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Chromatic pairs: Difference between revisions

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== Bridgetown ==
== Bridgetown ==
Bridgetown, the 5 & 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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== Tobago ==
== Tobago ==
Tobago, the 10 & 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 & 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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== Marveltri ==
== Marveltri ==
Marveltri, the 3 & 13 temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed 22 & 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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== Guanyintet ==
== Guanyintet ==
Guanyintet, the 4 & 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 & 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 & 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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== Indium ==
== Indium ==
Indium can be described as the 8 & 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 & 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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== 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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== Semidim ==
== Semidim ==
Semidim can be described as the 8 & 29 temperament in the 2.5/3.7/3.11/3.13/3 subgroup.
{{See also| Subgroup temperaments #Semidim }}
 
[[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]
 
[[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]]
[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Semidim in 770edo]]
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== Mothwelltri ==
== Mothwelltri ==
Mothwelltri, the 1 & 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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== 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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== 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:  
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