2 2], ⟨0 2 1 1 5], ⟨0 0 2 1 0]]

Mapping generators: ~2, ~11/9, ~10/7

Minimax tuning:

Template:Val list

Badness: 0.241 × 10-3

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

Music

Jovial

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 364/363, 441/440

Minimax tuning:

  • 13-odd-limit eigenmonzos: 2, 10/9, 13/10
  • 15-odd-limit eigenmonzos: 2, 15/13, 7/5

Mapping: [⟨1 1 1 2 2 1], ⟨0 2 1 1 5 11], ⟨0 0 2 1 0 -1]]

Mapping generators: ~2, ~11/9, ~10/7

Vals: Template:Val list

Badness: 0.624 × 10-3

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 243/242, 364/363, 441/440, 595/594

Mapping: [⟨1 1 1 2 2 1 3], ⟨0 2 1 1 5 11 9], ⟨0 0 2 1 0 -1 -3]]

Mapping generators: ~2, ~11/9, ~10/7

Minimax tuning:

  • 17-odd-limit eigenmonzos: 2, 18/17, 6/5

Vals: Template:Val list

Badness: 0.741 × 10-3

Jofur

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 196/195, 243/242

Mapping: [⟨1 1 1 2 2 4], ⟨0 2 1 1 5 -1], ⟨0 0 2 1 0 0]]

Mapping generators: ~2, ~11/9, ~10/7

Vals: Template:Val list

Badness: 0.749 × 10-3

Jovis

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 441/440

Mapping: [⟨1 1 1 2 2 2], ⟨0 2 1 1 5 -3], ⟨0 0 2 1 0 5]]

Mapping generators: ~2, ~11/9, ~10/7

Vals: Template:Val list

Badness: 0.542 × 10-3

Freya

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024

Mapping: [⟨1 1 3 3 2], ⟨0 2 3 2 1], ⟨0 0 -4 -2 3]]

Mapping generators: ~2, ~49/40, ~55/42

Minimax tuning:

  • 11-odd-limit eigenmonzos: 2, 14/11, 4/3

Template:Val list

Badness: 0.170 × 10-3

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

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2401/2400, 3025/3024, 4096/4095

Mapping: [⟨1 1 3 3 2 4], ⟨0 2 3 2 1 -9], ⟨0 0 -4 -2 3 6]]

Mapping generators: ~2, ~49/40, ~55/42

Vals: Template:Val list

Badness: 0.855 × 10-3

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

Baldur

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 9801/9800

Mapping: [⟨2 0 1 3 7], ⟨0 2 1 1 -2], ⟨0 0 2 1 3]]

Mapping generators: ~99/70, ~343/198, ~10/7

Minimax tuning:

[[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

Template:Val list

Badness: 0.166 × 10-3

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

Greenland

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1716/1715

Mapping: [⟨2 0 1 3 7 -1], ⟨0 2 1 1 -2 4], ⟨0 0 2 1 3 2]]

Vals: Template:Val list

Badness: 0.433 × 10-3

Complexity 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

Subgroup: 2.3.5.7.11

Comma list: 385/384, 1375/1372

Mapping: [⟨1 1 1 2 5], ⟨0 2 1 1 0], ⟨0 0 2 1 -3]]

Mapping generators: ~2, ~49/40, ~10/7

Map to lattice: [⟨0 2 1 1 0], ⟨0 0 2 1 -3]]

Lattice basis:

49/40 length = 0.756, 10/7 length = 0.819
Angle (49/40, 10/7) = 106.460 degrees

Minimax tuning:

[[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

Template:Val list

Badness: 0.494 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 625/624, 1375/1372

Mapping: [⟨1 1 1 2 5 -1], ⟨0 2 1 1 0 2], ⟨0 0 2 1 -3 8]]

Vals: Template:Val list

Badness: 0.923 × 10-3

Vili

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 391314/390625

Mapping: [⟨1 1 5 4 10], ⟨0 2 3 2 6], ⟨0 0 -6 -3 -14]]

Template:Val list

Badness: 1.26 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 2401/2400, 10985/10976

Mapping: [⟨1 1 5 4 10 4], ⟨0 2 3 2 6 1], ⟨0 0 -6 -3 -14 -1]]

Vals: Template:Val list

Badness: 0.738 × 10-3

Zisa

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 5632/5625

Mapping: [⟨1 1 1 2 -3], ⟨0 2 1 1 8], ⟨0 0 2 1 8]]

Template:Val list

Badness: 0.640 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2401/2400, 4096/4095, 5632/5625

Mapping: [⟨1 1 1 2 -3 7], ⟨0 2 1 1 8 -6], ⟨0 0 2 1 8 -3]]

Vals: Template:Val list

Badness: 0.830 × 10-3

Frigg

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 644204/643125

Mapping: [⟨1 1 3 3 4], ⟨0 2 3 2 4], ⟨0 0 -10 -5 -11]]

Template:Val list

Badness: 1.79 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 2401/2400, 10648/10647

Mapping: [⟨1 1 3 3 4 5], ⟨0 2 3 2 4 3], ⟨0 0 -10 -5 -11 -14]]

Vals: Template:Val list

Badness: 0.934 × 10-3

Ennealimmic

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 4375/4374

Mapping: [⟨9 1 1 12 0], ⟨0 2 3 2 0], ⟨0 0 0 0 1]]

Mapping generators: 27/25, 5/3, 11

Template:Val list

Badness: 0.275 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2401/2400, 4375/4374

Mapping: [⟨9 1 1 12 0 -31], ⟨0 2 3 2 0 5], ⟨0 0 0 0 1 1]]

Vals: Template:Val list

Badness: 0.755 × 10-3

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