View source for Catalog of 3.5.7 subgroup rank two temperaments

{{Todo|merge articles|inline=1|comment=Merge into [[No-twos subgroup temperaments]]}}
__FORCETOC__
== Table ==
{| class="wikitable"
|-
! Name
! Comma ratio
! Comma n/d
! Comma c
! Comma name
! a&amp;b (3)
! a&amp;b (2)
! Complexity
! Damage
! Mapping
! TE gen1
! TE gen2
! Per/3
! MOS
|-
| [[No-twos subgroup temperaments#Izar|Izar]]
| {{vector| -11 -7 12 }}
| style="text-align: center;" | 13841287201/13839609375
| 0.210
|
| b271 &amp; b1071
| [http://x31eq.com/cgi-bin/rt.cgi?ets=171p_676cd&limit=3_5_7 171p &amp; 676cd]
| 11.675
| 0.003
| {{ket|{{bra| 271 397 480 }} {{bra| 1071 1569 1897 }}}}
| 1901.9584
| 877.2825
| 1
| 2*,3,5,7,9,11*,13*,24,37,50,63,76,...258*,271*
|-
| [[Canopus|Canopus]]
| {{vector| 3 4 -5 }}
| style="text-align: center;" | 16875/16807
| 6.990
| small BP diesis, [[Mirkwai_clan|mirkwai]]
| b13 &amp; b101
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_64cd&limit=3_5_7 8d &amp; 64cd]
| 4.866
| 0.249
| {{ket|{{bra| 13 19 23 }} {{bra| 101 148 179 }}}}
| 1901.7828
| 583.9055
| 1
| 2,3*,4,7,10*,13*,23,36,49,62,75,88,101,114*
|-
| *Procyon
| {{vector| -8 -3 7 }}
| style="text-align: center;" | 823543/820125
| 7.200
|
| b13 &amp; b144
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_91p&limit=3_5_7 8d &amp; 91p]
| 6.810
| 0.183
| {{ket|{{bra| 13 19 23 }} {{bra| 144 211 255 }}}}
| 1902.198
| 145.4124
| 1
| ...13*,14,27,40,53,66,79,92,105,118,131,144,157*
|-
| *Gacrux
| {{vector| 6 8 -10 }}
| style="text-align: center;" | 284765625/282475249
| 13.981
|
|
|
|
|
|
|
|
|
|
|-
| [[BPS|BPS (Bohlen-Pierce-Stearns)]]
| {{vector| -5 1 2 }}
| style="text-align: center;" | 245/243
| 14.191
| minor BP diesis, [[Sensamagic_clan|sensamagic]]
| b13 &amp; b17
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_11cd&limit=3_5_7 8d &amp; 11cd]
| 2.749
| 0.895
| {{ket|{{bra| 13 19 23 }} {{bra| 17 25 30 }}}}
| 1903.7424
| 440.902
| 1
| 2,3,4*,5,9,13*,17,30,43,56,69,82*,95*
|-
| [[Sirius]]
| {{vector| -2 5 -3 }}
| style="text-align: center;" | 3125/3087
| 21.181
| major BP diesis, [[Gariboh_family|gariboh]]
| b13 &amp; b19
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_12p&limit=3_5_7 8d &amp; 12p]
| 4.021
| 0.913
| {{ket|{{bra| 13 19 23 }} {{bra| 19 28 34 }}}}
| 1902.4482
| 293.7397
| 1
| 2,3,4,5,6*,7,13*,19,32,45,58,71,84,97,110,123,136*
|-
| *Betelgeuse
| {{vector| -13 -2 9 }}
| style="text-align: center;" | 40353607/39858075
| 21.391
|
| b13 &amp; b148
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_93bccd&limit=3_5_7 8d &amp; 93bccd]
| 8.754
| 0.423
| {{ket|{{bra| 13 19 23 }} {{bra| 148 217 262 }}}}
| 1902.5991
| 732.4139
| 1
| 2*,3*,5*,8,13*,...226*
|-
| *Miaplacidus
| {{vector| 1 9 -8 }}
| style="text-align: center;" | 5859375/5764801
| 28.171
|
| b13 &amp; b94d
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_59ccdd&limit=3_5_7 8d &amp; 59ccdd]
| 7.788
| 0.627
| {{ket|{{bra| 13 19 23 }} {{bra| 94 138 167 }}}}
| 1901.88
| 585.8431
| 1
| 2,3*,4,7,10,13*,16,29,42,55,68,81,94,...224*
|-
| [[Arcturus]]
| {{vector| -7 6 -1 }}
| style="text-align: center;" | 15625/15309
| 35.371
| great BP diesis
| b13 &amp; b2
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_1cdd&limit=3_5_7 8d &amp; 1cdd]
| 4.823
| 1.271
| {{ket|{{bra| 13 19 23 }} {{bra| 2 3 4 }}}}
| 1903.8685
| 878.9253
| 1
| 2*,3,5,7,9,11,13*
|-
| *Pollux
| {{vector| -18 -1 11 }}
| style="text-align: center;" | 1977326743/1937102445
| 35.581
|
| b13 &amp; b139
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_88dd&limit=3_5_7 8d &amp; 88dd]
| 10.697
| 0.576
| {{ket|{{bra| 13 19 23 }} {{bra| 139 204 246 }}}}
| 1902.8625
| 438.6389
| 1
| 2,3,4*,5,9*,13
|-
| *Castor
| {{vector| -1 14 -11 }}
| style="text-align: center;" | 6103515625/5931980229
| 49.352
|
| b13 &amp; b113d
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_71ccddd&limit=3_5_7 8d &amp; 71ccddd]
| 11.259
| 0.760
| {{ket|{{bra| 13 19 23 }} {{bra| 113 166 201 }}}}
| 1902.0166
| 438.5094
| 1
| 2,3,4*,5,9*,13
|-
| *Muphrid
| {{vector| -12 7 1 }}
| style="text-align: center;" | 546875/531441
| 49.562
|
| b13 &amp; b2d
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_1c&limit=3_5_7 8d &amp; 1c]
| 6.599
| 1.302
| {{ket|{{bra| 13 19 23 }} {{bra| 2 3 3 }}}}
| 1904.3123
| 879.0503
| 1
| 2*,3,5,7,9,11,13*
|-
| *Rigel
| {{vector| -9 11 -4 }}
| style="text-align: center;" | 48828125/47258883
| 56.552
|
| b13 &amp; b21d
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d_5d&limit=3_5_7 8d &amp; 5d]
| 8.844
| 1.108
| {{ket|{{bra| 13 19 23 }} {{bra| 21 31 38 }}}}
| 1903.2571
| 731.7183
| 1
| 2*,3*,5*,8*,13*
|-
| *Mirzam
| {{vector| -17 8 3 }}
| style="text-align: center;" | 133984375/129140163
| 63.752
|
| b13 &amp; b32d
| [http://x31eq.com/cgi-bin/rt.cgi?ets=8d+20c&limit=3.5.7 8d &amp; 20c]
| 9.347
| 1.182
| {{ket|{{bra| 13 19 23 }} {{bra| 32 47 56 }}}}
| 1904.3391
| 293.1889
| 1
| 2,3,4,5,6*,7,13*
|-
|
| {{vector| 15 -9 -1 }}
| style="text-align: center;" | 14348907/13671875
| 83.676
|
| b17 &amp; b32
| [http://x31eq.com/cgi-bin/rt.cgi?ets=11cd_20cd&limit=3_5_7 11cd &amp; 20cd]
| 8.228
| 1.762
| {{ket|{{bra| 17 25 30 }} {{bra| 32 47 57 }}}}
| 1898.8326
| 891.5018
| 1
| 2*,3,5,7,9,11,13,15*,17*,32,49*,66,115,164*
|-
| *Capella
| {{vector| 10 -8 1 }}
| style="text-align: center;" | 413343/390625
| 97.866
| small link
| b17 &amp; b19
| [http://x31eq.com/cgi-bin/rt.cgi?ets=11cd_12p&limit=3_5_7 12p &amp; 11cd]
| 6.452
| 2.629
| {{ket|{{bra| 17 25 30 }} {{bra| 19 28 34 }}}}
| 1897.8856
| 895.415
| 1
| 2*,3,5,7,9,11,13,15,17*,19,36*,53*,89,142*,195*
|-
|
| {{vector| 13 -4 -4 }}
| style="text-align: center;" | 1594323/1500625
| 104.857
|
| b4 &amp; b32
| [http://x31eq.com/cgi-bin/rt.cgi?ets=3bcdd_20cd&limit=3_5_7 3bcdd &amp; 20cd]
| 7.126
| 2.550
| {{ket|{{bra| 4 6 7 }} {{bra| 32 47 57 }}}}
| 474.1446
| 55.0036
| 4
| ...32*,36*,68*,104*,172*,276*
|-
|
| {{vector| 16 0 -9 }}
| style="text-align: center;" | 43046721/40353607
| 111.847
|
| b9 &amp; b36
| [http://x31eq.com/cgi-bin/rt.cgi?ets=6bcd_23d&limit=3_5_7 6bcd &amp; 23d]
| 8.773
| 2.209
| {{ket|{{bra| 9 13 16 }} {{bra| 36 53 64 }}}}
| 210.9385
| 44.1126
| 9
| 18,27,36*,45*,81,126,171*,216*,387*
|-
| Toliman
| {{vector| 5 -7 3 }}
| style="text-align: center;" | 83349/78125
| 112.057
| minor link
| b6 &amp; b17
| [http://x31eq.com/cgi-bin/rt.cgi?ets=4p_11cd&limit=3_5_7 4p &amp; 11cd]
| 5.649
| 3.437
| {{ket|{{bra| 6 9 11 }} {{bra| 17 25 30 }}}}
| 1898.4178
| 333.298
| 1
| 2,3,4,5*,6*,11,17*,23,40,57*,74,131*
|-
| Vega
| {{vector| 8 -3 -2 }}
| style="text-align: center;" | 6561/6125
| 119.047
| major link
| b4 &amp; b15
| [http://x31eq.com/cgi-bin/rt.cgi?ets=3bcdd_10bccdd&limit=3_5_7 3bcdd &amp; 10bccdd]
| 4.377
| 4.713
| {{ket|{{bra| 4 6 7 }} {{bra| 15 22 27 }}}}
| 1892.0204
| 494.8658
| 1
| 2,3*,4*,7,11,15,19*,23*,42*,65*
|-
| *Achernar
| {{vector| 0 -6 5 }}
| style="text-align: center;" | 16807/15625
| 126.247
|
| b7 &amp; b17
| [http://x31eq.com/cgi-bin/rt.cgi?ets=4bcd_11cd&limit=3_5_7 4bcd &amp; 11cd]
| 4.847
| 4.514
| {{ket|{{bra| 7 10 12 }} {{bra| 17 25 30 }}}}
| 1901.955
| 559.351
| 1
| 2,3*,4,7*,10,17*
|-
| %
| {{vector| 3 -2 0 }}
| style="text-align: center;" | [[27/25|27/25]]
| 133.238
| large limma, BP small semitone
| b4 &amp; b6
| [http://x31eq.com/cgi-bin/rt.cgi?ets=b4+b6&limit=3_5_7 3bcdd &amp; 4p]
| 1.629
| 14.176
| {{ket|{{bra| 4 6 7 }} {{bra| 6 9 11 }}}}
| 939.6121
| 549.9897
| 2
| 4*,6,10*,14,24*,34,58,82*
|-
|
| {{vector| 6 2 -5 }}
| style="text-align: center;" | 18225/16807
| 140.228
| minimal BP chroma
| b9 &amp; b10
| [http://x31eq.com/cgi-bin/rt.cgi?ets=6bcd_6ccdd&limit=3_5_7 6bcd &amp; 6ccdd]
| 4.885
| 4.974
| {{ket|{{bra| 9 13 16 }} {{bra| 10 15 18 }}}}
| 1895.1156
| 201.762
| 1
| ...9*,10,19*,28*,47*
|-
| %
| {{vector| -2 -1 2 }}
| style="text-align: center;" | [[49/45|49/45]]
| 147.428
| BP minor semitone, [[Swetismic_temperaments|swetismic]] neutral second
| b4 &amp; b7
| [http://x31eq.com/cgi-bin/rt.cgi?ets=b4+b7&limit=3_5_7 3bcdd &amp; 4bcd]
| 1.925
| 13.274
| {{ket|{{bra| 4 6 7 }} {{bra| 7 10 12 }}}}
| 1917.7266
| 516.1077
| 1
| 2,3*,4*,7,11*,15*,26*
|-
|
| {{vector| 1 3 -3 }}
| style="text-align: center;" | 375/343
| 154.418
| BP major semitone, minor BP chroma
| b3 &amp; b6
| [http://x31eq.com/cgi-bin/rt.cgi?ets=2cd_4p&limit=3_5_7 2cd &amp; 4p]
| 2.941
| 9.098
| {{ket|{{bra| 3 4 5 }} {{bra| 6 9 11 }}}}
| 632.9248
| 234.1367
| 3
| 6*,9*,15,24*,33,57*,81*
|-
|
| {{vector| -7 0 4 }}
| style="text-align: center;" | 2401/2187
| 161.619
|
| b4 &amp; b40cd
| [http://x31eq.com/cgi-bin/rt.cgi?ets=b4+b25&limit=3_5_7 3bcdd &amp; 25p]
| 3.868
| 7.240
| {{ket|{{bra| 4 6 7 }} {{bra| 40 58 70 }}}}
| 478.34
| 41.8631
| 4
| ...44*,48,92*,136,228*,320*
|-
|
| {{vector| -4 4 -1 }}
| style="text-align: center;" | 625/567
| 168.609
| BP great semitone, major BP chroma
| b2 &amp; b7
| [http://x31eq.com/cgi-bin/rt.cgi?ets=1cdd_4bcd&limit=3_5_7 1cdd &amp; 4bcd]
| 3.195
| 9.146
| {{ket|{{bra| 2 3 4 }} {{bra| 7 10 12 }}}}
| 1914.567
| 1069.8876
| 1
| 2*,3,5,7*,9*,16,25,34*
|-
|
| {{vector| -9 5 1 }}
| style="text-align: center;" | 21875/19683
| 182.799
| maximal BP chroma
| b9 &amp; b11
| [http://x31eq.com/cgi-bin/rt.cgi?ets=6bcd_7d&limit=3_5_7 6bcd &amp; 7d]
| 4.970
| 6.373
| {{ket|{{bra| 9 13 16 }} {{bra| 11 16 19 }}}}
| 1913.8948
| 858.1831
| 1
| 2*,3,5,7,9*,11,20*,29*
|-
| %
| {{vector| 9 0 -5 }}
| style="text-align: center;" | 19683/16807
| 273.465
|
| b5 &amp; b10
| [http://x31eq.com/cgi-bin/rt.cgi?ets=3d_6ccdd&limit=3_5_7 3d &amp; 6ccdd]
| 4.904
| 9.663
| {{ket|{{bra| 5 7 9 }} {{bra| 10 15 18 }}}}
| 377.3036
| 145.1888
| 5
| 10*,15*,25*,40,65*
|}

names: * = proposed

names: % = not shown on PTS plots

MOS: * = maximally even

complexity = ln(n*d)/4

damage = 1200 *log(n/d) / log(n*d)

(complexity and damage are calculated as in the "Middle Path" tables)

[[Category:Lists of temperaments]]
[[Category:Non-octave temperaments]]