Chromatic pairs

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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 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.

terrain_3558edo.png

Nine note albitonic scale

Fifteen note chromatic scale

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 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

petrtri_385edo.png

Five note haplotonic scale

Eight note albitonic scale

Thirteen note chromatic scale

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 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

Five note haplotonic scale

Seven note albitonic scale

Nine note mega albitonic scale

Eleven note chromatic 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 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

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

tridec_235edo.png

Eight note albitonic scale

Thirteen note chromatic scale

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 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

nestoria_171edo.png

Seven note albitonic scale

Twelve note chromatic scale

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 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

orgone_308edo.jpg

Seven note albitonic scale

Eleven note chromatic scale

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 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

marveltwintri_321edo.png

Seven note albitonic scale

Eleven note chromatic scale

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 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

cata_246edo.jpg

Seven note albitonic scale

Eleven note mega albitonic scale

Fifteen note chromatic 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 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

bridgetown_29edo.png

Nine note albitonic scale

Fourteen note chromatic scale

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 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

Five note haplotonic scale

Nine note albitonic scale

Fourteen note chromatic scale

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 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

neutral_380edo.png

Seven note albitonic scale

Ten note chromatic scale

Seventeen note mega chromatic scale

Music

Mo - Happy - Happy play by Jake Freivald in Neutral[7], 24et tuning

Slendric

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

slendric_190edo.jpg

Five note haplotonic scale

Six note haplotonic scale

Eleven note albitonic scale

Sixteen note chromatic scale

Music

The 11th Slendric Fanfare

16 Slendric Virgins

by Chris Vaisvil

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 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

huntington_400edo.jpg

Seven note haplotonic scale

Ten note albitonic scale

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 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

Six note haplotonic scale

Ten note albitonic scale

Fourteen note chromatic scale

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 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

pepperoni_271edo.png

Seven note albitonic scale

Twelve note chromatic scale

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 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

Six note haplotonic scale

Ten note albitonic scale

Sixteen note chromatic scale

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 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

bossier_225edo.jpg

Eight note albitonic scale

Eleven note chromatic scale

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 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

Five note haplotonic scale

Eight note albitonic scale

Eleven note chromatic scale

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 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

Six note haplotonic scale

Seven note albitonic scale

Thirteen note chromatic scale

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 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

Seven note albitonic scale

Ten note chromatic scale

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 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

Five note haplotonic scale

Seven note albitonic scale

Twelve note chromatic scale

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 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

photia_65edo.png

Seven note albitonic scale

Twelve note chromatic scale

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 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

shoe_37edo.jpg

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 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

roulette_37edo.jpg

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 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

silver_487edo.jpg

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 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

baldy_147edo.jpg

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 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

Five note haplotonic scale

Nine note albitonic scale

Thirteen note chromatic scale

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 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

radon_128edo.jpg

Five note haplotonic scale

Eleven note albitonic scale

Sixteen note chromatic scale

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 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

Five note haplotonic scale

Nine note albitonic scale

Thirteen note chromatic scale

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 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

Seven note haplotonic scale

Ten note albitonic scale

Seventeen note chromatic scale

Sentry

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

Five note haplotonic scale

Eight note albitonic scale

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 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

hemif_58edo.jpg

Seven note haplotonic scale

Ten note albitonic scale

Seventeen note chromatic scale

Garibaldi

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

garibaldi_94edo.png

Twelve note albitonic scale

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 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

mabila_66edo.jpg

Seven note haplotonic scale

Nine note albitonic scale

Sixteen note chromatic scale

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 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

indium_253edo.png

Eight note albitonic scale

Seventeen note chromatic scale

Music

The Cry of Indium (in Indium 17) by Chris Vaisvil => details

Starlingtet

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

Four note haplotonic scale

Seven note albitonic scale

Eleven note chromatic scale

Lovecraft

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

lovecraft_116edo.png

Five note haplotonic scale

Nine note albitonic scale

Thirteen note chromatic scale

Blackbirds

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

Eight note albitonic scale

Twelve note chromatic scale

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 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

Five note haplotonic scale

Nine note albitonic scale

Thirteen note chromatic scale

Myna

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

myna_89edo.jpg

Seven note haplotonic scale

Eleven note albitonic scale

Fifteen note chromatic scale

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 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

greeley_100edo.png

Eight note albitonic scale

Fifteen note chromatic scale

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 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

semidim_770edo.png

Eight note albitonic scale

Thirteen note chromatic scale

Mothwelltri

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

Five note haplotonic scale

Nine note albitonic scale

Thirteen note chromatic scale

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 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

Seven note haplotonic scale

Ten note albitonic scale

Thirteen note chromatic scale

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 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

skwares_206edo.png

Eight note albitonic scale

Eleven note mega albitonic scale

Fourteen note chromatic scale

Orwell

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

orwell_84edo.png

Five note haplotonic scale

Nine note albitonic scale

Thirteen note chromatic scale

Magicaltet

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

Seven note albitonic scale

Eleven note chromatic scale

Fifteen note mega scale

Magic

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

magic_145edo.jpg

Seven note haplotonic scale

Ten note albitonic scale

Thirteen note chromatic scale

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 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

Thirteen note chromatic scale

Fourteen note chromatic scale

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 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

score_20edo.jpg

Five note haplotonic scale

Seven note albitonic scale

Nine note mega albitonic scale

Eleven note chromatic scale

Sensation

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

Five note haplotonic scale

Eight note albitonic scale

Eleven note mega albitonic scale

Nineteen note chromatic 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 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

sensi_46edo.jpg

Five note haplotonic scale

Eight note albitonic scale

Eleven note mega albitonic scale

Nineteen note chromatic 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 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

meantone_31edo.jpg

Five note haplotonic scale

Seven note albitonic scale

Twelve note chromatic scale

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 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

mohaha_131edo.png

Seven note albitonic scale

Ten note chromatic scale

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 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

Five note haplotonic scale

Seven note albitonic scale

Nine note mega albitonic scale

Eleven note chromatic 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 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

Six note haplotonic scale

Seven note albitonic scale

Thirteen note chromatic scale

tutone_99edo.png

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 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

Five note haplotonic scale

Eight note albitonic scale

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 map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]

Map: [<1 1 2 3 3|, <0 5 7 4 6|]

EDOs: 17, 43, 60c

RMS error: 1.752 cents

blue_60edo.png

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 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

Seven note haplotonic scale

Ten note albitonic scale

Thirteen note chromatic scale

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|]

Map: [<1 2 2|, <0 -1 2|]

EDOs: 5, 12, 17, 22, 27, 137bc

RMS error: 1.856 cents

Five note haplotonic scale

Seven note albitonic scale

Twelve note chromatic scale

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 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

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

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

supra_56edo.png

Seven note albitonic scale

Twelve note chromatic scale

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 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

machine_28edo.png

Five note haplotonic scale

Six note albitonic scale

Eleven note chromatic scale

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 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

deutone_44edo.png

Six note haplotonic scale

seven note albitonic scale

Thirteen note chromatic scale

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 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

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

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

Seven note haplotonic scale

Eight note albitonic scale

Fifteen note chromatic scale

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 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

Seven note haplotonic scale

Eleven note albitonic scale

Fifteen note chromatic scale

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 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

augment_21edo.png

Six note haplotonic scale

Nine note albitonic scale

Twelve note chromatic scale

Semaphore

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

semaphore_24edo.png

Five note haplotonic scale

Nine note albitonic scale

Fourteen note chromatic scale

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 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

Nine note albitonic scale

Ten note albitonic scale

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 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

Seven note haplotonic scale

Eleven note albitonic scale

Fifteen note chromatic scale

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 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

antikythera_28edo.png

Six note haplotonic scale

Ten note albitonic scale

Sixteen note chromatic scale

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 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

Six note haplotonic scale

Seven note albitonic scale

Thirteen note chromatic scale

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 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

leantone_81edo.png

Six note haplotonic scale

Seven note albitonic scale

Thirteen note chromatic scale