Chromatic pairs: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''chromatic pair''' is a pair of [[mos scale]]s in some [[rank-2 temperament]] (either a full [[Harmonic limit|''p''-limit]] temperament or a [[subgroup temperament]]) that are analogous to the familiar [[5L 2s|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.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">By a //chromatic pair// is meant a pair of MOS in some rank two temperament (which may often be a [[Just intonation subgroups|subgroup temperament]]) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it. Even so, note that many of these temperaments are quite accurate.


[[toc|flat]]
In the sections below, the pair temperaments are listed in order of increasing [[Tp tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full ''p''-limit groups.


=Terrain=
== Terrain ==
Subgroup: 2.9/5.9/7
{{See also| Subgroup temperaments #Terrain }}
Commas: 250047/250000
Related temperament: [[Minortonic family#Domain|domain]]
POTE generator: ~10/9 = 182.462


Map: [&lt;3 0 -4|, &lt;0 1 2|]
[[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]]
EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
Error: 0.0859 cents


Terrain 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.
Scales:
* [[Terrain9]] – 9-tone albitonic scale
* [[Terrain15]] – 15-tone chromatic scale


[[terrain9|Nine note albitonic scale]]
; Music
[[terrain15|Fifteen note chromatic scale]]
* ''5 5 1 mode of 33 equal'' (2013) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/ blog] | [https://www.youtube.com/watch?v=2gYdUOPHXSQ YouTube] | [https://web.archive.org/web/20201127015117/http://micro.soonlabel.com/33edo/20130827_551of33.mp3 play]


=Nestoria=
== Petrtri ==
Subgroup: 2.3.5.19
{{See also| Subgroup temperaments #Petrtri }}
Commas: 361/360, 513/512
Related temperament: [[Schismatic family|schismatic]]


POTE generator: ~3/2 = 701.746
[[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]]


Map: [&lt;1 0 15 9], &lt;0 1 -8 -3|]
Scales:  
EDOs: 7, 12, 17, 29, 41, 53, 118, 171
* [[Petrtri5]] – 5-tone haplotonic scale
Error: 0.611 cents
* [[Petrtri8]] – 8-tone albitonic scale
* [[Petrtri13]] – 13-tone chromatic scale


[[nestoria7|Seven note albitonic scale]]
== Barton ==
[[nestoria12|Twelve note chromatic scale]]
{{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}}
{{See also| The Jacobins #Barton }}


==Photia==
Scales:
Subgroup 2.3.5.17.19
* [[Barton5]] – 5-tone haplotonic scale
Commas: 171/170, 256/255, 324/323
* [[Barton7]] – 7-tone albitonic scale
Related temperament: [[Schismatic family|schismatic]]
* [[Barton9]] – 9-tone mega-albitonic scale
* [[Barton11]] – 11-tone chromatic scale
* [[Barton13]] – 13-tone mega-chromatic scale


POTE generator: ~3/2 = 701.470
== Tridec ==
{{See also| Subgroup temperaments #Tridec }}


Map: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]
[[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]]
EDOs: 7, 12, 17, 29, 41, 53, 65
Error: 1.512 cents


[[photia7|Seven note albitonic scale]]
Scales:
[[photia12|Twelve note chromatic scale]]
* [[Tridec8]] – 8-tone albitonic scale
* [[Tridec13]] – 13-tone chromatic scale


=Cata=
== Nestoria ==
Subgroup: 2.3.5.13
{{See also| Schismatic family #Nestoria (2.3.5.19)}}
Commas: 325/324, 625/624
Related temperament: [[Kleismic family|catakleismic]]


POTE generator: ~6/5 = 317.076
[[File:nestoria_171edo.png|right|alt=nestoria_171edo.png|Nestoria in 171edo]]


Map: [&lt;1 0 1 0|, &lt;0 6 5 14|]
Scales:  
EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246
* [[Nestoria7]] – 7-tone albitonic scale
Error: 0.735 cents
* [[Nestoria12]] – 12-tone chromatic scale
* [[Nestoria17]] – 17-tone mega chromatic scale


[[cata7|Seven note albitonic scale]]
== Orgone ==
[[cata11|Eleven note mega albitonic scale]]
{{Main| Orgone }}
[[cata15|Fifteen note chromatic scale]]
{{See also| Orgonia #Orgone }}
[[cata19|Nineteen note mega chromatic scale]]


=Bridgetown=
[[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]]
Subgroup: 2.3.11/5.13/5
Commas: 352/351, 676/675
Related temperament: [[The Archipelago|barabdos]]


POTE generator: ~15/13 = 248.285
Scales:  
* [[Orgone7]] – 7-tone albitonic scale
* [[Orgone11]] – 11-tone chromatic scale
* [[Orgone15]] – 15-tone mega-chromatic scale


Map: [&lt;1 0 -6 -1|, &lt;0 2 9 3|]
== Marveltwintri ==
EDOs: 5, 9, 14, 19, 24, 29
{{See also| Subgroup temperaments #Marveltwintri }}
Error: 0.8489 cents


[[bridgetown9|Nine note albitonic scale]]
[[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]]
[[bridgetown14|Fourteen note chromatic scale]]


=Huntington=
Scales:
Subgroup: 2.5.7.13
* [[Marveltwintri7]] – 7-tone albitonic scale
Commas: 640/637, 10985/10976
* [[Marveltwintri11]] – 11-tone chromatic scale
* [[Marveltwintri15]] – 15-tone mega-chromatic scale


POTE generator: ~16/13 = 357.002
== Cata ==
{{Main| Kleismic }}
{{See also| Kleismic family #Cata }}


Map: [&lt;1 5 4 4|, &lt;0 -9 -4 -1|]
[[File:cata_246edo.jpg|right|alt=cata_246edo.jpg|Cata in 246edo]]
EDOs: 7, 10, 17, 27, 37, 84, 121, 400
Error: 1.036 cents


[[huntington7|Seven note haplotonic scale]]
Scales:
[[huntington10|Ten note albitonic scale]]
* [[Cata7]] – 7-tone albitonic scale
[[huntington17|Seventeen note chromatic scale]]
* [[Cata11]] – 11-tone mega-albitonic scale
* [[Cata15]] – 15-tone chromatic scale
* [[Cata19]] – 19-tone mega-chromatic scale


=Bossier=
== Bridgetown ==
Subgroup: 2.7.11.13
{{See also| Subgroup temperaments #Bridgetown }}
Commas: 1573/1569, 15488/15379


POTE generator: ~14/11 = 421.309
[[File:bridgetown_29edo.png|right|alt=bridgetown_29edo.png|Bridgetown in 29edo]]


Map: [&lt;1 0 1 3|, &lt;0 8 7 2|]
Scales:  
EDOs: 17, 20, 37, 57, 94, 225
* [[Bridgetown9]] – 9-tone albitonic scale
Error: 1.213 cents
* [[Bridgetown14]] – 14-tone chromatic scale


[[bossier8|Eight note albitonic scale]]
; Music
[[bossier11|Eleven note chromatic scale]]
* [https://web.archive.org/web/20201127014201/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3 ''Paint in the Water 29''] (archived 2020) by [[Igliashon Jones]]
[[bossier14|Fourteen note mega chromatic scale]]
* ''Route 14 in Bridgetown'' (2011) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201127012744/http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 play] – in Bridgetown[14] for flute, bassoons, and contra-bassoon


=Roulette=
== Haumea ==
Subgroup: 2.5.7.11.13
{{See also| Subgroup temperaments #Haumea }}
Commas: 176/175, 1375/1372, 640/637
Related temperament: [[Wuerschmidt family|Hemiwuerschmidt]]


POTE generator: ~28/25 = 194.594
Scales:  
* [[Haumea5]] – 5-tone haplotonic scale
* [[Haumea9]] – 9-tone albitonic scale
* [[Haumea14]] – 14-tone chromatic scale
* [[Haumea19]] – 19-tone mega-chromatic scale


Map: [&lt;1 0 -3 -7 -13|, &lt;0 2 5 9 -8|]
== Neutral ==
EDOs: 6, 7, 13, 19, 25, 31, 37
{{See also| Rastmic clan #Neutral }}
Error: 1.363 cents


[[roulette6|Six note haplotonic scale]]
[[File:neutral_380edo.png|right|alt=neutral_380edo.png|Neutral in 380edo]]
[[roulette7|Seven note albitonic scale]]
[[roulette13|Thirteen note chromatic scale]]
[[roulette19|Nineteen note mega chromatic scale]]


=Baldy=
Scales:
Subgroup: 2.9.5.7.13
* [[Neutral7]] – 7-tone albitonic scale
Commas: 225/224, 325/325, 640/637
* [[Neutral10]] – 10-tone chromatic scale
Related temperament: [[Schismatic family|Garibaldi]]
* [[Neutral17]] – 17-tone mega-chromatic scale


POTE generator: ~9/8 = 204.090
; Music
* [https://soundcloud.com/jdfreivald/mo-happy-happy ''Mo - Happy - Happy''] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by [[Jake Freivald]] in Neutral[7], 24edo tuning


Map: [&lt;1 0 15 25 -8|, &lt;0 1 -4 -7 10|]
== Slendric ==
EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147
{{Main| Slendric }}
Error: 1.469 cents
:''See also: [[Gamelismic clan #Slendric]] and [[No-fives subgroup temperaments #Slendric]]''


[[baldy6|Six note haplotonic scale]]
[[File:slendric_190edo.jpg|right|alt=slendric_190edo.jpg|Slendric in 190edo]]
[[baldy11|Eleven note albitonic scale]]
[[baldy17|Seventeen note chromatic scale]]


=Hemif=
Scales:
Subgroup: 2.3.7.11.13
* [[Slendric5]] – 5-tone haplotonic scale
Commas: 144/143, 243/242, 364/363
* [[Slendric6]] – 6-tone haplotonic scale
Related temperament: [[Breedsmic temperaments|Hemififths]]
* [[Slendric11]] – 11-tone albitonic scale
* [[Slendric16]] – 16-tone chromatic scale


POTE generator: ~11/9 = 351.691
== Huntington ==
{{See also| No-threes subgroup temperaments #Huntington }}


Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]
[[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]]
EDOs: 7, 10, 17, 24, 41, 58
Error: 1.756


[[hemif7|Seven note haplotonic scale]]
Scales:
[[hemif10|Ten note albitonic scale]]
* [[Huntington7]] – 7-tone haplotonic scale
[[hemif17|Seventeen note chromatic scale]]
* [[Huntington10]] – 10-tone albitonic scale
* [[Huntington17]] – 17-tone chromatic scale


=Radon=
== Tobago ==
Subgroup: 2.3.7.11
{{See also| Subgroup temperaments #Tobago }}
Commas: 896/891, 1029/1024
Related temperament: [[Gamelismic clan|Rodan]]


POTE generator: ~8/7 = 234.381
Scales:  
* [[Tobago6]] – 6-tone haplotonic scale
* [[Tobago10]] – 10-tone albitonic scale
* [[Tobago14]] – 14-tone chromatic scale
* [[Tobago24]] – 24-tone quatertone scale


Map: [&lt;1 1 3 6|, &lt;0 3 -1 -13|]
== Pepperoni ==
EDOs: 5, 36, 41, 87, 128
{{See also| Parapyth }}
Error: 1.781 cents
{{See also| Subgroup temperaments #Pepperoni }}


[[radon5|Five note haplotonic scale]]
[[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]]
[[radon11|Eleven note albitonic scale]]
[[radon16|Sixteen note chromatic scale]]


=Pepperoni=
Scales:  
Subgroup: 2.3.11/7.13/7
* [[Pepperoni7]] – 7-tone albitonic scale
Commas: 352/351, 364/363
* [[Pepperoni12]] – 12-tone chromatic scale
Related temperament: [[Margo Schulter]]'s [[Pepper temperament|pepper temperament]]


POTE generator: ~3/2 = 704.052
== Wizz ==
{{See also| No-threes subgroup temperaments #Wizz }}


Map: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]
Scales:  
EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271
* [[Wizz6]] – 6-tone haplotonic scale
Error: 2.155 cents
* [[Wizz10]] – 10-tone albitonic scale
* [[Wizz16]] – 16-tone chromatic scale


[[pepperoni7|Seven note albitonic scale]]
== Bossier ==
[[pepperoni12|Twelve note chromatic scale]]
{{See also| No-threes subgroup temperaments #Bossier }}


=Skwares=
[[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]]
Subgroup: 2.3.7.11
Commas: 99/98, 243/242
Related temperament: [[Meantone family|squares]]


POTE generator: ~9/7 = 425.244
Scales:  
* [[Bossier8]] – 8-tone albitonic scale
* [[Bossier11]] – 11-tone chromatic scale
* [[Bossier14]] – 14-tone mega-chromatic scale


Map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]
== Penta a.k.a. mechanism ==
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206
{{See also| Subgroup temperaments #Penta a.k.a. mechanism }}
Error: 3.009 cents


[[skwares8|Eight note albitonic scale]]
Scales:
[[skwares11|Eleven note mega albitonic scale]]
* [[Penta5]] – 5-tone haplotonic scale
[[skwares14|Fourteen note chromatic scale]]
* [[Penta8]] – 8-tone albitonic scale
* [[Penta11]] – 11-tone chromatic scale
* [[Penta19]] – 19-tone mega-chromatic scale


=Tutone=
== Bluebirds ==
Subgroup: 2.9.5.7.11
{{See also| No-threes subgroup temperaments #Bluebirds }}
Commas: 81/80, 99/98, 126/125
Related temperament: [[Meantone family|meantone]]


POTE generator: ~9/8 = 193.937
Scales:  
* [[Bluebirds6]] – 6-tone haplotonic scale
* [[Bluebirds7]] – 7-tone albitonic scale
* [[Bluebirds13]] – 13-tone chromatic scale


Map: [&lt;1 0 -4 -13 -25|, &lt;0 1 2 5 9|]
== Marveltri ==
EDOs: 6, 7, 13, 19, 25, 31, 99
{{See also| Subgroup temperaments #Marveltri }}
Error: 3.218 cents


[[tutone6|Six note haplotonic scale]]
Scales:
[[tutone7|Seven note albitonic scale]]
* [[Marveltri7]] – 7-tone albitonic scale
[[tutone13|Thirteen note chromatic scale]]
* [[Marveltri10]] – 10-tone chromatic scale
* [[Marveltri13]] – 13-tone mega-chromatic scale


==Leantone==
== Edson ==
Subgroup: 2.9.5.7.11
{{See also| Subgroup temperaments #Edson }}
Commas: 45/44, 56/55, 81/80
Related temperament: [[Meantone family|flattone]]


POTE generator: ~9/8 = 192.500
Scales:  
* [[Edson5]] – 5-tone haplotonic scale
* [[Edson7]] – 7-tone albitonic scale
* [[Edson12]] – 12-tone chromatic scale
* [[Edson17]] – 17-tone mega-chromatic scale


Map: [&lt;1 0 -4 -13 -6|, &lt;0 1 2 5 3|]
== Photia ==
EDOs: 6, 7, 13, 19, 25, 31, 56, 81
{{See also| Schismatic family #Photia (2.3.5.17) }}
Error: 8.680 cents


[[leantone6|Six note haplotonic scale]]
[[File:photia_65edo.png|right|alt=photia_65edo.png|Photia in 65edo]]
[[leantone7|Seven note albitonic scale]]
[[leantone13|Thirteen note chromatic scale]]


=Mohaha=
Scales:  
Subgroup: 2.3.5.11
* [[Photia7]] – 7-tone albitonic scale
Commas: 81/80, 121/120
* [[Photia12]] – 12-tone chromatic scale
Related temperament: [[Meantone family|mohajira]]


POTE generator: ~11/9 = 348.094
== Shoe a.k.a. llywelyn ==
{{See also| Llywelynsmic clan #Llywelyn a.k.a. shoe }}


Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]
[[File:shoe_37edo.jpg|right|alt=shoe_37edo.jpg|Shoe in 37edo]]
EDOs: 7, 10, 17, 24, 31, 131
Error: 3.813 cents


[[mohaha7|Seven note albitonic scale]]
Scales:
[[mohaha10|Ten note chromatic scale]]
* [[Shoe5]] – 5-tone mini-haplotonic scale
* [[Shoe6]] – 6-tone haplotonic scale
* [[Shoe11]] – 11-tone albitonic scale
* [[Shoe16]] – 16-tone chromatic scale


==Mohoho==
== Roulette ==
Subgroup: 2.3.5.11.13
{{See also | Hemimean clan #Roulette }}
Commas: 66/65, 81/80, 121/120


POTE generator: ~11/9 = 348.916
[[File:roulette_37edo.jpg|right|alt=roulette_37edo.jpg|Roulette in 37edo]]


Map: [&lt;1 1 0 2 4|, &lt;0 2 8 5 -1|]
Scales:  
EDOs: 7, 10, 17, 24, 31, 55
* [[Roulette6]] – 6-tone haplotonic scale
Error: 4.829 cents
* [[Roulette7]] – 7-tone albitonic scale
* [[Roulette13]] – 13-tone chromatic scale
* [[Roulette19]] – 19-tone mega-chromatic scale


=Score=
== Silver ==
Subgroup: 2.7.11.13
{{See also | No-threes subgroup temperaments #Silver }}
Commas: 343/338, 847/832


POTE generator: ~11/8 = 540.099
[[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]]


Map: [&lt;1 1 3 1|, &lt;0 4 1 6|]
Scales:  
EDOs: 5, 7, 9, 11, 20
* [[Silver7]] – 7-tone haplotonic scale
Error: 3.846 cents
* [[Silver10]] – 10-tone albitonic scale
* [[Silver17]] – 17-tone chromatic scale


[[score5|Five note haplotonic scale]]
== Baldy ==
[[score7|Seven note albitonic scale]]
{{See also| Subgroup temperaments #Baldy }}
[[score9|Nine note mega albitonic scale]]
[[score11|Eleven note chromatic scale]]


=Supra=
[[File:baldy_147edo.jpg|right|alt=baldy_147edo.jpg|Baldy in 147edo]]
Subgroup: 2.3.7.11
Commas: 64/63, 99/98
Related temperament: [[Archytas clan|superpyth]]


POTE generator: ~3/2 = 707.192
Scales
* [[Baldy6]] – 6-tone haplotonic scale
* [[Baldy11]] – 11-tone albitonic scale
* [[Baldy17]] – 17-tone chromatic scale


Map: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]
EDOs: 5, 7, 12, 17, 22, 39, 56
Error: 5.414 cents


[[supra7|Seven note albitonic scale]]
== Guanyintet ==
[[supra12|Twelve note chromatic scale]]
{{See also | Subgroup temperaments #Guanyintet }}


==Supraphon==
Scales:
Subgroup: 2.3.7.11.13
* [[Guanyintet5]] – 5-tone haplotonic scale
Commas: 64/63, 78/77, 99/98
* [[Guanyintet9]] – 9-tone albitonic scale
* [[Guanyintet13]] – 13-tone chromatic scale


POTE generator: ~3/2 = 706.137
== Radon ==
{{See also| Gamelismic clan #Radon }}


Map: [&lt;1 0 6 13 18|, &lt;0 1 -2 -6 -9|]
[[File:radon_128edo.jpg|right|alt=radon_128edo.jpg|Radon in 128edo]]
EDOs: 5, 7, 12, 17
Error: 5.132 cents


==Machine==
* [[Radon5]] – 5-tone haplotonic scale
Subgroup: 2.9.7.11
* [[Radon11]] – 11-tone albitonic scale
Commas: 64/63, 99/98
* [[Radon16]] – 16-tone chromatic scale


POTE generator: ~9/8 = 214.384
== Gariberttet ==
{{See also | Subgroup temperaments #Gariberttet }}


Map: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]
Scales:  
EDOs: 5, 6, 11, 17, 28
* [[Gariberttet5]] – 5-tone haplotonic scale
Error: 5.414 cents
* [[Gariberttet9]] – 9-tone albitonic scale
* [[Gariberttet13]] – 13-tone chromatic scale


[[machine5|Five note haplotonic scale]]
== Namo ==
[[machine6|Six note albitonic scale]]
{{See also| Rastmic clan #Namo }}
[[machine11|Eleven note chromatic scale]]


=Augment=
Scales:
Subgroup: 2.5.7.11
* [[Namo7]] – 7-tone haplotonic scale
Commas: 56/55, 128/125
* [[Namo10]] – 10-tone albitonic scale
Related temperament: [[Augmented family|augmented]]
* [[Namo17]] – 17-tone chromatic scale


POTE generator: ~8/7
== Sentry ==
{{See also | Subgroup temperaments #Sentry }}


Map: [&lt;3 7 0 2|, &lt;0 0 1 1|]
Scales:  
EDOs: 3, 6, 9, 15, 21
* [[Sentry5]] – 5-tone haplotonic scale
Error: 6.632 cents
* [[Sentry8]] – 8-tone albitonic scale
* [[Sentry11]] – 11-tone chromatic scale


[[augment6|Six note haplotonic scale]]
== Hemif ==
[[augment9|Nine note albitonic scale]]
{{See also| No-fives subgroup temperaments #Hemif }}
[[augment12|Twelve note chromatic scale]]


=Greeley=
[[File:hemif_58edo.jpg|right|alt=hemif_58edo.jpg|Hemif in 58edo]]
Subgroup: 2.5/3.7/3.11/3
Commas: 121/120, 126/125


POTE generator: ~11/10 = 156.055
Scales:  
* [[Hemif7]] – 7-tone haplotonic scale
* [[Hemif10]] – 10-tone albitonic scale
* [[Hemif17]] – 17-tone chromatic scale


Map: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]
== Garibaldi ==
EDOs: 8, 15, 23, 77, 100
{{Main| Garibaldi temperament }}
Error: 7.555 cents
{{See also| Schismatic family #Garibaldi }}


[[greeley8|Eight note albitonic scale]]
[[File:garibaldi_94edo.png|right|alt=garibaldi_94edo.png|Garibaldi in 94edo]]
[[greeley15|Fifteen note chromatic scale]]
 
</pre></div>
Scales:
<h4>Original HTML content:</h4>
* [[Garibaldi12]] – 12-tone albitonic scale
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Chromatic pairs&lt;/title&gt;&lt;/head&gt;&lt;body&gt;By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of MOS in some rank two temperament (which may often be a &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup temperament&lt;/a&gt;) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called &amp;quot;albitonic&amp;quot; from the Latin word for &amp;quot;white&amp;quot;. Also included at times are &amp;quot;haplotonic&amp;quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it. Even so, note that many of these temperaments are quite accurate.&lt;br /&gt;
* [[Garibaldi17]] – 17-tone chromatic scale
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextTocRule:46:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;a href="#Terrain"&gt;Terrain&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt; | &lt;a href="#Nestoria"&gt;Nestoria&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Cata"&gt;Cata&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt; | &lt;a href="#Bridgetown"&gt;Bridgetown&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Huntington"&gt;Huntington&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Bossier"&gt;Bossier&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt; | &lt;a href="#Roulette"&gt;Roulette&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt; | &lt;a href="#Baldy"&gt;Baldy&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Hemif"&gt;Hemif&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt; | &lt;a href="#Radon"&gt;Radon&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Pepperoni"&gt;Pepperoni&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Skwares"&gt;Skwares&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Tutone"&gt;Tutone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Mohaha"&gt;Mohaha&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Score"&gt;Score&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt; | &lt;a href="#Supra"&gt;Supra&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Augment"&gt;Augment&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt; | &lt;a href="#Greeley"&gt;Greeley&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;
== Mabilic ==
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;br /&gt;
{{See also| No-threes subgroup temperaments #Mabilic }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Terrain"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Terrain&lt;/h1&gt;
 
Subgroup: 2.9/5.9/7&lt;br /&gt;
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]]
Commas: 250047/250000&lt;br /&gt;
 
Related temperament: &lt;a class="wiki_link" href="/Minortonic%20family#Domain"&gt;domain&lt;/a&gt;&lt;br /&gt;
Scales:  
POTE generator: ~10/9 = 182.462&lt;br /&gt;
* [[Mabilic7]] – 7-tone haplotonic scale
&lt;br /&gt;
* [[Mabilic9]] – 9-tone albitonic scale
Map: [&amp;lt;3 0 -4|, &amp;lt;0 1 2|]&lt;br /&gt;
* [[Mabilic16]] – 16-tone chromatic scale
EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558&lt;br /&gt;
 
Error: 0.0859 cents&lt;br /&gt;
== Indium ==
&lt;br /&gt;
{{See also | Subgroup temperaments #Indium }}
Terrain 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.&lt;br /&gt;
 
&lt;br /&gt;
[[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]]
&lt;a class="wiki_link" href="/terrain9"&gt;Nine note albitonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/terrain15"&gt;Fifteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
Scales:
&lt;br /&gt;
* [[Indium8]] – 8-tone albitonic scale
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Nestoria"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Nestoria&lt;/h1&gt;
* [[Indium17]] – 17-tone chromatic scale
Subgroup: 2.3.5.19&lt;br /&gt;
 
Commas: 361/360, 513/512&lt;br /&gt;
; Music
Related temperament: &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt;&lt;br /&gt;
* ''The Cry of Indium'' (2011) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/the-cry-of-indium/ blog] | [https://web.archive.org/web/20201127012551/http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3 play] – in Indium[17]
&lt;br /&gt;
 
POTE generator: ~3/2 = 701.746&lt;br /&gt;
== Starlingtet ==
&lt;br /&gt;
{{See also | Subgroup temperaments #Starlingtet }}
Map: [&amp;lt;1 0 15 9], &amp;lt;0 1 -8 -3|]&lt;br /&gt;
 
EDOs: 7, 12, 17, 29, 41, 53, 118, 171&lt;br /&gt;
Scales:
Error: 0.611 cents&lt;br /&gt;
* [[Starlingtet4]] – 4-tone haplotonic scale
&lt;br /&gt;
* [[Starlingtet7]] – 7-tone albitonic scale
&lt;a class="wiki_link" href="/nestoria7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
* [[Starlingtet11]] – 11-tone chromatic scale
&lt;a class="wiki_link" href="/nestoria12"&gt;Twelve note chromatic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
== Lovecraft ==
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Nestoria-Photia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Photia&lt;/h2&gt;
{{See also | No-threes subgroup temperaments #Lovecraft }}
Subgroup 2.3.5.17.19&lt;br /&gt;
 
Commas: 171/170, 256/255, 324/323&lt;br /&gt;
[[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]]
Related temperament: &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
POTE generator: ~3/2 = 701.470&lt;br /&gt;
* [[Lovecraft5]] – 5-tone haplotonic scale
&lt;br /&gt;
* [[Lovecraft9]] – 9-tone albitonic scale
Map: [&amp;lt;1 0 15 -7 9|, &amp;lt;0 1 -8 7 -3|]&lt;br /&gt;
* [[Lovecraft13]] – 13-tone chromatic scale
EDOs: 7, 12, 17, 29, 41, 53, 65&lt;br /&gt;
 
Error: 1.512 cents&lt;br /&gt;
== Blackbirds ==
&lt;br /&gt;
{{See also | No-threes subgroup temperaments #Blackbirds }}
&lt;a class="wiki_link" href="/photia7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/photia12"&gt;Twelve note chromatic scale&lt;/a&gt;&lt;br /&gt;
Scales:  
&lt;br /&gt;
* [[Blackbirds8]] – 8-tone albitonic scale
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Cata"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Cata&lt;/h1&gt;
* [[Blackbirds12]] – 12-tone chromatic scale
Subgroup: 2.3.5.13&lt;br /&gt;
* [[Blackbirds16]] – 16-tone mega-chromatic scale
Commas: 325/324, 625/624&lt;br /&gt;
 
Related temperament: &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic&lt;/a&gt;&lt;br /&gt;
== Laz ==
&lt;br /&gt;
{{See also | Subgroup temperaments #Laz }}
POTE generator: ~6/5 = 317.076&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
Map: [&amp;lt;1 0 1 0|, &amp;lt;0 6 5 14|]&lt;br /&gt;
* [[Laz5]] – 5-tone haplotonic scale
EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246&lt;br /&gt;
* [[Laz9]] – 9-tone albitonic scale
Error: 0.735 cents&lt;br /&gt;
* [[Laz13]] – 13-tone chromatic scale
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/cata7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
== Myna ==
&lt;a class="wiki_link" href="/cata11"&gt;Eleven note mega albitonic scale&lt;/a&gt;&lt;br /&gt;
{{Main| Myna }}
&lt;a class="wiki_link" href="/cata15"&gt;Fifteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
{{See also| Starling temperaments #Myna }}
&lt;a class="wiki_link" href="/cata19"&gt;Nineteen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
[[File:myna_89edo.jpg|right|alt=myna_89edo.jpg|Myna in 89edo]]
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Bridgetown"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Bridgetown&lt;/h1&gt;
 
Subgroup: 2.3.11/5.13/5&lt;br /&gt;
Scales:  
Commas: 352/351, 676/675&lt;br /&gt;
* [[Myna7]] – 7-tone haplotonic scale
Related temperament: &lt;a class="wiki_link" href="/The%20Archipelago"&gt;barabdos&lt;/a&gt;&lt;br /&gt;
* [[Myna11]] – 11-tone albitonic scale
&lt;br /&gt;
* [[Myna15]] – 15-tone chromatic scale
POTE generator: ~15/13 = 248.285&lt;br /&gt;
 
&lt;br /&gt;
== Greeley ==
Map: [&amp;lt;1 0 -6 -1|, &amp;lt;0 2 9 3|]&lt;br /&gt;
{{See also| Subgroup temperaments #Greeley }}
EDOs: 5, 9, 14, 19, 24, 29&lt;br /&gt;
 
Error: 0.8489 cents&lt;br /&gt;
[[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]]
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/bridgetown9"&gt;Nine note albitonic scale&lt;/a&gt;&lt;br /&gt;
Scales:  
&lt;a class="wiki_link" href="/bridgetown14"&gt;Fourteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
* [[Greeley8]] – 8-tone albitonic scale
&lt;br /&gt;
* [[Greeley15]] – 15-tone chromatic scale
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Huntington"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Huntington&lt;/h1&gt;
 
Subgroup: 2.5.7.13&lt;br /&gt;
; Music
Commas: 640/637, 10985/10976&lt;br /&gt;
* ''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]
&lt;br /&gt;
 
POTE generator: ~16/13 = 357.002&lt;br /&gt;
== Ammon ==
&lt;br /&gt;
{{See also| Subgroup temperaments #Ammon }}
Map: [&amp;lt;1 5 4 4|, &amp;lt;0 -9 -4 -1|]&lt;br /&gt;
 
EDOs: 7, 10, 17, 27, 37, 84, 121, 400&lt;br /&gt;
[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]]
Error: 1.036 cents&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
&lt;a class="wiki_link" href="/huntington7"&gt;Seven note haplotonic scale&lt;/a&gt;&lt;br /&gt;
* [[Ammon8]] – 8-tone albitonic scale
&lt;a class="wiki_link" href="/huntington10"&gt;Ten note albitonic scale&lt;/a&gt;&lt;br /&gt;
* [[Ammon13]] – 13-tone chromatic scale
&lt;a class="wiki_link" href="/huntington17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
== Mothwelltri ==
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Bossier"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Bossier&lt;/h1&gt;
{{See also| Subgroup temperaments #Mothwelltri }}
Subgroup: 2.7.11.13&lt;br /&gt;
 
Commas: 1573/1569, 15488/15379&lt;br /&gt;
Scales:  
&lt;br /&gt;
* [[Mothwelltri5]] – 5-tone haplotonic scale
POTE generator: ~14/11 = 421.309&lt;br /&gt;
* [[Mothwelltri9]] – 9-tone albitonic scale
&lt;br /&gt;
* [[Mothwelltri13]] – 13-tone chromatic scale
Map: [&amp;lt;1 0 1 3|, &amp;lt;0 8 7 2|]&lt;br /&gt;
 
EDOs: 17, 20, 37, 57, 94, 225&lt;br /&gt;
== Sulis ==
Error: 1.213 cents&lt;br /&gt;
{{See also| Subgroup temperaments #Sulis }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/bossier8"&gt;Eight note albitonic scale&lt;/a&gt;&lt;br /&gt;
Scales:
&lt;a class="wiki_link" href="/bossier11"&gt;Eleven note chromatic scale&lt;/a&gt;&lt;br /&gt;
* [[Sulis7]] – 7-tone haplotonic scale
&lt;a class="wiki_link" href="/bossier14"&gt;Fourteen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
* [[Sulis10]] – 10-tone albitonic scale
&lt;br /&gt;
* [[Sulis13]] – 13-tone chromatic scale
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Roulette"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Roulette&lt;/h1&gt;
 
Subgroup: 2.5.7.11.13&lt;br /&gt;
== Skwares ==
Commas: 176/175, 1375/1372, 640/637&lt;br /&gt;
{{Main| Squares }}
Related temperament: &lt;a class="wiki_link" href="/Wuerschmidt%20family"&gt;Hemiwuerschmidt&lt;/a&gt;&lt;br /&gt;
{{See also| No-fives subgroup temperaments #Skwares }}
&lt;br /&gt;
 
POTE generator: ~28/25 = 194.594&lt;br /&gt;
[[File:skwares_206edo.png|right|alt=skwares_206edo.png|Skwares in 206edo]]
&lt;br /&gt;
 
Map: [&amp;lt;1 0 -3 -7 -13|, &amp;lt;0 2 5 9 -8|]&lt;br /&gt;
Scales:  
EDOs: 6, 7, 13, 19, 25, 31, 37&lt;br /&gt;
* [[Skwares8]] – 8-tone albitonic scale
Error: 1.363 cents&lt;br /&gt;
* [[Skwares11]] – 11-tone mega-albitonic scale
&lt;br /&gt;
* [[Skwares14]] – 14-tone chromatic scale
&lt;a class="wiki_link" href="/roulette6"&gt;Six note haplotonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/roulette7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
== Orwell ==
&lt;a class="wiki_link" href="/roulette13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
{{Main| Orwell }}
&lt;a class="wiki_link" href="/roulette19"&gt;Nineteen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
{{See also| Semicomma family #Orwell }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Baldy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Baldy&lt;/h1&gt;
[[File:orwell_84edo.png|right|alt=orwell_84edo.png|Orwell in 84edo]]
Subgroup: 2.9.5.7.13&lt;br /&gt;
 
Commas: 225/224, 325/325, 640/637&lt;br /&gt;
Scales:  
Related temperament: &lt;a class="wiki_link" href="/Schismatic%20family"&gt;Garibaldi&lt;/a&gt;&lt;br /&gt;
* [[Orwell5]] – 5-tone haplotonic scale
&lt;br /&gt;
* [[Orwell9]] – 9-tone albitonic scale
POTE generator: ~9/8 = 204.090&lt;br /&gt;
* [[Orwell13]] – 13-tone chromatic scale
&lt;br /&gt;
 
Map: [&amp;lt;1 0 15 25 -8|, &amp;lt;0 1 -4 -7 10|]&lt;br /&gt;
== Magicaltet ==
EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147&lt;br /&gt;
{{See also| Subgroup temperaments #Magicaltet }}
Error: 1.469 cents&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
&lt;a class="wiki_link" href="/baldy6"&gt;Six note haplotonic scale&lt;/a&gt;&lt;br /&gt;
* [[Magicaltet7]] – 7-tone albitonic scale
&lt;a class="wiki_link" href="/baldy11"&gt;Eleven note albitonic scale&lt;/a&gt;&lt;br /&gt;
* [[Magicaltet11]] – 11-tone chromatic scale
&lt;a class="wiki_link" href="/baldy17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
* [[Magicaltet15]] – 15-tone mega-chromatic scale
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Hemif"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Hemif&lt;/h1&gt;
== Magic ==
Subgroup: 2.3.7.11.13&lt;br /&gt;
{{Main| Magic }}
Commas: 144/143, 243/242, 364/363&lt;br /&gt;
{{See also| Magic family #Magic }}
Related temperament: &lt;a class="wiki_link" href="/Breedsmic%20temperaments"&gt;Hemififths&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
[[File:magic_145edo.jpg|right|alt=magic_145edo.jpg|Magic in 145edo]]
POTE generator: ~11/9 = 351.691&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
Map: [&amp;lt;1 1 -1 2 4|, &amp;lt;0 2 13 5 -1|]&lt;br /&gt;
* [[Magic7]] – 7-tone haplotonic scale
EDOs: 7, 10, 17, 24, 41, 58&lt;br /&gt;
* [[Magic10]] – 10-tone albitonic scale
Error: 1.756&lt;br /&gt;
* [[Magic13]] – 13-tone chromatic scale
&lt;br /&gt;
* [[Magic16]] – 16-tone mega-chromatic scale
&lt;a class="wiki_link" href="/hemif7"&gt;Seven note haplotonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/hemif10"&gt;Ten note albitonic scale&lt;/a&gt;&lt;br /&gt;
== Kiribati ==
&lt;a class="wiki_link" href="/hemif17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
{{See also| Subgroup temperaments #Kiribati }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Radon"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Radon&lt;/h1&gt;
Scales:  
Subgroup: 2.3.7.11&lt;br /&gt;
* [[Kiribati13]] – 13-tone chromatic scale
Commas: 896/891, 1029/1024&lt;br /&gt;
* [[Kiribati14]] – 14-tone chromatic scale
Related temperament: &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;Rodan&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
== Score ==
POTE generator: ~8/7 = 234.381&lt;br /&gt;
{{See also|No-threes subgroup temperaments #Score }}
&lt;br /&gt;
 
Map: [&amp;lt;1 1 3 6|, &amp;lt;0 3 -1 -13|]&lt;br /&gt;
[[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]]
EDOs: 5, 36, 41, 87, 128&lt;br /&gt;
 
Error: 1.781 cents&lt;br /&gt;
Scales:
&lt;br /&gt;
* [[Score5]] – 5-tone haplotonic scale
&lt;a class="wiki_link" href="/radon5"&gt;Five note haplotonic scale&lt;/a&gt;&lt;br /&gt;
* [[Score7]] – 7-tone albitonic scale
&lt;a class="wiki_link" href="/radon11"&gt;Eleven note albitonic scale&lt;/a&gt;&lt;br /&gt;
* [[Score9]] – 9-tone mega-albitonic scale
&lt;a class="wiki_link" href="/radon16"&gt;Sixteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
* [[Score11]] – 11-tone chromatic scale
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Pepperoni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Pepperoni&lt;/h1&gt;
== Sensi ==
Subgroup: 2.3.11/7.13/7&lt;br /&gt;
{{Main| Sensi }}
Commas: 352/351, 364/363&lt;br /&gt;
{{See also| Sensipent family #Sensi }}
Related temperament: &lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt;'s &lt;a class="wiki_link" href="/Pepper%20temperament"&gt;pepper temperament&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
[[File:sensi_46edo.jpg|right|alt=sensi_46edo.jpg|Sensi in 46edo]]
POTE generator: ~3/2 = 704.052&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
Map: [&amp;lt;1 0 7 12|, &amp;lt;0 1 -4 -7|]&lt;br /&gt;
* [[Sensi5]] – 5-tone haplotonic scale
EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271&lt;br /&gt;
* [[Sensi8]] – 8-tone albitonic scale
Error: 2.155 cents&lt;br /&gt;
* [[Sensi11]] – 11-tone mega-albitonic scale
&lt;br /&gt;
* [[Sensi19]] – 19-tone chromatic scale
&lt;a class="wiki_link" href="/pepperoni7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/pepperoni12"&gt;Twelve note chromatic scale&lt;/a&gt;&lt;br /&gt;
=== Sensation ===
&lt;br /&gt;
{{Main| Sensi }}
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Skwares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Skwares&lt;/h1&gt;
{{See also| Sensipent family #Sensi }}
Subgroup: 2.3.7.11&lt;br /&gt;
 
Commas: 99/98, 243/242&lt;br /&gt;
Scales:  
Related temperament: &lt;a class="wiki_link" href="/Meantone%20family"&gt;squares&lt;/a&gt;&lt;br /&gt;
* [[Sensi5]] – 5-tone haplotonic scale
&lt;br /&gt;
* [[Sensi8]] – 8-tone albitonic scale
POTE generator: ~9/7 = 425.244&lt;br /&gt;
* [[Sensi11]] – 11-tone mega-albitonic scale
&lt;br /&gt;
* [[Sensi19]] – 19-tone chromatic scale
Map: [&amp;lt;1 3 6 7|, &amp;lt;0 -4 -9 -10|]&lt;br /&gt;
 
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206&lt;br /&gt;
== Meantone ==
Error: 3.009 cents&lt;br /&gt;
{{Main| Meantone }}
&lt;br /&gt;
{{See also| Meantone family #Meantone }}
&lt;a class="wiki_link" href="/skwares8"&gt;Eight note albitonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/skwares11"&gt;Eleven note mega albitonic scale&lt;/a&gt;&lt;br /&gt;
[[File:meantone_31edo.jpg|right|alt=meantone_31edo.jpg|Meantone in 31edo]]
&lt;a class="wiki_link" href="/skwares14"&gt;Fourteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Tutone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Tutone&lt;/h1&gt;
* [[Meantone5]] – 5-tone haplotonic scale
Subgroup: 2.9.5.7.11&lt;br /&gt;
* [[Meantone7]] – 7-tone albitonic scale
Commas: 81/80, 99/98, 126/125&lt;br /&gt;
* [[Meantone12]] – 12-tone chromatic scale
Related temperament: &lt;a class="wiki_link" href="/Meantone%20family"&gt;meantone&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
== Mohaha ==
POTE generator: ~9/8 = 193.937&lt;br /&gt;
{{See also| Rastmic clan #Mohaha }}
&lt;br /&gt;
 
Map: [&amp;lt;1 0 -4 -13 -25|, &amp;lt;0 1 2 5 9|]&lt;br /&gt;
[[File:mohaha_131edo.png|right|alt=mohaha_131edo.png|Mohaha in 131edo]]
EDOs: 6, 7, 13, 19, 25, 31, 99&lt;br /&gt;
 
Error: 3.218 cents&lt;br /&gt;
Scales:  
&lt;br /&gt;
* [[Mohaha7]] – 7-tone albitonic scale
&lt;a class="wiki_link" href="/tutone6"&gt;Six note haplotonic scale&lt;/a&gt;&lt;br /&gt;
* [[Mohaha10]] – 10-tone chromatic scale
&lt;a class="wiki_link" href="/tutone7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/tutone13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
Music:
&lt;br /&gt;
; [[Billy Stiltner]]
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Tutone-Leantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Leantone&lt;/h2&gt;
* [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 ''Mohaha10ping2'']{{dead link}}
Subgroup: 2.9.5.7.11&lt;br /&gt;
 
Commas: 45/44, 56/55, 81/80&lt;br /&gt;
=== Mohoho ===
Related temperament: &lt;a class="wiki_link" href="/Meantone%20family"&gt;flattone&lt;/a&gt;&lt;br /&gt;
{{See also| Rastmic clan #Mohoho }}
&lt;br /&gt;
 
POTE generator: ~9/8 = 192.500&lt;br /&gt;
== Joan ==
&lt;br /&gt;
{{See also| Subgroup temperaments #Joan }}
Map: [&amp;lt;1 0 -4 -13 -6|, &amp;lt;0 1 2 5 3|]&lt;br /&gt;
 
EDOs: 6, 7, 13, 19, 25, 31, 56, 81&lt;br /&gt;
Scales:  
Error: 8.680 cents&lt;br /&gt;
* [[Joan5]] – 5-tone haplotonic scale
&lt;br /&gt;
* [[Joan7]] – 7-tone albitonic scale
&lt;a class="wiki_link" href="/leantone6"&gt;Six note haplotonic scale&lt;/a&gt;&lt;br /&gt;
* [[Joan9]] – 9-tone mega-albitonic scale
&lt;a class="wiki_link" href="/leantone7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
* [[Joan11]] – 11-tone chromatic scale
&lt;a class="wiki_link" href="/leantone13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
== Tutone ==
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Mohaha"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Mohaha&lt;/h1&gt;
{{See also| Hemimean clan #Tutone }}
Subgroup: 2.3.5.11&lt;br /&gt;
 
Commas: 81/80, 121/120&lt;br /&gt;
[[File:tutone_99edo.png|right|alt=tutone_99edo.png|Tutone in 99edo]]
Related temperament: &lt;a class="wiki_link" href="/Meantone%20family"&gt;mohajira&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
POTE generator: ~11/9 = 348.094&lt;br /&gt;
* [[Tutone6]] – 6-tone haplotonic scale
&lt;br /&gt;
* [[Tutone7]] – 7-tone albitonic scale
Map: [&amp;lt;1 1 0 2|, &amp;lt;0 2 8 5|]&lt;br /&gt;
* [[Tutone13]] – 13-tone chromatic scale
EDOs: 7, 10, 17, 24, 31, 131&lt;br /&gt;
 
Error: 3.813 cents&lt;br /&gt;
== Stacks ==
&lt;br /&gt;
{{See also|Subgroup temperaments #Stacks (a.k.a. 2magic) }}
&lt;a class="wiki_link" href="/mohaha7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/mohaha10"&gt;Ten note chromatic scale&lt;/a&gt;&lt;br /&gt;
Scales:  
&lt;br /&gt;
* [[Stacks5]] – 5-tone haplotonic scale
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Mohaha-Mohoho"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Mohoho&lt;/h2&gt;
* [[Stacks8]] – 8-tone albitonic scale
Subgroup: 2.3.5.11.13&lt;br /&gt;
* [[Stacks11]] – 11-tone chromatic scale
Commas: 66/65, 81/80, 121/120&lt;br /&gt;
* [[Stacks19]] – 19-tone mega-chromatic scale
&lt;br /&gt;
 
POTE generator: ~11/9 = 348.916&lt;br /&gt;
== Bleu ==
&lt;br /&gt;
{{See also| No-fives subgroup temperaments #Bleu }}
Map: [&amp;lt;1 1 0 2 4|, &amp;lt;0 2 8 5 -1|]&lt;br /&gt;
 
EDOs: 7, 10, 17, 24, 31, 55&lt;br /&gt;
Scales:  
Error: 4.829 cents&lt;br /&gt;
* [[Bleu8]] – 8-tone haplotonic scale
&lt;br /&gt;
* [[Bleu9]] – 9-tone albitonic scale
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Score"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Score&lt;/h1&gt;
* [[Bleu17]] – 17-tone chromatic scale
Subgroup: 2.7.11.13&lt;br /&gt;
 
Commas: 343/338, 847/832&lt;br /&gt;
== Sephiroth ==
&lt;br /&gt;
{{See also| No-threes subgroup temperaments #Sephiroth }}
POTE generator: ~11/8 = 540.099&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
Map: [&amp;lt;1 1 3 1|, &amp;lt;0 4 1 6|]&lt;br /&gt;
* [[Sephiroth7]] – 7-tone haplotonic scale
EDOs: 5, 7, 9, 11, 20&lt;br /&gt;
* [[Sephiroth10]] – 10-tone albitonic scale
Error: 3.846 cents&lt;br /&gt;
* [[Sephiroth13]] – 13-tone chromatic scale
&lt;br /&gt;
* [[Sephiroth16]] – 16-tone mega-chromatic scale
&lt;a class="wiki_link" href="/score5"&gt;Five note haplotonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/score7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
== Archy ==
&lt;a class="wiki_link" href="/score9"&gt;Nine note mega albitonic scale&lt;/a&gt;&lt;br /&gt;
{{Main| Superpyth }}
&lt;a class="wiki_link" href="/score11"&gt;Eleven note chromatic scale&lt;/a&gt;&lt;br /&gt;
{{See also| Archytas clan #Archy }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Supra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Supra&lt;/h1&gt;
Scales:  
Subgroup: 2.3.7.11&lt;br /&gt;
* [[Archy5]] – 5-tone haplotonic scale
Commas: 64/63, 99/98&lt;br /&gt;
* [[Archy7]] – 7-tone albitonic scale
Related temperament: &lt;a class="wiki_link" href="/Archytas%20clan"&gt;superpyth&lt;/a&gt;&lt;br /&gt;
* [[Archy12]] – 12-tone chromatic scale
&lt;br /&gt;
 
POTE generator: ~3/2 = 707.192&lt;br /&gt;
=== Supra ===
&lt;br /&gt;
{{Main| Superpyth }}
Map: [&amp;lt;1 0 6 13|, &amp;lt;0 1 -2 -6|]&lt;br /&gt;
{{See also| Archytas clan #Supra }}
EDOs: 5, 7, 12, 17, 22, 39, 56&lt;br /&gt;
 
Error: 5.414 cents&lt;br /&gt;
[[File:supra_56edo.png|right|alt=supra_56edo.png|Supra in 56edo]]
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/supra7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
Scales:  
&lt;a class="wiki_link" href="/supra12"&gt;Twelve note chromatic scale&lt;/a&gt;&lt;br /&gt;
* [[Supra7]] – 7-tone [[albitonic scale]]
&lt;br /&gt;
* [[Supra12]] – 12-tone [[chromatic scale]]
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Supra-Supraphon"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Supraphon&lt;/h2&gt;
 
Subgroup: 2.3.7.11.13&lt;br /&gt;
=== Supraphon ===
Commas: 64/63, 78/77, 99/98&lt;br /&gt;
{{Main| Superpyth }}
&lt;br /&gt;
{{See also| Archytas clan #Supraphon }}
POTE generator: ~3/2 = 706.137&lt;br /&gt;
 
&lt;br /&gt;
== Suhajira ==
Map: [&amp;lt;1 0 6 13 18|, &amp;lt;0 1 -2 -6 -9|]&lt;br /&gt;
{{See also| Archytas clan #Suhajira }}
EDOs: 5, 7, 12, 17&lt;br /&gt;
 
Error: 5.132 cents&lt;br /&gt;
Scales:
&lt;br /&gt;
* [[Suhajira7]] – 7-tone haplotonic scale
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Supra-Machine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Machine&lt;/h2&gt;
* [[Suhajira10]] – 10-tone albitonic scale
Subgroup: 2.9.7.11&lt;br /&gt;
* [[Suhajira17]] – 17-tone chromatic scale
Commas: 64/63, 99/98&lt;br /&gt;
 
&lt;br /&gt;
== Machine ==
POTE generator: ~9/8 = 214.384&lt;br /&gt;
{{See also| Subgroup temperaments #Machine}}
&lt;br /&gt;
 
Map: [&amp;lt;1 0 6 13|, &amp;lt;0 1 -1 -3|]&lt;br /&gt;
[[File:machine_28edo.png|right|alt=machine_28edo.png|Machine in 28edo]]
EDOs: 5, 6, 11, 17, 28&lt;br /&gt;
 
Error: 5.414 cents&lt;br /&gt;
Scales:  
&lt;br /&gt;
* [[Machine5]] – 5-tone haplotonic scale
&lt;a class="wiki_link" href="/machine5"&gt;Five note haplotonic scale&lt;/a&gt;&lt;br /&gt;
* [[Machine6]] – 6-tone albitonic scale
&lt;a class="wiki_link" href="/machine6"&gt;Six note albitonic scale&lt;/a&gt;&lt;br /&gt;
* [[Machine11]] – 11-tone chromatic scale
&lt;a class="wiki_link" href="/machine11"&gt;Eleven note chromatic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
== Deutone ==
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Augment"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Augment&lt;/h1&gt;
{{See also| Hemimean clan #Deutone }}
Subgroup: 2.5.7.11&lt;br /&gt;
 
Commas: 56/55, 128/125&lt;br /&gt;
[[File:deutone_44edo.png|right|alt=deutone_44edo.png|Deutone in 44edo]]
Related temperament: &lt;a class="wiki_link" href="/Augmented%20family"&gt;augmented&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
Scales:  
POTE generator: ~8/7&lt;br /&gt;
* [[Deutone6]] – 6-tone haplotonic scale
&lt;br /&gt;
* [[Deutone7]] – 7-tone albitonic scale
Map: [&amp;lt;3 7 0 2|, &amp;lt;0 0 1 1|]&lt;br /&gt;
* [[Deutone13]] – 13-tone chromatic scale
EDOs: 3, 6, 9, 15, 21&lt;br /&gt;
 
Error: 6.632 cents&lt;br /&gt;
== Negra ==
&lt;br /&gt;
{{Main| Negri }}
&lt;a class="wiki_link" href="/augment6"&gt;Six note haplotonic scale&lt;/a&gt;&lt;br /&gt;
{{See also| Marvel temperaments #Negri }}
&lt;a class="wiki_link" href="/augment9"&gt;Nine note albitonic scale&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/augment12"&gt;Twelve note chromatic scale&lt;/a&gt;&lt;br /&gt;
== Porkypine ==
&lt;br /&gt;
{{Main| Porcupine }}
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Greeley"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Greeley&lt;/h1&gt;
{{See also| Porcupine family #Porcupine }}
Subgroup: 2.5/3.7/3.11/3&lt;br /&gt;
 
Commas: 121/120, 126/125&lt;br /&gt;
Scales:  
&lt;br /&gt;
* [[Porkypine7]] – 7-tone haplotonic scale
POTE generator: ~11/10 = 156.055&lt;br /&gt;
* [[Porkypine8]] – 8-tone albitonic scale
&lt;br /&gt;
* [[Porkypine15]] – 15-tone chromatic scale
Map: [&amp;lt;1 1 2 2|, &amp;lt;0 -2 -6 -1|]&lt;br /&gt;
 
EDOs: 8, 15, 23, 77, 100&lt;br /&gt;
== Skateboard ==
Error: 7.555 cents&lt;br /&gt;
{{See also| Subgroup temperaments #Skateboard }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/greeley8"&gt;Eight note albitonic scale&lt;/a&gt;&lt;br /&gt;
Scales:  
&lt;a class="wiki_link" href="/greeley15"&gt;Fifteen note chromatic scale&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[Skateboard7]] – 7-tone haplotonic scale
* [[Skateboard11]] – 11-tone albitonic scale
* [[Skateboard15]] – 15-tone chromatic scale
 
== Augment ==
{{See also| No-threes subgroup temperaments #Augment }}
 
[[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]]
 
Scales:  
* [[Augment6]] – 6-tone haplotonic scale
* [[Augment9]] – 9-tone albitonic scale
* [[Augment12]] – 12-tone chromatic scale
 
== Semaphore ==
{{Main| Semaphore and godzilla }}
{{See also| Semaphoresmic clan #Semaphore }}
 
[[File:semaphore_24edo.png|right|alt=semaphore_24edo.png|Semaphore in 24edo]]
 
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 }}
 
[[File:antikythera_28edo.png|right|alt=antikythera_28edo.png|Antikythera in 28edo]]
 
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 }}
 
[[File:leantone_81edo.png|right|alt=leantone_81edo.png|Leantone in 81edo]]
 
Scales:  
* [[Leantone6]] – 6-tone haplotonic scale
* [[Leantone7]] – 7-tone albitonic scale
* [[Leantone13]] – 13-tone chromatic scale
 
== Notes ==
 
[[Category:Lists of scales]]
[[Category:Tempered scales| ]]
[[Category:Listen]]
[[Category:Rank 2]]
 
{{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

See also: Subgroup temperaments § Terrain
terrain_3558edo.png
Terrain in 3558edo

Scales:

Music

Petrtri

See also: Subgroup temperaments § Petrtri
petrtri_385edo.png
Petrtri in 385edo

Scales:

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
tridec_235edo.png
Tridec in 235edo

Scales:

Nestoria

See also: Schismatic family § Nestoria (2.3.5.19)
nestoria_171edo.png
Nestoria in 171edo

Scales:

Orgone

Main article: Orgone
See also: Orgonia § Orgone
orgone_308edo.jpg
Orgone in 308edo

Scales:

Marveltwintri

See also: Subgroup temperaments § Marveltwintri
marveltwintri_321edo.png
Marveltwintri in 321edo

Scales:

Cata

Main article: Kleismic
See also: Kleismic family § Cata
cata_246edo.jpg
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

See also: Subgroup temperaments § Bridgetown
bridgetown_29edo.png
Bridgetown in 29edo

Scales:

Music

Haumea

See also: Subgroup temperaments § Haumea

Scales:

Neutral

See also: Rastmic clan § Neutral
neutral_380edo.png
Neutral in 380edo

Scales:

Music

Slendric

Main article: Slendric
See also: Gamelismic clan #Slendric and No-fives subgroup temperaments #Slendric
slendric_190edo.jpg
Slendric in 190edo

Scales:

Huntington

See also: No-threes subgroup temperaments § Huntington
huntington_400edo.jpg
Huntington in 400edo

Scales:

Tobago

See also: Subgroup temperaments § Tobago

Scales:

Pepperoni

See also: Parapyth
See also: Subgroup temperaments § Pepperoni
pepperoni_271edo.png
Pepperoni in 271edo

Scales:

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
bossier_225edo.jpg
Bossier in 225edo

Scales:

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:

Marveltri

See also: Subgroup temperaments § Marveltri

Scales:

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)
photia_65edo.png
Photia in 65edo

Scales:

Shoe a.k.a. llywelyn

See also: Llywelynsmic clan § Llywelyn a.k.a. shoe
shoe_37edo.jpg
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_37edo.jpg
Roulette in 37edo

Scales:

Silver

See also: No-threes subgroup temperaments § Silver
silver_487edo.jpg
Silver in 487edo

Scales:

Baldy

See also: Subgroup temperaments § Baldy
baldy_147edo.jpg
Baldy in 147edo

Scales

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


Guanyintet

See also: Subgroup temperaments § Guanyintet

Scales:

Radon

See also: Gamelismic clan § Radon
radon_128edo.jpg
Radon in 128edo
  • Radon5 – 5-tone haplotonic scale
  • Radon11 – 11-tone albitonic scale
  • Radon16 – 16-tone chromatic scale

Gariberttet

See also: Subgroup temperaments § Gariberttet

Scales:

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:

Hemif

See also: No-fives subgroup temperaments § Hemif
hemif_58edo.jpg
Hemif in 58edo

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
garibaldi_94edo.png
Garibaldi in 94edo

Scales:

Mabilic

See also: No-threes subgroup temperaments § Mabilic
mabila_66edo.jpg
Mabilic in 66edo

Scales:

Indium

See also: Subgroup temperaments § Indium
indium_253edo.png
Indium in 253edo

Scales:

Music

Starlingtet

See also: Subgroup temperaments § Starlingtet

Scales:

Lovecraft

See also: No-threes subgroup temperaments § Lovecraft
lovecraft_116edo.png
Lovecraft in 116edo

Scales:

Blackbirds

See also: No-threes subgroup temperaments § Blackbirds

Scales:

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
myna_89edo.jpg
Myna in 89edo

Scales:

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

Greeley

See also: Subgroup temperaments § Greeley
greeley_100edo.png
Greeley in 100edo

Scales:

Music

Ammon

See also: Subgroup temperaments § Ammon
semidim_770edo.png
Ammon in 770edo

Scales:

  • Ammon8 – 8-tone albitonic scale
  • Ammon13 – 13-tone chromatic scale

Mothwelltri

See also: Subgroup temperaments § Mothwelltri

Scales:

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
skwares_206edo.png
Skwares in 206edo

Scales:

Orwell

Main article: Orwell
See also: Semicomma family § Orwell
orwell_84edo.png
Orwell in 84edo

Scales:

Magicaltet

See also: Subgroup temperaments § Magicaltet

Scales:

Magic

Main article: Magic
See also: Magic family § Magic
magic_145edo.jpg
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

See also: Subgroup temperaments § Kiribati

Scales:

Score

See also: No-threes subgroup temperaments § Score
score_20edo.jpg
Score in 20edo

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
sensi_46edo.jpg
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: 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_31edo.jpg
Meantone in 31edo

Scales:

Mohaha

See also: Rastmic clan § Mohaha
mohaha_131edo.png
Mohaha in 131edo

Scales:

Music:

Billy Stiltner

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
tutone_99edo.png
Tutone in 99edo

Scales:

Stacks

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

Scales:

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:

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
supra_56edo.png
Supra in 56edo

Scales:

Supraphon

Main article: Superpyth
See also: Archytas clan § Supraphon

Suhajira

See also: Archytas clan § Suhajira

Scales:

Machine

See also: Subgroup temperaments § Machine
machine_28edo.png
Machine in 28edo

Scales:

Deutone

See also: Hemimean clan § Deutone
deutone_44edo.png
Deutone in 44edo

Scales:

Negra

Main article: Negri
See also: Marvel temperaments § Negri

Porkypine

Main article: Porcupine
See also: Porcupine family § Porcupine

Scales:

Skateboard

See also: Subgroup temperaments § Skateboard

Scales:

Augment

See also: No-threes subgroup temperaments § Augment
augment_21edo.png
Augment in 21edo

Scales:

Semaphore

Main article: Semaphore and godzilla
See also: Semaphoresmic clan § Semaphore
semaphore_24edo.png
Semaphore in 24edo

Scales:

Kryptonite

See also: Subgroup temperaments § Kryptonite

Scales:

Oregon

See also: Orgonia § Oregon

Scales:

Antikythera

See also: Jubilismic clan § Antikythera
antikythera_28edo.png
Antikythera in 28edo

Scales:

Glacial

See also: Subgroup temperaments § Glacial

Scales:

Leantone

See also: Hemimean clan § Leantone
leantone_81edo.png
Leantone in 81edo

Scales:

Notes

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