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Chromatic pairs: Difference between revisions

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== Terrain ==
== Terrain ==
{{Redirect|Terrain|the scale|Terrain (scale)}}
{{See also| Subgroup temperaments #Terrain }}
{{See also| Subgroup temperaments #Terrain }}


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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]] ([[Tp tuning|subgroup]] [[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]]
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== Barton ==
== Barton ==
{{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}}
{{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}}
 
{{See also| The Jacobins #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>.
 
[[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:  
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* [[Barton11]] – 11-tone chromatic scale
* [[Barton11]] – 11-tone chromatic scale
* [[Barton13]] – 13-tone mega-chromatic scale
* [[Barton13]] – 13-tone mega-chromatic scale
== 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 }}
[[Tp tuning #T2 tuning|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]] ([[Tp tuning|subgroup]] [[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]]
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== 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]]
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== 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]] ([[Tp tuning|subgroup]] [[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]]
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== Cata ==
== Cata ==
{{Main| Hanson and cata }}
{{Main| Kleismic }}
{{See also| Kleismic family #Cata }}
{{See also| Kleismic family #Cata }}


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== 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]] ([[Tp tuning|subgroup]] [[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]]
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== 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]] ([[Tp tuning|subgroup]] [[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:  
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== 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]]
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== 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]] ([[Tp tuning|subgroup]] [[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:  
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== 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]] ([[Tp tuning|subgroup]] [[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]]
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== 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:  
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== 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]]
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== Bluebirds ==
== Bluebirds ==
[[Subgroup]]: 2.11.13
{{See also| No-threes subgroup temperaments #Bluebirds }}
 
[[Comma list]]: [[265837/262144]]
 
{{Mapping|legend=2| 1 0 6 | 0 3 -2 }}
 
{{Mapping|legend=3| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }}
 
: [[gencom]]: [2 143/128; 265837/262144]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~143/128 = 182.368
 
{{Optimal ET sequence|legend=1| 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4444 cents


Scales:  
Scales:  
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== Marveltri ==
== Marveltri ==
Marveltri, the 3 &amp; 13 temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed 22 &amp; 47 temperament.
{{See also| Subgroup temperaments #Marveltri }}
 
[[Subgroup]]: 2.5.9/7
 
[[Comma list]]: [[225/224]]
 
{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
 
{{Mapping|legend=3| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }}
 
: [[gencom]]: [2 5/4; 225/224]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~5/4 = 383.638
 
{{Optimal ET sequence|legend=1| 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents


Scales:  
Scales:  
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== Edson ==
== Edson ==
Edson is related to [[pele]] and [[andromeda]].
{{See also| Subgroup temperaments #Edson }}
 
[[Subgroup]]: 2.3.7/5.11/5.13/5
 
[[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


Scales:  
Scales:  
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== Silver ==
== Silver ==
Silver can be described as the 10 &amp; 27 temperament in the 2.5.7.13.17 subgroup.
{{See also | No-threes subgroup temperaments #Silver }}
 
[[Subgroup]]: 2.5.7.13.17
 
[[Comma list]]: [[170/169]], [[640/637]], [[5525/5488]]
 
{{Mapping|legend=2| 1 5 4 4 2 | 0 -9 -4 -1 7 }}
 
{{Mapping|legend=3| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}
 
: [[gencom]]: [2 13/8; 170/169 640/637 5525/5488]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/8 = 842.711
 
{{Optimal ET sequence|legend=1| 7, 10, 17, 27, 37, 47, 84, 131, 178e, 309cde, 487bcdee }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.5886 cents


[[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]]
[[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]]
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== Baldy ==
== Baldy ==
{{See also| Subgroup temperaments #Baldy }}
{{See also| Subgroup temperaments #Baldy }}
Baldy is every other step of [[garibaldi]], without the mapping of prime 11. It can be described as the 6 &amp; 35 temperament.
[[Subgroup]]: 2.9.5.7.13
[[Comma list]]: [[225/224]], [[325/324]], [[640/637]]
{{Mapping|legend=2| 1 0 15 25 -28 | 0 1 -4 -7 10 }}
{{Mapping|legend=3| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }}
: [[gencom]]: [2 9/8; 225/224 325/324 640/637]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.090
{{Optimal ET sequence|legend=1| 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|right|alt=baldy_147edo.jpg|Baldy in 147edo]]
[[File:baldy_147edo.jpg|right|alt=baldy_147edo.jpg|Baldy in 147edo]]
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* [[Baldy11]] – 11-tone albitonic scale
* [[Baldy11]] – 11-tone albitonic scale
* [[Baldy17]] – 17-tone chromatic scale
* [[Baldy17]] – 17-tone chromatic scale


== Guanyintet ==
== Guanyintet ==
Guanyintet, the 4 &amp; 9 temperament in the 2.5.7/3.11/3 subgroup, is related to [[guanyin]] as well as to [[orwell]].
{{See also | Subgroup temperaments #Guanyintet }}
 
[[Subgroup]]: 2.5.7/3.11/3
 
[[Comma list]]: [[176/175]], [[540/539]]
 
{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}
 
{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}
 
: [[gencom]]: [2 7/6; 176/175 540/539]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 270.093
 
{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents


Scales:  
Scales:  
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== Gariberttet ==
== Gariberttet ==
Gariberttet can be described as the 4 &amp; 29 temperament in the 2.5/3.7/3.13/11 subgroup.
{{See also | Subgroup temperaments #Gariberttet }}
 
[[Subgroup]]: 2.5/3.7/3.13/11
 
[[Comma list]]: [[275/273]], [[847/845]]
 
{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
 
{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}
 
: [[gencom]]: [2 13/11; 275/273 847/845]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/11 = 293.679
 
{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents


Scales:  
Scales:  
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== Sentry ==
== Sentry ==
Sentry, the 3 &amp; 5 temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
{{See also | Subgroup temperaments #Sentry }}
 
[[Subgroup]]: 2.5/3.9/7
 
[[Comma list]]: [[245/243]]
 
{{Mapping|legend=2| 1 0 0 | 0 2 1 }}
 
{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
 
: [[gencom]]: [2 9/7; 245/243]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~9/7 = 440.902
 
{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents


Scales:  
Scales:  
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== Mabilic ==
== Mabilic ==
Given below is the no-three version of [[Mabila family#Semabila|semabila]], or equivalently the no-threes version of [[Magic family#Trismegistus|trismegistus]]. It is the 7 &amp; 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.
{{See also| No-threes subgroup temperaments #Mabilic }}


[[Subgroup]]: 2.5.7
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]]
 
[[Comma list]]: 1071875/1048576
 
{{Mapping|legend=2| 1 1 5 | 0 3 -5 }}
 
{{Mapping|legend=3| 1 0 1 5 | 0 0 3 -5 }}
 
: [[gencom]]: [2 175/128; 1071875/1048576]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~175/128 = 527.236
 
{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41, 66, 305bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.7729 cents
 
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabila in 66edo]]


Scales:  
Scales:  
* [[Mabila7]] – 7-tone haplotonic scale
* [[Mabilic7]] – 7-tone haplotonic scale
* [[Mabila9]] – 9-tone albitonic scale
* [[Mabilic9]] – 9-tone albitonic scale
* [[Mabila16]] – 16-tone chromatic scale
* [[Mabilic16]] – 16-tone chromatic scale


== Indium ==
== Indium ==
Indium can be described as the 8 &amp; 33 temperament in the 2.5/3.7/3.11/3 subgroup.
{{See also | Subgroup temperaments #Indium }}
 
[[Subgroup]]: 2.5/3.7/3.11/3
 
[[Comma list]]: [[3025/3024]], [[3125/3087]]
 
{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
 
{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}
 
: [[gencom]]: [2 12/11; 3025/3024 3125/3087]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~12/11 = 147.010
 
{{Optimal ET sequence|legend=1| 33, 41, 49, 57, 106, 204, 253 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents


[[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]]
[[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]]
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== Starlingtet ==
== Starlingtet ==
Starlingtet, the 4 &amp; 15 temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]].
{{See also | Subgroup temperaments #Starlingtet }}
 
[[Subgroup]]: 2.5/3.7/3
 
[[Comma list]]: [[126/125]]
 
{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
 
{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
 
: [[gencom]]: [2 6/5; 126/125]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 311.154
 
{{Optimal ET sequence|legend=1| 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents


Scales:  
Scales:  
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== Lovecraft ==
== Lovecraft ==
Lovecraft, the 4 & 13 temperament in the 2.11.13 subgroup, is generated by ~13/11. Two generator steps give ~11/8 and three generator steps give ~13/8.
{{See also | No-threes subgroup temperaments #Lovecraft }}
 
[[Subgroup]]: 2.11.13
 
[[Comma list]]: [[1352/1331]]
 
{{Mapping|legend=2| 1 3 3 | 0 2 3 }}
 
{{Mapping|legend=3| 1 0 0 0 3 3 | 0 0 0 0 2 3 }}
 
: [[gencom]]: [2 13/11; 1352/1331]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/11 = 279.318
 
{{Optimal ET sequence|legend=1| 13, 30, 43, 73, 116b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8449 cents


[[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]]
[[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]]
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== Blackbirds ==
== Blackbirds ==
Blackbirds is a fairly straightforward temperament. It simply equates ~13/11 to 1/4 of the octave with a generator for prime 11 or 13.
{{See also | No-threes subgroup temperaments #Blackbirds }}
 
[[Subgroup]]: 2.11.13
 
[[Comma list]]: [[29282/28561]]
 
{{Mapping|legend=2| 4 0 1 | 0 1 1 }}
 
{{Mapping|legend=3| 4 0 0 0 12 13 | 0 0 0 0 1 1 }}
 
: [[gencom]]: [13/11 11/8; 29282/28561]
 
[[Optimal tuning]] ([[POTE]]): ~13/11 = 1\4, ~11/8 = 546.660
 
{{Optimal ET sequence|legend=1| 4, 16, 20, 24, 44, 68, 112c, 180bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8685 cents


Scales:  
Scales:  
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== Laz ==
== Laz ==
Laz is related to [[georgian]] as well as to [[winston]].
{{See also | Subgroup temperaments #Laz }}
 
[[Subgroup]]: 2.5.7/3.11/3.13/3
 
[[Comma list]]: [[144/143]], [[176/175]], [[196/195]]
 
{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
 
{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}
 
: [[gencom]]: [2 7/6; 144/143 176/175 196/195]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300
 
{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 58, 156bde, 205bde }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents


Scales:  
Scales:  
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== Greeley ==
== Greeley ==
Greeley is related to [[opossum]] as well as to [[nusecond]].
{{See also| Subgroup temperaments #Greeley }}
 
[[Subgroup]]: 2.5/3.7/3.11/3
 
[[Comma list]]: [[121/120]], [[126/125]]
 
{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1}}
 
{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}
 
: [[gencom]]: [2 11/10; 121/120 126/125]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~11/10 = 155.776
 
{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131d, 208bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents


[[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]]
[[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]]
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* ''A Greeley Steals Halloween'' by [[Chris Vaisvil]] (2011) – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201201174756/http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3 play] – in Greeley[15]
* ''A Greeley Steals Halloween'' by [[Chris Vaisvil]] (2011) – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201201174756/http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3 play] – in Greeley[15]


== Semidim ==
== Ammon ==
Semidim can be described as the 8 &amp; 29 temperament in the 2.5/3.7/3.11/3.13/3 subgroup.
{{See also| Subgroup temperaments #Ammon }}
 
[[Subgroup]]: 2.5/3.7/3.11/3.13/3
 
[[Comma list]]: [[121/120]], [[169/168]], [[275/273]]
 
{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
 
{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}


: [[gencom]]: [2 13/10; 121/120 169/168 275/273]
[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 453.242
 
{{Optimal ET sequence|legend=1| 5, 8, 13, 21, 29, 37, 44, 45, 188bde }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
 
[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Semidim in 770edo]]


Scales:  
Scales:  
* [[Semidim8]] – 8-tone albitonic scale
* [[Ammon8]] – 8-tone albitonic scale
* [[Semidim13]] – 13-tone chromatic scale
* [[Ammon13]] – 13-tone chromatic scale


== Mothwelltri ==
== Mothwelltri ==
Mothwelltri, the 1 &amp; 4 temperament in the 2.7/3.11 subgroup, is related to [[orwell]].
{{See also| Subgroup temperaments #Mothwelltri }}
 
[[Subgroup]]: 2.7/3.11
 
[[Comma list]]: [[99/98]]
 
{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
 
{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
 
: [[gencom]]: [2 7/6; 99/98]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 273.174
 
{{Optimal ET sequence|legend=1| 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents


Scales:  
Scales:  
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== Sulis ==
== Sulis ==
Sulis is related to [[minerva]] as well as to [[würschmidt]].
{{See also| Subgroup temperaments #Sulis }}
 
[[Subgroup]]: 2.5.9/7.11/9
 
[[Comma list]]: [[99/98]], [[176/175]]
 
{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}
 
{{Mapping|legend=3| 1 4/9 2 -1/9 -1/9 | 0 -4/3 1 -2/3 4/3 }}
 
: [[gencom]]: [2 5/4; 99/98 176/175]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~5/4 = 386.558
 
{{Optimal ET sequence|legend=1| 22, 25, 28, 31, 59, 90c, 149c }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents


Scales:  
Scales:  
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== Magicaltet ==
== Magicaltet ==
Magicaltet is related to [[supermagic]], [[superkleismic]], and [[magic]].
{{See also| Subgroup temperaments #Magicaltet }}
 
[[Subgroup]]: 2.5/3.7.11
 
[[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


Scales:  
Scales:  
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== Kiribati ==
== Kiribati ==
Kiribati is related to [[nakika]] as well as to [[octacot]].
{{See also| Subgroup temperaments #Kiribati }}
 
[[Subgroup]]: 2.9/5.7/3.11/9
 
[[Comma list]]: 100/99, 245/242
 
{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
 
{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
 
: [[gencom]]: [2 21/20; 100/99 245/242]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892
 
{{Optimal ET sequence|legend=1| 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents


Scales:  
Scales:  
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== Score ==
== Score ==
[[Subgroup]]: 2.7.11.13
{{See also|No-threes subgroup temperaments #Score }}
 
[[Comma list]]: 343/338, 847/832
 
{{Mapping|legend=2| 1 1 3 1 | 0 4 1 6 }}
 
{{Mapping|legend=3| 1 0 0 1 3 1| 0 0 0 4 1 6 }}
 
: [[gencom]]: [2 11/8; 343/338 847/832]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 540.099
 
{{Optimal ET sequence|legend=1| 5, 7, 9, 11, 20 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.282 cents


[[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]]
[[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]]
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== Joan ==
== Joan ==
Joan is related to [[casablanca]] as well as to [[orwell]].
{{See also| Subgroup temperaments #Joan }}
 
[[Subgroup]]: 2.9.7.11
 
[[Comma list]]: 99/98, 9317/9216
 
{{Mapping|legend=2| 1 0 1 3 | 0 7 4 1 }}
 
{{Mapping|legend=3| 1 0 0 1 3 | 0 7/2 0 4 1 }}
 
: [[gencom]]: [2 11/8; 99/98 9317/9216]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents
 
{{Optimal ET sequence|legend=1| 11, 20, 31, 42, 115bd, 157bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.424 cents


Scales:  
Scales:  
Line 1,156: Line 579:


== Sephiroth ==
== Sephiroth ==
Sephiroth is the no-7 restriction of [[muggles]].
{{See also| No-threes subgroup temperaments #Sephiroth }}
 
[[Subgroup]]: 2.5.11.13.17
 
[[Comma list]]: 65/64, 170/169, 221/220
 
{{Mapping|legend=2| 1 0 15 6 11 | 0 1 -5 -1 -3 }}
 
{{Mapping|legend=3| 1 0 2 0 5 4 5 | 0 0 1 0 -5 -1 -3 }}
 
: [[gencom]]: [2 5/4; 65/64 170/169 221/220]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 372.236
 
{{Optimal ET sequence|legend=1| 10, 13, 16, 29 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.774 cents


Scales:  
Scales:  
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== Skateboard ==
== Skateboard ==
Skateboard is related to [[thrasher]].
{{See also| Subgroup temperaments #Skateboard }}
 
[[Subgroup]]: 2.5/3.7/3.11.13/9
 
[[Comma list]]: 56/55, 91/90, 100/99
 
{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
 
{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}
 
: [[gencom]]: [2 6/5; 56/55 91/90 100/99]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 313.842
 
{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents


Scales:  
Scales:  
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== Augment ==
== Augment ==
Augment is related to [[augmented]].
{{See also| No-threes subgroup temperaments #Augment }}
 
[[Subgroup]]: 2.5.7.11
 
[[Comma list]]: 56/55, 128/125
 
{{Mapping|legend=2| 3 7 0 2 | 0 0 1 1 }}
 
{{Mapping|legend=3| 3 0 7 9 11| 0 0 0 -1 -1 }}
 
: [[gencom]]: [5/4 8/7; 56/55 128/125]
 
[[Optimal tuning]] ([[POTE]]): ~5/4 = 1\3, ~8/7 = 228.275
 
{{Optimal ET sequence|legend=1| 3, 6, 9, 15, 21 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.422 cents


[[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]]
[[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]]
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== Kryptonite ==
== Kryptonite ==
Kryptonite is related to [[krypton]].
{{See also| Subgroup temperaments #Kryptonite }}
 
[[Subgroup]]: 2.5.7/3.11/3.13/3
 
[[Comma list]]: 56/55, 78/77, 91/90
 
{{Mapping|legend=2| 1 2 1 2 2 | 0 -3 -2 1 -1 }}
 
{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}
 
: [[gencom]]: [2 13/12; 56/55 78/77 91/90]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/12 = 132.428
 
{{Optimal ET sequence|legend=1| 9, 63, 82bd, 91bde }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents


Scales:  
Scales:  
Line 1,330: Line 689:


== Oregon ==
== Oregon ==
[[Subgroup]]: 2.9.15.7.11
{{See also| Orgonia #Oregon }}
 
[[Comma list]]: 55/54, 64/63, 100/99
 
{{Mapping|legend=2| 1 1 1 5 2 | 0 3 4 -3 2 }}
 
{{Mapping|legend=3| 1 2 3 2 4 | 0 -3/2 -5/2 3 -2 }}
 
: [[gencom]]: [2 6/5; 55/54 64/63 100/99]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495
 
{{Optimal ET sequence|legend=1| 7, 11, 37b, 48b, 59b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.550 cents


Scales:  
Scales:  
Line 1,362: Line 707:


== Glacial ==
== Glacial ==
[[Subgroup]]: 2.9.5.11.13
{{See also| Subgroup temperaments #Glacial }}
 
[[Comma list]]: 45/44, 65/64, 81/80
 
{{Mapping|legend=2| 1 0 -4 -6 10 | 0 1 2 3 -2 }}
 
{{Mapping|legend=3| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }}
 
: [[gencom]]: [2 9/8; 45/44 65/64 81/80]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151
 
{{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.887 cents


Scales:  
Scales:  
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[[Category:Listen]]
[[Category:Listen]]
[[Category:Rank 2]]
[[Category:Rank 2]]
{{todo|cleanup}}
{{todo|cleanup}}
Retrieved from "https://en.xen.wiki/w/Chromatic_pairs"