Subgroup temperaments
Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on Chromatic pairs.
2.3.7[edit]
Semaphore[edit]
Comma: 49/48
POL2 generator: ~15/13= 250.385
Gencom: [2 8/7; 49/48]
Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|]
Map: [<1 2 3|, <0 -2 -1|]
EDOs: 5, 14, 19, 24, 67c, 91c
RMS error: 2.523 cents
Archy[edit]
Archy can be thought of as "no-5's dominant" or "no-5's superpyth". The name comes from the fact that it tempers out 64/63, the Archytas comma.
Comma: 64/63
POL2 generator: ~3/2 = 709.321
Gencom: [2 3/2; 64/63]
Gencom mapping: [<1 1 0 4|, <0 1 0 -2|]
Map: [<1 2 2|, <0 -1 2|]
EDOs: 5, 12, 17, 22, 27, 137bc
RMS error: 1.856 cents
Slendric[edit]
Comma: 1029/1024
POL2 generator: ~8/7 = 233.688
Gencom: [2 8/7; 1029/1024]
Gencom mapping: [<1 1 0 3|, <0 3 0 -1|]
Map: [<1 1 3|, <0 3 -1|]
EDOs: 5, 21, 26, 31, 36, 77, 113, 190
RMS error: 0.3202 cents
Lee[edit]
Comma: 177147/175616
POL2 generator: ~13/9 = 633.525
Map: [<1 0 -3|, <0 3 11|]
EDOs: 17, 36, 89, 125, 161, 358, 519b
RMS error: 0.3519 cents
Skwares[edit]
Comma: 19683/19208
POL2 generator: ~23/18 = 425.365 cents
Map: [<1 3 6|, <0 -4 -9|]
EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc
RMS error: 1.149 cents
2.3.11[edit]
Neutral[edit]
Neutral can be thought of as the 2.3.11 version of either mohajira or maqamic, as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the neutral tetrad.
Comma: 243/242
POL2 generator: ~11/9 = 350.525
Gencom: [2 11/9; 243/242]
Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|]
Map: [<1 1 2|, <0 2 5|]
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380
RMS error: 0.3021 cents
Seventeen note mega chromatic scale
2.3.5.11[edit]
Porkypine[edit]
Commas: 55/54, 100/99
POL2 generator: ~11/10 = 164.078
Gencom: [2 10/9; 55/54, 100/99]
Gencom mapping: [<1 2 3 0 4|, <0 -3 -5 0 -4|]
Map: [<1 2 3 4|, <0 -3 -5 -4|]
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd
RMS error: 2.287 cents
Mohaha[edit]
Commas: 81/80, 121/120
POL2 generator: ~11/9 = 348.094
Gencom: [2 11/9; 81/80 121/120]
Gencom mapping: [<1 1 0 0 2|, <0 2 8 0 5|]
Map: [<1 1 0 2|, <0 2 8 5|]
EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd
RMS error: 1.392 cents
Music[edit]
Mohaha10ping2 by Billy Stiltner
2.3.7.11[edit]
Ennea[edit]
Commas: 41503/41472, 43923/43904
POL2 generator: ~99/98 = 17.6258
Gencom: [2 99/98; 41503/41472, 43923/43904]
Gencom mapping: [<1 14/9 0 25/9 31/9|, <0 2 0 2 1|]
Sval map: [<9 0 11 24|, <0 2 2 1|]
EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd
RMS error: 0.0383 cents
Supra[edit]
Commas: 64/63, 99/98
POTE generator: ~3/2 = 707.192
Gencom: [2 3/2; 64/63 99/98]
Gencom mapping: [<1 1 0 4 7|, <0 1 0 -2 -6|]
Sval map: [<1 0 6 13|, <0 1 -2 -6|]
EDOs: 5, 12, 17, 39c, 56c
RMS error: 1.977 cents
Skwares[edit]
Commas: 99/98, 243/242
POTE generator: ~23/18 = 425.244
Gencom: [2 9/7; 99/98 243/242]
Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10]]
Sval map: [<1 3 6 7|, <0 -4 -9 -10|]
EDOs: 14, 17, 31, 48, 79, 127, 206bcd
RMS error: 1.099 cents
Hemif[edit]
Commas: 243/242, 896/891
POTE generator: ~11/9 = 351.535
Gencom: [2 11/9; 243/242 896/891]
Gencom mapping: [<1 1 0 -1 2|, <0 2 0 13 5|]
Sval map: [<1 1 -1 2|, <0 2 13 5|]
EDOs: 7, 17, 41, 58, 99d
RMS error: 0.6108 cents
Bleu[edit]
Commas: 99/98, 864/847
POTE generator: ~13/12 = 140.005
Map: [<1 1 2 3|, <0 5 7 4|]
EDOs: 9, 17, 43, 60c
RMS error: 1.829 cents
2.3.7.11.13[edit]
Suhajira[edit]
Commas: 64/63, 78/77, 144/143
Gencom: [2 11/9; 64/63 78/77 144/143]
Gencom map: [<1 1 0 4 2 4|, <0 2 0 -4 5 -1|]
POT2 generator: ~11/9 = 353.775
Map: [<1 1 4 2 4|, <0 2 -4 5 -1|]
EDOs: 7, 10, 17, 44d, 61cd, 78cd
RMS error: 1.953 cents
Hemif[edit]
Commas: 144/143, 243/242, 364/363
Related temperament: Hemififths, namo
POT2 generator: ~11/9 = 351.691
Gencom: [2 11/9; 144/143 243/242 364/363]
Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]
Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]
EDOs: 7, 10, 17, 24, 41, 58
RMS error: 0.7167 cents
Skwares[edit]
Commas: 78/77, 99/98, 243/242
POT2 generator: ~23/18 = 424.457
Map: [<1 3 6 7 9|, <0 -4 -9 -10 -15|]
EDOs: 17, 48e, 65de, 82c, 147ce
RMS error: 1.769 cents
Leapfrog[edit]
Commas: 169/168, 352/351, 364/363
POL2 generator: ~3/2 = 704.745 cents
Gencom: [2 3/2; 169/169 352/351 364/363]
Gencom mapping: [<1 1 0 -6 -3 -1|, <0 1 0 15 11 8|]
Sval map: [<1 0 -21 -14 -9|, <0 1 15 11 8|]
EDOs: 17, 46, 63
RMS error: 0.7541 cents
Bleu[edit]
Group: 2.3.7.11.13
Commas: 78/77, 99/98, 144/143
Sval name: 9&17
POL2 generator: ~13/12 = 139.990
Gencom: [2 13/12; 78/77 99/98 144/143]
Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]
Map: [<1 1 2 3 3|, <0 5 7 4 6|]
RMS error: 1.752 cents
Parapyth (Rank 3)[edit]
Commas: 352/351, 364/363
POL2 tuning: <1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|
The gencom below gives Margo Schulter's favored basis
Gencom: [2 3/2 28/27; 352/351 364/363]
Gencom mapping: [<1 1 0 1 4 6|, <0 1 0 3 -1 -4|, <0 0 0 1 1 1|]
Sval map: [<1 0 0 7 12|, <0 1 0 -4 -7|, <0 0 1 1 1|]
EDOs: 17, 41, 46, 58, 87, 104
RMS error: 0.3789 cents
2.3.5.11[edit]
Larry[edit]
Commas: 243/242, 4000/3993
Related temperaments: gravity, harry
POTE generator: ~40/27 = 683.166
Gencom: [2 40/27; 243/242 4000/3993]
Gencom mapping: [<1 5 12 0 12|, <0 -6 -17 0 -15|]
Map: [<1 5 12 12|, <0 -6 -17 -15|]
EDOs: 7, 58, 65, 137, 202
RMS error: 0.3025 cents
2.9.7.11[edit]
Machine[edit]
Commas: 64/63, 99/98
POTE generator: ~17/15 = 214.384
Gencom: [2 8/7; 64/63 99/98]
Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]
Sval map: [<1 0 6 13|, <0 1 -1 -3|]
EDOs: 5, 6, 11, 17, 28
RMS error: 1.977 cents
Apparatus[edit]
Commas: 41503/41472, 322102/321489
POTE generator: ~31/29 = 115.570
Gencom: [2 77/72; 41503/41472 322102/321489]
Gencom mapping: [<1 5/2 0 3 5|, <0 -19/2 0 -2 -16|]
Sval map: [<1 5 3 5|, <0 -19 -2 -16|]
EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623
RMS error: 0.0673 cents
Mechanism[edit]
Commas: 896/891, 26411/26244
POTE generator: ~9/7 = 438.465
Gencom: [2 9/7; 896/891 26411/26244]
Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]
Sval map: [<1 5 5 2|, <0 -5 -6 4|]
EDOs: 8, 11, 30, 41, 52
RMS error: 0.4262 cents
2.9.15.7.11.13[edit]
Stacks (aka 2magic)[edit]
Commas: 100/99, 105/104, 144/143, 196/195
POL2 generator: ~9/7 = 438.977
Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|]
Sval map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef
RMS error: 1.540 cents
2.9.15.7.11 stacks[edit]
Commas: 100/99, 225/224, 245/243
POL2 generator: ~9/7 = 438.607
Gencom: [2 9/7; 100/99 225/224 245/243]
Gencom mapping: [<1 5/2 5/2 5 2|, <0 -5/2 -1/2 -6 4|]
Sval map: [<1 0 2 -1 6|, <0 5 3 6 -4|]
EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce,
RMS error: 1.226 cents
2.9.15.7 stacks[edit]
Commas: 225/224, 245/243
POL2 generator: ~9/7 = 439.296
Gencom: [2 9/7; 225/224 245/243]
Gencom mapping: [<1 5/2 5/2 5|, <0 -5/2 -1/2 -6|]
Sval map: [<1 0 2 -1|, <0 5 3 6|]
EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c
RMS error: 1.074 cents
2.9.21[edit]
A-team[edit]
Commas: 1029/1024
POL2 generator: ~17/13 = 467.375
Gencom: [2 21/16; 1029/1024]
Gencom mapping: [<1 1 0 3|, <0 3/2 0 -1/2|]
Sval map: [<1 2 4|, <0 3 1|]
EDOs: 5, 13, 18, 41, 59, 77, 95
RMS error: 0.3202 cents
2.3.7/5.11/5.13/5[edit]
Historical[edit]
Subgroup: 2.3.7/5.11/5.13/5
Commas: 364/363, 441/440, 1001/1000
POL2 generator: ~21/20 = 83.016
Gencom: [2 21/20; 364/363 441/440 1001/1000]
Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|]
Sval map: [<1 2 0 1 2|, <0 -6 7 2 -9|]
EDOs: 14, 29, 72, 101, 130, 159
RMS error: 0.2562 cents
2.3.7.11/5.13[edit]
Hypnosis[edit]
Subgroup: 2.3.7.11/5.13
Commas: 169/168, 540/539, 729/728
Related temperament: hypnos, tricot
Gencom: [2 13/9; 169/168, 540/539, 729/728]
Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|]
Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|]
EDOs: 17, 36, 118e, 125e, 161e, 197e
RMS error: 0.5379 cents
2.5.7[edit]
Didacus[edit]
Subgroup: 2.5.7
Commas: 3136/3125
Related temperaments: Chromatic+pairs#Roulette
Gencom: [2 28/25 3136/3125]
Gencom map: [<1 0 2 2|, <0 0 2 5|]
Sval map: [<1 2 2|, <0 2 5|]
EDOs: 6, 19, 25, 31, 37, 99, 130, 161, 353
RMS error: 0.2138 cents