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

See also: Subgroup temperaments § Terrain

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

See also: Subgroup temperaments § Petrtri

Scales:

• Petrtri5 – 5-tone haplotonic scale
• Petrtri8 – 8-tone albitonic scale
• Petrtri13 – 13-tone chromatic scale

Barton

"Barton" redirects here. For Jacob Barton's scale, see Barton (scale).

See also: The Jacobins § Barton

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

Tridec

See also: Subgroup temperaments § Tridec

Scales:

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

Nestoria

See also: Schismatic family § Nestoria (2.3.5.19)

Scales:

• Nestoria7 – 7-tone albitonic scale
• Nestoria12 – 12-tone chromatic scale
• Nestoria17 – 17-tone mega chromatic scale

Orgone

Main article: Orgone

See also: Orgonia § Orgone

Scales:

• Orgone7 – 7-tone albitonic scale
• Orgone11 – 11-tone chromatic scale
• Orgone15 – 15-tone mega-chromatic scale

Marveltwintri

See also: Subgroup temperaments § Marveltwintri

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

Scales:

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

Bridgetown

See also: Subgroup temperaments § 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

See also: Subgroup temperaments § Haumea

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

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

Scales:

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

Huntington

See also: No-threes subgroup temperaments § Huntington

Scales:

• Huntington7 – 7-tone haplotonic scale
• Huntington10 – 10-tone albitonic scale
• Huntington17 – 17-tone chromatic scale

Tobago

See also: Subgroup temperaments § Tobago

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

See also: Subgroup temperaments § Pepperoni

Scales:

• Pepperoni7 – 7-tone albitonic scale
• Pepperoni12 – 12-tone chromatic scale

Wizz

See also: No-threes subgroup temperaments § Wizz

Scales:

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

Bossier

See also: No-threes subgroup temperaments § Bossier

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

See also: No-threes subgroup temperaments § Bluebirds

Scales:

• Bluebirds6 – 6-tone haplotonic scale
• Bluebirds7 – 7-tone albitonic scale
• Bluebirds13 – 13-tone chromatic scale

Marveltri

See also: Subgroup temperaments § Marveltri

Scales:

• Marveltri7 – 7-tone albitonic scale
• Marveltri10 – 10-tone chromatic scale
• Marveltri13 – 13-tone mega-chromatic scale

Edson

See also: Subgroup temperaments § Edson

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)

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

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

Scales:

• Roulette6 – 6-tone haplotonic scale
• Roulette7 – 7-tone albitonic scale
• Roulette13 – 13-tone chromatic scale
• Roulette19 – 19-tone mega-chromatic scale

Silver

See also: No-threes subgroup temperaments § Silver

Scales:

• Silver7 – 7-tone haplotonic scale
• Silver10 – 10-tone albitonic scale
• Silver17 – 17-tone chromatic scale

Baldy

See also: Subgroup temperaments § Baldy

Scales

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

Guanyintet

See also: Subgroup temperaments § Guanyintet

Scales:

• Guanyintet5 – 5-tone haplotonic scale
• Guanyintet9 – 9-tone albitonic scale
• Guanyintet13 – 13-tone chromatic scale

Radon

See also: Gamelismic clan § Radon

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

Gariberttet

See also: Subgroup temperaments § Gariberttet

Scales:

• Gariberttet5 – 5-tone haplotonic scale
• Gariberttet9 – 9-tone albitonic scale
• Gariberttet13 – 13-tone 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

See also: Subgroup temperaments § Sentry

Scales:

• Sentry5 – 5-tone haplotonic scale
• Sentry8 – 8-tone albitonic scale
• Sentry11 – 11-tone chromatic scale

Hemif

See also: No-fives subgroup temperaments § Hemif

Scales:

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

Garibaldi

Main article: Garibaldi temperament

See also: Schismatic family § Garibaldi

Scales:

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

Mabilic

See also: No-threes subgroup temperaments § Mabilic

Scales:

• Mabila7 – 7-tone haplotonic scale
• Mabila9 – 9-tone albitonic scale
• Mabila16 – 16-tone chromatic scale

Indium

See also: Subgroup temperaments § Indium

Scales:

• Indium8 – 8-tone albitonic scale
• Indium17 – 17-tone chromatic scale

Music

• The Cry of Indium (2011) by Chris Vaisvil – blog | play – in Indium[17]

Starlingtet

See also: Subgroup temperaments § Starlingtet

Scales:

• Starlingtet4 – 4-tone haplotonic scale
• Starlingtet7 – 7-tone albitonic scale
• Starlingtet11 – 11-tone chromatic scale

Lovecraft

See also: No-threes subgroup temperaments § Lovecraft

Scales:

• Lovecraft5 – 5-tone haplotonic scale
• Lovecraft9 – 9-tone albitonic scale
• Lovecraft13 – 13-tone chromatic scale

Blackbirds

See also: No-threes subgroup temperaments § Blackbirds

Scales:

• Blackbirds8 – 8-tone albitonic scale
• Blackbirds12 – 12-tone chromatic scale
• Blackbirds16 – 16-tone mega-chromatic scale

Laz

See also: Subgroup temperaments § Laz

Scales:

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

Myna

Main article: Myna

See also: Starling temperaments § Myna

Scales:

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

Greeley

See also: Subgroup temperaments § Greeley

Scales:

• Greeley8 – 8-tone albitonic scale
• Greeley15 – 15-tone chromatic scale

Music

• A Greeley Steals Halloween by Chris Vaisvil (2011) – blog | play – in Greeley[15]

Semidim

See also: Subgroup temperaments § Semidim

Scales:

• Semidim8 – 8-tone albitonic scale
• Semidim13 – 13-tone chromatic scale

Mothwelltri

See also: Subgroup temperaments § Mothwelltri

Scales:

• Mothwelltri5 – 5-tone haplotonic scale
• Mothwelltri9 – 9-tone albitonic scale
• Mothwelltri13 – 13-tone chromatic scale

Sulis

See also: Subgroup temperaments § Sulis

Scales:

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

Skwares

Main article: Squares

See also: No-fives subgroup temperaments § Skwares

Scales:

• Skwares8 – 8-tone albitonic scale
• Skwares11 – 11-tone mega-albitonic scale
• Skwares14 – 14-tone chromatic scale

Orwell

Main article: Orwell

See also: Semicomma family § Orwell

Scales:

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

Magicaltet

See also: Subgroup temperaments § Magicaltet

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

Scales:

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

Kiribati

See also: Subgroup temperaments § Kiribati

Scales:

• Kiribati13 – 13-tone chromatic scale
• Kiribati14 – 14-tone chromatic scale

Score

See also: No-threes subgroup temperaments § Score

Scales:

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

Sensi

Main article: 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

Sensation

Main article: 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

Scales:

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

Mohaha

See also: Rastmic clan § Mohaha

Scales:

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

Music:

Billy Stiltner

• Mohaha10ping2⁠ ⁠^[dead link]

Mohoho

See also: Rastmic clan § Mohoho

Joan

See also: Subgroup temperaments § Joan

Scales:

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

Tutone

See also: Hemimean clan § Tutone

Scales:

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

Stacks

See also: Subgroup temperaments § Stacks (a.k.a. 2magic)

Scales:

• Stacks5 – 5-tone haplotonic scale
• Stacks8 – 8-tone albitonic scale
• Stacks11 – 11-tone chromatic scale
• Stacks19 – 19-tone mega-chromatic scale

Bleu

See also: No-fives subgroup temperaments § Bleu

Scales:

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

Sephiroth

See also: No-threes subgroup temperaments § Sephiroth

Scales:

• Sephiroth7 – 7-tone haplotonic scale
• Sephiroth10 – 10-tone albitonic scale
• Sephiroth13 – 13-tone chromatic scale
• Sephiroth16 – 16-tone mega-chromatic scale

Archy

Main article: Superpyth

See also: Archytas clan § Archy

Scales:

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

Supra

Main article: Superpyth

See also: Archytas clan § Supra

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

See also: Subgroup temperaments § Machine

Scales:

• Machine5 – 5-tone haplotonic scale
• Machine6 – 6-tone albitonic scale
• Machine11 – 11-tone chromatic scale

Deutone

See also: Hemimean clan § Deutone

Scales:

• Deutone6 – 6-tone haplotonic scale
• Deutone7 – 7-tone albitonic scale
• Deutone13 – 13-tone 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

See also: Subgroup temperaments § Skateboard

Scales:

• Skateboard7 – 7-tone haplotonic scale
• Skateboard11 – 11-tone albitonic scale
• Skateboard15 – 15-tone chromatic scale

Augment

See also: No-threes subgroup temperaments § Augment

Scales:

• Augment6 – 6-tone haplotonic scale
• Augment9 – 9-tone albitonic scale
• Augment12 – 12-tone chromatic scale

Semaphore

Main article: Semaphore and godzilla

See also: Semaphoresmic clan § Semaphore

Scales:

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

Kryptonite

See also: Subgroup temperaments § Kryptonite

Scales:

• Kryptonite9 – 9-tone albitonic scale
• Kryptonite10 – 10-tone albitonic scale
• Kryptonite19 – 19-tone mega-chromatic scale

Oregon

See also: Orgonia § Oregon

Scales:

• Oregon7 – 7-tone haplotonic scale
• Oregon11 – 11-tone albitonic scale
• Oregon15 – 15-tone chromatic scale

Antikythera

See also: Jubilismic clan § Antikythera

Scales:

• Antikythera6 – 6-tone haplotonic scale
• Antikythera10 – 10-tone albitonic scale
• Antikythera16 – 16-tone chromatic scale

Glacial

See also: Subgroup temperaments § Glacial

Scales:

• Glacial6 – 6-tone haplotonic scale
• Glacial7 – 7-tone albitonic scale
• Glacial13 – 13-tone chromatic scale

Leantone

See also: Hemimean clan § Leantone

Scales:

• Leantone6 – 6-tone haplotonic scale
• Leantone7 – 7-tone albitonic scale
• Leantone13 – 13-tone chromatic scale