Catalog of 3.5.7 subgroup rank two temperaments
Jump to navigation
Jump to search
Todo: merge articles Merge into No-twos subgroup temperaments |
Table
name | comma 3.5.7 |> | 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)
Graphs
Complexity vs. damage plot. z<1 corresponds to the "Middle Path" inclusion criterion. |
Projective tuning space diagrams
Temperaments supported by 13edt, labeled by name |
Temperaments supported by 13edt, labeled by comma |
Temperaments not supported by 13edt, labeled by name |
Temperaments not supported by 13edt, labeled by comma |
Both sets, labeled by name |
Both sets, labeled by comma |