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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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* [[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 & 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 ==
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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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== 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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== 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
 
[[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]]
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic 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 ==
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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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* ''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 ==
{{See also| Subgroup temperaments #Semidim }}
{{See also| Subgroup temperaments #Ammon }}


[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Semidim in 770edo]]
[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon 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 ==
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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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== 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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== 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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[[Category:Listen]]
[[Category:Listen]]
[[Category:Rank 2]]
[[Category:Rank 2]]
{{todo|cleanup}}
{{todo|cleanup}}
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