Chromatic pairs: Difference between revisions
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== Terrain == | == Terrain == | ||
{{See also| Subgroup temperaments #Terrain }} | {{See also| Subgroup temperaments #Terrain }} | ||
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* [[Barton11]] – 11-tone chromatic scale | * [[Barton11]] – 11-tone chromatic scale | ||
* [[Barton13]] – 13-tone mega-chromatic scale | * [[Barton13]] – 13-tone mega-chromatic scale | ||
== Tridec == | == Tridec == | ||
| Line 99: | Line 77: | ||
== Cata == | == Cata == | ||
{{Main| | {{Main| Kleismic }} | ||
{{See also| Kleismic family #Cata }} | {{See also| Kleismic family #Cata }} | ||
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== Huntington == | == Huntington == | ||
{{See also| No-threes subgroup temperaments #Huntington }} | |||
{{ | |||
[[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]] | [[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]] | ||
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== Wizz == | == Wizz == | ||
{{See also| No-threes subgroup temperaments #Wizz }} | |||
{{ | |||
Scales: | Scales: | ||
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== Bossier == | == Bossier == | ||
{{See also| No-threes subgroup temperaments #Bossier }} | |||
{{ | |||
[[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]] | [[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]] | ||
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== Bluebirds == | == Bluebirds == | ||
{{See also| No-threes subgroup temperaments #Bluebirds }} | |||
{{ | |||
Scales: | Scales: | ||
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== Silver == | == Silver == | ||
{{See also | No-threes subgroup temperaments #Silver }} | |||
{{ | |||
[[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]] | [[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]] | ||
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== Mabilic == | == Mabilic == | ||
{{See also| No-threes subgroup temperaments #Mabilic }} | |||
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]] | |||
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg| | |||
Scales: | Scales: | ||
* [[ | * [[Mabilic7]] – 7-tone haplotonic scale | ||
* [[ | * [[Mabilic9]] – 9-tone albitonic scale | ||
* [[ | * [[Mabilic16]] – 16-tone chromatic scale | ||
== Indium == | == Indium == | ||
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== Lovecraft == | == Lovecraft == | ||
{{See also | No-threes subgroup temperaments #Lovecraft }} | |||
{{ | |||
[[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]] | [[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]] | ||
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== Blackbirds == | == Blackbirds == | ||
{{See also | No-threes subgroup temperaments #Blackbirds }} | |||
{{ | |||
Scales: | Scales: | ||
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* ''A Greeley Steals Halloween'' by [[Chris Vaisvil]] (2011) – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201201174756/http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3 play] – in Greeley[15] | * ''A Greeley Steals Halloween'' by [[Chris Vaisvil]] (2011) – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201201174756/http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3 play] – in Greeley[15] | ||
== | == Ammon == | ||
{{See also| Subgroup temperaments # | {{See also| Subgroup temperaments #Ammon }} | ||
[[File:semidim_770edo.png|right|alt=semidim_770edo.png| | [[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]] | ||
Scales: | Scales: | ||
* [[ | * [[Ammon8]] – 8-tone albitonic scale | ||
* [[ | * [[Ammon13]] – 13-tone chromatic scale | ||
== Mothwelltri == | == Mothwelltri == | ||
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== Score == | == Score == | ||
{{See also|No-threes subgroup temperaments #Score }} | |||
{{ | |||
[[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]] | [[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]] | ||
| Line 741: | Line 579: | ||
== Sephiroth == | == Sephiroth == | ||
{{See also| No-threes subgroup temperaments #Sephiroth }} | |||
{{ | |||
Scales: | Scales: | ||
| Line 838: | Line 660: | ||
== Augment == | == Augment == | ||
{{See also| No-threes subgroup temperaments #Augment }} | |||
{{ | |||
[[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]] | [[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]] | ||
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[[Category:Listen]] | [[Category:Listen]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
{{todo|cleanup}} | {{todo|cleanup}} | ||
Latest revision as of 00:23, 24 June 2025
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
Scales:
- Music
- 5 5 1 mode of 33 equal (2013) by Chris Vaisvil – blog | YouTube | play
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).
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
Scales:
Nestoria
Scales:
- Nestoria7 – 7-tone albitonic scale
- Nestoria12 – 12-tone chromatic scale
- Nestoria17 – 17-tone mega chromatic scale
Orgone
Scales:
- Orgone7 – 7-tone albitonic scale
- Orgone11 – 11-tone chromatic scale
- Orgone15 – 15-tone mega-chromatic scale
Marveltwintri
Scales:
- Marveltwintri7 – 7-tone albitonic scale
- Marveltwintri11 – 11-tone chromatic scale
- Marveltwintri15 – 15-tone mega-chromatic scale
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
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:
- Haumea5 – 5-tone haplotonic scale
- Haumea9 – 9-tone albitonic scale
- Haumea14 – 14-tone chromatic scale
- Haumea19 – 19-tone mega-chromatic scale
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:
- Tobago6 – 6-tone haplotonic scale
- Tobago10 – 10-tone albitonic scale
- Tobago14 – 14-tone chromatic scale
- Tobago24 – 24-tone quatertone scale
Pepperoni
Scales:
- Pepperoni7 – 7-tone albitonic scale
- Pepperoni12 – 12-tone chromatic scale
Wizz
Scales:
Bossier
Scales:
- Bossier8 – 8-tone albitonic scale
- Bossier11 – 11-tone chromatic scale
- Bossier14 – 14-tone mega-chromatic scale
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
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:
- Edson5 – 5-tone haplotonic scale
- Edson7 – 7-tone albitonic scale
- Edson12 – 12-tone chromatic scale
- Edson17 – 17-tone mega-chromatic scale
Photia
Scales:
Shoe a.k.a. llywelyn
Scales:
- Shoe5 – 5-tone mini-haplotonic scale
- Shoe6 – 6-tone haplotonic scale
- Shoe11 – 11-tone albitonic scale
- Shoe16 – 16-tone chromatic scale
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:
- Silver7 – 7-tone haplotonic scale
- Silver10 – 10-tone albitonic scale
- Silver17 – 17-tone chromatic scale
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
- Radon5 – 5-tone haplotonic scale
- Radon11 – 11-tone albitonic scale
- Radon16 – 16-tone chromatic scale
Gariberttet
Scales:
- Gariberttet5 – 5-tone haplotonic scale
- Gariberttet9 – 9-tone albitonic scale
- Gariberttet13 – 13-tone chromatic scale
Namo
Scales:
Sentry
Scales:
- Sentry5 – 5-tone haplotonic scale
- Sentry8 – 8-tone albitonic scale
- Sentry11 – 11-tone chromatic scale
Hemif
Scales:
- Hemif7 – 7-tone haplotonic scale
- Hemif10 – 10-tone albitonic scale
- Hemif17 – 17-tone chromatic scale
Garibaldi
Scales:
- Garibaldi12 – 12-tone albitonic scale
- Garibaldi17 – 17-tone chromatic scale
Mabilic
Scales:
- Mabilic7 – 7-tone haplotonic scale
- Mabilic9 – 9-tone albitonic scale
- Mabilic16 – 16-tone chromatic scale
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
Scales:
- Lovecraft5 – 5-tone haplotonic scale
- Lovecraft9 – 9-tone albitonic scale
- Lovecraft13 – 13-tone chromatic scale
Blackbirds
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]
Ammon
Scales:
Mothwelltri
Scales:
- Mothwelltri5 – 5-tone haplotonic scale
- Mothwelltri9 – 9-tone albitonic scale
- Mothwelltri13 – 13-tone chromatic scale
Sulis
Scales:
- Sulis7 – 7-tone haplotonic scale
- Sulis10 – 10-tone albitonic scale
- Sulis13 – 13-tone chromatic scale
Skwares
Scales:
- Skwares8 – 8-tone albitonic scale
- Skwares11 – 11-tone mega-albitonic scale
- Skwares14 – 14-tone chromatic scale
Orwell
Scales:
- Orwell5 – 5-tone haplotonic scale
- Orwell9 – 9-tone albitonic scale
- Orwell13 – 13-tone chromatic scale
Magicaltet
Scales:
- Magicaltet7 – 7-tone albitonic scale
- Magicaltet11 – 11-tone chromatic scale
- Magicaltet15 – 15-tone mega-chromatic scale
Magic
Scales:
- Magic7 – 7-tone haplotonic scale
- Magic10 – 10-tone albitonic scale
- Magic13 – 13-tone chromatic scale
- Magic16 – 16-tone mega-chromatic scale
Kiribati
Scales:
- Kiribati13 – 13-tone chromatic scale
- Kiribati14 – 14-tone chromatic scale
Score
Scales:
- Score5 – 5-tone haplotonic scale
- Score7 – 7-tone albitonic scale
- Score9 – 9-tone mega-albitonic scale
- Score11 – 11-tone chromatic scale
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:
- Sensi5 – 5-tone haplotonic scale
- Sensi8 – 8-tone albitonic scale
- Sensi11 – 11-tone mega-albitonic scale
- Sensi19 – 19-tone chromatic scale
Meantone
Scales:
- Meantone5 – 5-tone haplotonic scale
- Meantone7 – 7-tone albitonic scale
- Meantone12 – 12-tone chromatic scale
Mohaha
Scales:
Music:
Mohoho
Joan
Scales:
- Joan5 – 5-tone haplotonic scale
- Joan7 – 7-tone albitonic scale
- Joan9 – 9-tone mega-albitonic scale
- Joan11 – 11-tone chromatic scale
Tutone
Scales:
- Tutone6 – 6-tone haplotonic scale
- Tutone7 – 7-tone albitonic scale
- Tutone13 – 13-tone chromatic scale
Stacks
Scales:
- Stacks5 – 5-tone haplotonic scale
- Stacks8 – 8-tone albitonic scale
- Stacks11 – 11-tone chromatic scale
- Stacks19 – 19-tone mega-chromatic scale
Bleu
Scales:
Sephiroth
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:
- Machine5 – 5-tone haplotonic scale
- Machine6 – 6-tone albitonic scale
- Machine11 – 11-tone chromatic scale
Deutone
Scales:
- Deutone6 – 6-tone haplotonic scale
- Deutone7 – 7-tone albitonic scale
- Deutone13 – 13-tone chromatic scale
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
Scales:
- Augment6 – 6-tone haplotonic scale
- Augment9 – 9-tone albitonic scale
- Augment12 – 12-tone chromatic scale
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:
- Oregon7 – 7-tone haplotonic scale
- Oregon11 – 11-tone albitonic scale
- Oregon15 – 15-tone chromatic scale
Antikythera
Scales:
- Antikythera6 – 6-tone haplotonic scale
- Antikythera10 – 10-tone albitonic scale
- Antikythera16 – 16-tone chromatic scale
Glacial
Scales:
- Glacial6 – 6-tone haplotonic scale
- Glacial7 – 7-tone albitonic scale
- Glacial13 – 13-tone chromatic scale
Leantone
Scales:
- Leantone6 – 6-tone haplotonic scale
- Leantone7 – 7-tone albitonic scale
- Leantone13 – 13-tone chromatic scale