Chromatic pairs: Difference between revisions

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== Terrain ==
== Terrain ==
{{Redirect|Terrain|the scale|Terrain (scale)}}
{{See also| Subgroup temperaments #Terrain }}
 
Terrain, the 6 & 21 temperament in the 2.9/5.9/7 subgroup, is related to [[domain (temperament)|domain]]. It is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1–7/5–9/5 and 1–9/7–9/5 chords are characteristic.
 
[[Subgroup]]: 2.9/5.9/7
 
[[Comma list]]: 250047/250000
 
{{Mapping|legend=2| 3 0 -4 | 0 1 2 }}
 
{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
 
: [[gencom]]: [63/50 10/9; 250047/250000]
 
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
 
{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents


[[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]]
[[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]]


Scales:  
Scales:  
* [[terrain9]] – 9-tone albitonic scale
* [[Terrain9]] – 9-tone albitonic scale
* [[terrain15]] – 15-tone chromatic scale
* [[Terrain15]] – 15-tone chromatic scale


; Music
; Music
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== Petrtri ==
== Petrtri ==
Petrtri can be described as 3 & 5 temperament in the 2.11/5.13/5 subgroup.
{{See also| Subgroup temperaments #Petrtri }}
 
[[Subgroup]]: 2.11/5.13/5
 
[[Comma list]]: 2200/2197
 
{{Mapping|legend=2| 1 0 1| 0 3 1 }}
 
{{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}
 
: [[gencom]]: [2 13/10; 2200/2197]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/10 = 455.012
 
{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents


[[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]]
[[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]]


Scales:  
Scales:  
* [[petrtri5]] – 5-tone haplotonic scale
* [[Petrtri5]] – 5-tone haplotonic scale
* [[petrtri8]] – 8-tone albitonic scale
* [[Petrtri8]] – 8-tone albitonic scale
* [[petrtri13]] – 13-tone chromatic scale
* [[Petrtri13]] – 13-tone chromatic scale


== Barton ==
== Barton ==
Barton may be described as the 11 &amp; 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group | "father" variant?]</ref>.
{{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}}
 
{{See also| The Jacobins #Barton }}
[[Subgroup]]: 2.5.11.13
 
[[Comma list]]: 2200/2197, 6656/6655
 
{{Mapping|legend=2| 1 6 3 6 | 0 -8 1 -5 }}
 
{{Mapping|legend=3| 1 0 6 0 3 6 | 0 0 -8 0 1 -5 }}
 
: gencom: [2 11/8; 2200/2197 6656/6655]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 551.699
 
{{Optimal ET sequence|legend=1| 11, 13, 24, 37, 50, 87, 298, 385, 472, 559, 1590cd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.0822 cents


Scales:  
Scales:  
* [[Barton5]] – 5-tone [[haplotonic scale]]
* [[Barton5]] – 5-tone haplotonic scale
* [[Barton7]] – 7-tone [[albitonic scale]]
* [[Barton7]] – 7-tone albitonic scale
* [[Barton9]] – 9-tone [[mega-albitonic scale]]
* [[Barton9]] – 9-tone mega-albitonic scale
* [[Barton11]] – 11-tone [[chromatic scale]]
* [[Barton11]] – 11-tone chromatic scale
* [[Barton13]] – 13-tone [[mega-chromatic scale]]
* [[Barton13]] – 13-tone mega-chromatic scale
 
== Voltage ==
Voltage is the 3 &amp; 7 temperament in the 2.7.13 subgroup.
 
[[Subgroup]]: 2.7.13
 
[[Comma list]]: 28672/28561
 
{{Mapping|legend=2| 1 4 4 | 0 -4 -1 }}
 
{{Mapping|legend=3| 1 0 0 4 0 4 | 0 0 0 -4 0 -1 }}
 
: [[gencom]]: [2, 16/13; 28672/28561]
 
[[Optimal tuning]]:
* [[POTE]]: ~2 = 1\1, ~16/13 = 357.677
* [[TOP tuning|POTT]]: ~2 = 1\1, ~16/13 = 357.794 (1200 - 300 log<sub>2</sub>(7))
 
{{Optimal ET sequence|legend=1| 3, 7, 10, 27, 37, 47, 57, 104 }}
 
RMS error: 0.1423


== Tridec ==
== Tridec ==
Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[petrtri]].
{{See also| Subgroup temperaments #Tridec }}
 
[[Subgroup]]: 2.7/5.11/5.13/5
 
[[Comma list]]: 847/845, 1001/1000
 
{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
 
{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}
 
: [[gencom]]: [2 13/10; 847/845 1001/1000]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/10 = 454.556
 
{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents


[[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]]
[[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]]


Scales:
* [[Tridec8]] – 8-tone albitonic scale
* [[Tridec8]] – 8-tone albitonic scale
* [[Tridec13]] – 13-tone chromatic scale
* [[Tridec13]] – 13-tone chromatic scale
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Scales:  
Scales:  
* [[nestoria7]] – 7-tone albitonic scale
* [[Nestoria7]] – 7-tone albitonic scale
* [[nestoria12]] – 12-tone chromatic scale
* [[Nestoria12]] – 12-tone chromatic scale
* [[nestoria17]] – 7-tone mega chromatic scale
* [[Nestoria17]] – 17-tone mega chromatic scale


== Orgone ==
== Orgone ==
{{Main| Orgone }}
{{Main| Orgone }}
{{See also| Orgonia }}
{{See also| Orgonia #Orgone }}
 
Orgone, the 4 &amp; 7 temperament in the 2.7.11 subgroup, is related to [[superkleismic]].
 
[[Subgroup]]: 2.7.11
 
[[Comma list]]: 65536/65219
 
{{Mapping|legend=2| 1 2 4 | 0 3 -2 }}
 
{{Mapping|legend=3| 1 0 0 2 4 | 0 0 0 3 -2 }}
 
: [[gencom]]: [2 77/64; 65536/65219]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~77/64 = 323.372
 
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475bc, 783bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.1888 cents


[[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]]
[[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]]


Scales:  
Scales:  
* [[orgone7]] – 7-tone albitonic scale
* [[Orgone7]] – 7-tone albitonic scale
* [[orgone11]] – 11-tone chromatic scale
* [[Orgone11]] – 11-tone chromatic scale
* [[orgone15]] – 15-tone mega chromatic scale
* [[Orgone15]] – 15-tone mega-chromatic scale


== Marveltwintri ==
== Marveltwintri ==
Marveltwintri can be described as the 3 &amp; 4 temperament in the 2.5/3.13/9 subgroup.
{{See also| Subgroup temperaments #Marveltwintri }}
 
[[Subgroup]]: 2.5/3.13/9
 
[[Comma list]]: 325/324
 
{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
 
{{Mapping|legend=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}
 
: [[gencom]]: [2 6/5; 325/324]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 317.139
 
{{Optimal ET sequence|legend=1| 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents


[[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]]
[[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]]


Scales:  
Scales:  
* [[marveltwintri7]] – 7-tone albitonic scale
* [[Marveltwintri7]] – 7-tone albitonic scale
* [[marveltwintri11]] – 11-tone chromatic scale
* [[Marveltwintri11]] – 11-tone chromatic scale
* [[marveltwintri15]] – 15-tone mega chromatic scale
* [[Marveltwintri15]] – 15-tone mega-chromatic scale


== Cata ==
== Cata ==
{{Main| Hanson and cata }}
{{Main| Kleismic }}
{{See also| Kleismic family #Cata }}
{{See also| Kleismic family #Cata }}


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Scales:  
Scales:  
* [[Cata7]] – 7-tone [[albitonic scale]]
* [[Cata7]] – 7-tone albitonic scale
* [[Cata11]] – 11-tone [[mega-albitonic scale]]
* [[Cata11]] – 11-tone mega-albitonic scale
* [[Cata15]] – 15-tone [[chromatic scale]]
* [[Cata15]] – 15-tone chromatic scale
* [[Cata19]] – 19-tone [[mega-chromatic scale]]
* [[Cata19]] – 19-tone mega-chromatic scale


== Bridgetown ==
== Bridgetown ==
Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[haumea]] and [[barbados]].
{{See also| Subgroup temperaments #Bridgetown }}
 
[[Subgroup]]: 2.3.11/5.13/5
 
[[Comma list]]: 352/351, 676/675
 
{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
 
{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}
 
: [[gencom]]: [2 15/13; 352/351 676/675]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/13 = 248.399
 
{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents


[[File:bridgetown_29edo.png|right|alt=bridgetown_29edo.png|Bridgetown in 29edo]]
[[File:bridgetown_29edo.png|right|alt=bridgetown_29edo.png|Bridgetown in 29edo]]


Scales:  
Scales:  
* [[bridgetown9]] – 9-tone albitonic scale
* [[Bridgetown9]] – 9-tone albitonic scale
* [[bridgetown14]] – 14-tone chromatic scale
* [[Bridgetown14]] – 14-tone chromatic scale


; Music
; Music
* [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]]
* [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]]
* [https://web.archive.org/web/20201127012744/http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 ''Route 14 in Bridgetown''] (archived 2020) by [[Chris Vaisvil]]
* ''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


== Haumea ==
== Haumea ==
Related temperaments include [[bridgetown]], [[namaka]], [[hemigari]], [[barbados]], and [[parizekmic]].
{{See also| Subgroup temperaments #Haumea }}
 
[[Subgroup]]: 2.3.7/5.11/5.13/5
 
[[Comma list]]: 352/351, 676/675, 847/845
 
{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
 
{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}
 
: [[gencom]]: [2 15/13; 352/351 676/675 847/845]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/13 = 248.491
 
{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents


Scales:  
Scales:  
* [[haumea5]] – 5-tone haplotonic scale
* [[Haumea5]] – 5-tone haplotonic scale
* [[haumea9]] – 9-tone albitonic scale
* [[Haumea9]] – 9-tone albitonic scale
* [[haumea14]] – 14-tone chromatic scale
* [[Haumea14]] – 14-tone chromatic scale
* [[haumea19]] – 19-tone mega chromatic scale
* [[Haumea19]] – 19-tone mega-chromatic scale


== Neutral ==
== Neutral ==
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Scales:  
Scales:  
* [[neutral7]] – 7-tone [[albitonic scale]]
* [[Neutral7]] – 7-tone albitonic scale
* [[neutral10]] – 10-tone [[chromatic scale]]
* [[Neutral10]] – 10-tone chromatic scale
* [[neutral17]] – 17-tone [[mega-chromatic scale]]
* [[Neutral17]] – 17-tone mega-chromatic scale


; Music
; Music
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Scales:  
Scales:  
* [[Slendric5]] – 5-tone [[haplotonic scale]]
* [[Slendric5]] – 5-tone haplotonic scale
* [[Slendric6]] – 6-tone [[haplotonic scale]]
* [[Slendric6]] – 6-tone haplotonic scale
* [[Slendric11]] – 11-tone [[albitonic scale]]
* [[Slendric11]] – 11-tone albitonic scale
* [[Slendric16]] – 16-tone [[chromatic scale]]
* [[Slendric16]] – 16-tone chromatic scale


== Huntington ==
== Huntington ==
Huntington may be described as the 10 &amp; 27 temperament in the 2.5.7.13 subgroup.
{{See also| No-threes subgroup temperaments #Huntington }}
 
[[Subgroup]]: 2.5.7.13
 
[[Comma list]]: 640/637, 10985/10976
 
{{Mapping|legend=2| 1 5 4 4 | 0 -9 -4 -1 }}
 
{{Mapping|legend=3| 1 0 5 4 0 4 | 0 0 -9 -4 0 -1 }}
 
: [[gencom]]: [2 16/13; 640/637 10985/10976]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/13 = 357.002
 
{{Optimal ET sequence|legend=1| 7, 10, 17, 27, 37, 84, 121, 279cd, 400cd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3452 cents


[[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]]
[[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]]


Scales:  
Scales:  
* [[huntington7]] – 7-tone haplotonic scale
* [[Huntington7]] – 7-tone haplotonic scale
* [[huntington10]] – 10-tone albitonic scale
* [[Huntington10]] – 10-tone albitonic scale
* [[huntington17]] – 17-tone chromatic scale
* [[Huntington17]] – 17-tone chromatic scale


== Tobago ==
== Tobago ==
Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
{{See also| Subgroup temperaments #Tobago }}
 
[[Subgroup]]: 2.3.11.13/5
 
[[Comma list]]: 243/242, 676/675
 
{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}
 
{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}
 
: [[gencom]]: [55/39 15/13; 243/242 676/675]
 
[[Optimal tuning]] ([[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
 
{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents


Scales:  
Scales:  
* [[tobago6]] – 6-tone haplotonic scale
* [[Tobago6]] – 6-tone haplotonic scale
* [[tobago10]] – 10-tone albitonic scale
* [[Tobago10]] – 10-tone albitonic scale
* [[tobago14]] – 14-tone chromatic scale
* [[Tobago14]] – 14-tone chromatic scale
* [[tobago24]] – 24-tone quatertone scale
* [[Tobago24]] – 24-tone quatertone scale


== Pepperoni ==
== Pepperoni ==
{{See also| Parapyth }}
{{See also| Parapyth }}
 
{{See also| Subgroup temperaments #Pepperoni }}
Pepperoni is generated by a fifth and can be described as the 5 &amp; 12 temperament in the 2.3.11/7.13/7. It is the single-chain retraction of [[parapyth]]. The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
 
[[Subgroup]]: 2.3.11/7.13/7
 
[[Comma list]]: 352/351, 364/363
 
{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
 
{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
 
: [[gencom]]: [2 3/2; 352/351 364/363]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.856
 
{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents


[[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]]
[[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]]


Scales:  
Scales:  
* [[pepperoni7]] – 7-tone albitonic scale
* [[Pepperoni7]] – 7-tone albitonic scale
* [[pepperoni12]] – 12-tone chromatic scale
* [[Pepperoni12]] – 12-tone chromatic scale


== Wizz ==
== Wizz ==
Wizz, the 6 &amp; 16 temperament in the 2.5.11 subgroup, is related to [[wizard]].
{{See also| No-threes subgroup temperaments #Wizz }}
 
[[Subgroup]]: 2.5.11
 
[[Comma list]]: 15625/15488
 
{{Mapping|legend=2| 2 0 -7 | 0 1 3 }}
 
{{Mapping|legend=3| 2 0 4 0 5 | 0 0 1 0 3 }}
 
: [[gencom]]: [125/88 5/4; 15625/15488]
 
[[Optimal tuning]] ([[POTE]]): ~125/88 = 1\2, ~5/4 = 383.768
 
{{Optimal ET sequence|legend=1| 6, 16, 22, 28, 50, 122, 172, 222 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3997


Scales:  
Scales:  
* [[wizz6]] – 6-tone haplotonic scale
* [[Wizz6]] – 6-tone haplotonic scale
* [[wizz10]] – 10-tone albitonic scale
* [[Wizz10]] – 10-tone albitonic scale
* [[wizz16]] – 16-tone chromatic scale
* [[Wizz16]] – 16-tone chromatic scale


== Bossier ==
== Bossier ==
Bossier can be described as the 3 &amp; 17 in the 2.7.11.13 subgroup.
{{See also| No-threes subgroup temperaments #Bossier }}
 
[[Subgroup]]: 2.7.11.13
 
[[Comma list]]: 1573/1568, 15488/15379
 
{{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }}
 
{{Mapping|legend=3| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}
 
: [[gencom]]: [2 14/11; 1573/1568 15488/15379]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/11 = 421.309
 
{{Optimal ET sequence|legend=1| 17, 20, 37, 57, 94, 225, 319cd, 413bcd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4043 cents


[[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]]
[[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]]


Scales:  
Scales:  
* [[bossier8]] – 8-tone albitonic scale
* [[Bossier8]] – 8-tone albitonic scale
* [[bossier11]] – 11-tone chromatic scale
* [[Bossier11]] – 11-tone chromatic scale
* [[bossier14]] – 14-tone mega-chromatic scale
* [[Bossier14]] – 14-tone mega-chromatic scale
 
== Penta aka mechanism ==
Penta, also known as mechanism, is the 8 &amp; 11 temperament in the 2.9.7.11 subgroup.
 
[[Subgroup]]: 2.9.7.11
 
[[Comma list]]: 896/891, 26411/26244
 
{{Mapping|legend=2| 1 0 -1 6 | 0 5 6 -4 }}
 
{{Mapping|legend=3| 1 5/2 0 5 2 | 0 -5/2 0 -6 4 }}
 
: [[gencom]]: [2 9/7; 896/891 26411/26244]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 438.465
== Penta a.k.a. mechanism ==
 
{{See also| Subgroup temperaments #Penta a.k.a. mechanism }}
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents


Scales:  
Scales:  
* [[penta5]] – 5-tone haplotonic scale
* [[Penta5]] – 5-tone haplotonic scale
* [[penta8]] – 8-tone albitonic scale
* [[Penta8]] – 8-tone albitonic scale
* [[penta11]] – 11-tone chromatic scale
* [[Penta11]] – 11-tone chromatic scale
* [[penta19]] – 19-tone mega-chromatic scale
* [[Penta19]] – 19-tone mega-chromatic scale


== Bluebirds ==
== Bluebirds ==
Subgroup: 2.11.13
{{See also| No-threes subgroup temperaments #Bluebirds }}


Comma: 265837/262144
Scales:  
 
* [[Bluebirds6]] – 6-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~143/128 = 182.368
* [[Bluebirds7]] – 7-tone albitonic scale
 
* [[Bluebirds13]] – 13-tone chromatic scale
Gencom: [2 143/128; 265837/262144]
 
Gencom mapping: [&lt;1 0 0 0 3 4|, &lt;0 0 0 0 3 -2|]
 
Mapping: [&lt;1 0 6|, &lt;0 3 -2|]
 
EDOs: {{EDOs|6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.4444 cents
 
[[bluebirds6|Six note haplotonic scale]]
 
[[bluebirds7|Seven note albitonic scale]]
 
[[bluebirds13|Thirteen note chromatic scale]]


== Marveltri ==
== Marveltri ==
Subgroup: 2.5.9/7
{{See also| Subgroup temperaments #Marveltri }}


Comma: 225/224
Scales:  
 
* [[Marveltri7]] – 7-tone albitonic scale
Sval name: 3&amp;13
* [[Marveltri10]] – 10-tone chromatic scale
 
* [[Marveltri13]] – 13-tone mega-chromatic scale
Related temperaments: marvel, 22&amp;47, magic
 
[[Tp_tuning|POT2 generator]]: ~5/4 = 383.638
 
[[Gencom|Gencom]]: [2 5/4; 225/224]
 
Gencom mapping: [&lt;1 2/5 2 -1/5|, &lt;0 -4/5 1 2/5|]
 
Mapping: [&lt;1 0 5|, &lt;0 1 -2|]
 
EDOs: {{EDOs|12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.4801 cents
 
[[marveltri7|Seven note albitonic scale]]
 
[[marveltri10|Ten note chromatic scale]]
 
[[marveltri13|Thirteen note mega chromatic scale]]


== Edson ==
== Edson ==
[[Subgroup]]: 2.3.7/5.11/5.13/5
{{See also| Subgroup temperaments #Edson }}
 
[[Comma list]]: 196/195 = {{monzo| 2 -1 2 0 -1 }}, 352/351 = {{monzo| 5 -3 0 1 -1 }}, 364/363 = {{monzo| 2 -1 1 -2 1 }}
 
{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
 
: mapping generators: ~2, ~3
 
{{Mapping|legend=3| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }}
 
: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363]
 
[[Optimal tuning]]s:
* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~3/2 = 703.4398
* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~3/2 = 703.414
 
{{Optimal ET sequence|legend=1| 12, 17, 29 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
 
Related temperaments: [[pele]], [[cassandra]]


Scales:  
Scales:  
* [[edson5]] – 5-tone [[haplotonic scale]]
* [[Edson5]] – 5-tone haplotonic scale
* [[edson7]] – 7-tone [[albitonic scale]]
* [[Edson7]] – 7-tone albitonic scale
* [[edson12]] – 12-tone [[chromatic scale]]
* [[Edson12]] – 12-tone chromatic scale
* [[edson17]] – 17-tone [[mega-chromatic scale]]
* [[Edson17]] – 17-tone mega-chromatic scale


== Photia ==
== Photia ==
Subgroup: 2.3.5.17.19
{{See also| Schismatic family #Photia (2.3.5.17) }}


Commas: 171/170, 256/255, 324/323
[[File:photia_65edo.png|right|alt=photia_65edo.png|Photia in 65edo]]


Sval name: 12&amp;41
Scales:  
 
* [[Photia7]] – 7-tone albitonic scale
Related temperament: [[Schismatic_family|schismatic]]
* [[Photia12]] – 12-tone chromatic scale
 
[[Tp_tuning|POT2 generator]]: ~3/2 = 701.470
 
[[Gencom|Gencom]]: [2 3/2; 171/170 256/255 324/323]
 
Gencom mapping: [&lt;1 1 7 0 0 0 0 6|, &lt;0 1 -8 0 0 0 7 -3|]
 
Mapping: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]
 
EDOs: {{EDOs|7, 12, 17, 29, 41, 53, 65, 142d, 207d, 272d}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5374 cents
 
[[File:photia_65edo.png|alt=photia_65edo.png|photia_65edo.png]]
 
[[photia7|Seven note albitonic scale]]
 
[[photia12|Twelve note chromatic scale]]
 
== Shoe ==
Subgroup: 2.5.7.11.13
 
Commas: 176/175, 640/637, 847/845
 
Sval name: 16&amp;21
 
[[Tp_tuning|POT2 generator]]: ~8/7 = 227.108
 
[[Gencom|Gencom]]: [2 8/7; 176/175 640/637 847/845]
 
Gencom mapping: [&lt;1 0 1 3 1 2|, &lt;0 0 7 -1 13 9|]
 
Mapping: [&lt;1 1 3 1 2|, &lt;0 7 -1 13 9|]
 
EDOs: {{EDOs|16, 21, 37, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce}}


[[Tp_tuning#T2 tuning|RMS error]]: 0.5433 cents
== Shoe a.k.a. llywelyn ==
{{See also| Llywelynsmic clan #Llywelyn a.k.a. shoe }}


[[File:shoe_37edo.jpg|alt=shoe_37edo.jpg|shoe_37edo.jpg]]
[[File:shoe_37edo.jpg|right|alt=shoe_37edo.jpg|Shoe in 37edo]]


[[shoe5|shoe5]] - five note mini [[haplotonic_scale|haplotonic scale]]
Scales:
 
* [[Shoe5]] – 5-tone mini-haplotonic scale
[[shoe6|shoe6]] - six note [[haplotonic_scale|haplotonic scale]]
* [[Shoe6]] – 6-tone haplotonic scale
 
* [[Shoe11]] – 11-tone albitonic scale
[[shoe11|shoe11]] - eleven note note [[albitonic_scale|albitonic scale]]
* [[Shoe16]] – 16-tone chromatic scale
 
[[shoe16|shoe16]] - sixteen note [[chromatic_scale|chromatic scale]]


== Roulette ==
== Roulette ==
{{ See also | Mediantone }}
{{See also | Hemimean clan #Roulette }}


Subgroup: 2.5.7.11.13
[[File:roulette_37edo.jpg|right|alt=roulette_37edo.jpg|Roulette in 37edo]]


Commas: 176/175, 1375/1372, 640/637
Scales:  
 
* [[Roulette6]] – 6-tone haplotonic scale
Sval name: 6&amp;25
* [[Roulette7]] – 7-tone albitonic scale
 
* [[Roulette13]] – 13-tone chromatic scale
Related temperament: [[Würschmidt_family|Hemiwürschmidt]]
* [[Roulette19]] – 19-tone mega-chromatic scale
 
[[Tp_tuning|POT2 generator]]: ~28/25 = 194.594
 
[[Gencom|Gencom]]: [2 28/25; 176/175 1375/1372 640/637]
 
Gencom mapping: [&lt;1 0 2 2 2 5|, &lt;0 0 2 5 9 -8|]
 
Mapping: [&lt;1 0 -3 -7 13|, &lt;0 2 5 9 -8|]
 
EDOs: {{EDOs|6, 7, 13, 19, 25, 31, 37}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5567 cents
 
[[File:roulette_37edo.jpg|alt=roulette_37edo.jpg|roulette_37edo.jpg]]
 
[[roulette6|roulette6]] - six note [[haplotonic_scale|haplotonic scale]]
 
[[roulette7|roulette7]] - seven note [[albitonic_scale|albitonic scale]]
 
[[roulette13|roulette13]] - thirteen note [[chromatic_scale|chromatic scale]]
 
[[roulette19|roulette19]] - nineteen note [[mega_chromatic_scale|mega chromatic scale]]


== Silver ==
== Silver ==
Subgroup: 2.5.7.13.17
{{See also | No-threes subgroup temperaments #Silver }}


Commas: 170/169, 640/637, 5525/5488
[[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]]


Sval name: 10&amp;27
Scales:  
 
* [[Silver7]] – 7-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~13/8 = 842.711
* [[Silver10]] – 10-tone albitonic scale
 
* [[Silver17]] – 17-tone chromatic scale
[[Gencom|Gencom]]: [2 13/8; 170/169 640/637 5525/5488]
 
Gencom mapping: [&lt;1 0 -4 0 0 3 9|, &lt;0 0 9 4 0 1 -7|]
 
Mapping: [&lt;1 5 4 4 2|, &lt;0 -9 -4 -1 7|]
 
EDOs: {{EDOs|7, 10, 17, 27, 37, 47, 84, 131, 178e, 309cde, 487bcdee}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5886 cents
 
[[File:silver_487edo.jpg|alt=silver_487edo.jpg|silver_487edo.jpg]]
 
[[silver7|silver7]] -seven note [[haplotonic_scale|haplotonic scale]]
 
[[silver10|silver10]] - ten note [[albitonic_scale|albitonic scale]]
 
[[silver17|silver17]] - seventeen note [[chromatic_scale|chromatic scale]]


== Baldy ==
== Baldy ==
{{See also| Subgroup temperaments #Baldy }}
{{See also| Subgroup temperaments #Baldy }}


Subgroup: 2.9.5.7.13
[[File:baldy_147edo.jpg|right|alt=baldy_147edo.jpg|Baldy in 147edo]]
 
Commas: 225/224, 325/324, 640/637
 
Sval name: 6&amp;35
 
Related temperament: [[Schismatic_family|Garibaldi]]
 
[[Tp_tuning|POT2 generator]]: ~9/8 = 204.090
 
[[Gencom|Gencom]]: [2 9/8; 225/224 325/324 640/637]


Gencom mapping: [&lt;1 3/2 3 4 0 2|, &lt;0 1/2 -4 -7 0 10|]
Scales
* [[Baldy6]] – 6-tone haplotonic scale
* [[Baldy11]] – 11-tone albitonic scale
* [[Baldy17]] – 17-tone chromatic scale


Mapping: [&lt;1 0 15 25 -28|, &lt;0 1 -4 -7 10|]
EDOs: {{EDOs|6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd}}
[[Tp_tuning#T2 tuning|RMS error]]: 0.5999 cents
[[File:baldy_147edo.jpg|alt=baldy_147edo.jpg|baldy_147edo.jpg]]
[[baldy6|baldy6]] - six note [[haplotonic_scale|haplotonic scale]]
[[baldy11|baldy11]] - eleven note [[albitonic_scale|albitonic scale]]
[[baldy17|baldy17]] - seventeen note [[chromatic_scale|chromatic scale]]


== Guanyintet ==
== Guanyintet ==
Subgroup: 2.5.7/3.11/3
{{See also | Subgroup temperaments #Guanyintet }}


Commas: 176/175, 540/539
Scales:  
 
* [[Guanyintet5]] – 5-tone haplotonic scale
Svalname: 4&amp;9
* [[Guanyintet9]] – 9-tone albitonic scale
 
* [[Guanyintet13]] – 13-tone chromatic scale
Related temperaments: guanyin, orwell
 
[[Tp_tuning|POT2 generator]]: ~7/6 = 270.093
 
[[Gencom|Gencom]]: [2 7/6; 176/175 540/539]
 
Gencom mapping: [&lt;1 -4/3 3 -1/3 5/3|, &lt;0 4/3 -3 7/3 -11/3|]
 
Mapping: [&lt;1 0 2 -2|, &lt;0 3 -1 5|]
 
EDOs: {{EDOs|9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.6028 cents
 
[[guanyintet5|Five note haplotonic scale]]
 
[[guanyintet9|Nine note albitonic scale]]
 
[[guanyintet13|Thirteen note chromatic scale]]


== Radon ==
== Radon ==
Line 697: Line 281:
[[File:radon_128edo.jpg|right|alt=radon_128edo.jpg|Radon in 128edo]]
[[File:radon_128edo.jpg|right|alt=radon_128edo.jpg|Radon in 128edo]]


* [[Radon5]] – 5-tone [[haplotonic scale]]
* [[Radon5]] – 5-tone haplotonic scale
* [[Radon11]] – 11-tone [[albitonic scale]]
* [[Radon11]] – 11-tone albitonic scale
* [[Radon16]] – 16-tone [[chromatic scale]]
* [[Radon16]] – 16-tone chromatic scale


== Gariberttet ==
== Gariberttet ==
Subgroup: 2.5/3.7/3.13/11
{{See also | Subgroup temperaments #Gariberttet }}


Commas: 275/273, 847/845
Scales:  
 
* [[Gariberttet5]] – 5-tone haplotonic scale
Svalname: 4&amp;29
* [[Gariberttet9]] – 9-tone albitonic scale
 
* [[Gariberttet13]] – 13-tone chromatic scale
[[Tp_tuning|POT2 generator]]: ~13/11 = 293.679
 
[[Gencom|Gencom]]: [2 13/11; 275/273 847/845]
 
Gencom mapping: [&lt;1 0 0 0 0 0|, &lt;0 -8/3 1/3 7/3 -1/2 1/2|]
 
Mapping: [&lt;1 0 0 0|, &lt;0 3 5 1|]
 
EDOs: {{EDOs|29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.6914 cents
 
[[gariberttet5|Five note haplotonic scale]]
 
[[gariberttet9|Nine note albitonic scale]]
 
[[gariberttet13|Thirteen note chromatic scale]]


== Namo ==
== Namo ==
Line 730: Line 297:


Scales:  
Scales:  
* [[namo7]]| – 7-tone [[haplotonic scale]]
* [[Namo7]] – 7-tone haplotonic scale
* [[namo10]] – 10-tone [[albitonic scale]]
* [[Namo10]] – 10-tone albitonic scale
* [[namo17]] – 17-tone [[chromatic scale]]
* [[Namo17]] – 17-tone chromatic scale


== Sentry ==
== Sentry ==
Subgroup: 2.5/3.9/7
{{See also | Subgroup temperaments #Sentry }}


Commas: 245/243
Scales:  
 
* [[Sentry5]] – 5-tone haplotonic scale
Svalname: 3&amp;5
* [[Sentry8]] – 8-tone albitonic scale
 
* [[Sentry11]] – 11-tone chromatic scale
Related temperaments: sensi
 
[[Tp_tuning|POT2 generator]]: ~9/7 = 440.902
 
[[Gencom|Gencom]]: [2 9/7; 245/243]
 
Gencom mapping: [&lt;1 0 0 0|, &lt;0 0 2 -1|]
 
Mapping: [&lt;1 0 0|, &lt;0 2 1|]
 
EDOs: {{EDOs|8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.7105 cents
 
[[sentry5|Five note haplotonic scale]]
 
[[sentry8|Eight note albitonic scale]]
 
[[sentry11|Eleven note note chromatic scale]]


== Hemif ==
== Hemif ==
Subgroup: 2.3.7.11.13
{{See also| No-fives subgroup temperaments #Hemif }}


Commas: 144/143, 243/242, 364/363
[[File:hemif_58edo.jpg|right|alt=hemif_58edo.jpg|Hemif in 58edo]]


Related temperament: [[Breedsmic_temperaments|Hemififths]], namo
Scales:  
 
* [[Hemif7]] – 7-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~11/9 = 351.691
* [[Hemif10]] – 10-tone albitonic scale
 
* [[Hemif17]] – 17-tone chromatic scale
[[Gencom|Gencom]]: [2 11/9; 144/143 243/242 364/363]
 
Gencom mapping: [&lt;1 1 0 -1 2 4|, &lt;0 2 0 13 5 -1|]
 
Mapping: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]
 
EDOs: {{EDOs|7, 10, 17, 24, 41, 58}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.7167 cents
 
[[File:hemif_58edo.jpg|alt=hemif_58edo.jpg|hemif_58edo.jpg]]
 
[[hemif7|Seven note haplotonic scale]]
 
[[hemif10|Ten note albitonic scale]]
 
[[hemif17|Seventeen note chromatic scale]]


== Garibaldi ==
== Garibaldi ==
Line 795: Line 326:


Scales:  
Scales:  
* [[Garibaldi12]] – 12-tone [[albitonic scale]]
* [[Garibaldi12]] – 12-tone albitonic scale
* [[Garibaldi17]] – 17-tone [[chromatic scale]]
* [[Garibaldi17]] – 17-tone chromatic scale


== Mabila ==
== Mabilic ==
Subgroup: 2.5.7
{{See also| No-threes subgroup temperaments #Mabilic }}


Comma: 1071875/1048576
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]]


Sval name: 7&amp;9
Scales:  
 
* [[Mabilic7]] – 7-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~175/128 = 527.236
* [[Mabilic9]] – 9-tone albitonic scale
 
* [[Mabilic16]] – 16-tone chromatic scale
[[Gencom|Gencom]]: [2 175/128; 1071875/1048576]
 
Gencom mapping: [&lt;1 0 1 5}, &lt;0, 0, 3, -5|]
 
Mapping: [&lt;1 1 5|, &lt;0 3 -5|]
 
EDOs: {{EDOs|7, 9, 16, 25, 41, 66, 305bc}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.7729 cents
 
[[File:mabila_66edo.jpg|alt=mabila_66edo.jpg|mabila_66edo.jpg]]
 
[[mabila7|Seven note haplotonic scale]]
 
[[mabila9|Nine note albitonic scale]]
 
[[mabila16|Sixteen note chromatic scale]]


== Indium ==
== Indium ==
Subgroup: 2.5/3.7/3.11/3
{{See also | Subgroup temperaments #Indium }}


Commas: 3025/3024, 3125/3087
[[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]]


Sval name: 8&amp;33
Scales:  
* [[Indium8]] – 8-tone albitonic scale
* [[Indium17]] – 17-tone chromatic scale


[[Tp_tuning|POT2 generator]]: ~12/11 = 147.010
; Music
 
* ''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]
[[Gencom|Gencom]]: [2 12/11; 3025/3024 3125/3087]
 
Gencom mapping: [&lt;1 -1/2 -1/2 -1/2 3/2|, &lt;0 -15/4 9/4 25/4 -19/4|]
 
Mapping: [&lt;1 0 0 2|, &lt;0 6 10 -1|]
 
EDOs: {{EDOs|33, 41, 49, 57, 106, 204, 253}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.7788 cents
 
[[File:indium_253edo.png|alt=indium_253edo.png|indium_253edo.png]]
 
[[indium8|Eight note albitonic scale]]
 
[[indium17|Seventeen note chromatic scale]]
 
=== Music ===
<span style=""><span style="">[http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3 The Cry of Indium]</span></span> (in Indium 17) by [http://www.chrisvaisvil.com/ Chris Vaisvil] =&gt; [http://chrisvaisvil.com/?p=1532 details]


== Starlingtet ==
== Starlingtet ==
Subgroup: 2.5/3.7/3
{{See also | Subgroup temperaments #Starlingtet }}


Comma: 126/125
Scales:  
 
* [[Starlingtet4]] – 4-tone haplotonic scale
Svalname: 4&amp;15
* [[Starlingtet7]] – 7-tone albitonic scale
 
* [[Starlingtet11]] – 11-tone chromatic scale
Related temperaments: starling; becomes myna
 
[[Tp_tuning|POT2 generator]]: ~6/5 = 311.154
 
[[Gencom|Gencom]]: [2 6/5; 126/125]
 
Gencom mapping: [&lt;1 -1 0 1|, &lt;0 4/3 1/3 -5/3|]
 
Mapping: [&lt;1 0 -1|, &lt;0 1 3|]
 
EDOs: {{EDOs|15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.8398 cents
 
[[starlingtet4|Four note haplotonic scale]]
 
[[starlingtet7|Seven note albitonic scale]]
 
[[starlingtet11|Eleven note chromatic scale]]


== Lovecraft ==
== Lovecraft ==
Subgroup: 2.11.13
{{See also | No-threes subgroup temperaments #Lovecraft }}


Commas: 1352/1331
[[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]]


[[Tp_tuning|POT2 generator]]: ~13/11 = 279.318
Scales:  
 
* [[Lovecraft5]] – 5-tone haplotonic scale
[[Gencom|Gencom]]: [2 13/11; 1352/1331]
* [[Lovecraft9]] – 9-tone albitonic scale
 
* [[Lovecraft13]] – 13-tone chromatic scale
Gencom mapping: [&lt;1 0 0 0 3 3|, &lt;0 0 0 0 2 3|]
 
Mapping: [&lt;1 1 0|, &lt;0 2 3|]
 
EDOS: {{EDOs|13, 30, 43, 73, 116b}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.8449 cents
 
[[File:lovecraft_116edo.png|alt=lovecraft_116edo.png|lovecraft_116edo.png]]
 
[[lovecraft5|Five note haplotonic scale]]
 
[[lovecraft9|Nine note albitonic scale]]
 
[[lovecraft13|Thirteen note chromatic scale]]


== Blackbirds ==
== Blackbirds ==
Subgroup: 2.11.13
{{See also | No-threes subgroup temperaments #Blackbirds }}


Comma: 29282/28561
Scales:  
 
* [[Blackbirds8]] – 8-tone albitonic scale
[[Tp_tuning|POT2 generator]]: ~11/8 = 546.660
* [[Blackbirds12]] – 12-tone chromatic scale
 
* [[Blackbirds16]] – 16-tone mega-chromatic scale
Gencom: [13/11 11/8; 29282/28561]
 
Gencom mapping: [&lt;4 0 0 0 12 13|, &lt;0 0 0 0 1 1|]
 
Mapping: [&lt;4 0 1|, &lt;0 1 1|]
 
EDOs: {{EDOs|4, 16, 20, 24, 44, 68, 112c, 180bc}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.8685 cents
 
[[blackbirds8|Eight note albitonic scale]]
 
[[blackbirds12|Twelve note chromatic scale]]
 
[[blackbirds16|Sixteen note mega chromatic scale]]


== Laz ==
== Laz ==
Subgroup: 2.5.7/3.11/3.13/3
{{See also | Subgroup temperaments #Laz }}


Commas: 144/143, 176/175, 196/195
Scales:  
 
* [[Laz5]] – 5-tone haplotonic scale
Related temperaments: [[Orwellismic_family#Guanyin-Georgian|georgian]], winston
* [[Laz9]] – 9-tone albitonic scale
 
* [[Laz13]] – 13-tone chromatic scale
[[Tp_tuning|POT2 generator]]: ~7/6 = 269.300
 
[[Gencom|Gencom]]: [2 7/6; 144/143 176/175 196/195]
 
Gencom mapping: [&lt;1 -5/4 3 -1/4 7/4 -1/4|, &lt;0 -1/4 -3 3/4 -21/4 19/4|]
 
Mapping: [&lt;1 0 2 -2 6|, &lt;0 3 -1 5 -5|]
 
EDOs: {{EDOs|9, 31, 40, 49, 58, 156bde, 205bde}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.8790 cents
 
[[laz5|Five note haplotonic scale]]
 
[[laz9|Nine note albitonic scale]]
 
[[laz13|Thirteen note chromatic scale]]


== Myna ==
== Myna ==
Line 960: Line 392:


Scales:  
Scales:  
* [[Myna7]] – 7-tone [[haplotonic scale]]
* [[Myna7]] – 7-tone haplotonic scale
* [[Myna11]] – 11-tone [[albitonic scale]]
* [[Myna11]] – 11-tone albitonic scale
* [[Myna15]] – 15-tone [[chromatic scale]]
* [[Myna15]] – 15-tone chromatic scale


== Greeley ==
== Greeley ==
Subgroup: 2.5/3.7/3.11/3
{{See also| Subgroup temperaments #Greeley }}


Commas: 121/120, 126/125
[[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]]


Related temperament: [[Porcupine_family#Opossum|Opossum]], [[Starling_temperaments#Nusecond temperament|Nusecond]]
Scales:  
* [[Greeley8]] – 8-tone albitonic scale
* [[Greeley15]] – 15-tone chromatic scale


[[Tp_tuning|POT2 generator]]: ~11/10 = 155.776
; Music
* ''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]


[[Gencom|Gencom]]: [2 11/10; 121/120 126/125]
== Ammon ==
{{See also| Subgroup temperaments #Ammon }}


Gencom mapping: &lt;1 -5/4 -1/4 3/4 3/4|, &lt;0 9/4 1/4 -15/4 5/4|]
[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]]


Mapping: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]
Scales:  
 
* [[Ammon8]] – 8-tone albitonic scale
EDOs: {{EDOs|8, 15, 23, 54, 77, 100, 131d, 208bd}}
* [[Ammon13]] – 13-tone chromatic scale
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.034 cents
 
[[File:greeley_100edo.png|alt=greeley_100edo.png|greeley_100edo.png]]
 
[[greeley8|Eight note albitonic scale]]
 
[[greeley15|Fifteen note chromatic scale]]
 
=== Music ===
<span style=""><span style="">[http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3 A Greeley Steals Halloween]</span></span> by [http://chrisvaisvil.com/?p=1485 Chris Vaisvil] in Greeley 15
 
== Semidim ==
Subgroup: 2.5/3.7/3.11/3.13/3
 
Commas: 121/120, 169/168, 275/273
 
Sval name: 8&amp;29
 
[[Tp_tuning|POT2 generator]]: ~13/10 = 453.242
 
[[Gencom|Gencom]]: [2 13/10; 121/120 169/168 275/273]
 
Gencom mapping: [&lt;1 -3 0 2 0 1|, &lt;0 24/5 -6/5 -26/5 9/5 -1/5|]
 
Mapping: [&lt;1 3 5 3 4|, &lt;0 -6 -10 -3 -5|]
 
EDOs: {{EDOs|5, 8, 13, 21, 29, 37, 44, 45, 188bde}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.052 cents
 
[[File:semidim_770edo.png|alt=semidim_770edo.png|semidim_770edo.png]]
 
[[semidim8|Eight note albitonic scale]]
 
[[semidim13|Thirteen note chromatic scale]]


== Mothwelltri ==
== Mothwelltri ==
Subgroup: 2.7/3.11
{{See also| Subgroup temperaments #Mothwelltri }}


Comma: 99/98
Scales:  
 
* [[Mothwelltri5]] – 5-tone haplotonic scale
Svalname: 1&amp;4
* [[Mothwelltri9]] – 9-tone albitonic scale
 
* [[Mothwelltri13]] – 13-tone chromatic scale
Related temperament: Orwell
 
[[Tp_tuning|POT2 generator]]: ~7/6 = 273.174
 
[[Gencom|Gencom]]: [2 7/6; 99/98]
 
Gencom mapping: [&lt;1 -1/2 0 1/2 3|, &lt;0 -1/2 0 1/2 2|]
 
Mapping: [&lt;1 0 1|, &lt;0 1 2|]
 
EDOs: {{EDOs|9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.064 cents
 
[[mothwelltri5|Five note haplotonic scale]]
 
[[mothwelltri9|Nine note albitonic scale]]
 
[[mothwelltri13|Thirteen note chromatic scale]]


== Sulis ==
== Sulis ==
Subgroup: 2.5.9/7.11/9
{{See also| Subgroup temperaments #Sulis }}


Commas: 99/98, 176/175
Scales:  
 
* [[Sulis7]] – 7-tone haplotonic scale
Related temperament: [[Marvel_family#Minerva|minerva]], würschmidt
* [[Sulis10]] – 10-tone albitonic scale
 
* [[Sulis13]] – 13-tone chromatic scale
[[Tp_tuning|POT2 generator]]: ~5/4 = 386.558
 
[[Gencom|Gencom]]: [2 5/4; 99/98 176/175]
 
Gencom mapping: [&lt;1 4/9 2 -1/9 -1/9|, &lt;0 -4/3 1 -2/3 4/3|]
 
Mapping: [&lt;1 0 5 -9|, &lt;0 1 -2 4|]
 
EDOs: {{EDOs|22, 25, 28, 31, 59, 90c, 149c}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.074 cents
 
[[sulis7|Seven note haplotonic scale]]
 
[[sulis10|Ten note albitonic scale]]
 
[[sulis13|Thirteen note chromatic scale]]


== Skwares ==
== Skwares ==
Subgroup: 2.3.7.11
{{Main| Squares }}
{{See also| No-fives subgroup temperaments #Skwares }}


Commas: 99/98, 243/242
[[File:skwares_206edo.png|right|alt=skwares_206edo.png|Skwares in 206edo]]


Related temperament: [[Meantone_family|squares]]
Scales:  
 
* [[Skwares8]] – 8-tone albitonic scale
[[Tp_tuning|POT2 generator]]: ~9/7 = 425.244
* [[Skwares11]] – 11-tone mega-albitonic scale
 
* [[Skwares14]] – 14-tone chromatic scale
[[Gencom|Gencom]]: [2 9/7; 99/98 243/242]
 
Gencom mapping: [&lt;1 3 0 6 7|, &lt;0 -4 0 -9 -10|]
 
Mapping: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]
 
EDOs: {{EDOs|5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.099 cents
 
[[File:skwares_206edo.png|alt=skwares_206edo.png|skwares_206edo.png]]
 
[[skwares8|Eight note albitonic scale]]
 
[[skwares11|Eleven note mega albitonic scale]]
 
[[skwares14|Fourteen note chromatic scale]]


== Orwell ==
== Orwell ==
Line 1,103: Line 451:


Scales:  
Scales:  
* [[Orwell5]] – 5-tone [[haplotonic scale]]
* [[Orwell5]] – 5-tone haplotonic scale
* [[Orwell9]] – 9-tone [[albitonic scale]]
* [[Orwell9]] – 9-tone albitonic scale
* [[Orwell13]] – 13-tone [[chromatic scale]]
* [[Orwell13]] – 13-tone chromatic scale


== Magicaltet ==
== Magicaltet ==
[[Subgroup]]: 2.5/3.7.11
{{See also| Subgroup temperaments #Magicaltet }}
 
[[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }}
 
{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
 
: mapping generators: ~2, ~5/3
 
{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
 
: [[gencom]]: [2 6/5; 100/99 385/384]
 
[[Optimal tuning]]s:
* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~5/3 = 877.3426
* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~5/3 = 877.351
 
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
 
<nowiki>*</nowiki> wart for 5/3
 
[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents
 
Related temperaments: [[supermagic]], [[superkleismic]], [[magic]]


Scales:  
Scales:  
* [[magicaltet7]] – 7-tone [[albitonic scale]]
* [[Magicaltet7]] – 7-tone albitonic scale
* [[magicaltet11]] – 11-tone [[chromatic scale]]
* [[Magicaltet11]] – 11-tone chromatic scale
* [[magicaltet15]] – 15-tone [[mega-chromatic scale]]
* [[Magicaltet15]] – 15-tone mega-chromatic scale


== Magic ==
== Magic ==
Line 1,144: Line 470:


Scales:  
Scales:  
* [[Magic7]] – 7-tone [[haplotonic scale]]
* [[Magic7]] – 7-tone haplotonic scale
* [[Magic10]] – 10-tone [[albitonic scale]]
* [[Magic10]] – 10-tone albitonic scale
* [[Magic13]] – 13-tone [[chromatic scale]]
* [[Magic13]] – 13-tone chromatic scale
* [[Magic16]] – 16-tone [[mega-chromatic scale]]
* [[Magic16]] – 16-tone mega-chromatic scale


== Kiribati ==
== Kiribati ==
Subgroup: 2.9/5.7/3.11/9
{{See also| Subgroup temperaments #Kiribati }}


Commas: 100/99, 245/242
Scales:  
 
* [[Kiribati13]] – 13-tone chromatic scale
Related temperament: [[Octagar_family|nakika]], octacot
* [[Kiribati14]] – 14-tone chromatic scale
 
[[Tp_tuning|POT2 generator]]: ~21/20 = 87.892
 
[[Gencom|Gencom]]: [2 21/20; 100/99 245/242]
 
Gencom mapping: [&lt;1 1/10 -4/5 11/10 1/5|, &lt;0 -3/2 -1 3/2 1|]
 
Mapping: [&lt;1 1 1 0|, &lt;0 -2 3 4|]
 
EDOs: {{EDOs|13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.245 cents
 
[[kiribati13|Thirteen note chromatic scale]]
 
[[kiribati14|Fourteen note chromatic scale]]


== Score ==
== Score ==
Subgroup: 2.7.11.13
{{See also|No-threes subgroup temperaments #Score }}


Commas: 343/338, 847/832
[[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]]


[[Tp_tuning|POT2 generator]]: ~11/8 = 540.099
Scales:  
 
* [[Score5]] – 5-tone haplotonic scale
[[Gencom|Gencom]]: [2 11/8; 343/338 847/832]
* [[Score7]] – 7-tone albitonic scale
 
* [[Score9]] – 9-tone mega-albitonic scale
Gencom mapping: [&lt;1 0 0 1 3 1|, &lt;0 0 0 4 1 6|]
* [[Score11]] – 11-tone chromatic scale
 
Mapping: [&lt;1 1 3 1|, &lt;0 4 1 6|]
 
EDOs: {{EDOs|5, 7, 9, 11, 20}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.282 cents
 
[[File:score_20edo.jpg|alt=score_20edo.jpg|score_20edo.jpg]]
 
[[score5|Five note haplotonic scale]]
 
[[score7|Seven note albitonic scale]]
 
[[score9|Nine note mega albitonic scale]]
 
[[score11|Eleven note chromatic scale]]


== Sensi ==
== Sensi ==
{{Main| Sensi }}
{{Main| Sensi }}
{{See also| Sensamagic clan #Sensi }}
{{See also| Sensipent family #Sensi }}
{{See also| Sensipent family #Sensi }}


Line 1,207: Line 500:


Scales:  
Scales:  
* [[Sensi5]] – 5-tone [[haplotonic scale]]
* [[Sensi5]] – 5-tone haplotonic scale
* [[Sensi8]] – 8-tone [[albitonic scale]]
* [[Sensi8]] – 8-tone albitonic scale
* [[Sensi11]] – 11-tone [[mega-albitonic scale]]
* [[Sensi11]] – 11-tone mega-albitonic scale
* [[Sensi19]] – 19-tone [[chromatic scale]]
* [[Sensi19]] – 19-tone chromatic scale


=== Sensation ===
=== Sensation ===
{{Main| Sensi }}
{{Main| Sensi }}
{{See also| Sensamagic clan #Sensi }}
{{See also| Sensipent family #Sensi }}
{{See also| Sensipent family #Sensi }}


Scales:  
Scales:  
* [[Sensi5]] – 5-tone [[haplotonic scale]]
* [[Sensi5]] – 5-tone haplotonic scale
* [[Sensi8]] – 8-tone [[albitonic scale]]
* [[Sensi8]] – 8-tone albitonic scale
* [[Sensi11]] – 11-tone [[mega-albitonic scale]]
* [[Sensi11]] – 11-tone mega-albitonic scale
* [[Sensi19]] – 19-tone [[chromatic scale]]
* [[Sensi19]] – 19-tone chromatic scale


== Meantone ==
== Meantone ==
Line 1,230: Line 522:


Scales:  
Scales:  
* [[Meantone5]] – 5-tone [[haplotonic scale]]
* [[Meantone5]] – 5-tone haplotonic scale
* [[Meantone7]] – 7-tone [[albitonic scale]]
* [[Meantone7]] – 7-tone albitonic scale
* [[Meantone12]] – 12-tone [[chromatic scale]]
* [[Meantone12]] – 12-tone chromatic scale


== Mohaha ==
== Mohaha ==
Line 1,240: Line 532:


Scales:  
Scales:  
* [[Mohaha7]] – 7-tone [[albitonic scale]]
* [[Mohaha7]] – 7-tone albitonic scale
* [[Mohaha10]] – 10-tone [[chromatic scale]]
* [[Mohaha10]] – 10-tone chromatic scale


Music:  
Music:  
Line 1,251: Line 543:


== Joan ==
== Joan ==
Subgroup: 2.9.7.11
{{See also| Subgroup temperaments #Joan }}


Commas: 99/98, 9317/9216
Scales:  
 
* [[Joan5]] – 5-tone haplotonic scale
Related temperaments: casablanca, orwell
* [[Joan7]] – 7-tone albitonic scale
 
* [[Joan9]] – 9-tone mega-albitonic scale
[[Tp_tuning|POT2 generator]]: ~11/8 = 542.672 cents
* [[Joan11]] – 11-tone chromatic scale
 
Gencom: [2 11/8; 99/98 9317/9216]
 
Gencom mapping: [&lt;1 0 0 1 3|, &lt;0 7/2 0 4 1|]
 
Mapping: [&lt;1 0 1 3|, &lt;0 7 4 1|]
 
EDOs: {{EDOs|11, 20, 31, 42, 115bd, 157bd}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.424 cents
 
[[joan5|Five note haplotonic scale]]
 
[[joan7|Seven note albitonic scale]]
 
[[joan9|Nine note mega albitonic scale]]
 
[[joan11|Eleven note chromatic scale]]


== Tutone ==
== Tutone ==
Line 1,283: Line 557:


Scales:  
Scales:  
* [[Tutone6]] – 6-tone [[haplotonic scale]]
* [[Tutone6]] – 6-tone haplotonic scale
* [[Tutone7]] – 7-tone [[albitonic scale]]
* [[Tutone7]] – 7-tone albitonic scale
* [[Tutone13]] – 13-tone [[chromatic scale]]
* [[Tutone13]] – 13-tone chromatic scale


== Stacks ==
== Stacks ==
Subgroup: 2.9.15.7.11.13
{{See also|Subgroup temperaments #Stacks (a.k.a. 2magic) }}


Commas: 100/99, 105/104, 144/143, 196/195
Scales:  
 
* [[Stacks5]] – 5-tone haplotonic scale
Related temperament: [[Magic_family#Magic-13-limit|magic]]
* [[Stacks8]] – 8-tone albitonic scale
 
* [[Stacks11]] – 11-tone chromatic scale
Svalname: 11&amp;30
* [[Stacks19]] – 19-tone mega-chromatic scale
 
[[Tp_tuning|POT2 generator]]: ~9/7 = 439.146
 
[[Gencom|Gencom]]: [2 9/7; 100/99 105/104 144/143 196/195]
 
Gencom mapping: [&lt;1 5/2 5/2 5 2 7|, &lt;0 -5/2 -1/2 -6 4 -9|]
 
Mapping: [&lt;1 0 2 -1 6 -2|, &lt;0 5 3 6 -4 9|]
 
EDOs: {{EDOs|11, 30, 41, 153cdef, 194cdef, 235cdef}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.540 cents
 
[[stacks5|Five note haplotonic scale]]
 
[[stacks8|Eight note albitonic scale]]
 
[[stacks11|Eleven note note chromatic scale]]
 
[[stacks19|Nineteen note note mega chromatic scale]]


== Bleu ==
== Bleu ==
Subgroup: 2.3.7.11.13
{{See also| No-fives subgroup temperaments #Bleu }}


Commas: 78/77, 99/98, 144/143
Scales:  
 
* [[Bleu8]] – 8-tone haplotonic scale
Sval name: 9&amp;17
* [[Bleu9]] – 9-tone albitonic scale
 
* [[Bleu17]] – 17-tone chromatic scale
[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990
 
[[Gencom|Gencom]]: [2 13/12; 78/77 99/98 144/143]
 
Gencom mapping: [&lt;1 1 0 2 3 3|, &lt;0 5 0 7 4 6|]
 
Mapping: [&lt;1 1 2 3 3|, &lt;0 5 7 4 6|]
 
EDOs: [[17edo|17]], [[43edo|43]], [[60edo|60c]]
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.752 cents
 
[[File:blue_60edo.png|alt=blue_60edo.png|blue_60edo.png]]
 
[[bleu8|bleu8]] - Eight note [[haplotonic_scale|haplotonic scale]]
 
[[bleu9|bleu9]] - Nine note [[albitonic_scale|albitonic scale]]
 
[[bleu17|bleu17]] - Seventeen note [[chromatic_scale|chromatic scale]]
 
[http://micro.soonlabel.com/temperaments/Bleu/20131103_2-11-13-subgroup-Bleu17_a-well-worn-riff.mp3 On a Well Worn Riff (Bleu 17)] by [http://chrisvaisvil.com/on-a-well-worn-riff-bleu-17/ Chris Vaisvil]


== Sephiroth ==
== Sephiroth ==
Subgroup: 2.5.11.13.17
{{See also| No-threes subgroup temperaments #Sephiroth }}


Commas: 65/64, 170/169, 221/220
Scales:  
 
* [[Sephiroth7]] – 7-tone haplotonic scale
Related temperament: [[Muggles]]
* [[Sephiroth10]] – 10-tone albitonic scale
 
* [[Sephiroth13]] – 13-tone chromatic scale
[[Tp_tuning|POT2 generator]]: ~5/4 = 372.236
* [[Sephiroth16]] – 16-tone mega-chromatic scale
 
[[Gencom|Gencom]]: [2 5/4; 65/64 170/169 221/220]
 
Gencom mapping: [&lt;1 0 2 0 5 4 5|, &lt;0 0 1 0 -5 -1 -3|]
 
Mapping: [&lt;1 0 15 6 11|, &lt;0 1 -5 -1 -3|]
 
EDOs: {{EDOs|10, 13, 16, 29}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.774 cents
 
[[sephiroth7|Seven note haplotonic scale]]
 
[[sephiroth10|Ten note albitonic scale]]
 
[[sephiroth13|Thirteen note chromatic scale]]
 
[[sephiroth16|Sixteen note mega chromatic scale]]


== Archy ==
== Archy ==
Line 1,377: Line 592:


Scales:  
Scales:  
* [[Archy5|5-tone haplotonic scale]]
* [[Archy5]] – 5-tone haplotonic scale
* [[Archy7|7-tone albitonic scale]]
* [[Archy7]] – 7-tone albitonic scale
* [[Archy12|12-tone chromatic scale]]
* [[Archy12]] – 12-tone chromatic scale


=== Supra ===
=== Supra ===
Line 1,399: Line 614:


Scales:  
Scales:  
* [[Suhajira7]] – 7-tone [[haplotonic scale]]
* [[Suhajira7]] – 7-tone haplotonic scale
* [[Suhajira10]] – 10-tone [[albitonic scale]]
* [[Suhajira10]] – 10-tone albitonic scale
* [[Suhajira17]] – 17-tone [[chromatic scale]]
* [[Suhajira17]] – 17-tone chromatic scale


== Machine ==
== Machine ==
Subgroup: 2.9.7.11
{{See also| Subgroup temperaments #Machine}}


Commas: 64/63, 99/98
[[File:machine_28edo.png|right|alt=machine_28edo.png|Machine in 28edo]]


[[Tp_tuning|POT2 generator]]: ~9/8 = 214.384
Scales:  
 
* [[Machine5]] – 5-tone haplotonic scale
[[Gencom|Gencom]]: [2 9/8; 64/63 99/98]
* [[Machine6]] – 6-tone albitonic scale
 
* [[Machine11]] – 11-tone chromatic scale
Gencom mapping: [&lt;1 3/2 0 3 4|, &lt;0 1/2 0 -1 -3|]
 
Mapping: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]
 
EDOs: {{EDOs|5, 6, 11, 17, 28}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.977 cents
 
[[File:machine_28edo.png|alt=machine_28edo.png|machine_28edo.png]]
 
[[machine5|Five note haplotonic scale]]
 
[[machine6|Six note albitonic scale]]
 
[[machine11|Eleven note chromatic scale]]


== Deutone ==
== Deutone ==
Subgroup: 2.9.5.7.13
{{See also| Hemimean clan #Deutone }}


Commas: 65/64, 81/80, 91/90
[[File:deutone_44edo.png|right|alt=deutone_44edo.png|Deutone in 44edo]]


Related temperament: [[Meantone_family|meanpop]]
Scales:  
 
* [[Deutone6]] – 6-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~9/8 = 191.059
* [[Deutone7]] – 7-tone albitonic scale
 
* [[Deutone13]] – 13-tone chromatic scale
[[Gencom|Gencom]]: [2 9/8; 65/64 81/80 91/90]
 
Gencom mapping: [&lt;1 3/2 2 2 0 4|, &lt;0 1/2 2 5 0 -2|]
 
Mapping: [&lt;1 0 -4 -13 10|, &lt;0 1 2 5 -2|]
 
EDOs: {{EDOs|6, 7, 13, 19, 25e, 44de}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.003 cents
 
[[File:deutone_44edo.png|alt=deutone_44edo.png|deutone_44edo.png]]
 
[[deutone6|Six note haplotonic scale]]
 
[[deutone7|seven note albitonic scale]]
 
[[deutone13|Thirteen note chromatic scale]]


== Negra ==
== Negra ==
Line 1,464: Line 647:


Scales:  
Scales:  
* [[Porkypine7]] – 7-tone [[haplotonic scale]]
* [[Porkypine7]] – 7-tone haplotonic scale
* [[Porkypine8]] – 8-tone [[albitonic scale]]
* [[Porkypine8]] – 8-tone albitonic scale
* [[Porkypine15]] – 15-tone [[chromatic scale]]
* [[Porkypine15]] – 15-tone chromatic scale


== Skateboard ==
== Skateboard ==
Subgroup: 2.5/3.7/3.11.13/9
{{See also| Subgroup temperaments #Skateboard }}


Commas: 56/55, 91/90, 100/99
Scales:  
 
* [[Skateboard7]] – 7-tone haplotonic scale
Related temperament: [[Starling_family#Thrasher-13-limit|thrasher]]
* [[Skateboard11]] – 11-tone albitonic scale
 
* [[Skateboard15]] – 15-tone chromatic scale
[[Tp_tuning|POT2 generator]]: ~6/5 = 313.842
 
[[Gencom|Gencom]]: [2 6/5; 56/55 91/90 100/99]
 
Gencom mapping: [&lt;1 -3/7 4/7 11/7 4 -6/7|, &lt;0 0 -1 -3 -2 2|]
 
Mapping: [&lt;1 0 -1 2 2|, &lt;0 1 3 2 -2|]
 
EDOs: {{EDOs|11, 15, 19, 23, 42d, 65d}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.396 cents
 
[[skateboard7|Seven note haplotonic scale]]
 
[[skateboard11|Eleven note albitonic scale]]
 
[[skateboard15|Fifteen note chromatic scale]]


== Augment ==
== Augment ==
Subgroup: 2.5.7.11
{{See also| No-threes subgroup temperaments #Augment }}


Commas: 56/55, 128/125
[[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]]


Related temperament: [[Augmented_family|augmented]]
Scales:  
 
* [[Augment6]] – 6-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~8/7 = 228.275
* [[Augment9]] – 9-tone albitonic scale
 
* [[Augment12]] – 12-tone chromatic scale
[[Gencom|Gencom]]: [5/4 8/7; 56/55 128/125]
 
Gencom mapping: [&lt;3 0 7 9 11|, &lt;0 0 0 -1 -1|]
 
Mapping: [&lt;3 7 0 2|, &lt;0 0 1 1|]
 
EDOs: {{EDOs|3, 6, 9, 15, 21}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.422 cents
 
[[File:augment_21edo.png|alt=augment_21edo.png|augment_21edo.png]]
 
[[augment6|Six note haplotonic scale]]
 
[[augment9|Nine note albitonic scale]]
 
[[augment12|Twelve note chromatic scale]]


== Semaphore ==
== Semaphore ==
{{Main| Semaphore and godzilla }}
{{Main| Semaphore and godzilla }}
{{See also| Slendro clan #Semaphore }}
{{See also| Semaphoresmic clan #Semaphore }}


[[File:semaphore_24edo.png|right|alt=semaphore_24edo.png|Semaphore in 24edo]]
[[File:semaphore_24edo.png|right|alt=semaphore_24edo.png|Semaphore in 24edo]]


Scales:  
Scales:  
* [[Semaphore5]] – 5-tone [[haplotonic scale]]
* [[Semaphore5]] – 5-tone haplotonic scale
* [[Semaphore9]] – 9-tone [[albitonic scale]]
* [[Semaphore9]] – 9-tone albitonic scale
* [[Semaphore14]] – 14-tone [[chromatic scale]]
* [[Semaphore14]] – 14-tone chromatic scale


== Kryptonite ==
== Kryptonite ==
Subgroup: 2.5.7/3.11/3.13/3
{{See also| Subgroup temperaments #Kryptonite }}


Commas: 56/55, 78/77, 91/90
Scales:  
 
* [[Kryptonite9]] – 9-tone albitonic scale
Related temperaments: [[Sengic_family|krypton]]
* [[Kryptonite10]] – 10-tone albitonic scale
 
* [[Kryptonite19]] – 19-tone mega-chromatic scale
[[Tp_tuning|POT2 generator]]: ~13/12 = 132.428
 
[[Gencom|Gencom]]: [2 13/12; 56/55 78/77 91/90]
 
Gencom mapping: [&lt;1 -5/4 2 -1/4 3/4 3/4|, &lt;0 -1/2 3 3/2 -3/2 1/2|]
 
Mapping: [&lt;1 2 1 2 2|, &lt;0 -3 -2 1 -1|]
 
EDOs: {{EDOs|9, 63, 82bd, 91bde}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.545 cents
 
[[kryptonite9|Nine note albitonic scale]]
 
[[kryptonite10|Ten note albitonic scale]]
 
[[kryptonite19|Nineteen note mega chromatic scale]]


== Oregon ==
== Oregon ==
Subgroup: 2.9.15.7.11
{{See also| Orgonia #Oregon }}


Commas: 55/54, 64/63, 100/99
Scales:  
 
* [[Oregon7]] – 7-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~6/5 = 325.495
* [[Oregon11]] – 11-tone albitonic scale
 
* [[Oregon15]] – 15-tone chromatic scale
[[Gencom|Gencom]]: [2 6/5; 55/54 64/63 100/99]
 
Gencom mapping: [&lt;1 2 3 2 4|, &lt;0 -3/2 -5/2 3 -2|]
 
Mapping: [&lt;1 1 1 5 2|, &lt;0 3 4 -3 2|]
 
EDOs: {{EDOs|7, 11, 37b, 48b, 59b}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.550 cents
 
[[oregon7|Seven note haplotonic scale]]
 
[[oregon11|Eleven note albitonic scale]]
 
[[oregon15|Fifteen note chromatic scale]]


== Antikythera ==
== Antikythera ==
Subgroup: 2.9.5.7
{{See also| Jubilismic clan #Antikythera }}


Commas: 50/49, 64/63
[[File:antikythera_28edo.png|right|alt=antikythera_28edo.png|Antikythera in 28edo]]


Related temperament: [[pajara|pajara]]
Scales:  
 
* [[Antikythera6]] – 6-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~8/7 = 214.095
* [[Antikythera10]] – 10-tone albitonic scale
 
* [[Antikythera16]] – 16-tone chromatic scale
[[Gencom|Gencom]]: [7/5 8/7; 50/49 64/63]
 
Gencom mapping: [&lt;2 3 5 6|, &lt;0 1/2 -1 -1|]
 
Mapping: [&lt;2 0 11 12|, &lt;0 1 -1 -1|]
 
EDOS: {{EDOs|4, 6, 10, 16, 22, 28}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.572 cents
 
[[File:antikythera_28edo.png|alt=antikythera_28edo.png|antikythera_28edo.png]]
 
[[antikythera6|Six note haplotonic scale]]
 
[[antikythera10|Ten note albitonic scale]]
 
[[antikythera16|Sixteen note chromatic scale]]


== Glacial ==
== Glacial ==
Subgroup: 2.9.5.11.13
{{See also| Subgroup temperaments #Glacial }}


Commas: 45/44, 65/64, 81/80
Scales:  
 
* [[Glacial6]] – 6-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~9/8 = 186.151
* [[Glacial7]] – 7-tone albitonic scale
 
* [[Glacial13]] – 13-tone chromatic scale
[[Gencom|Gencom]]: [2 9/8; 45/44 65/64 81/80]
 
Gencom mapping: [&lt;1 3/2 2 0 3 4|, &lt;0 1/2 2 0 3 -2|]
 
Mapping: [&lt;1 0 -4 -6 10|, &lt;0 1 2 3 -2|]
 
EDOs: {{EDOs|6, 13, 45be, 58bce, 71bce, 84bce}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.887 cents
 
[[glacial6|Six note haplotonic scale]]
 
[[glacial7|Seven note albitonic scale]]
 
[[glacial13|Thirteen note chromatic scale]]


== Leantone ==
== Leantone ==
Subgroup: 2.9.5.7.11
{{See also| Hemimean clan #Leantone }}


Commas: 45/44, 56/55, 81/80
[[File:leantone_81edo.png|right|alt=leantone_81edo.png|Leantone in 81edo]]


Related temperament: [[Meanenneadecal|meanenneadecal]]
Scales:  
* [[Leantone6]] – 6-tone haplotonic scale
* [[Leantone7]] – 7-tone albitonic scale
* [[Leantone13]] – 13-tone chromatic scale


[[Tp_tuning|POT2 generator]]: ~9/8 = 192.500
== Notes ==
 
[[Gencom|Gencom]]: [2 9/8; 45/44 56/55 81/80]
 
Gencom mapping: [&lt;1 3/2 2 2 3|, &lt;0 1/2 2 5 3|]
 
Mapping: [&lt;1 0 -4 -13 -6|, &lt;0 1 2 5 3|]
 
EDOs: {{EDOs|6, 7, 13, 19, 25, 31, 56, 81}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 3.882 cents
 
[[File:leantone_81edo.png|alt=leantone_81edo.png|leantone_81edo.png]]
 
* [[leantone6|Six note haplotonic scale]]
* [[leantone7|Seven note albitonic scale]]
* [[leantone13|Thirteen note chromatic scale]]


[[Category:Lists of scales]]
[[Category:Lists of scales]]
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[[Category:Listen]]
[[Category:Rank 2]]
[[Category:Rank 2]]
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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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