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

"Terrain" redirects here. For the scale, see Terrain (scale).

Terrain, the 6 & 21 temperament in the 2.9/5.9/7 subgroup, is related to domain. It 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.

Subgroup: 2.9/5.9/7

Comma list: 250047/250000

Sval mapping[3 0 -4], 0 1 2]]

Gencom mapping[3 10/9 -7/9 2/9], 0 -2/3 -1/3 2/3]]

gencom: [63/50 10/9; 250047/250000]

Optimal tuning (subgroup POTE): ~63/50 = 1\3, ~10/9 = 182.461

Optimal ET sequence6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558

RMS error: 0.00844 cents

terrain_3558edo.png

Scales:

Music

Petrtri

Petrtri can be described as 3 & 5 temperament in the 2.11/5.13/5 subgroup.

Subgroup: 2.11/5.13/5

Comma list: 2200/2197

Sval mapping[1 0 1], 0 3 1]]

Gencom mapping[1 0 -1/3 0 -1/3 2/3], 0 0 -4/3 0 5/3 -1/3]]

gencom: [2 13/10; 2200/2197]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~13/10 = 455.012

Optimal ET sequence21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c

RMS error: 0.0749 cents

petrtri_385edo.png

Scales:

Barton

Barton may be described as the 11 & 13 temperament in the 2.5.11.13 subgroup. It was named after Jacob Barton by Gene Ward Smith and Carl Lumma in 2006[1].

Subgroup: 2.5.11.13

Comma list: 2200/2197, 6656/6655

Sval mapping[1 6 3 6], 0 -8 1 -5]]

Gencom mapping[1 0 6 0 3 6], 0 0 -8 0 1 -5]]

gencom: [2 11/8; 2200/2197 6656/6655]

Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 551.699

Optimal ET sequence11, 13, 24, 37, 50, 87, 298, 385, 472, 559, 1590cd

RMS error: 0.0822 cents

Scales:

  • Barton5 – 5-tone haplotonic scale
  • Barton7 – 7-tone albitonic scale
  • Barton9 – 9-tone mega-albitonic scale
  • Barton11 – 11-tone chromatic scale
  • Barton13 – 13-tone mega-chromatic scale

Voltage

Voltage is the 3 & 7 temperament in the 2.7.13 subgroup.

Subgroup: 2.7.13

Comma list: 28672/28561

Sval mapping[1 4 4], 0 -4 -1]]

Gencom mapping[1 0 0 4 0 4], 0 0 0 -4 0 -1]]

gencom: [2, 16/13; 28672/28561]

Optimal tuning:

  • POTE: ~2 = 1\1, ~16/13 = 357.677
  • POTT: ~2 = 1\1, ~16/13 = 357.794 (1200 - 300 log2(7))

Optimal ET sequence3, 7, 10, 27, 37, 47, 57, 104

RMS error: 0.1423

Tridec

Tridec, the 5 & 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends petrtri.

Subgroup: 2.7/5.11/5.13/5

Comma list: 847/845, 1001/1000

Sval mapping[1 2 0 1], 0 -4 3 1]]

Gencom mapping[1 0 -3/4 5/4 -3/4 1/4], 0 0 0 -4 3 1]]

gencom: [2 13/10; 847/845 1001/1000]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~13/10 = 454.556

Optimal ET sequence5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc

RMS error: 0.1613 cents

tridec_235edo.png

Scales:

Nestoria

nestoria_171edo.png

Scales:

Orgone

Orgone, the 4 & 7 temperament in the 2.7.11 subgroup, is related to superkleismic.

Subgroup: 2.7.11

Comma list: 65536/65219

Sval mapping[1 2 4], 0 3 -2]]

Gencom mapping[1 0 0 2 4], 0 0 0 3 -2]]

gencom: [2 77/64; 65536/65219]

Optimal tuning (POTE): ~2 = 1\1, ~77/64 = 323.372

Optimal ET sequence4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475bc, 783bc

RMS error: 0.1888 cents

orgone_308edo.jpg

Scales:

Marveltwintri

Marveltwintri can be described as the 3 & 4 temperament in the 2.5/3.13/9 subgroup.

Subgroup: 2.5/3.13/9

Comma list: 325/324

Sval mapping[1 0 2], 0 1 -2]]

Gencom mapping[1 -1/6 5/6 0 0 -1/3], 0 -1/2 -3/2 0 0 1]]

gencom: [2 6/5; 325/324]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~6/5 = 317.139

Optimal ET sequence11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b

RMS error: 0.2444 cents

marveltwintri_321edo.png

Scales:

Cata

cata_246edo.jpg

Scales:

  • Cata7 – 7-tone albitonic scale
  • Cata11 – 11-tone mega-albitonic scale
  • Cata15 – 15-tone chromatic scale
  • Cata19 – 19-tone mega-chromatic scale

Bridgetown

Bridgetown, the 5 & 24 temperament in the 2.3.11/5.13/5 subgroup, is related to haumea and barbados.

Subgroup: 2.3.11/5.13/5

Comma list: 352/351, 676/675

Sval mapping[1 0 -6 -1], 0 2 9 3]]

Gencom mapping[1 2 -5/3 0 4/3 1/3], 0 -2 4 0 -5 1]]

gencom: [2 15/13; 352/351 676/675]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~15/13 = 248.399

Optimal ET sequence5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314

RMS error: 0.2513 cents

bridgetown_29edo.png

Scales:

Music

Haumea

Related temperaments include bridgetown, namaka, hemigari, barbados, and parizekmic.

Subgroup: 2.3.7/5.11/5.13/5

Comma list: 352/351, 676/675, 847/845

Sval mapping[1 0 10 -6 -1], 0 2 -12 9 3]]

Gencom mapping[1 2 -3/4 -11/4 9/4 5/4], 0 -2 0 12 -9 -3]]

gencom: [2 15/13; 352/351 676/675 847/845]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~15/13 = 248.491

Optimal ET sequence24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd

RMS error: 0.2668 cents

Scales:

Neutral

neutral_380edo.png

Scales:

Music

Slendric

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

Scales:

Huntington

Huntington may be described as the 10 & 27 temperament in the 2.5.7.13 subgroup.

Subgroup: 2.5.7.13

Comma list: 640/637, 10985/10976

Sval mapping[1 5 4 4], 0 -9 -4 -1]]

Gencom mapping[1 0 5 4 0 4], 0 0 -9 -4 0 -1]]

gencom: [2 16/13; 640/637 10985/10976]

Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 357.002

Optimal ET sequence7, 10, 17, 27, 37, 84, 121, 279cd, 400cd

RMS error: 0.3452 cents

huntington_400edo.jpg

Scales:

Tobago

Tobago, the 10 & 14 temperament in the 2.3.11.13/5 subgroup, extends neutral and barbados.

Subgroup: 2.3.11.13/5

Comma list: 243/242, 676/675

Sval mapping[2 0 -1 -2], 0 2 5 3]]

Gencom mapping[2 4 -2 0 9 2], 0 -2 3/2 0 -5 -3/2]]

gencom: [55/39 15/13; 243/242 676/675]

Optimal tuning (subgroup POTE): ~55/39 = 1\2, ~15/13 = 249.312

Optimal ET sequence10, 14, 24, 58, 82, 130

RMS error: 0.3533 cents

Scales:

Pepperoni

Pepperoni is generated by a fifth and can be described as the 5 & 12 temperament in the 2.3.11/7.13/7. It is the single-chain retraction of parapyth. The Pepper fifth, which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.

Subgroup: 2.3.11/7.13/7

Comma list: 352/351, 364/363

Sval mapping[1 0 7 12], 0 1 -4 -7]]

Gencom mapping[1 1 0 -8/3 1/3 7/3], 0 1 0 11/3 -1/3 -10/3]]

gencom: [2 3/2; 352/351 364/363]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~3/2 = 703.856

Optimal ET sequence5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd

RMS error: 0.3789 cents

pepperoni_271edo.png

Scales:

Wizz

Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, is related to wizard.

Subgroup: 2.5.11

Comma list: 15625/15488

Sval mapping[2 0 -7], 0 1 3]]

Gencom mapping[2 0 4 0 5], 0 0 1 0 3]]

gencom: [125/88 5/4; 15625/15488]

Optimal tuning (POTE): ~125/88 = 1\2, ~5/4 = 383.768

Optimal ET sequence6, 16, 22, 28, 50, 122, 172, 222

RMS error: 0.3997

Scales:

  • Wizz6 – 6-tone haplotonic scale
  • Wizz10 – 10-tone albitonic scale
  • Wizz16 – 16-tone chromatic scale

Bossier

Bossier can be described as the 3 & 17 in the 2.7.11.13 subgroup.

Subgroup: 2.7.11.13

Comma list: 1573/1568, 15488/15379

Sval mapping[1 0 1 3], 0 8 7 2]]

Gencom mapping[1 0 0 0 1 3], 0 0 0 8 7 2]]

gencom: [2 14/11; 1573/1568 15488/15379]

Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 421.309

Optimal ET sequence17, 20, 37, 57, 94, 225, 319cd, 413bcd

RMS error: 0.4043 cents

bossier_225edo.jpg

Scales:

Penta a.k.a. mechanism

Scales:

  • Penta5 – 5-tone haplotonic scale
  • Penta8 – 8-tone albitonic scale
  • Penta11 – 11-tone chromatic scale
  • Penta19 – 19-tone mega-chromatic scale

Bluebirds

Subgroup: 2.11.13

Comma list: 265837/262144

Sval mapping[1 0 6], 0 3 -2]]

Gencom mapping[1 0 0 0 3 4], 0 0 0 0 3 -2]]

gencom: [2 143/128; 265837/262144]

Optimal tuning (POTE): ~2 = 1\1, ~143/128 = 182.368

Optimal ET sequence6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc

RMS error: 0.4444 cents

Scales:

Marveltri

Marveltri, the 3 & 13 temperament in the 2.5.9/7 subgroup, is related to marvel, magic, and the unnamed 22 & 47 temperament.

Subgroup: 2.5.9/7

Comma list: 225/224

Sval mapping[1 0 5], 0 1 -2]]

Gencom mapping[1 2/5 2 -1/5], 0 -4/5 1 2/5]]

gencom: [2 5/4; 225/224]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~5/4 = 383.638

Optimal ET sequence13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc

RMS error: 0.4801 cents

Scales:

Edson

Edson is related to pele and andromeda.

Subgroup: 2.3.7/5.11/5.13/5

Comma list: 196/195 = [2 -1 2 0 -1, 352/351 = [5 -3 0 1 -1, 364/363 = [2 -1 1 -2 1

Sval mapping[1 0 10 17 22], 0 1 -6 -10 -13]]

mapping generators: ~2, ~3

Gencom mapping[1 1 -5 -1 2 4], 0 1 29/4 5/4 -11/4 -23/4]]

gencom: [2 3/2; 196/195, 352/351, 364/363]

Optimal tunings:

Optimal ET sequence12, 17, 29

RMS error: 0.5102 cents

Scales:

  • Edson5 – 5-tone haplotonic scale
  • Edson7 – 7-tone albitonic scale
  • Edson12 – 12-tone chromatic scale
  • Edson17 – 17-tone mega-chromatic scale

Photia

photia_65edo.png

Scales:

Shoe a.k.a. llywelyn

shoe_37edo.jpg

Scales:

  • Shoe5 – 5-tone mini-haplotonic scale
  • Shoe6 – 6-tone haplotonic scale
  • Shoe11 – 11-tone albitonic scale
  • Shoe16 – 16-tone chromatic scale

Roulette

roulette_37edo.jpg

Scales:

Silver

Silver can be described as the 10 & 27 temperament in the 2.5.7.13.17 subgroup.

Subgroup: 2.5.7.13.17

Comma list: 170/169, 640/637, 5525/5488

Sval mapping[1 5 4 4 2], 0 -9 -4 -1 7]]

Gencom mapping[1 0 -4 0 0 3 9], 0 0 9 4 0 1 -7]]

gencom: [2 13/8; 170/169 640/637 5525/5488]

Optimal tuning (POTE): ~2 = 1\1, ~13/8 = 842.711

Optimal ET sequence7, 10, 17, 27, 37, 47, 84, 131, 178e, 309cde, 487bcdee

RMS error: 0.5886 cents

silver_487edo.jpg

Scales:

Baldy

Baldy is every other step of garibaldi, without the mapping of prime 11. It can be described as the 6 & 35 temperament.

Subgroup: 2.9.5.7.13

Comma list: 225/224, 325/324, 640/637

Sval mapping[1 0 15 25 -28], 0 1 -4 -7 10]]

Gencom mapping[1 3/2 3 4 0 2], 0 1/2 -4 -7 0 10]]

gencom: [2 9/8; 225/224 325/324 640/637]

Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.090

Optimal ET sequence6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd

RMS error: 0.5999 cents

baldy_147edo.jpg

Scales

  • Baldy6 – 6-tone haplotonic scale
  • Baldy11 – 11-tone albitonic scale
  • Baldy17 – 17-tone chromatic scale

Guanyintet

Guanyintet, the 4 & 9 temperament in the 2.5.7/3.11/3 subgroup, is related to guanyin as well as to orwell.

Subgroup: 2.5.7/3.11/3

Comma list: 176/175, 540/539

Sval mapping[1 0 2 -2], 0 3 -1 5]]

Gencom mapping[1 -4/3 3 -1/3 5/3], 0 4/3 -3 7/3 -11/3]]

gencom: [2 7/6; 176/175 540/539]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~7/6 = 270.093

Optimal ET sequence9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd

RMS error: 0.6028 cents

Scales:

Radon

radon_128edo.jpg
  • Radon5 – 5-tone haplotonic scale
  • Radon11 – 11-tone albitonic scale
  • Radon16 – 16-tone chromatic scale

Gariberttet

Gariberttet can be described as the 4 & 29 temperament in the 2.5/3.7/3.13/11 subgroup.

Subgroup: 2.5/3.7/3.13/11

Comma list: 275/273, 847/845

Sval mapping[1 0 0 0], 0 3 5 1]]

Gencom mapping[1 0 0 0 0 0], 0 -8/3 1/3 7/3 -1/2 1/2]]

gencom: [2 13/11; 275/273 847/845]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~13/11 = 293.679

Optimal ET sequence29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd

RMS error: 0.6914 cents

Scales:

Namo

Scales:

  • Namo7 – 7-tone haplotonic scale
  • Namo10 – 10-tone albitonic scale
  • Namo17 – 17-tone chromatic scale

Sentry

Sentry, the 3 & 5 temperament in the 2.5/3.9/7 subgroup, is related to sensi.

Subgroup: 2.5/3.9/7

Comma list: 245/243

Sval mapping[1 0 0], 0 2 1]]

Gencom mapping[1 0 0 0], 0 0 2 -1]]

gencom: [2 9/7; 245/243]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~9/7 = 440.902

Optimal ET sequence8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc

RMS error: 0.7105 cents

Scales:

Hemif

hemif_58edo.jpg

Scales:

  • Hemif7 – 7-tone haplotonic scale
  • Hemif10 – 10-tone albitonic scale
  • Hemif17 – 17-tone chromatic scale

Garibaldi

garibaldi_94edo.png

Scales:

Mabila

Given below is the no-3 version of mabila, the 7 & 9 temperament.

Subgroup: 2.5.7

Comma list: 1071875/1048576

Sval mapping[1 1 5], 0 3 -5]]

Gencom mapping[1 0 1 5], 0 0 3 -5]]

gencom: [2 175/128; 1071875/1048576]

Optimal tuning (POTE): ~2 = 1\1, ~175/128 = 527.236

Optimal ET sequence7, 9, 16, 25, 41, 66, 305bc

RMS error: 0.7729 cents

mabila_66edo.jpg

Scales:

Indium

Indium can be described as the 8 & 33 temperament in the 2.5/3.7/3.11/3 subgroup.

Subgroup: 2.5/3.7/3.11/3

Comma list: 3025/3024, 3125/3087

Sval mapping[1 0 0 2], 0 6 10 -1]]

Gencom mapping[1 -1/2 -1/2 -1/2 3/2], 0 -15/4 9/4 25/4 -19/4]]

gencom: [2 12/11; 3025/3024 3125/3087]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~12/11 = 147.010

Optimal ET sequence33, 41, 49, 57, 106, 204, 253

RMS error: 0.7788 cents

indium_253edo.png

Scales:

Music

Starlingtet

Starlingtet, the 4 & 15 temperament in the 2.5/3.7/3 subgroup, is related to starling as well as to myna.

Subgroup: 2.5/3.7/3

Comma list: 126/125

Sval mapping[1 0 -1], 0 1 3]]

Gencom mapping[1 -1 0 1], 0 4/3 1/3 -5/3]]

gencom: [2 6/5; 126/125]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~6/5 = 311.154

Optimal ET sequence15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b

RMS error: 0.8398 cents

Scales:

Lovecraft

Lovecraft, the 4 & 13 temperament in the 2.11.13 subgroup, is generated by ~13/11. Two generator steps give ~11/8 and three generator steps give ~13/8.

Subgroup: 2.11.13

Comma list: 1352/1331

Sval mapping[1 3 3], 0 2 3]]

Gencom mapping[1 0 0 0 3 3], 0 0 0 0 2 3]]

gencom: [2 13/11; 1352/1331]

Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 279.318

Optimal ET sequence13, 30, 43, 73, 116b

RMS error: 0.8449 cents

lovecraft_116edo.png

Scales:

Blackbirds

Blackbirds is a fairly straightforward temperament. It simply equates ~13/11 to 1/4 of the octave with a generator for prime 11 or 13.

Subgroup: 2.11.13

Comma list: 29282/28561

Sval mapping[4 0 1], 0 1 1]]

Gencom mapping[4 0 0 0 12 13], 0 0 0 0 1 1]]

gencom: [13/11 11/8; 29282/28561]

Optimal tuning (POTE): ~13/11 = 1\4, ~11/8 = 546.660

Optimal ET sequence4, 16, 20, 24, 44, 68, 112c, 180bc

RMS error: 0.8685 cents

Scales:

Laz

Laz is related to georgian as well as to winston.

Subgroup: 2.5.7/3.11/3.13/3

Comma list: 144/143, 176/175, 196/195

Sval mapping[1 0 2 -2 6], 0 3 -1 5 -5]]

Gencom mapping[1 -5/4 3 -1/4 7/4 -1/4], 0 -1/4 -3 3/4 -21/4 19/4]]

gencom: [2 7/6; 144/143 176/175 196/195]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~7/6 = 269.300

Optimal ET sequence9, 31, 40, 49, 58, 156bde, 205bde

RMS error: 0.8790 cents

Scales:

  • Laz5 – 5-tone haplotonic scale
  • Laz9 – 9-tone albitonic scale
  • Laz13 – 13-tone chromatic scale

Myna

myna_89edo.jpg

Scales:

  • Myna7 – 7-tone haplotonic scale
  • Myna11 – 11-tone albitonic scale
  • Myna15 – 15-tone chromatic scale

Greeley

Greeley is related to opossum as well as to nusecond.

Subgroup: 2.5/3.7/3.11/3

Comma list: 121/120, 126/125

Sval mapping[1 1 2 2], 0 -2 -6 -1]]

Gencom mapping[1 -5/4 -1/4 3/4 3/4], 0 9/4 1/4 -15/4 5/4]]

gencom: [2 11/10; 121/120 126/125]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~11/10 = 155.776

Optimal ET sequence8, 15, 23, 54, 77, 100, 131d, 208bd

RMS error: 1.034 cents

greeley_100edo.png

Scales:

Music

Semidim

Semidim can be described as the 8 & 29 temperament in the 2.5/3.7/3.11/3.13/3 subgroup.

Subgroup: 2.5/3.7/3.11/3.13/3

Comma list: 121/120, 169/168, 275/273

Sval mapping[1 3 5 3 4], 0 -6 -10 -3 -5]]

Gencom mapping[1 -3 0 2 0 1], 0 24/5 -6/5 -26/5 9/5 -1/5]]

gencom: [2 13/10; 121/120 169/168 275/273]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~13/10 = 453.242

Optimal ET sequence5, 8, 13, 21, 29, 37, 44, 45, 188bde

RMS error: 1.052 cents

semidim_770edo.png

Scales:

Mothwelltri

Mothwelltri, the 1 & 4 temperament in the 2.7/3.11 subgroup, is related to orwell.

Subgroup: 2.7/3.11

Comma list: 99/98

Sval mapping[1 0 1], 0 1 2]]

Gencom mapping[1 -1/2 0 1/2 3], 0 -1/2 0 1/2 2]]

gencom: [2 7/6; 99/98]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~7/6 = 273.174

Optimal ET sequence9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc

RMS error: 1.064 cents

Scales:

Sulis

Sulis is related to minerva as well as to würschmidt.

Subgroup: 2.5.9/7.11/9

Comma list: 99/98, 176/175

Sval mapping[1 0 5 -9], 0 1 -2 4]]

Gencom mapping[1 4/9 2 -1/9 -1/9], 0 -4/3 1 -2/3 4/3]]

gencom: [2 5/4; 99/98 176/175]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~5/4 = 386.558

Optimal ET sequence22, 25, 28, 31, 59, 90c, 149c

RMS error: 1.074 cents

Scales:

  • Sulis7 – 7-tone haplotonic scale
  • Sulis10 – 10-tone albitonic scale
  • Sulis13 – 13-tone chromatic scale

Skwares

skwares_206edo.png

Scales:

Orwell

orwell_84edo.png

Scales:

Magicaltet

Magicaltet is related to supermagic, superkleismic, and magic.

Subgroup: 2.5/3.7.11

Comma list: 100/99 = [2 2 0 -1, 385/384 = [-7 1 1 1

Sval mapping[1 0 5 2], 0 1 -3 2]]

mapping generators: ~2, ~5/3

Gencom mapping[1 -1/2 1/2 2 4], 0 1/2 -1/2 3 -2]]

gencom: [2 6/5; 100/99 385/384]

Optimal tunings:

Optimal ET sequence4, 7, 11, 15, 26, 67, 93*

* wart for 5/3

RMS error: 1.206 cents

Scales:

Magic

magic_145edo.jpg

Scales:

  • Magic7 – 7-tone haplotonic scale
  • Magic10 – 10-tone albitonic scale
  • Magic13 – 13-tone chromatic scale
  • Magic16 – 16-tone mega-chromatic scale

Kiribati

Kiribati is related to nakika as well as to octacot.

Subgroup: 2.9/5.7/3.11/9

Comma list: 100/99, 245/242

Sval mapping[1 1 1 0], 0 -2 3 4]]

Gencom mapping[1 1/10 -4/5 11/10 1/5], 0 -3/2 -1 3/2 1]]

gencom: [2 21/20; 100/99 245/242]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~21/20 = 87.892

Optimal ET sequence13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd

RMS error: 1.245 cents

Scales:

Score

Subgroup: 2.7.11.13

Comma list: 343/338, 847/832

Sval mapping[1 1 3 1], 0 4 1 6]]

Gencom mapping[1 0 0 1 3 1], 0 0 0 4 1 6]]

gencom: [2 11/8; 343/338 847/832]

Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 540.099

Optimal ET sequence5, 7, 9, 11, 20

RMS error: 1.282 cents

score_20edo.jpg

Scales:

  • Score5 – 5-tone haplotonic scale
  • Score7 – 7-tone albitonic scale
  • Score9 – 9-tone mega-albitonic scale
  • Score11 – 11-tone chromatic scale

Sensi

sensi_46edo.jpg

Scales:

  • Sensi5 – 5-tone haplotonic scale
  • Sensi8 – 8-tone albitonic scale
  • Sensi11 – 11-tone mega-albitonic scale
  • Sensi19 – 19-tone chromatic scale

Sensation

Scales:

  • Sensi5 – 5-tone haplotonic scale
  • Sensi8 – 8-tone albitonic scale
  • Sensi11 – 11-tone mega-albitonic scale
  • Sensi19 – 19-tone chromatic scale

Meantone

meantone_31edo.jpg

Scales:

Mohaha

mohaha_131edo.png

Scales:

Music:

Billy Stiltner

Mohoho

Joan

Joan is related to casablanca as well as to orwell.

Subgroup: 2.9.7.11

Comma list: 99/98, 9317/9216

Sval mapping[1 0 1 3], 0 7 4 1]]

Gencom mapping[1 0 0 1 3], 0 7/2 0 4 1]]

gencom: [2 11/8; 99/98 9317/9216]

Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 542.672 cents

Optimal ET sequence11, 20, 31, 42, 115bd, 157bd

RMS error: 1.424 cents

Scales:

  • Joan5 – 5-tone haplotonic scale
  • Joan7 – 7-tone albitonic scale
  • Joan9 – 9-tone mega-albitonic scale
  • Joan11 – 11-tone chromatic scale

Tutone

tutone_99edo.png

Scales:

Stacks

Scales:

Bleu

Scales:

  • Bleu8 – 8-tone haplotonic scale
  • Bleu9 – 9-tone albitonic scale
  • Bleu17 – 17-tone chromatic scale

Sephiroth

Sephiroth is the no-7 restriction of muggles.

Subgroup: 2.5.11.13.17

Comma list: 65/64, 170/169, 221/220

Sval mapping[1 0 15 6 11], 0 1 -5 -1 -3]]

Gencom mapping[1 0 2 0 5 4 5], 0 0 1 0 -5 -1 -3]]

gencom: [2 5/4; 65/64 170/169 221/220]

Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 372.236

Optimal ET sequence10, 13, 16, 29

RMS error: 1.774 cents

Scales:

Archy

Scales:

  • Archy5 – 5-tone haplotonic scale
  • Archy7 – 7-tone albitonic scale
  • Archy12 – 12-tone chromatic scale

Supra

supra_56edo.png

Scales:

Supraphon

Suhajira

Scales:

Machine

machine_28edo.png

Scales:

Deutone

Deutone is every other step of meanpop.

Subgroup: 2.9.5.7.13

Comma list: 65/64, 81/80, 91/90

Sval mapping[1 0 -4 -13 10], 0 1 2 5 -2]]

Gencom mapping[1 3/2 2 2 0 4], 0 1/2 2 5 0 -2]]

gencom: [2 9/8; 65/64 81/80 91/90]

Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 191.059

Optimal ET sequence6, 7, 13, 19, 25e, 44de

RMS error: 2.003 cents

deutone_44edo.png

Scales:

Negra

Porkypine

Scales:

Skateboard

Skateboard is related to thrasher.

Subgroup: 2.5/3.7/3.11.13/9

Comma list: 56/55, 91/90, 100/99

Sval mapping[1 0 -1 2 2], 0 1 3 2 -2]]

Gencom mapping[1 -3/7 4/7 11/7 4 -6/7], 0 0 -1 -3 -2 2]]

gencom: [2 6/5; 56/55 91/90 100/99]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~6/5 = 313.842

Optimal ET sequence11, 15, 19, 23, 42d, 65d

RMS error: 2.396 cents

Scales:

Augment

Augment is related to augmented.

Subgroup: 2.5.7.11

Comma list: 56/55, 128/125

Sval mapping[3 7 0 2], 0 0 1 1]]

Gencom mapping[3 0 7 9 11], 0 0 0 -1 -1]]

gencom: [5/4 8/7; 56/55 128/125]

Optimal tuning (POTE): ~5/4 = 1\3, ~8/7 = 228.275

Optimal ET sequence3, 6, 9, 15, 21

RMS error: 2.422 cents

augment_21edo.png

Scales:

Semaphore

semaphore_24edo.png

Scales:

Kryptonite

Kryptonite is related to krypton.

Subgroup: 2.5.7/3.11/3.13/3

Comma list: 56/55, 78/77, 91/90

Sval mapping[1 2 1 2 2], 0 -3 -2 1 -1]]

Gencom mapping[1 -5/4 2 -1/4 3/4 3/4], 0 -1/2 3 3/2 -3/2 1/2]]

gencom: [2 13/12; 56/55 78/77 91/90]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~13/12 = 132.428

Optimal ET sequence9, 63, 82bd, 91bde

RMS error: 2.545 cents

Scales:

Oregon

Subgroup: 2.9.15.7.11

Comma list: 55/54, 64/63, 100/99

Sval mapping[1 1 1 5 2], 0 3 4 -3 2]]

Gencom mapping[1 2 3 2 4], 0 -3/2 -5/2 3 -2]]

gencom: [2 6/5; 55/54 64/63 100/99]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~6/5 = 325.495

Optimal ET sequence7, 11, 37b, 48b, 59b

RMS error: 2.550 cents

Scales:

Antikythera

antikythera_28edo.png

Scales:

Glacial

Subgroup: 2.9.5.11.13

Comma list: 45/44, 65/64, 81/80

Sval mapping[1 0 -4 -6 10], 0 1 2 3 -2]]

Gencom mapping[1 3/2 2 0 3 4], 0 1/2 2 0 3 -2]]

gencom: [2 9/8; 45/44 65/64 81/80]

Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 186.151

Optimal ET sequence6, 13, 45be, 58bce, 71bce, 84bce

RMS error: 2.887 cents

Scales:

Leantone

Leantone is every other step of meanenneadecal.

Subgroup: 2.9.5.7.11

Comma list: 45/44, 56/55, 81/80

Sval mapping[1 0 -4 -13 -6], 0 1 2 5 3]]

Gencom mapping[1 3/2 2 2 3], 0 1/2 2 5 3]]

gencom: [2 9/8; 45/44 56/55 81/80]

Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 192.500

Optimal ET sequence6, 7, 13, 19, 25, 31, 56, 81

RMS error: 3.882 cents

leantone_81edo.png

Scales:

Notes