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Subgroup temperaments: Difference between revisions

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Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic_pairs|Chromatic pairs]].
Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]].


=2.3.7=
=2.3.7=
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[[Lp_tuning|POL2 generator]]: ~15/13= 250.385
[[Lp_tuning|POL2 generator]]: ~15/13= 250.385


[[Gencom|Gencom]]: [2 8/7; 49/48]
[[Gencom]]: [2 8/7; 49/48]


Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|]
Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|]
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==Archy==
==Archy==
Archy can be thought of as "no-5's [[dominant|dominant]]" or "no-5's [[Superpyth|superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma.
Archy can be thought of as "no-5's [[dominant]]" or "no-5's [[superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma.


Comma: 64/63
Comma: 64/63
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[[Tp_tuning#T2 tuning|RMS error]]: 1.856 cents
[[Tp_tuning#T2 tuning|RMS error]]: 1.856 cents


==[[Slendric|Slendric]]==
==[[Slendric]]==
Comma: 1029/1024
Comma: 1029/1024


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==Neutral==
==Neutral==
Neutral can be thought of as the 2.3.11 version of either [[Mohajira|mohajira]] or [[maqamic|maqamic]], as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the [[neutral_tetrad|neutral tetrad]].
Neutral can be thought of as the 2.3.11 version of either [[mohajira]] or [[maqamic]], as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the [[neutral tetrad]].


Comma: 243/242
Comma: 243/242
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===Music===
===Music===
[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 Mohaha10ping2] by [[Billy_Stiltner|Billy Stiltner]]
[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 Mohaha10ping2] by [[Billy Stiltner]]


=2.3.7.11=
=2.3.7.11=
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[[Tp_tuning|POT2 generator]]: ~11/9 = 351.691
[[Tp_tuning|POT2 generator]]: ~11/9 = 351.691


[[Gencom|Gencom]]: [2 11/9; 144/143 243/242 364/363]
[[Gencom]]: [2 11/9; 144/143 243/242 364/363]


Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]
Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]
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[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990
[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990


[[Gencom|Gencom]]: [2 13/12; 78/77 99/98 144/143]
[[Gencom]]: [2 13/12; 78/77 99/98 144/143]


Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]
Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]
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[[Lp_tuning|POL2 tuning]]: <1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|
[[Lp_tuning|POL2 tuning]]: <1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|


The gencom below gives [[Margo_Schulter|Margo Schulter]]'s favored basis
The gencom below gives [[Margo Schulter]]'s favored basis


Gencom: [2 3/2 28/27; 352/351 364/363]
Gencom: [2 3/2 28/27; 352/351 364/363]
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[[Lp_tuning|POL2 generator]]: ~21/20 = 83.016
[[Lp_tuning|POL2 generator]]: ~21/20 = 83.016


[[Gencom|Gencom]]: [2 21/20; 364/363 441/440 1001/1000]
[[Gencom]]: [2 21/20; 364/363 441/440 1001/1000]


Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|]
Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|]
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Related temperament: [[Swetismic_temperaments#Hypnos-13-limit|hypnos]], [[Hemifamity_temperaments#Tricot-13-limit|tricot]]
Related temperament: [[Swetismic_temperaments#Hypnos-13-limit|hypnos]], [[Hemifamity_temperaments#Tricot-13-limit|tricot]]


[[Gencom|Gencom]]: [2 13/9; 169/168, 540/539, 729/728]
[[Gencom]]: [2 13/9; 169/168, 540/539, 729/728]


Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|]
Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|]
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Commas: 3136/3125
Commas: 3136/3125


Related temperaments: [[Chromatic+pairs#Roulette]]
Related temperaments: [[Chromatic_pairs#Roulette|roulette]]


[[Gencom|Gencom]]: [2 28/25 3136/3125]
[[Gencom]]: [2 28/25 3136/3125]


Gencom map: [<1 0 2 2|, <0 0 2 5|]
Gencom map: [<1 0 2 2|, <0 0 2 5|]
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[[Category:subgroup]]
[[Category:subgroup]]
[[Category:temperaments]]
[[Category:temperament]]
Retrieved from "https://en.xen.wiki/w/Subgroup_temperaments"