Chromatic pairs: Difference between revisions
m →Magic: Rename "group" field to "subgroup". |
m →Sensation: Rename "group" field to "subgroup". |
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== Sensation == | == Sensation == | ||
Subgroup: 2.3.5.7.13 | |||
Commas: 91/90, 126/125, 169/168 | Commas: 91/90, 126/125, 169/168 | ||
Revision as of 14:49, 2 August 2022
Definitions
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
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 mapping: [<3 10/9 -7/9 2/9|, <0 -2/3 -1/3 2/3|]
Mapping: [<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
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 mapping: [<1 0 -1/3 0 -1/3 2/3|, <0 0 -4/3 0 5/3 -1/3|]
Mapping: [<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
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 mapping: [<1 0 6 0 3 6|, <0 0 -8 0 1 -5|]
Mapping: [<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
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 mapping: [<1 0 0 4 0 4|, <0 0 0 -4 0 -1|]
Mapping: [<1 4 4|, <0 -4 -1|]
EDOS: 3, 7, 10, 27, 37, 47, 57, 104
RMS error: 0.1423
Tridec
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 mapping: [<1 0 -3/4 5/4 -3/4 1/4|, <0 0 0 -4 3 1|]
Mapping: [<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
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 mapping: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 0 -3|]
Mapping: [<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
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 mapping: [<1 0 0 2 4|, <0 0 0 3 -2|]
Mapping: [<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
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 mapping: [<1 -1/6 5/6 0 0 -1/3|, <0 -1/2 -3/2 0 0 1|]
Mapping: [<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
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 mapping: [<1 0 1 0 0 0|, <0 6 5 0 0 14|]
Mapping: [<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
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 mapping: [<1 2 -5/3 0 4/3 1/3|, <0 -2 4 0 -5 1|]
Mapping: [<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
Paint in the Water 29 by Igliashon Jones
Route 14 in Bridgetown by Chris Vaisvil
Haumea
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 mapping: [<1 2 -3/4 -11/4 9/4 5/4|, <0 -2 0 12 -9 -3|]
Mapping: [<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
Subgroup: 2.3.11
Commas: 243/242
Svalname: 7&17
POT2 generator: ~11/9 = 350.525
Gencom: [2 11/9; 243/242]
Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|]
Mapping: [<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
Mo - Happy - Happy play by Jake Freivald in Neutral[7], 24et tuning
Slendric
Subgroup: 2.3.7
Comma list: 1029/1024
Sval name: 5&21
POT2 generator: ~8/7 = 233.688
Gencom: [2 8/7; 1029/1024]
Gencom mapping: [⟨1 1 0 3], ⟨0 3 0 -1]]
Mapping: [⟨1 1 3], ⟨0 3 -1]]
EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190
RMS error: 0.3202 cents
Huntington
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 mapping: [<1 0 5 4 0 4|, <0 0 -9 -4 0 -1|]
Mapping: [<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
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 mapping: [<2 4 -2 0 9 2|, <0 -2 3/2 0 -5 -3/2|]
Mapping: [<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
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 mapping: [<1 1 0 -8/3 1/3 7/3|, <0 1 0 11/3 -1/3 -10/3|]
Mapping: [<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
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 mapping: [<2 0 4 0 5| <0 0 1 0 3|]
Mapping: [<2 0 -7|, <0 1 3|]
EDOs: 6, 16, 22, 28, 50, 122, 172, 222
RMS error: 0.3997
Bossier
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 mapping: [<1 0 0 0 1 3|, <0 0 0 8 7 2|]
Mapping: [<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
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 mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]
Mapping: [<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
Subgroup: 2.11.13
Comma: 265837/262144
POT2 generator: ~143/128 = 182.368
Gencom: [2 143/128; 265837/262144]
Gencom mapping: [<1 0 0 0 3 4|, <0 0 0 0 3 -2|]
Mapping: [<1 0 6|, <0 3 -2|]
EDOs: 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc
RMS error: 0.4444 cents
Marveltri
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 mapping: [<1 2/5 2 -1/5|, <0 -4/5 1 2/5|]
Mapping: [<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
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 mapping: [<1 1 -5 -1 2 4|, <0 1 29/4 5/4 -11/4 -23/4|]
Mapping: [<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
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 mapping: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 7 -3|]
Mapping: [<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
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 mapping: [<1 0 1 3 1 2|, <0 0 7 -1 13 9|]
Mapping: [<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
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 mapping: [<1 0 2 2 2 5|, <0 0 2 5 9 -8|]
Mapping: [<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
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 mapping: [<1 0 -4 0 0 3 9|, <0 0 9 4 0 1 -7|]
Mapping: [<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
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 mapping: [<1 3/2 3 4 0 2|, <0 1/2 -4 -7 0 10|]
Mapping: [<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
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 mapping: [<1 -4/3 3 -1/3 5/3|, <0 4/3 -3 7/3 -11/3|]
Mapping: [<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
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 mapping: [<1 1 0 3 6|, <0 3 0 -1 -13|]
Mapping: [<1 1 3 6|, <0 3 -1 -13|]
RMS error: 0.6502 cents
Gariberttet
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 mapping: [<1 0 0 0 0 0|, <0 -8/3 1/3 7/3 -1/2 1/2|]
Mapping: [<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
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 mapping: [<1 1 0 0 2 4|, <0 2 0 0 5 -1|]
Mapping: [<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
Subgroup: 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 mapping: [<1 0 0 0|, <0 0 2 -1|]
Mapping: [<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
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 mapping: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]
Mapping: [<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
Subgroup: 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 mapping: [<1 1 7 11], <0 1 -8 -14|]
Mapping: [<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
Subgroup: 2.5.7
Comma: 1071875/1048576
Sval name: 7&9
POT2 generator: ~175/128 = 527.236
Gencom: [2 175/128; 1071875/1048576]
Gencom mapping: [<1 0 1 5}, <0, 0, 3, -5|]
Mapping: [<1 1 5|, <0 3 -5|]
EDOs: 7, 9, 16, 25, 41, 66, 305bc
RMS error: 0.7729 cents
Indium
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 mapping: [<1 -1/2 -1/2 -1/2 3/2|, <0 -15/4 9/4 25/4 -19/4|]
Mapping: [<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
The Cry of Indium (in Indium 17) by Chris Vaisvil => details
Starlingtet
Subgroup: 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 mapping: [<1 -1 0 1|, <0 4/3 1/3 -5/3|]
Mapping: [<1 0 -1|, <0 1 3|]
EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b
RMS error: 0.8398 cents
Lovecraft
Subgroup: 2.11.13
Commas: 1352/1331
POT2 generator: ~13/11 = 279.318
Gencom: [2 13/11; 1352/1331]
Gencom mapping: [<1 0 0 0 3 3|, <0 0 0 0 2 3|]
Mapping: [<1 1 0|, <0 2 3|]
EDOS: 13, 30, 43, 73, 116b
RMS error: 0.8449 cents
Blackbirds
Subgroup: 2.11.13
Comma: 29282/28561
POT2 generator: ~11/8 = 546.660
Gencom: [13/11 11/8; 29282/28561]
Gencom mapping: [<4 0 0 0 12 13|, <0 0 0 0 1 1|]
Mapping: [<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
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 mapping: [<1 -5/4 3 -1/4 7/4 -1/4|, <0 -1/4 -3 3/4 -21/4 19/4|]
Mapping: [<1 0 2 -2 6|, <0 3 -1 5 -5|]
EDOs: 9, 31, 40, 49, 58, 156bde, 205bde
RMS error: 0.8790 cents
Myna
Subgroup: 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 mapping: [<1 -1 0 1|,<0 10 9 7|]
Mapping: [<1 9 9 8|, <0 -10 -9 -7|]
EDOs: 4, 27, 31, 58, 89, 236c, 325cd
RMS error: 0.9516 cents
Greeley
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 mapping: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|]
Mapping: [<1 1 2 2|, <0 -2 -6 -1|]
EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd
RMS error: 1.034 cents
Music
A Greeley Steals Halloween by Chris Vaisvil in Greeley 15
Semidim
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 mapping: [<1 -3 0 2 0 1|, <0 24/5 -6/5 -26/5 9/5 -1/5|]
Mapping: [<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
Subgroup: 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 mapping: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|]
Mapping: [<1 0 1|, <0 1 2|]
EDOs: 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc
RMS error: 1.064 cents
Sulis
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 mapping: [<1 4/9 2 -1/9 -1/9|, <0 -4/3 1 -2/3 4/3|]
Mapping: [<1 0 5 -9|, <0 1 -2 4|]
EDOs: 22, 25, 28, 31, 59, 90c, 149c
RMS error: 1.074 cents
Skwares
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 mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10|]
Mapping: [<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
Subgroup: 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 mapping: [<1 0 3 1 3|, <0 7 -3 8 2|]
Mapping: [<1 0 3 1 3|, <0 7 -3 8 2|]
EDOs: 9, 22, 31, 53, 84e
RMS error: 1.151 cents
Magicaltet
Subgroup: 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 mapping: [<1 -1/2 1/2 2 4|, <0 1/2 -1/2 3 -2|]
Mapping: [<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
Subgroup: 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 mapping: [<1 0 2 -1 6|, <0 5 1 12 -8|]
Mapping: [<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
Chromatic piece in magic 16 Chris Vaisvil
Kiribati
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 mapping: [<1 1/10 -4/5 11/10 1/5|, <0 -3/2 -1 3/2 1|]
Mapping: [<1 1 1 0|, <0 -2 3 4|]
EDOs: 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd
RMS error: 1.245 cents
Score
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 mapping: [<1 0 0 1 3 1|, <0 0 0 4 1 6|]
Mapping: [<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
Subgroup: 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 mapping: [<1 -1 -1 -2 0 0|, <0 7 9 13 0 10|]
Mapping: [<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
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 mapping: [<1 -1 -1 -2|, <0 7 9 13|]
Mapping: [<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
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 mapping: [<1 1 0 -3|, <0 1 4 10|]
Mapping: [<1 0 -4 -13|, <0 1 4 10|]
EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b
RMS error: 1.382 cents
Mohaha
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 mapping: [<1 1 0 0 2|, <[0 2 8 0 5|]
Mapping: [<1 1 0 2|, <0 2 8 5|]
EDOs: 24, 31, 55, 69d, 100d, 131bd
RMS error: 1.392 cents
Music
Mohaha10ping2 by Billy Stiltner
Joan
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 mapping: [<1 0 0 1 3|, <0 7/2 0 4 1|]
Mapping: [<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
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 mapping: [<1 3/2 2 2 2|, <0 1/2 2 5 9|]
Mapping: [<1 0 -4 -13 -25|, <0 1 2 5 9|]
EDOs: 25, 31, 68b, 99b
RMS error: 1.439 cents
Stacks
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 mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|]
Mapping: [<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
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 mapping: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]
Mapping: [<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
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 mapping: [<1 0 2 0 5 4 5|, <0 0 1 0 -5 -1 -3|]
Mapping: [<1 0 15 6 11|, <0 1 -5 -1 -3|]
EDOs: 10, 13, 16, 29
RMS error: 1.774 cents
Sixteen note mega chromatic scale
Archy
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|]
Mapping: [<1 2 2|, <0 -1 2|]
EDOs: 5, 12, 17, 22, 27, 137bc
RMS error: 1.856 cents
Suhajira
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 mapping: [<1 1 0 4 2|, <0 2 0 -4 5|]
Mapping: [<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
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 mapping: [<1 1 0 0 2 4|, <0 2 8 0 5 -1|]
Mapping: [<1 1 0 2 4|, <0 2 8 5 -1|]
EDOs: 17c, 24, 31, 55, 86de, 141cde
RMS error: 1.971 cents
Supra
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 mapping: [<1 1 0 4 7|, <0 1 0 -2 -6|]
Mapping: [<1 0 6 13|, <0 1 -2 -6|]
EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c
RMS error: 1.977 cents
Machine
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 mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]
Mapping: [<1 0 6 13|, <0 1 -1 -3|]
EDOs: 5, 6, 11, 17, 28
RMS error: 1.977 cents
Deutone
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 mapping: [<1 3/2 2 2 0 4|, <0 1/2 2 5 0 -2|]
Mapping: [<1 0 -4 -13 10|, <0 1 2 5 -2|]
EDOs: 6, 7, 13, 19, 25e, 44de
RMS error: 2.003 cents
Supraphon
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 mapping: [<1 1 0 4 7 9|, <0 1 0 -2 -6 -9|]
Mapping: [<1 0 6 13 18|, <0 1 -2 -6 -9|]
EDOs: 5, 7, 12, 17
RMS error: 2.095 cents
Negra
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 mapping: [<1 2 2 3 0 4|, <0 -4 3 -2 0 -3|]
Mapping: [<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
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 mapping: [<1 2 3 0 4|], <0 -3 -5 0 -4|]
Mapping: [<1 2 3 4|, <0 3 5 4|]
EDOs: 7, 15, 22, 73cd, 95cd, 117bcd, 256bcdd
RMS error: 2.287 cents
Skateboard
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 mapping: [<1 -3/7 4/7 11/7 4 -6/7|, <0 0 -1 -3 -2 2|]
Mapping: [<1 0 -1 2 2|, <0 1 3 2 -2|]
EDOs: 11, 15, 19, 23, 42d, 65d
RMS error: 2.396 cents
Augment
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 mapping: [<3 0 7 9 11|, <0 0 0 -1 -1|]
Mapping: [<3 7 0 2|, <0 0 1 1|]
EDOs: 3, 6, 9, 15, 21
RMS error: 2.422 cents
Semaphore
Subgroup: 2.3.7
Comma: 49/48
POT2 generator: ~7/6 = 250.385
Gencom: [2 7/6; 49/48]
Gencom mapping: [<1 2 0 3}, <0 -2 0 -1|]
Mapping: [<1 0 2|, <0 2 1|]
EDOs: 5, 9, 14, 19, 24, 67c, 91c
RMS error: 2.523 cents
Kryptonite
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 mapping: [<1 -5/4 2 -1/4 3/4 3/4|, <0 -1/2 3 3/2 -3/2 1/2|]
Mapping: [<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
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 mapping: [<1 2 3 2 4|, <0 -3/2 -5/2 3 -2|]
Mapping: [<1 1 1 5 2|, <0 3 4 -3 2|]
EDOs: 7, 11, 37b, 48b, 59b
RMS error: 2.550 cents
Antikythera
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 mapping: [<2 3 5 6|, <0 1/2 -1 -1|]
Mapping: [<2 0 11 12|, <0 1 -1 -1|]
EDOS: 4, 6, 10, 16, 22, 28
RMS error: 2.572 cents
Glacial
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 mapping: [<1 3/2 2 0 3 4|, <0 1/2 2 0 3 -2|]
Mapping: [<1 0 -4 -6 10|, <0 1 2 3 -2|]
EDOs: 6, 13, 45be, 58bce, 71bce, 84bce
RMS error: 2.887 cents
Leantone
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 mapping: [<1 3/2 2 2 3|, <0 1/2 2 5 3|]
Mapping: [<1 0 -4 -13 -6|, <0 1 2 5 3|]
EDOs: 6, 7, 13, 19, 25, 31, 56, 81
RMS error: 3.882 cents
