Xenharmonic Wiki

Chromatic pairs: Difference between revisions

← Older editNewer edit →
VisualWikitext
Cleanup (2/)
Cleanup (3/)
Line 237: Line 237:


== Haumea ==
== Haumea ==
Subgroup: 2.3.7/5.11/5.13/5
Related temperaments include [[bridgetown]], [[namaka]], [[hemigari]], [[barbados]], and [[parizekmic]].  


Commas: 352/351, 676/675, 847/845
[[Subgroup]]: 2.3.7/5.11/5.13/5


Related temperaments: [[Chromatic_pairs#Bridgetown|bridgetown]], [[Hemifamity_family#Namaka|namaka]], hemigari, barbados, parizekmic
[[Comma list]]: 352/351, 676/675, 847/845


[[Tp_tuning|POT2 generator]]: ~15/13 = 248.491
{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}


[[Gencom|Gencom]]: [2 15/13; 352/351 676/675 847/845]
{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}


Gencom mapping: [<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]


Mapping: [<1 0 10 -6 -1|, <0 2 -12 9 3|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/13 = 248.491


EDOs: {{EDOs|24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd}}
{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.2668 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents


[[haumea5|Five note haplotonic scale]]
Scales:
 
* [[haumea5]] – 5-tone haplotonic scale
[[haumea9|Nine note albitonic scale]]
* [[haumea9]] – 9-tone albitonic scale
 
* [[haumea14]] – 14-tone chromatic scale
[[haumea14|Fourteen note chromatic scale]]
* [[haumea19]] – 19-tone mega chromatic scale
 
[[haumea19|Nineteen note mega chromatic scale]]


== Neutral ==
== Neutral ==
Line 273: Line 271:
* [[neutral17]] – 17-tone [[mega-chromatic scale]]
* [[neutral17]] – 17-tone [[mega-chromatic scale]]


=== Music ===
; Music
[https://soundcloud.com/jdfreivald/mo-happy-happy ''Mo - Happy - Happy''] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by [[Jake Freivald]] in Neutral[7], 24et tuning
* [https://soundcloud.com/jdfreivald/mo-happy-happy ''Mo - Happy - Happy''] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by [[Jake Freivald]] in Neutral[7], 24edo tuning


== Slendric ==
== Slendric ==
Line 289: Line 287:


== Huntington ==
== Huntington ==
Subgroup: 2.5.7.13
Huntington may be described as the 10 & 27 temperament in the 2.5.7.13 subgroup.


Commas: 640/637, 10985/10976
[[Subgroup]]: 2.5.7.13


Sval name: 10&27
[[Comma list]]: 640/637, 10985/10976


[[Tp_tuning|POT2 generator]]: ~16/13 = 357.002
{{Mapping|legend=2| 1 5 4 4 | 0 -9 -4 -1 }}


[[Gencom|Gencom]]: [2 16/13; 640/637 10985/10976]
{{Mapping|legend=3| 1 0 5 4 0 4 | 0 0 -9 -4 0 -1 }}


Gencom mapping: [<1 0 5 4 0 4|, <0 0 -9 -4 0 -1|]
: [[gencom]]: [2 16/13; 640/637 10985/10976]


Mapping: [<1 5 4 4|, <0 -9 -4 -1|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/13 = 357.002


EDOs: {{EDOs|7, 10, 17, 27, 37, 84, 121, 279cd, 400cd}}
{{Optimal ET sequence|legend=1| 7, 10, 17, 27, 37, 84, 121, 279cd, 400cd }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.3452 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3452 cents


[[File:huntington_400edo.jpg|alt=huntington_400edo.jpg|huntington_400edo.jpg]]
[[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]]


[[huntington7|Seven note haplotonic scale]]
Scales:
 
* [[huntington7]] – 7-tone haplotonic scale
[[huntington10|Ten note albitonic scale]]
* [[huntington10]] – 10-tone albitonic scale
 
* [[huntington17]] – 17-tone chromatic scale
[[huntington17|Seventeen note chromatic scale]]


== Tobago ==
== Tobago ==
Subgroup: 2.3.11.13/5
Tobago, the 10 & 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].


Commas: 243/242, 676/675
[[Subgroup]]: 2.3.11.13/5


Sval name: 10&14
[[Comma list]]: 243/242, 676/675


Related temperaments: [[Chromatic_pairs#Neutral|neutral]], [[The_Archipelago|barbados]]
{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}


[[Tp_tuning|POT2 generator]]: ~15/13 = 249.312
{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}


[[Gencom|Gencom]]: [55/39 15/13; 243/242 676/675]
: [[gencom]]: [55/39 15/13; 243/242 676/675]


Gencom mapping: [<2 4 -2 0 9 2|, <0 -2 3/2 0 -5 -3/2|]
[[Optimal tuning]] ([[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312


Mapping: [<2 0 -1 -2], <0 2 5 3]]
{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}


EDOs: {{EDOs|10, 14, 24, 58, 82, 130}}
[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents


[[Tp_tuning#T2 tuning|RMS error]]: 0.3533 cents
Scales:  
 
* [[tobago6]] – 6-tone haplotonic scale
[[tobago6|Six note haplotonic scale]]
* [[tobago10]] – 10-tone albitonic scale
 
* [[tobago14]] – 14-tone chromatic scale
[[tobago10|Ten note albitonic scale]]
* [[tobago24]] – 24-tone quatertone scale
 
[[tobago14|Fourteen note chromatic scale]]
 
[[tobago24|Twentyfour note quatertone scale]]


== Pepperoni ==
== Pepperoni ==
Subgroup: 2.3.11/7.13/7
{{See also| Parapyth }}


Commas: 352/351, 364/363
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.


Sval name: 5&12
[[Subgroup]]: 2.3.11/7.13/7


Related temperament: The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
[[Comma list]]: 352/351, 364/363


[[Tp_tuning|POT2 generator]]: ~3/2 = 703.856
{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}


[[Gencom|Gencom]]: [2 3/2; 352/351 364/363]
{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}


Gencom mapping: [<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]


Mapping: [<1 0 7 12|, <0 1 -4 -7|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.856


EDOs: {{EDOs|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 }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.3789 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents


[[File:pepperoni_271edo.png|alt=pepperoni_271edo.png|pepperoni_271edo.png]]
[[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]]


[[pepperoni7|Seven note albitonic scale]]
Scales:
 
* [[pepperoni7]] – 7-tone albitonic scale
[[pepperoni12|Twelve note chromatic scale]]
* [[pepperoni12]] – 12-tone chromatic scale


== Wizz ==
== Wizz ==
Subgroup: 2.5.11
Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, is related to [[wizard]].


Commas: 15625/15488
[[Subgroup]]: 2.5.11


Sval name: 6&16
[[Comma list]]: 15625/15488


Related temperaments: [[Marvel_temperaments#Wizard-11-limit|wizard]]
{{Mapping|legend=2| 2 0 -7 | 0 1 3 }}


Generator: ~5/4 = 383.768
{{Mapping|legend=3| 2 0 4 0 5 | 0 0 1 0 3 }}


[[Gencom|Gencom]]: [125/88 5/4; 15625/15488]
: [[gencom]]: [125/88 5/4; 15625/15488]


Gencom mapping: [<2 0 4 0 5| <0 0 1 0 3|]
[[Optimal tuning]] ([[POTE]]): ~125/88 = 1\2, ~5/4 = 383.768


Mapping: [<2 0 -7|, <0 1 3|]
{{Optimal ET sequence|legend=1| 6, 16, 22, 28, 50, 122, 172, 222 }}


EDOs: {{EDOs|6, 16, 22, 28, 50, 122, 172, 222}}
[[Tp tuning #T2 tuning|RMS error]]: 0.3997


[[Tp_tuning#T2 tuning|RMS error]]: 0.3997
Scales:  
 
* [[wizz6]] – 6-tone haplotonic scale
[[wizz6|Six note haplotonic scale]]
* [[wizz10]] – 10-tone albitonic scale
 
* [[wizz16]] – 16-tone chromatic scale
[[wizz10|Ten note albitonic scale]]
 
[[wizz16|Sixteen note chromatic scale]]


== Bossier ==
== Bossier ==
Subgroup: 2.7.11.13
Bossier can be described as the 3 & 17 in the 2.7.11.13 subgroup.


Commas: 1573/1568, 15488/15379
[[Subgroup]]: 2.7.11.13


Sval name: 3&17
[[Comma list]]: 1573/1568, 15488/15379


[[Tp_tuning|POT2 generator]]: ~14/11 = 421.309
{{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }}


[[Gencom|Gencom]]: [2 14/11; 1573/1568 15488/15379]
{{Mapping|legend=3| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}


Gencom mapping: [<1 0 0 0 1 3|, <0 0 0 8 7 2|]
: [[gencom]]: [2 14/11; 1573/1568 15488/15379]


Mapping: [<1 0 1 3|, <0 8 7 2|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/11 = 421.309


EDOs: {{EDOs|17, 20, 37, 57, 94, 225, 319cd, 413bcd}}
{{Optimal ET sequence|legend=1| 17, 20, 37, 57, 94, 225, 319cd, 413bcd }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.4043 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.4043 cents


[[File:bossier_225edo.jpg|alt=bossier_225edo.jpg|bossier_225edo.jpg]]
[[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]]


[[bossier8|Eight note albitonic scale]]
Scales:
* [[bossier8]] – 8-tone albitonic scale
* [[bossier11]] – 11-tone chromatic scale
* [[bossier14]] – 14-tone mega-chromatic scale


[[bossier11|Eleven note chromatic scale]]
== Penta aka mechanism ==
Penta, also known as mechanism, is the 8 & 11 temperament in the 2.9.7.11 subgroup.


[[bossier14|Fourteen note mega chromatic scale]]
[[Subgroup]]: 2.9.7.11


== Penta (aka Mechanism) ==
[[Comma list]]: 896/891, 26411/26244
Subgroup: 2.9.7.11


Commas: 896/891, 26411/26244
{{Mapping|legend=2| 1 0 -1 6 | 0 5 6 -4 }}


Svalname: 8&11
{{Mapping|legend=3| 1 5/2 0 5 2 | 0 -5/2 0 -6 4 }}


[[Tp_tuning|POT2 generator]]: ~9/7 = 438.465
: [[gencom]]: [2 9/7; 896/891 26411/26244]


[[Gencom|Gencom]]: [2 9/7; 896/891 26411/26244]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 438.465


Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}


Mapping: [<1 0 -1 6|, <0 5 6 -4|]
[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents


EDOs: {{EDOs|8, 11, 30, 41, 52}}
Scales:  
 
* [[penta5]] – 5-tone haplotonic scale
[[Tp_tuning#T2 tuning|RMS error]]: 0.4262 cents
* [[penta8]] – 8-tone albitonic scale
 
* [[penta11]] – 11-tone chromatic scale
[[penta5|Five note haplotonic scale]]
* [[penta19]] – 19-tone mega-chromatic scale
 
[[penta8|Eight note albitonic scale]]
 
[[penta11|Eleven note chromatic scale]]
 
[[penta19|Nineteen note mega chromatic scale]]


== Bluebirds ==
== Bluebirds ==
Retrieved from "https://en.xen.wiki/w/Chromatic_pairs"