Chromatic pairs
Definitions[edit]
By a chromatic pair is meant a pair of MOS in some rank two temperament (which may often be a subgroup temperament) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing RMS error, which is an appropriate error measure for subgroups as well as full p-limit groups.
Terrain[edit]
Subgroup: 2.9/5.9/7
Commas: 250047/250000
Sval name: 6&21
Related temperament: domain
POT2 generator: ~10/9 = 182.461
Gencom: [63/50 10/9; 250047/250000]
Gencom map: [<3 10/9 -7/9 2/9|, <0 -2/3 -1/3 2/3|]
Map: [<3 0 -4|, <0 1 2|]
EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
RMS error: 0.00844 cents
Terrain is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1-7/5-9/5 and 1-9/7-9/5 chords are characteristic.
5 5 1 mode of 33 equal (with video) play by Chris Vaisvil
Petrtri[edit]
Subgroup: 2.11/5.13/5
Comma: 2200/2197
Svalname: 3&5
POT2 generator: ~13/10 = 455.012
Gencom: [2 13/10; 2200/2197]
Gencom map: [<1 0 -1/3 0 -1/3 2/3|, <0 0 -4/3 0 5/3 -1/3|]
Map: [<1 0 1|, <0 3 1|]
EDOs: 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c
RMS error: 0.0749 cents
Barton[edit]
Subgroup: 2.5.11.13
Commas: 2200/2197, 6656/6655
Svalname: 11&13
POT2 generator: ~11/8 = 551.699
Gencom: [2 11/8; 2200/2197 6656/6655]
Gencom map: [<1 0 6 0 3 6|, <0 0 -8 0 1 -5|]
Map: [<1 6 3 6|, <0 -8 1 -5|]
EDOs: 11, 13, 24, 37, 50, 87, 298, 385, 472, 559, 1590cd
RMS error: 0.0822 cents
Nine note mega albitonic scale
Thirteen note mega chromatic scale
Voltage[edit]
Subgroup: 2.7.13
Comma: 28672/28561
Sval name: 3&7
POT2 generator: ~16/13 = 357.677
POTT generator: ~16/13 = 1200 - 300 log₂(7) (357.794)
Gencom: [2, 16/13; 28672/28561]
Gencom map: [<1 0 0 4 0 4|, <0 0 0 -4 0 -1|]
Map: [<1 4 4|, <0 -4 -1|]
EDOS: 3, 7, 10, 27, 37, 47, 57, 104
RMS error: 0.1423
Tridec[edit]
Subgroup: 2.7/5.11/5.13/5
Commas: 847/845, 1001/1000
Sval name: 5&8
POT2 generator: ~13/10 = 454.556
Gencom: [2 13/10; 847/845 1001/1000]
Gencom map: [<1 0 -3/4 5/4 -3/4 1/4|, <0 0 0 -4 3 1|]
Map: [<1 2 0 1|, <0 -4 3 1|]
EDOs: 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc
RMS error: 0.1613 cents
Nestoria[edit]
Subgroup: 2.3.5.19
Commas: 361/360, 513/512
Sval name: 12&29
Related temperament: schismatic
POT2 generator: ~3/2 = 701.746
Gencom: [2 3/2; 361/360 513/512]
Gencom map: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 0 -3|]
Map: [<1 0 15 9|, <0 1 -8 -3|]
EDOs: 7, 12, 17, 29, 41, 53, 118, 171, 460d, 631d
RMS error: 0.1763 cents
Seventeen note mega chromatic scale
Orgone[edit]
Subgroup: 2.7.11
Commas: 65536/65219
Svals: 4&7
Related temperament: superkleismic
POT2 generator: ~77/64 = 323.372
Gencom: [2 77/64; 65536/65219]
Gencom map: [<1 0 0 2 4|, <0 0 0 3 -2|]
Map: [<1 2 4|, <0 3 -2|]
EDOs: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475bc, 783bc
RMS error: 0.1888 cents
Fifteen note mega chromatic scale
Marveltwintri[edit]
Subgroup: 2.5/3.13/9
Comma: 325/324
Svalname: 3&4
POT2 generator: ~6/5 = 317.139
Gencom: [2 6/5; 325/324]
Gencom map: [<1 -1/6 5/6 0 0 -1/3|, <0 -1/2 -3/2 0 0 1|]
Map: [<1 0 2|, <0 1 -2|]
EDOs: 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b
RMS error: 0.2444 cents
Fifteen note mega chromatic scale
Cata[edit]
Subgroup: 2.3.5.13
Commas: 325/324, 625/624
Sval name: 15&19
Related temperament: catakleismic
POT2 generator: ~6/5 = 317.076
Gencom: [2 6/5; 325/324 625/624]
Gencom map: [<1 0 1 0 0 0|, <0 6 5 0 0 14|]
Map: [<1 0 1 0|, <0 6 5 14|]
EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd
RMS error: 0.2450 cents
Eleven note mega albitonic scale
Nineteen note mega chromatic scale
Bridgetown[edit]
Subgroup: 2.3.11/5.13/5
Commas: 352/351, 676/675
Sval name: 5&24
Related temperaments: haumea, barbados
POT2 generator: ~15/13 = 248.399
Gencom: [2 15/13; 352/351 676/675]
Gencom map: [<1 2 -5/3 0 4/3 1/3|, <0 -2 4 0 -5 1|]
Map: [<1 0 -6 -1|, <0 2 9 3|]
EDOs: 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314
RMS error: 0.2513 cents
Music[edit]
Paint in the Water 29 by Igliashon Jones
Route 14 in Bridgetown by Chris Vaisvil
Haumea[edit]
Subgroup: 2.3.7/5.11/5.13/5
Commas: 352/351, 676/675, 847/845
Related temperaments: bridgetown, namaka, hemigari, barbados, parizekmic
POT2 generator: ~15/13 = 248.491
Gencom: [2 15/13; 352/351 676/675 847/845]
Gencom map: [<1 2 -3/4 -11/4 9/4 5/4|, <0 -2 0 12 -9 -3|]
Map: [<1 0 10 -6 -1|, <0 2 -12 9 3|]
EDOs: 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd
RMS error: 0.2668 cents
Nineteen note mega chromatic scale
Neutral[edit]
Subgroup: 2.3.11
Commas: 243/242
Svalname: 7&17
POT2 generator: ~11/9 = 350.525
Gencom: [2 11/9; 243/242]
Gencom map: [<1 1 0 0 2|, <0 2 0 0 5|]
Map: [<1 1 2|, <0 2 5|]
EDOs: 7, 17, 24, 65, 89, 202, 291, 380
RMS error: 0.3021 cents
Seventeen note mega chromatic scale
Music[edit]
Mo - Happy - Happy play by Jake Freivald in Neutral[7], 24et tuning
Slendric[edit]
Subgroup: 2.3.7
Comma: 1029/1024
Sval name: 5&21
POT2 generator: ~8/7 = 233.688
Gencom: [2 8/7; 1029/1024]
Gencom map: [<1 1 0 3|, <0 3 0 -1|]
Map: [<1 1 3|, <0 3 -1|]
EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190
RMS error: 0.3202 cents
Music[edit]
Huntington[edit]
Subgroup: 2.5.7.13
Commas: 640/637, 10985/10976
Sval name: 10&27
POT2 generator: ~16/13 = 357.002
Gencom: [2 16/13; 640/637 10985/10976]
Gencom map: [<1 0 5 4 0 4|, <0 0 -9 -4 0 -1|]
Map: [<1 5 4 4|, <0 -9 -4 -1|]
EDOs: 7, 10, 17, 27, 37, 84, 121, 279cd, 400cd
RMS error: 0.3452 cents
Seventeen note chromatic scale
Tobago[edit]
Subgroup: 2.3.11.13/5
Commas: 243/242, 676/675
Sval name: 10&14
Related temperaments: neutral, barbados
POT2 generator: ~15/13 = 249.312
Gencom: [55/39 15/13; 243/242 676/675]
Gencom map: [<2 4 -2 0 9 2|, <0 -2 3/2 0 -5 -3/2|]
Map: [<2 0 -1 -2], <0 2 5 3]]
EDOs: 10, 14, 24, 58, 82, 130
RMS error: 0.3533 cents
Twentyfour note quatertone scale
Pepperoni[edit]
Subgroup: 2.3.11/7.13/7
Commas: 352/351, 364/363
Sval name: 5&12
Related temperament: The Pepper fifth, which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
POT2 generator: ~3/2 = 703.856
Gencom: [2 3/2; 352/351 364/363]
Gencom map: [<1 1 0 -8/3 1/3 7/3|, <0 1 0 11/3 -1/3 -10/3|]
Map: [<1 0 7 12|, <0 1 -4 -7|]
EDOs: 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd
RMS error: 0.3789 cents
Wizz[edit]
Subgroup: 2.5.11
Commas: 15625/15488
Sval name: 6&16
Related temperaments: wizard
Generator: ~5/4 = 383.768
Gencom: [125/88 5/4; 15625/15488]
Gencom map: [<2 0 4 0 5| <0 0 1 0 3|]
Map: [<2 0 -7|, <0 1 3|]
EDOs: 6, 16, 22, 28, 50, 122, 172, 222
RMS error: 0.3997
Bossier[edit]
Subgroup: 2.7.11.13
Commas: 1573/1568, 15488/15379
Sval name: 3&17
POT2 generator: ~14/11 = 421.309
Gencom: [2 14/11; 1573/1568 15488/15379]
Gencom map: [<1 0 0 0 1 3|, <0 0 0 8 7 2|]
Map: [<1 0 1 3|, <0 8 7 2|]
EDOs: 17, 20, 37, 57, 94, 225, 319cd, 413bcd
RMS error: 0.4043 cents
Fourteen note mega chromatic scale
Penta[edit]
Subgroup: 2.9.7.11
Commas: 896/891, 26411/26244
Svalname: 8&11
POT2 generator: ~9/7 = 438.465
Gencom: [2 9/7; 896/891 26411/26244]
Gencom map: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]
Map: [<1 0 -1 6|, <0 5 6 -4|]
EDOs: 8, 11, 30, 41, 52
RMS error: 0.4262 cents
Nineteen note mega chromatic scale
Bluebirds[edit]
Subgroup: 2.11.13
Comma: 265837/262144
POT2 generator: ~143/128 = 182.368
Gencom: [2 143/128; 265837/262144]
Gencom map: [<1 0 0 0 3 4|, <0 0 0 0 3 -2|]
Map: [<1 0 6|, <0 3 -2|]
EDOs: 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc
RMS error: 0.4444 cents
Marveltri[edit]
Subgroup: 2.5.9/7
Comma: 225/224
Sval name: 3&13
Related temperaments: marvel, 22&47, magic
POT2 generator: ~5/4 = 383.638
Gencom: [2 5/4; 225/224]
Gencom map: [<1 2/5 2 -1/5|, <0 -4/5 1 2/5|]
Map: [<1 0 5|, <0 1 -2|]
EDOs: 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc
RMS error: 0.4801 cents
Thirteen note mega chromatic scale
Edson[edit]
Subgroup: 2.3.7/5.11/5.13/5
Commas: 196/195, 352/351, 364/363
Related temperaments: pele, cassandra
POT2 generator: ~3/2 = 703.414
Gencom: [2 3/2; 196/195, 352/351, 364/363]
Gencom map: [<1 1 -5 -1 2 4|, <0 1 29/4 5/4 -11/4 -23/4|]
Map: [<1 0 10 17 22|, <0 1 -6 -10 -13|]
EDOs: 12, 17, 29, 621bcde
RMS error: 0.5102 cents
Seventeen note mega chromatic scale
Photia[edit]
Subgroup: 2.3.5.17.19
Commas: 171/170, 256/255, 324/323
Sval name: 12&41
Related temperament: schismatic
POT2 generator: ~3/2 = 701.470
Gencom: [2 3/2; 171/170 256/255 324/323]
Gencom map: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 7 -3|]
Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|]
EDOs: 7, 12, 17, 29, 41, 53, 65, 142d, 207d, 272d
RMS error: 0.5374 cents
Shoe[edit]
Subgroup: 2.5.7.11.13
Commas: 176/175, 640/637, 847/845
Sval name: 16&21
POT2 generator: ~8/7 = 227.108
Gencom: [2 8/7; 176/175 640/637 847/845]
Gencom map: [<1 0 1 3 1 2|, <0 0 7 -1 13 9|]
Map: [<1 1 3 1 2|, <0 7 -1 13 9|]
EDOs: 16, 21, 37, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce
RMS error: 0.5433 cents
shoe5 - five note mini haplotonic scale
shoe6 - six note haplotonic scale
shoe11 - eleven note note albitonic scale
shoe16 - sixteen note chromatic scale
Roulette[edit]
Subgroup: 2.5.7.11.13
Commas: 176/175, 1375/1372, 640/637
Sval name: 6&25
Related temperament: Hemiwürschmidt
POT2 generator: ~28/25 = 194.594
Gencom: [2 28/25; 176/175 1375/1372 640/637]
Gencom map: [<1 0 2 2 2 5|, <0 0 2 5 9 -8|]
Map: [<1 0 -3 -7 13|, <0 2 5 9 -8|]
EDOs: 6, 7, 13, 19, 25, 31, 37
RMS error: 0.5567 cents
roulette6 - six note haplotonic scale
roulette7 - seven note albitonic scale
roulette13 - thirteen note chromatic scale
roulette19 - nineteen note mega chromatic scale
Silver[edit]
Subgroup: 2.5.7.13.17
Commas: 170/169, 640/637, 5525/5488
Sval name: 10&27
POT2 generator: ~13/8 = 842.711
Gencom: [2 13/8; 170/169 640/637 5525/5488]
Gencom map: [<1 0 -4 0 0 3 9|, <0 0 9 4 0 1 -7|]
Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|]
EDOs: 7, 10, 17, 27, 37, 47, 84, 131, 178e, 309cde, 487bcdee
RMS error: 0.5886 cents
silver7 -seven note haplotonic scale
silver10 - ten note albitonic scale
silver17 - seventeen note chromatic scale
Baldy[edit]
Subgroup: 2.9.5.7.13
Commas: 225/224, 325/324, 640/637
Sval name: 6&35
Related temperament: Garibaldi
POT2 generator: ~9/8 = 204.090
Gencom: [2 9/8; 225/224 325/324 640/637]
Gencom map: [<1 3/2 3 4 0 2|, <0 1/2 -4 -7 0 10|]
Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|]
EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd
RMS error: 0.5999 cents
baldy6 - six note haplotonic scale
baldy11 - eleven note albitonic scale
baldy17 - seventeen note chromatic scale
Guanyintet[edit]
Subgroup: 2.5.7/3.11/3
Commas: 176/175, 540/539
Svalname: 4&9
Related temperaments: guanyin, orwell
POT2 generator: ~7/6 = 270.093
Gencom: [2 7/6; 176/175 540/539]
Gencom map: [<1 -4/3 3 -1/3 5/3|, <0 4/3 -3 7/3 -11/3|]
Map: [<1 0 2 -2|, <0 3 -1 5|]
EDOs: 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd
RMS error: 0.6028 cents
Radon[edit]
Subgroup: 2.3.7.11
Commas: 896/891, 1029/1024
Sval name: 5&36
Related temperament: Rodan
POT2 generator: ~8/7 = 234.381
Gencom: [2 8/7; 896/891 1029/1024]
Gencom map: [<1 1 0 3 6|, <0 3 0 -1 -13|]
Map: [<1 1 3 6|, <0 3 -1 -13|]
EDOs: 5, 36, 41, 87, 128
RMS error: 0.6502 cents
Gariberttet[edit]
Subgroup: 2.5/3.7/3.13/11
Commas: 275/273, 847/845
Svalname: 4&29
POT2 generator: ~13/11 = 293.679
Gencom: [2 13/11; 275/273 847/845]
Gencom map: [<1 0 0 0 0 0|, <0 -8/3 1/3 7/3 -1/2 1/2|]
Map: [<1 0 0 0|, <0 3 5 1|]
EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd
RMS error: 0.6914 cents
Namo[edit]
Subgroup: 2.3.11.13
Commas: 144/143, 243/242
Related temperament: mandos, mohajira, hemif
POT2 generator: ~11/9 = 351.488
Gencom: [2 11/9; 144/143 243/242]
Gencom map: [<1 1 0 0 2 4|, <0 2 0 0 5 -1|]
Map: [<1 1 2 4|, <0 2 5 -1|]
EDOs: 7, 10, 17, 41, 58, 99cd
RMS error: 0.7038 cents
Seventeen note chromatic scale
Sentry[edit]
Group: 2.5/3.9/7
Commas: 245/243
Svalname: 3&5
Related temperaments: sensi
POT2 generator: ~9/7 = 440.902
Gencom: [2 9/7; 245/243]
Gencom map: [<1 0 0 0|, <0 0 2 -1|]
Map: [<1 0 0|, <0 2 1|]
EDOs: 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc
RMS error: 0.7105 cents
Eleven note note chromatic scale
Hemif[edit]
Subgroup: 2.3.7.11.13
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
Seventeen note chromatic scale
Garibaldi[edit]
Group: 2.3.5.7
Commas: 225/224, 3125/3087
Val name: 12&29
POT2 generator: ~3/2 = 702.085
Gencom: [2 3/2; 225/224 3125/3087]
Gencom map: [<1 1 7 11], <0 1 -8 -14|]
Map: [<1 0 15 25|, <0 1 -8 -14|]
EDOs: 7, 12, 17, 29, 41, 53, 94, 241c
RMS error: 0.7257 cents
Seventeen note chromatic scale
Mabila[edit]
Subgroup: 2.5.7
Comma: 1071875/1048576
Sval name: 7&9
POT2 generator: ~175/128 = 527.236
Gencom: [2 175/128; 1071875/1048576]
Gencom map: [<1 0 1 5}, <0, 0, 3, -5|]
Map: [<1 1 5|, <0 3 -5|]
EDOs: 7, 9, 16, 25, 41, 66, 305bc
RMS error: 0.7729 cents
Indium[edit]
Subgroup: 2.5/3.7/3.11/3
Commas: 3025/3024, 3125/3087
Sval name: 8&33
POT2 generator: ~12/11 = 147.010
Gencom: [2 12/11; 3025/3024 3125/3087]
Gencom map: [<1 -1/2 -1/2 -1/2 3/2|, <0 -15/4 9/4 25/4 -19/4|]
Map: [<1 0 0 2|, <0 6 10 -1|]
EDOs: 33, 41, 49, 57, 106, 204, 253
RMS error: 0.7788 cents
Seventeen note chromatic scale
Music[edit]
The Cry of Indium (in Indium 17) by Chris Vaisvil => details
Starlingtet[edit]
Group: 2.5/3.7/3
Comma: 126/125
Svalname: 4&15
Related temperaments: starling; becomes myna
POT2 generator: ~6/5 = 311.154
Gencom: [2 6/5; 126/125]
Gencom map: [<1 -1 0 1|, <0 4/3 1/3 -5/3|]
Map: [<1 0 -1|, <0 1 3|]
EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b
RMS error: 0.8398 cents
Lovecraft[edit]
Group: 2.11.13
Commas: 1352/1331
POT2 generator: ~13/11 = 279.318
Gencom: [2 13/11; 1352/1331]
Gencom map: [<1 0 0 0 3 3|, <0 0 0 0 2 3|]
Map: [<1 1 0|, <0 2 3|]
EDOS: 13, 30, 43, 73, 116b
RMS error: 0.8449 cents
Blackbirds[edit]
Subgroup: 2.11.13
Comma: 29282/28561
POT2 generator: ~11/8 = 546.660
Gencom: [13/11 11/8; 29282/28561]
Gencom map: [<4 0 0 0 12 13|, <0 0 0 0 1 1|]
Map: [<4 0 1|, <0 1 1|]
EDOs: 4, 16, 20, 24, 44, 68, 112c, 180bc
RMS error: 0.8685 cents
Sixteen note mega chromatic scale
Laz[edit]
Subgroup: 2.5.7/3.11/3.13/3
Commas: 144/143, 176/175, 196/195
Related temperaments: georgian, winston
POT2 generator: ~7/6 = 269.300
Gencom: [2 7/6; 144/143 176/175 196/195]
Gencom map: [<1 -5/4 3 -1/4 7/4 -1/4|, <0 -1/4 -3 3/4 -21/4 19/4|]
Map: [<1 0 2 -2 6|, <0 3 -1 5 -5|]
EDOs: 9, 31, 40, 49, 58, 156bde, 205bde
RMS error: 0.8790 cents
Myna[edit]
Group: 2.3.5.7
Commas: 126/125, 1728/1715
Val name: 4&27
POT2 generator: ~6/5 = 310.146
Gencom: [2 6/5; 126/125 1728/1715]
Gencom map: [<1 -1 0 1|,<0 10 9 7|]
Map: [<1 9 9 8|, <0 -10 -9 -7|]
EDOs: 4, 27, 31, 58, 89, 236c, 325cd
RMS error: 0.9516 cents
Greeley[edit]
Subgroup: 2.5/3.7/3.11/3
Commas: 121/120, 126/125
Related temperament: Opossum, Nusecond
POT2 generator: ~11/10 = 155.776
Gencom: [2 11/10; 121/120 126/125]
Gencom map: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|]
Map: [<1 1 2 2|, <0 -2 -6 -1|]
EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd
RMS error: 1.034 cents
Music[edit]
A Greeley Steals Halloween by Chris Vaisvil in Greeley 15
Semidim[edit]
Subgroup: 2.5/3.7/3.11/3.13/3
Commas: 121/120, 169/168, 275/273
Sval name: 8&29
POT2 generator: ~13/10 = 453.242
Gencom: [2 13/10; 121/120 169/168 275/273]
Gencom map: [<1 -3 0 2 0 1|, <0 24/5 -6/5 -26/5 9/5 -1/5|]
Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]
EDOs: 5, 8, 13, 21, 29, 37, 44, 45, 188bde,
RMS error: 1.052 cents
Mothwelltri[edit]
Group: 2.7/3.11
Comma: 99/98
Svalname: 1&4
Related temperament: Orwell
POT2 generator: ~7/6 = 273.174
Gencom: [2 7/6; 99/98]
Gencom map: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|]
Map: [<1 0 1|, <0 1 2|]
EDOs: 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc
RMS error: 1.064 cents
Sulis[edit]
Subgroup: 2.5.9/7.11/9
Commas: 99/98, 176/175
Related temperament: minerva, würschmidt
POT2 generator: ~5/4 = 386.558
Gencom: [2 5/4; 99/98 176/175]
Gencom map: [<1 4/9 2 -1/9 -1/9|, <0 -4/3 1 -2/3 4/3|]
Map: [<1 0 5 -9|, <0 1 -2 4|]
EDOs: 22, 25, 28, 31, 59, 90c, 149c
RMS error: 1.074 cents
Skwares[edit]
Subgroup: 2.3.7.11
Commas: 99/98, 243/242
Related temperament: squares
POT2 generator: ~9/7 = 425.244
Gencom: [2 9/7; 99/98 243/242]
Gencom map: [<1 3 0 6 7|, <0 -4 0 -9 -10|]
Map: [<1 3 6 7|, <0 -4 -9 -10|]
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd
RMS error: 1.099 cents
Eleven note mega albitonic scale
Orwell[edit]
Group: 2.3.5.7.11
Commas: 99/98, 121/120, 176/175
Val name: 9&22
POT2 generator: ~7/6 = 271.426
Gencom: [2 7/6; 99/98 121/120 176/175]
Gencom map: [<1 0 3 1 3|, <0 7 -3 8 2|]
Map: [<1 0 3 1 3|, <0 7 -3 8 2|]
EDOs: 9, 22, 31, 53, 84e
RMS error: 1.151 cents
Magicaltet[edit]
Group: 2.5/3.7.11
Commas: 100/99, 385/384
Related temperaments: 4&7&15, superkleismic, magic
POT2 generator: ~6/5 = 322.659
Gencom: [2 6/5; 100/99 385/384]
Gencom map: [<1 -1/2 1/2 2 4|, <0 1/2 -1/2 3 -2|]
Map: [<1 0 5 2|, <0 1 -3 2|]
EDOs: 11, 15, 26, 67, 79cd, 93b, 94cd, 109cd, 119b, 124cd, 139cd, 212bd
RMS error: 1.206 cents
Magic[edit]
Group: 2.3.5.7.11
Commas: 100/99, 225/224, 245/243
Val name: 19&22
POT2 generator: ~5/4 = 380.696
Gencom: [2 5/4; 100/99 225/224 245/243]
Gencom map: [<1 0 2 -1 6|, <0 5 1 12 -8|]
Map: [<1 0 2 -1 6|, <0 5 1 12 -8|]
EDOs: 19, 22, 41, 104, 145
RMS error: 1.226 cents
Sixteen note mega chromatic scale
Music[edit]
Chromatic piece in magic 16 Chris Vaisvil
Kiribati[edit]
Subgroup: 2.9/5.7/3.11/9
Commas: 100/99, 245/242
Related temperament: nakika, octacot
POT2 generator: ~21/20 = 87.892
Gencom: [2 21/20; 100/99 245/242]
Gencom map: [<1 1/10 -4/5 11/10 1/5|, <0 -3/2 -1 3/2 1|]
Map: [<1 1 1 0|, <0 -2 3 4|]
EDOs: 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd
RMS error: 1.245 cents
Score[edit]
Subgroup: 2.7.11.13
Commas: 343/338, 847/832
POT2 generator: ~11/8 = 540.099
Gencom: [2 11/8; 343/338 847/832]
Gencom map: [<1 0 0 1 3 1|, <0 0 0 4 1 6|]
Map: [<1 1 3 1|, <0 4 1 6|]
EDOs: 5, 7, 9, 11, 20
RMS error: 1.282 cents
Nine note mega albitonic scale
Sensation[edit]
Group: 2.3.5.7.13
Commas: 91/90, 126/125, 169/168
Related temperaments: Sensi, Sensis, Sensus
POT2 generator: ~9/7 = 443.322
Gencom: [2 9/7; 91/90 126/125 169/168]
Gencom map: [<1 -1 -1 -2 0 0|, <0 7 9 13 0 10|]
Map: [<1 6 8 11 10|, <0 -7 -9 -13 -10|]
EDOs: 19, 27, 46, 111de, 157de
RMS error: 1.321 cents
Eleven note mega albitonic scale
Sensi[edit]
Group: 2.3.5.7
Commas: 126/125, 245/243
Val name: 19&27
POT2 generator: ~9/7 = 443.383
Gencom: [2 9/7; 126/125 245/243]
Gencom map: [<1 -1 -1 -2|, <0 7 9 13|]
Map: [<1 6 8 11|, <0 -7 -9 -13|]
EDOs: 5, 8, 11, 19, 27, 46, 157d, 203cd, 249cd, 295cd
RMS error: 1.323 cents
Eleven note mega albitonic scale
Meantone[edit]
Group: 2.3.5.7
Commas: 81/80, 126/125
Val name: 12&19
POT2 generator: ~3/2 = 696.495
Gencom: [2 3/2; 81/80 126/125]
Gencom map: [<1 1 0 -3|, <0 1 4 10|]
Map: [<1 0 -4 -13|, <0 1 4 10|]
EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b
RMS error: 1.382 cents
Mohaha[edit]
Subgroup: 2.3.5.11
Commas: 81/80, 121/120
Related temperament: mohajira
POT2 generator: ~11/9 = 348.094
Gencom: [2 11/9; 81/80 121/120]
Gencom map: [<1 1 0 0 2|, <[0 2 8 0 5|]
Map: [<1 1 0 2|, <0 2 8 5|]
EDOs: 24, 31, 55, 69d, 100d, 131bd
RMS error: 1.392 cents
Music[edit]
Mohaha10ping2 by Billy Stiltner
Joan[edit]
Subgroup: 2.9.7.11
Commas: 99/98, 9317/9216
Related temperaments: casablanca, orwell
POT2 generator: ~11/8 = 542.672 cents
Gencom: [2 11/8; 99/98 9317/9216]
Gencom map: [<1 0 0 1 3|, <0 7/2 0 4 1|]
Map: [<1 0 1 3|, <0 7 4 1|]
EDOs: 11, 20, 31, 42, 115bd, 157bd
RMS error: 1.424 cents
Nine note mega albitonic scale
Tutone[edit]
Subgroup: 2.9.5.7.11
Commas: 81/80, 99/98, 126/125
Related temperaments: meantone, belobog, hemithirds, hemiwürschmidt
POT2 generator: ~9/8 = 193.937
Gencom: [2 9/8; 81/80 99/98 126/125]
Gencom map: [<1 3/2 2 2 2|, <0 1/2 2 5 9|]
Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]
EDOs: 25, 31, 68b, 99b
RMS error: 1.439 cents
Stacks[edit]
Subgroup: 2.9.15.7.11.13
Commas: 100/99, 105/104, 144/143, 196/195
Related temperament: magic
Svalname: 11&30
POT2 generator: ~9/7 = 439.146
Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
Gencom map: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|]
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
Eleven note note chromatic scale
Nineteen note note mega chromatic scale
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
bleu8 - Eight note haplotonic scale
bleu9 - Nine note albitonic scale
bleu17 - Seventeen note chromatic scale
On a Well Worn Riff (Bleu 17) by Chris Vaisvil
Sephiroth[edit]
Subgroup: 2.5.11.13.17
Commas: 65/64, 170/169, 221/220
Related temperament: muggles
POT2 generator: ~5/4 = 372.236
Gencom: [2 5/4; 65/64 170/169 221/220]
Gencom map: [<1 0 2 0 5 4 5|, <0 0 1 0 -5 -1 -3|]
Map: [<1 0 15 6 11|, <0 1 -5 -1 -3|]
EDOs: 10, 13, 16, 29c
RMS error: 1.774 cents
Sixteen note mega chromatic scale
Archy[edit]
Subgroup: 2.3.7
Comma: 64/63
POT2 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
Suhajira[edit]
Subgroup: 2.3.7.11
Commas: 64/63, 243/242
POL2 generator: ~11/9 = 353.958
Gencom: [2 11/9; 64/63 243/242]
Gencom map: [<1 1 0 4 2|, <0 2 0 -4 5|]
Map: [<1 1 4 2|, <0 2 -4 5|]
EDOs: 7, 10, 17, 61de
RMS error: 1.968 cents
suhajira7 - Seven note haplotonic scale
suhajira10 - Ten note albitonic scale
suhajira17 - note chromatic scale
Mohoho[edit]
Subgroup: 2.3.5.11.13
Commas: 66/65, 81/80, 121/120
POT2 generator: ~11/9 = 348.916
Gencom: [2 11/9; 66/65 81/80 121/120]
Gencom map: [<1 1 0 0 2 4|, <0 2 8 0 5 -1|]
Map: [<1 1 0 2 4|, <0 2 8 5 -1|]
EDOs: 17c, 24, 31, 55, 86de, 141cde
RMS error: 1.971 cents
Supra[edit]
Subgroup: 2.3.7.11
Commas: 64/63, 99/98
Related temperament: suprapyth
POT2 generator: ~3/2 = 707.192
Gencom: [2 3/2; 64/63 99/98]
Gencom map: [<1 1 0 4 7|, <0 1 0 -2 -6|]
Map: [<1 0 6 13|, <0 1 -2 -6|]
EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c
RMS error: 1.977 cents
Machine[edit]
Subgroup: 2.9.7.11
Commas: 64/63, 99/98
POT2 generator: ~9/8 = 214.384
Gencom: [2 9/8; 64/63 99/98]
Gencom map: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]
Map: [<1 0 6 13|, <0 1 -1 -3|]
EDOs: 5, 6, 11, 17, 28
RMS error: 1.977 cents
Deutone[edit]
Subgroup: 2.9.5.7.13
Commas: 65/64, 81/80, 91/90
Related temperament: meanpop
POT2 generator: ~9/8 = 191.059
Gencom: [2 9/8; 65/64 81/80 91/90]
Gencom map: [<1 3/2 2 2 0 4|, <0 1/2 2 5 0 -2|]
Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|]
EDOs: 6, 7, 13, 19, 25e, 44de
RMS error: 2.003 cents
Supraphon[edit]
Subgroup: 2.3.7.11.13
Commas: 64/63, 78/77, 99/98
POT2 generator: ~3/2 = 706.137
Gencom: [2 3/2; 64/63 78/77 99/98]
Gencom map: [<1 1 0 4 7 9|, <0 1 0 -2 -6 -9|]
Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]
EDOs: 5, 7, 12, 17
RMS error: 2.095 cents
Negra[edit]
Subgroup: 2.3.5.7.13
Commas: 49/48, 65/64, 91/90
Related temperament: negri
POT2 generator: ~14/13~13/12 = 125.567 cents
Gencom: [2 14/13;
Gencom map: [<1 2 2 3 0 4|, <0 -4 3 -2 0 -3|]
Map: [<1 2 2 3 4|, <0 -4 3 -2 -3|]
EDOs: 9, 10, 19, 29, 67cd*f, 86cd*f
RMS error: 2.147 cents
Porkypine[edit]
Subgroup: 2.3.5.11
Commas: 55/54, 100/99
POT2 generator: ~10/9 = 164.078
Gencom: [2 10/9; 55/54 100/99]
Gencom map: [<1 2 3 0 4|], <0 -3 -5 0 -4|]
Map: [<1 2 3 4|, <0 3 5 4|]
EDOs: 7, 15, 22, 73cd, 95cd, 117bcd, 256bcdd
RMS error: 2.287 cents
Skateboard[edit]
Subgroup: 2.5/3.7/3.11.13/9
Commas: 56/55, 91/90, 100/99
Related temperament: thrasher
POT2 generator: ~6/5 = 313.842
Gencom: [2 6/5; 56/55 91/90 100/99]
Gencom map: [<1 -3/7 4/7 11/7 4 -6/7|, <0 0 -1 -3 -2 2|]
Map: [<1 0 -1 2 2|, <0 1 3 2 -2|]
EDOs: 11, 15, 19, 23, 42d, 65d
RMS error: 2.396 cents
Augment[edit]
Subgroup: 2.5.7.11
Commas: 56/55, 128/125
Related temperament: augmented
POT2 generator: ~8/7 = 228.275
Gencom: [5/4 8/7; 56/55 128/125]
Gencom map: [<3 0 7 9 11|, <0 0 0 -1 -1|]
Map: [<3 7 0 2|, <0 0 1 1|]
EDOs: 3, 6, 9, 15, 21
RMS error: 2.422 cents
Semaphore[edit]
Subgroup: 2.3.7
Comma: 49/48
POT2 generator: ~7/6 = 250.385
Gencom: [2 7/6; 49/48]
Gencom map: [<1 2 0 3}, <0 -2 0 -1|]
Map: [<1 0 2|, <0 2 1|]
EDOs: 5, 9, 14, 19, 24, 67c, 91c
RMS error: 2.523 cents
Kryptonite[edit]
Subgroup: 2.5.7/3.11/3.13/3
Commas: 56/55, 78/77, 91/90
Related temperaments: krypton
POT2 generator: ~13/12 = 132.428
Gencom: [2 13/12; 56/55 78/77 91/90]
Gencom map: [<1 -5/4 2 -1/4 3/4 3/4|, <0 -1/2 3 3/2 -3/2 1/2|]
Map: [<1 2 1 2 2|, <0 -3 -2 1 -1|]
EDOs: 9, 63, 82bd, 91bde
RMS error: 2.545 cents
Nineteen note mega chromatic scale
Oregon[edit]
Subgroup: 2.9.15.7.11
Commas: 55/54, 64/63, 100/99
POT2 generator: ~6/5 = 325.495
Gencom: [2 6/5; 55/54 64/63 100/99]
Gencom map: [<1 2 3 2 4|, <0 -3/2 -5/2 3 -2|]
Map: [<1 1 1 5 2|, <0 3 4 -3 2|]
EDOs: 7, 11, 37b, 48b, 59b
RMS error: 2.550 cents
Antikythera[edit]
Subgroup: 2.9.5.7
Commas: 50/49, 64/63
Related temperament: pajara
POT2 generator: ~8/7 = 214.095
Gencom: [7/5 8/7; 50/49 64/63]
Gencom map: [<2 3 5 6|, <0 1/2 -1 -1|]
Map: [<2 0 11 12|, <0 1 -1 -1|]
EDOS: 4, 6, 10, 16, 22, 28
RMS error: 2.572 cents
Glacial[edit]
Subgroup: 2.9.5.11.13
Commas: 45/44, 65/64, 81/80
POT2 generator: ~9/8 = 186.151
Gencom: [2 9/8; 45/44 65/64 81/80]
Gencom map: [<1 3/2 2 0 3 4|, <0 1/2 2 0 3 -2|]
Map: [<1 0 -4 -6 10|, <0 1 2 3 -2|]
EDOs: 6, 13, 45be, 58bce, 71bce, 84bce
RMS error: 2.887 cents
Leantone[edit]
Subgroup: 2.9.5.7.11
Commas: 45/44, 56/55, 81/80
Related temperament: meanenneadecal
POT2 generator: ~9/8 = 192.500
Gencom: [2 9/8; 45/44 56/55 81/80]
Gencom map: [<1 3/2 2 2 3|, <0 1/2 2 5 3|]
Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]
EDOs: 6, 7, 13, 19, 25, 31, 56, 81
RMS error: 3.882 cents
