Chromatic pairs

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A chromatic pair is a pair of mos scales in some rank-2 temperament (either a full p-limit temperament or a subgroup temperament) that are analogous to the familiar diatonic and chromatic scales of standard tuning. The smaller scale is an albitonic scale (from Latin albus, "white"), named such since the diatonic scale can be played using the white keys of a piano, and the larger of the two is a chromatic scale, analogous to the chromatic scale of standard tuning. Other related scales can be associated to chromatic pairs, namely a haplotonic scale (from Greek haplóos, "single, simple"), analogous to the pentatonic scale of standard tuning and played using the black keys of a piano.

In the sections below, 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.

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 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

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 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

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 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

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 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

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 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

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 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

marveltwintri_321edo.png

Seven note albitonic scale

Eleven note chromatic scale

Fifteen note mega chromatic scale

Cata

Main article: Catakleismic
See also: Kleismic family #Cata
cata_246edo.jpg

Scales:

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

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 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

Five note haplotonic scale

Nine note albitonic scale

Fourteen note chromatic scale

Nineteen note mega chromatic scale

Neutral

See also: Rastmic clan #Neutral
neutral_380edo.png

Scales:

Music

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

Slendric

Main article: Slendric
See also: Gamelismic clan #Slendric and No-fives subgroup temperaments #Slendric
slendric_190edo.jpg

Scales:

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

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 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

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 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

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 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

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 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

bossier_225edo.jpg

Eight note albitonic scale

Eleven note chromatic scale

Fourteen note mega chromatic scale

Penta (aka Mechanism)

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

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 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

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 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

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 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

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 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

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 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

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 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

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 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

silver_487edo.jpg

silver7 -seven note haplotonic scale

silver10 - ten note albitonic scale

silver17 - seventeen note chromatic scale

Baldy

See also: Subgroup temperaments #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

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 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

Five note haplotonic scale

Nine note albitonic scale

Thirteen note chromatic scale

Radon

See also: Gamelismic clan #Radon
radon_128edo.jpg

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

Five note haplotonic scale

Nine note albitonic scale

Thirteen note chromatic scale

Namo

See also: Rastmic clan #Namo

Scales:

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

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 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

hemif_58edo.jpg

Seven note haplotonic scale

Ten note albitonic scale

Seventeen note chromatic scale

Garibaldi

Main article: Garibaldi temperament
See also: Schismatic family #Garibaldi
garibaldi_94edo.png

Scales:

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

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 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

indium_253edo.png

Eight note albitonic scale

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

Four note haplotonic scale

Seven note albitonic scale

Eleven note chromatic scale

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

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 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

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 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

Five note haplotonic scale

Nine note albitonic scale

Thirteen note chromatic scale

Myna

Main article: Myna
See also: Starling temperaments #Myna
myna_89edo.jpg

Scales:

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

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 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

semidim_770edo.png

Eight note albitonic scale

Thirteen note chromatic scale

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

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 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

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 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

skwares_206edo.png

Eight note albitonic scale

Eleven note mega albitonic scale

Fourteen note chromatic scale

Orwell

Main article: Orwell
See also: Semicomma family #Orwell
orwell_84edo.png

Scales:

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

Seven note albitonic scale

Eleven note chromatic scale

Fifteen note mega scale

Magic

Main article: Magic
See also: Magic family #Magic
magic_145edo.jpg

Scales:

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

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 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

score_20edo.jpg

Five note haplotonic scale

Seven note albitonic scale

Nine note mega albitonic scale

Eleven note chromatic scale

Sensi

Main article: Sensi
See also: Sensamagic clan #Sensi
See also: Sensipent family #Sensi
sensi_46edo.jpg

Scales:

Sensation

Main article: Sensi
See also: Sensamagic clan #Sensi
See also: Sensipent family #Sensi

Scales:

Meantone

Main article: Meantone
See also: Meantone family #Meantone
meantone_31edo.jpg

Scales:

Mohaha

See also: Rastmic clan #Mohaha
mohaha_131edo.png

Scales:

Music:

Billy Stiltner

Mohoho

See also: Rastmic clan #Mohoho

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

Five note haplotonic scale

Seven note albitonic scale

Nine note mega albitonic scale

Eleven note chromatic scale

Tutone

See also: Hemimean clan #Tutone
tutone_99edo.png

Scales:

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

Five note haplotonic scale

Eight note albitonic scale

Eleven note note chromatic scale

Nineteen note note mega chromatic scale

Bleu

Subgroup: 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|]

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 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

Seven note haplotonic scale

Ten note albitonic scale

Thirteen note chromatic scale

Sixteen note mega chromatic scale

Archy

Main article: Superpyth
See also: Archytas clan #Archy

Scales:

Supra

Main article: Superpyth
See also: Archytas clan #Supra
supra_56edo.png

Scales:

Supraphon

Main article: Superpyth
See also: Archytas clan #Supraphon

Suhajira

See also: Archytas clan #Suhajira

Scales:

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

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 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

deutone_44edo.png

Six note haplotonic scale

seven note albitonic scale

Thirteen note chromatic scale

Negra

Main article: Negri
See also: Marvel temperaments #Negri

Porkypine

Main article: Porcupine
See also: Porcupine family #Porcupine

Scales:

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

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 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

augment_21edo.png

Six note haplotonic scale

Nine note albitonic scale

Twelve note chromatic scale

Semaphore

Main article: Semaphore and godzilla
See also: Slendro clan #Semaphore
semaphore_24edo.png

Scales:

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

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 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

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 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

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 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

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 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

leantone_81edo.png