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