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Chromatic pairs: Difference between revisions

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: [[gencom]]: [63/50 10/9; 250047/250000]
: [[gencom]]: [63/50 10/9; 250047/250000]


[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[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 }}
{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
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: [[gencom]]: [2 13/10; 2200/2197]
: [[gencom]]: [2 13/10; 2200/2197]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/10 = 455.012
[[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 }}
{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
Line 119: Line 119:
: [[gencom]]: [2 13/10; 847/845 1001/1000]
: [[gencom]]: [2 13/10; 847/845 1001/1000]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/10 = 454.556
[[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 }}
{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
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: [[gencom]]: [2 6/5; 325/324]
: [[gencom]]: [2 6/5; 325/324]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 317.139
[[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 }}
{{Optimal ET sequence|legend=1| 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b }}
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: [[gencom]]: [2 15/13; 352/351 676/675]
: [[gencom]]: [2 15/13; 352/351 676/675]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/13 = 248.399
[[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 }}
{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
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: [[gencom]]: [2 15/13; 352/351 676/675 847/845]
: [[gencom]]: [2 15/13; 352/351 676/675 847/845]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/13 = 248.491
[[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 }}
{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
Line 325: Line 325:
: [[gencom]]: [55/39 15/13; 243/242 676/675]
: [[gencom]]: [55/39 15/13; 243/242 676/675]


[[Optimal tuning]] ([[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
[[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 }}
{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
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: [[gencom]]: [2 3/2; 352/351 364/363]
: [[gencom]]: [2 3/2; 352/351 364/363]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.856
[[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 }}
{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd }}
Line 414: Line 414:
* [[bossier14]] – 14-tone mega-chromatic scale
* [[bossier14]] – 14-tone mega-chromatic scale


== Penta aka mechanism ==
== Penta a.k.a. mechanism ==
Penta, also known as mechanism, is the 8 & 11 temperament in the 2.9.7.11 subgroup.
{{See also| Subgroup temperaments #Penta a.k.a. mechanism }}
 
[[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
 
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents


Scales:  
Scales:  
Line 440: Line 424:


== Bluebirds ==
== Bluebirds ==
Subgroup: 2.11.13
[[Subgroup]]: 2.11.13


Comma: 265837/262144
[[Comma list]]: 265837/262144


[[Tp_tuning|POT2 generator]]: ~143/128 = 182.368
{{Mapping|legend=2| 1 0 6 | 0 3 -2 }}


Gencom: [2 143/128; 265837/262144]
{{Mapping|legend=3| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }}


Gencom mapping: [<1 0 0 0 3 4|, <0 0 0 0 3 -2|]
: [[gencom]]: [2 143/128; 265837/262144]


Mapping: [<1 0 6|, <0 3 -2|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~143/128 = 182.368


EDOs: {{EDOs|6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc}}
{{Optimal ET sequence|legend=1| 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.4444 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.4444 cents


[[bluebirds6|Six note haplotonic scale]]
Scales:
 
* [[bluebirds6]] – 6-tone haplotonic scale
[[bluebirds7|Seven note albitonic scale]]
* [[bluebirds7]] – 7-tone albitonic scale
 
* [[bluebirds13]] – 13-tone chromatic scale
[[bluebirds13|Thirteen note chromatic scale]]


== Marveltri ==
== Marveltri ==
Subgroup: 2.5.9/7
Marveltri, the 3 & 13 temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed 22 & 47 temperament.


Comma: 225/224
[[Subgroup]]: 2.5.9/7


Sval name: 3&13
[[Comma list]]: 225/224


Related temperaments: marvel, 22&47, magic
{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}


[[Tp_tuning|POT2 generator]]: ~5/4 = 383.638
{{Mapping|legend=3| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }}


[[Gencom|Gencom]]: [2 5/4; 225/224]
: [[gencom]]: [2 5/4; 225/224]


Gencom mapping: [<1 2/5 2 -1/5|, <0 -4/5 1 2/5|]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~5/4 = 383.638


Mapping: [<1 0 5|, <0 1 -2|]
{{Optimal ET sequence|legend=1| 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc }}


EDOs: {{EDOs|12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc}}
[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents


[[Tp_tuning#T2 tuning|RMS error]]: 0.4801 cents
Scales:
* [[marveltri7]] – 7-tone albitonic scale
* [[marveltri10]] – 10-tone chromatic scale
* [[marveltri13]] – 13-tone mega-chromatic scale


[[marveltri7|Seven note albitonic scale]]
== Edson ==
 
Edson is related to [[pele]] and [[andromeda]].
[[marveltri10|Ten note chromatic scale]]
 
[[marveltri13|Thirteen note mega chromatic scale]]


== Edson ==
[[Subgroup]]: 2.3.7/5.11/5.13/5
[[Subgroup]]: 2.3.7/5.11/5.13/5


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[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents
Related temperaments: [[pele]], [[cassandra]]


Scales:  
Scales:  
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