Chromatic pairs

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 sequence: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558

RMS error: 0.00844 cents

Terrain in 3558edo

Scales:

• terrain9 – 9-tone albitonic scale
• terrain15 – 15-tone chromatic scale

Music

• 5 5 1 mode of 33 equal (2013) by Chris Vaisvil – blog | YouTube | play

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 sequence: 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c

RMS error: 0.0749 cents

Petrtri in 385edo

Scales:

• petrtri5 – 5-tone haplotonic scale
• petrtri8 – 8-tone albitonic scale
• petrtri13 – 13-tone chromatic scale

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.

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 sequence: 11, 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 sequence: 3, 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 sequence: 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc

RMS error: 0.1613 cents

Tridec in 235edo

• Tridec8 – 8-tone albitonic scale
• Tridec13 – 13-tone chromatic scale

Nestoria

See also: Schismatic family § Nestoria (2.3.5.19)

Nestoria in 171edo

Scales:

• nestoria7 – 7-tone albitonic scale
• nestoria12 – 12-tone chromatic scale
• nestoria17 – 7-tone mega chromatic scale

Orgone

Main article: Orgone

See also: Orgonia

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 sequence: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475bc, 783bc

RMS error: 0.1888 cents

Orgone in 308edo

Scales:

• orgone7 – 7-tone albitonic scale
• orgone11 – 11-tone chromatic scale
• orgone15 – 15-tone mega chromatic scale

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 sequence: 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b

RMS error: 0.2444 cents

Marveltwintri in 321edo

Scales:

• marveltwintri7 – 7-tone albitonic scale
• marveltwintri11 – 11-tone chromatic scale
• marveltwintri15 – 15-tone mega chromatic scale

Cata

Main article: Hanson and cata

See also: Kleismic family § Cata

Cata in 246edo

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 sequence: 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314

RMS error: 0.2513 cents

Bridgetown in 29edo

Scales:

• bridgetown9 – 9-tone albitonic scale
• bridgetown14 – 14-tone chromatic scale

Music

• Paint in the Water 29 (archived 2020) by Igliashon Jones
• Route 14 in Bridgetown (archived 2020) by Chris Vaisvil

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 sequence: 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd

RMS error: 0.2668 cents

Scales:

• haumea5 – 5-tone haplotonic scale
• haumea9 – 9-tone albitonic scale
• haumea14 – 14-tone chromatic scale
• haumea19 – 19-tone mega chromatic scale

Neutral

See also: Rastmic clan § Neutral

Neutral in 380edo

Scales:

• neutral7 – 7-tone albitonic scale
• neutral10 – 10-tone chromatic scale
• neutral17 – 17-tone mega-chromatic scale

Music

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

Slendric

Main article: Slendric

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

Slendric in 190edo

Scales:

• Slendric5 – 5-tone haplotonic scale
• Slendric6 – 6-tone haplotonic scale
• Slendric11 – 11-tone albitonic scale
• Slendric16 – 16-tone chromatic scale

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 sequence: 7, 10, 17, 27, 37, 84, 121, 279cd, 400cd

RMS error: 0.3452 cents

Huntington in 400edo

Scales:

• huntington7 – 7-tone haplotonic scale
• huntington10 – 10-tone albitonic scale
• huntington17 – 17-tone chromatic scale

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 sequence: 10, 14, 24, 58, 82, 130

RMS error: 0.3533 cents

Scales:

• tobago6 – 6-tone haplotonic scale
• tobago10 – 10-tone albitonic scale
• tobago14 – 14-tone chromatic scale
• tobago24 – 24-tone quatertone scale

Pepperoni

See also: Parapyth

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 sequence: 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd

RMS error: 0.3789 cents

Pepperoni in 271edo

Scales:

• pepperoni7 – 7-tone albitonic scale
• pepperoni12 – 12-tone chromatic scale

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 sequence: 6, 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 sequence: 17, 20, 37, 57, 94, 225, 319cd, 413bcd

RMS error: 0.4043 cents

Bossier in 225edo

Scales:

• bossier8 – 8-tone albitonic scale
• bossier11 – 11-tone chromatic scale
• bossier14 – 14-tone mega-chromatic scale

Penta a.k.a. mechanism

See also: Subgroup temperaments § 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 sequence: 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc

RMS error: 0.4444 cents

Scales:

• bluebirds6 – 6-tone haplotonic scale
• bluebirds7 – 7-tone albitonic scale
• bluebirds13 – 13-tone chromatic scale

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 sequence: 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc

RMS error: 0.4801 cents

Scales:

• marveltri7 – 7-tone albitonic scale
• marveltri10 – 10-tone chromatic scale
• marveltri13 – 13-tone mega-chromatic scale

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:

• subgroup CTE: ~2 = 1\1, ~3/2 = 703.4398
• subgroup POTE: ~2 = 1\1, ~3/2 = 703.414

Optimal ET sequence: 12, 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

See also: Schismatic family § Photia (2.3.5.17)

Photia in 65edo

Scales:

• photia7 – 7-tone albitonic scale
• photia12 – 12-tone chromatic scale

Shoe a.k.a. llywelyn

See also: Llywelynsmic clan § Llywelyn a.k.a. shoe

Shoe in 37edo

Scales:

• shoe5 – 5-tone mini-haplotonic scale
• shoe6 – 6-tone haplotonic scale
• shoe11 – 11-tone albitonic scale
• shoe16 – 16-tone chromatic scale

Roulette

See also: Hemimean clan § Roulette

Roulette in 37edo

Scales:

• roulette6 – 6-tone haplotonic scale
• roulette7 – 7-tone albitonic scale
• roulette13 – 13-tone chromatic scale
• roulette19 – 19-tone 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

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

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 in 128edo

• Radon5 – 5-tone haplotonic scale
• Radon11 – 11-tone albitonic scale
• Radon16 – 16-tone 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 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:

• namo7| – 7-tone haplotonic scale
• namo10 – 10-tone albitonic scale
• namo17 – 17-tone 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

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

Seven note haplotonic scale

Ten note albitonic scale

Seventeen note chromatic scale

Garibaldi

Main article: Garibaldi temperament

See also: Schismatic family § Garibaldi

Garibaldi in 94edo

Scales:

• Garibaldi12 – 12-tone albitonic scale
• Garibaldi17 – 17-tone 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

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

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

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 in 89edo

Scales:

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

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

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

Eight note albitonic scale

Eleven note mega albitonic scale

Fourteen note chromatic scale

Orwell

Main article: Orwell

See also: Semicomma family § Orwell

Orwell in 84edo

Scales:

• Orwell5 – 5-tone haplotonic scale
• Orwell9 – 9-tone albitonic scale
• Orwell13 – 13-tone chromatic scale

Magicaltet

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:

• subgroup CTE: ~2 = 1\1, ~5/3 = 877.3426
• subgroup POTE: ~2 = 1\1, ~5/3 = 877.351

Optimal ET sequence: 4, 7, 11, 15, 26, 67, 93*

* wart for 5/3

RMS error: 1.206 cents

Related temperaments: supermagic, superkleismic, magic

Scales:

• magicaltet7 – 7-tone albitonic scale
• magicaltet11 – 11-tone chromatic scale
• magicaltet15 – 15-tone mega-chromatic scale

Magic

Main article: Magic

See also: Magic family § Magic

Magic in 145edo

Scales:

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

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

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 in 46edo

Scales:

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

Sensation

Main article: Sensi

See also: Sensamagic clan § Sensi

See also: Sensipent family § Sensi

Scales:

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

Meantone

Main article: Meantone

See also: Meantone family § Meantone

Meantone in 31edo

Scales:

• Meantone5 – 5-tone haplotonic scale
• Meantone7 – 7-tone albitonic scale
• Meantone12 – 12-tone chromatic scale

Mohaha

See also: Rastmic clan § Mohaha

Mohaha in 131edo

Scales:

• Mohaha7 – 7-tone albitonic scale
• Mohaha10 – 10-tone chromatic scale

Music:

Billy Stiltner

• Mohaha10ping2^{[dead link]}

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 in 99edo

Scales:

• Tutone6 – 6-tone haplotonic scale
• Tutone7 – 7-tone albitonic scale
• Tutone13 – 13-tone chromatic scale

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

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:

• 5-tone haplotonic scale
• 7-tone albitonic scale
• 12-tone chromatic scale

Supra

Main article: Superpyth

See also: Archytas clan § Supra

Supra in 56edo

Scales:

• Supra7 – 7-tone albitonic scale
• Supra12 – 12-tone chromatic scale

Supraphon

Main article: Superpyth

See also: Archytas clan § Supraphon

Suhajira

See also: Archytas clan § Suhajira

Scales:

• Suhajira7 – 7-tone haplotonic scale
• Suhajira10 – 10-tone albitonic scale
• Suhajira17 – 17-tone 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 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

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

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:

• Porkypine7 – 7-tone haplotonic scale
• Porkypine8 – 8-tone albitonic scale
• Porkypine15 – 15-tone 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 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

Six note haplotonic scale

Nine note albitonic scale

Twelve note chromatic scale

Semaphore

Main article: Semaphore and godzilla

See also: Slendro clan § Semaphore

Semaphore in 24edo

Scales:

• Semaphore5 – 5-tone haplotonic scale
• Semaphore9 – 9-tone albitonic scale
• Semaphore14 – 14-tone 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 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

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

• Six note haplotonic scale
• Seven note albitonic scale
• Thirteen note chromatic scale