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).
Scales:
- Music
- 5 5 1 mode of 33 equal (2013) by Chris Vaisvil – blog | YouTube | play
Petrtri
Scales:
Barton
- "Barton" redirects here. For Jacob Barton's scale, see Barton (scale).
Scales:
Voltage
Voltage is the 3 & 7 temperament in the 2.7.13 subgroup.
Subgroup: 2.7.13
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 ET sequence: 3, 7, 10, 27, 37, 47, 57, 104
RMS error: 0.1423
Tridec
Scales:
Nestoria
Scales:
- Nestoria7 – 7-tone albitonic scale
- Nestoria12 – 12-tone chromatic scale
- Nestoria17 – 17-tone mega chromatic scale
Orgone
Scales:
Marveltwintri
Scales:
- Marveltwintri7 – 7-tone albitonic scale
- Marveltwintri11 – 11-tone chromatic scale
- Marveltwintri15 – 15-tone mega-chromatic scale
Cata
Scales:
Bridgetown
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 (2011) by Chris Vaisvil – blog | play – in Bridgetown[14] for flute, bassoons, and contra-bassoon
Haumea
Scales:
Neutral
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
Scales:
- Slendric5 – 5-tone haplotonic scale
- Slendric6 – 6-tone haplotonic scale
- Slendric11 – 11-tone albitonic scale
- Slendric16 – 16-tone chromatic scale
Huntington
Scales:
- Huntington7 – 7-tone haplotonic scale
- Huntington10 – 10-tone albitonic scale
- Huntington17 – 17-tone chromatic scale
Tobago
Scales:
Pepperoni
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
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:
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
Scales:
Penta a.k.a. mechanism
Scales:
Bluebirds
Subgroup: 2.11.13
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
Scales:
- Marveltri7 – 7-tone albitonic scale
- Marveltri10 – 10-tone chromatic scale
- Marveltri13 – 13-tone mega-chromatic scale
Edson
Scales:
Photia
Scales:
Shoe a.k.a. llywelyn
Scales:
Roulette
Scales:
- Roulette6 – 6-tone haplotonic scale
- Roulette7 – 7-tone albitonic scale
- Roulette13 – 13-tone chromatic scale
- Roulette19 – 19-tone mega-chromatic scale
Silver
Scales:
Baldy
Scales
- Baldy6 – 6-tone haplotonic scale
- Baldy11 – 11-tone albitonic scale
- Baldy17 – 17-tone chromatic scale
Guanyintet
Scales:
- Guanyintet5 – 5-tone haplotonic scale
- Guanyintet9 – 9-tone albitonic scale
- Guanyintet13 – 13-tone chromatic scale
Radon
Gariberttet
Scales:
- Gariberttet5 – 5-tone haplotonic scale
- Gariberttet9 – 9-tone albitonic scale
- Gariberttet13 – 13-tone chromatic scale
Namo
Scales:
Sentry
Scales:
Hemif
Scales:
Garibaldi
Scales:
- Garibaldi12 – 12-tone albitonic scale
- Garibaldi17 – 17-tone chromatic scale
Mabilic
Given below is the no-three version of semabila, or equivalently the no-threes version of trismegistus. It is the 7 & 9 temperament in the 2.5.7 subgroup, and tempers out 1071875/1048576, the mabilisma.
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 sequence: 7, 9, 16, 25, 41, 66, 305bc
RMS error: 0.7729 cents
Scales:
Indium
Scales:
- Music
- The Cry of Indium (2011) by Chris Vaisvil – blog | play – in Indium[17]
Starlingtet
Scales:
- Starlingtet4 – 4-tone haplotonic scale
- Starlingtet7 – 7-tone albitonic scale
- Starlingtet11 – 11-tone chromatic scale
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
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 sequence: 13, 30, 43, 73, 116b
RMS error: 0.8449 cents
Scales:
- Lovecraft5 – 5-tone haplotonic scale
- Lovecraft9 – 9-tone albitonic scale
- Lovecraft13 – 13-tone chromatic scale
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
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 sequence: 4, 16, 20, 24, 44, 68, 112c, 180bc
RMS error: 0.8685 cents
Scales:
- Blackbirds8 – 8-tone albitonic scale
- Blackbirds12 – 12-tone chromatic scale
- Blackbirds16 – 16-tone mega-chromatic scale
Laz
Scales:
Myna
Scales:
Greeley
Scales:
- Music
- A Greeley Steals Halloween by Chris Vaisvil (2011) – blog | play – in Greeley[15]
Semidim
Scales:
Mothwelltri
Scales:
- Mothwelltri5 – 5-tone haplotonic scale
- Mothwelltri9 – 9-tone albitonic scale
- Mothwelltri13 – 13-tone chromatic scale
Sulis
Scales:
Skwares
Scales:
Orwell
Scales:
Magicaltet
Scales:
- Magicaltet7 – 7-tone albitonic scale
- Magicaltet11 – 11-tone chromatic scale
- Magicaltet15 – 15-tone mega-chromatic scale
Magic
Scales:
Kiribati
Scales:
- Kiribati13 – 13-tone chromatic scale
- Kiribati14 – 14-tone chromatic scale
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 sequence: 5, 7, 9, 11, 20
RMS error: 1.282 cents
Scales:
Sensi
Scales:
- Sensi5 – 5-tone haplotonic scale
- Sensi8 – 8-tone albitonic scale
- Sensi11 – 11-tone mega-albitonic scale
- Sensi19 – 19-tone chromatic scale
Sensation
Scales:
Meantone
Scales:
- Meantone5 – 5-tone haplotonic scale
- Meantone7 – 7-tone albitonic scale
- Meantone12 – 12-tone chromatic scale
Mohaha
Scales:
Music:
Mohoho
Joan
Scales:
Tutone
Scales:
Stacks
Scales:
Bleu
Scales:
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 sequence: 10, 13, 16, 29
RMS error: 1.774 cents
Scales:
- Sephiroth7 – 7-tone haplotonic scale
- Sephiroth10 – 10-tone albitonic scale
- Sephiroth13 – 13-tone chromatic scale
- Sephiroth16 – 16-tone mega-chromatic scale
Archy
Scales:
Supra
Scales:
- Supra7 – 7-tone albitonic scale
- Supra12 – 12-tone chromatic scale
Supraphon
Suhajira
Scales:
- Suhajira7 – 7-tone haplotonic scale
- Suhajira10 – 10-tone albitonic scale
- Suhajira17 – 17-tone chromatic scale
Machine
Scales:
Deutone
Scales:
Negra
Porkypine
Scales:
- Porkypine7 – 7-tone haplotonic scale
- Porkypine8 – 8-tone albitonic scale
- Porkypine15 – 15-tone chromatic scale
Skateboard
Scales:
- Skateboard7 – 7-tone haplotonic scale
- Skateboard11 – 11-tone albitonic scale
- Skateboard15 – 15-tone chromatic scale
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 sequence: 3, 6, 9, 15, 21
RMS error: 2.422 cents
Scales:
Semaphore
Scales:
- Semaphore5 – 5-tone haplotonic scale
- Semaphore9 – 9-tone albitonic scale
- Semaphore14 – 14-tone chromatic scale
Kryptonite
Scales:
- Kryptonite9 – 9-tone albitonic scale
- Kryptonite10 – 10-tone albitonic scale
- Kryptonite19 – 19-tone mega-chromatic scale
Oregon
Scales:
Antikythera
Scales:
- Antikythera6 – 6-tone haplotonic scale
- Antikythera10 – 10-tone albitonic scale
- Antikythera16 – 16-tone chromatic scale
Glacial
Scales:
Leantone
Scales:
- Leantone6 – 6-tone haplotonic scale
- Leantone7 – 7-tone albitonic scale
- Leantone13 – 13-tone chromatic scale