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Chromatic pairs: Difference between revisions

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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 ==
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* [[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 ==
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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 ==
Line 267: Line 267:


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 ==
Line 493: Line 493:


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 ==
Line 530: Line 530:


== Silver ==
== Silver ==
Subgroup: 2.5.7.13.17
Silver can be described as the 10 & 27 temperament in the 2.5.7.13.17 subgroup.


Commas: 170/169, 640/637, 5525/5488
[[Subgroup]]: 2.5.7.13.17


Sval name: 10&27
[[Comma list]]: 170/169, 640/637, 5525/5488


[[Tp_tuning|POT2 generator]]: ~13/8 = 842.711
{{Mapping|legend=2| 1 5 4 4 2 | 0 -9 -4 -1 7 }}


[[Gencom|Gencom]]: [2 13/8; 170/169 640/637 5525/5488]
{{Mapping|legend=3| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}


Gencom mapping: [<1 0 -4 0 0 3 9|, <0 0 9 4 0 1 -7|]
: [[gencom]]: [2 13/8; 170/169 640/637 5525/5488]


Mapping: [<1 5 4 4 2|, <0 -9 -4 -1 7|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/8 = 842.711


EDOs: {{EDOs|7, 10, 17, 27, 37, 47, 84, 131, 178e, 309cde, 487bcdee}}
{{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
[[Tp tuning #T2 tuning|RMS error]]: 0.5886 cents


[[File:silver_487edo.jpg|alt=silver_487edo.jpg|silver_487edo.jpg]]
[[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]]


[[silver7|silver7]] -seven note [[haplotonic_scale|haplotonic scale]]
Scales:
 
* [[silver7]] – 7-tone haplotonic scale
[[silver10|silver10]] - ten note [[albitonic_scale|albitonic scale]]
* [[silver10]] – 10-tone albitonic scale
 
* [[silver17]] – 17-tone chromatic 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
Baldy is every other step of [[garibaldi]], without the mapping of prime 11. It can be described as the 6 & 35 temperament.  


Commas: 225/224, 325/324, 640/637
[[Subgroup]]: 2.9.5.7.13


Sval name: 6&35
[[Comma list]]: 225/224, 325/324, 640/637


Related temperament: [[Schismatic_family|Garibaldi]]
{{Mapping|legend=2| 1 0 15 25 -28 | 0 1 -4 -7 10 }}


[[Tp_tuning|POT2 generator]]: ~9/8 = 204.090
{{Mapping|legend=3| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }}


[[Gencom|Gencom]]: [2 9/8; 225/224 325/324 640/637]
: [[gencom]]: [2 9/8; 225/224 325/324 640/637]


Gencom mapping: [<1 3/2 3 4 0 2|, <0 1/2 -4 -7 0 10|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.090


Mapping: [<1 0 15 25 -28|, <0 1 -4 -7 10|]
{{Optimal ET sequence|legend=1| 6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd }}


EDOs: {{EDOs|6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd}}
[[Tp tuning #T2 tuning|RMS error]]: 0.5999 cents


[[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|alt=baldy_147edo.jpg|baldy_147edo.jpg]]
Scales
 
* [[baldy6]] – 6-tone haplotonic scale
[[baldy6|baldy6]] - six note [[haplotonic_scale|haplotonic scale]]
* [[baldy11]] – 11-tone albitonic scale
 
* [[baldy17]] – 17-tone chromatic 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
Guanyintet, the 4 & 9 temperament in the 2.5.7/3.11/3 subgroup, is related to [[guanyin]] as well as to [[orwell]].


Commas: 176/175, 540/539
[[Subgroup]]: 2.5.7/3.11/3


Svalname: 4&9
[[Comma list]]: 176/175, 540/539


Related temperaments: guanyin, orwell
{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}


[[Tp_tuning|POT2 generator]]: ~7/6 = 270.093
{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}


[[Gencom|Gencom]]: [2 7/6; 176/175 540/539]
: [[gencom]]: [2 7/6; 176/175 540/539]


Gencom mapping: [<1 -4/3 3 -1/3 5/3|, <0 4/3 -3 7/3 -11/3|]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 270.093


Mapping: [<1 0 2 -2|, <0 3 -1 5|]
{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd }}


EDOs: {{EDOs|9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd}}
[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents


[[Tp_tuning#T2 tuning|RMS error]]: 0.6028 cents
Scales:  
 
* [[guanyintet5]] – 5-tone haplotonic scale
[[guanyintet5|Five note haplotonic scale]]
* [[guanyintet9]] – 9-tone albitonic scale
 
* [[guanyintet13]] – 13-tone chromatic scale
[[guanyintet9|Nine note albitonic scale]]
 
[[guanyintet13|Thirteen note chromatic scale]]


== Radon ==
== Radon ==
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[[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
Gariberttet can be described as the 4 & 29 temperament in the 2.5/3.7/3.13/11 subgroup.


Commas: 275/273, 847/845
[[Subgroup]]: 2.5/3.7/3.13/11


Svalname: 4&29
[[Comma list]]: 275/273, 847/845


[[Tp_tuning|POT2 generator]]: ~13/11 = 293.679
{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}


[[Gencom|Gencom]]: [2 13/11; 275/273 847/845]
{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}


Gencom mapping: [<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]


Mapping: [<1 0 0 0|, <0 3 5 1|]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/11 = 293.679


EDOs: {{EDOs|29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd}}
{{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
[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents


[[gariberttet5|Five note haplotonic scale]]
Scales:
 
* [[gariberttet5]] – 5-tone haplotonic scale
[[gariberttet9|Nine note albitonic scale]]
* [[gariberttet9]] – 9-tone albitonic scale
 
* [[gariberttet13]] – 13-tone chromatic scale
[[gariberttet13|Thirteen note chromatic scale]]


== Namo ==
== Namo ==
Line 652: Line 644:


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
Sentry, the 3 & 5 temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].


Commas: 245/243
[[Subgroup]]: 2.5/3.9/7


Svalname: 3&5
[[Comma list]]: 245/243


Related temperaments: sensi
{{Mapping|legend=2| 1 0 0 | 0 2 1 }}


[[Tp_tuning|POT2 generator]]: ~9/7 = 440.902
{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}


[[Gencom|Gencom]]: [2 9/7; 245/243]
: [[gencom]]: [2 9/7; 245/243]


Gencom mapping: [<1 0 0 0|, <0 0 2 -1|]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~9/7 = 440.902


Mapping: [<1 0 0|, <0 2 1|]
{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc }}


EDOs: {{EDOs|8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc}}
[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents


[[Tp_tuning#T2 tuning|RMS error]]: 0.7105 cents
Scales:  
 
* [[sentry5]] – 5-tone haplotonic scale
[[sentry5|Five note haplotonic scale]]
* [[sentry8]] – 8-tone albitonic scale
 
* [[sentry11]] – 11-tone chromatic 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: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]
 
Mapping: [<1 1 -1 2 4|, <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 717: Line 689:


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


== Mabila ==
== Mabila ==
Subgroup: 2.5.7
Given below is the no-3 version of mabila, the 7 & 9 temperament.  


Comma: 1071875/1048576
[[Subgroup]]: 2.5.7


Sval name: 7&9
[[Comma list]]: 1071875/1048576


[[Tp_tuning|POT2 generator]]: ~175/128 = 527.236
{{Mapping|legend=2| 1 1 5 | 0 3 -5 }}


[[Gencom|Gencom]]: [2 175/128; 1071875/1048576]
{{Mapping|legend=3| 1 0 1 5 | 0 0 3 -5 }}


Gencom mapping: [<1 0 1 5}, <0, 0, 3, -5|]
: [[gencom]]: [2 175/128; 1071875/1048576]


Mapping: [<1 1 5|, <0 3 -5|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~175/128 = 527.236


EDOs: {{EDOs|7, 9, 16, 25, 41, 66, 305bc}}
{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41, 66, 305bc }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.7729 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.7729 cents


[[File:mabila_66edo.jpg|alt=mabila_66edo.jpg|mabila_66edo.jpg]]
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabila in 66edo]]


[[mabila7|Seven note haplotonic scale]]
Scales:
 
* [[mabila7]] – 7-tone haplotonic scale
[[mabila9|Nine note albitonic scale]]
* [[mabila9]] – 9-tone albitonic scale
 
* [[mabila16]] – 16-tone chromatic scale
[[mabila16|Sixteen note chromatic scale]]


== Indium ==
== Indium ==
Subgroup: 2.5/3.7/3.11/3
Indium can be described as the 8 & 33 temperament in the 2.5/3.7/3.11/3 subgroup.


Commas: 3025/3024, 3125/3087
[[Subgroup]]: 2.5/3.7/3.11/3


Sval name: 8&33
[[Comma list]]: 3025/3024, 3125/3087


[[Tp_tuning|POT2 generator]]: ~12/11 = 147.010
{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}


[[Gencom|Gencom]]: [2 12/11; 3025/3024 3125/3087]
{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}


Gencom mapping: [<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]


Mapping: [<1 0 0 2|, <0 6 10 -1|]
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~12/11 = 147.010


EDOs: {{EDOs|33, 41, 49, 57, 106, 204, 253}}
{{Optimal ET sequence|legend=1| 33, 41, 49, 57, 106, 204, 253 }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.7788 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents


[[File:indium_253edo.png|alt=indium_253edo.png|indium_253edo.png]]
[[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]]


[[indium8|Eight note albitonic scale]]
Scales:
* [[indium8]] – 8-tone albitonic scale
* [[indium17]] – 17-tone chromatic scale


[[indium17|Seventeen note chromatic scale]]
; 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]
=== 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 ==
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