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Hemimage temperaments: Difference between revisions

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'''Hemimage temperaments''' temper out the [[hemimage comma]], {{monzo| 5 -7 -1 3 }} = 10976/10935.  
'''Hemimage temperaments''' temper out the [[hemimage comma]], {{monzo| 5 -7 -1 3 }} = 10976/10935.  


Discussed elsewhere are [[Archytas clan #quasisuper|quasisuper]], [[Meantone family #Liese|liese]], [[Marvel temperaments #Pluto|pluto]], [[Magic family #magic|magic]], [[Diaschismic family #Echidna|echidna]], [[Breedsmic temperaments #hemififths|hemififths]], [[Ragismic microtemperaments #Parakleismic|parakleismic]], [[Porwell temperaments #Hendecatonic|hendecatonic]], [[Schismatic family #Guiron|guiron]], [[Turkish maqam music temperaments|yarman]], and [[Unicorn family #Alicorn|alicorn]].
Discussed elsewhere are:
* [[Archytas clan #quasisuper|Quasisuper]]
* [[Meantone family #Liese|Liese]]
* [[Unicorn family #Alicorn|Alicorn]]
* [[Magic family #magic|Magic]]
* [[Schismatic family #Guiron|Guiron]]
* [[Diaschismic family #Echidna|Echidna]]
* [[Breedsmic temperaments #hemififths|Hemififths]]
* [[Ragismic microtemperaments #Parakleismic|Parakleismic]]
* [[Mirkwai clan #Pluto|Pluto]]
* [[Porwell temperaments #Hendecatonic|Hendecatonic]]
* [[Turkish maqam music temperaments|Yarman]]


= Commatic =
= Commatic =
Commas: 10976/10935, 50421/50000
Subgroup: 2.3.5.7


POTE generator: ~81/80 = 20.377
Comma list: 10976/10935, 50421/50000


Map: [<2 3 4 5|, <0 5 19 18|]
Mapping: [<2 3 4 5|, <0 5 19 18|]


Wedgie: <<10 38 36 37 29 -23||
Wedgie: <<10 38 36 37 29 -23||
POTE generator: ~81/80 = 20.377


EDOs: 58, 118, 294, 412d, 530d
EDOs: 58, 118, 294, 412d, 530d
Line 17: Line 30:


== 11-limit ==
== 11-limit ==
Commas: 441/440, 3388/3375, 8019/8000
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 3388/3375, 8019/8000
 
Mapping: [<2 3 4 5 6|, <0 5 19 18 27|]


POTE generator: ~81/80 = 20.390
POTE generator: ~81/80 = 20.390
Map: [<2 3 4 5 6|, <0 5 19 18 27|]


EDOs: 58, 118, 294, 412d
EDOs: 58, 118, 294, 412d
Line 30: Line 45:
{{see also|Amity family}}
{{see also|Amity family}}


Commas: 10976/10935, 235298/234375
Subgroup: 2.3.5.7


POTE generator: ~28/27 = 60.528
Comma list: 10976/10935, 235298/234375


Map: [<3 4 5 6|, <0 5 13 16|]
Mapping: [<3 4 5 6|, <0 5 13 16|]


Wedgie: <<15 39 48 27 34 2||
Wedgie: <<15 39 48 27 34 2||
POTE generator: ~28/27 = 60.528


EDOs: 60, 99, 258, 357, 456
EDOs: 60, 99, 258, 357, 456
Line 43: Line 60:


= Degrees =
= Degrees =
Commas: 10976/10935, 390625/388962
Subgroup: 2.3.5.7


POTE generator: ~3/2 = 703.015
Comma list: 10976/10935, 390625/388962


Map: [<20 0 -17 -39|, <0 1 2 3|]
Mapping: [<20 0 -17 -39|, <0 1 2 3|]


Wedgie: <<20 40 60 17 39 27||
Wedgie: <<20 40 60 17 39 27||
POTE generator: ~3/2 = 703.015


EDOs: 60, 80, 140, 640b, 780b, 920b
EDOs: 60, 80, 140, 640b, 780b, 920b
Line 56: Line 75:


== 11-limit ==
== 11-limit ==
Commas: 1331/1323, 1375/1372, 2200/2187
Subgroup: 2.3.5.7.11
 
Comma list: 1331/1323, 1375/1372, 2200/2187
 
Mapping: [<20 0 -17 -39 -26|, <0 1 2 3 3|]


POTE generator: ~3/2 = 703.231
POTE generator: ~3/2 = 703.231
Map: [<20 0 -17 -39 -26|, <0 1 2 3 3|]


EDOs: 80, 140, 360, 500be, 860bde
EDOs: 80, 140, 360, 500be, 860bde
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== 13-limit ==
== 13-limit ==
Commas: 325/324, 352/351, 1001/1000, 1331/1323
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 352/351, 1001/1000, 1331/1323
 
Mapping: [<20 0 -17 -39 -26 74|, <0 1 2 3 3 0|]


POTE generator: ~3/2 = 703.080
POTE generator: ~3/2 = 703.080
Map: [<20 0 -17 -39 -26 74|, <0 1 2 3 3 0|]


EDOs: 60e, 80, 140, 500be, 640be, 780be
EDOs: 60e, 80, 140, 500be, 640be, 780be
Line 78: Line 101:


= Subfourth =
= Subfourth =
Commas: 10976/10935, 65536/64827
Subgroup: 2.3.5.7
 
Comma list: 10976/10935, 65536/64827
 
Mapping: [<1 0 17 4|, <0 4 -37 -3|]


POTE generator: ~21/16 = 475.991
POTE generator: ~21/16 = 475.991
Map: [<1 0 17 4|, <0 4 -37 -3|]


EDOs: 58, 121, 179, 300bd, 479bcd
EDOs: 58, 121, 179, 300bd, 479bcd
Line 89: Line 114:


== 11-limit ==
== 11-limit ==
Commas: 540/539, 896/891, 12005/11979
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 896/891, 12005/11979
 
Mapping: [<1 0 17 4 11|, <0 4 -37 -3 -19|]


POTE generator: ~21/16 = 475.995
POTE generator: ~21/16 = 475.995
Map: [<1 0 17 4 11|, <0 4 -37 -3 -19|]


EDOs: 58, 121, 179e, 300bde
EDOs: 58, 121, 179e, 300bde
Line 100: Line 127:


== 13-limit ==
== 13-limit ==
Commas: 352/351, 364/363, 540/539, 676/675
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 364/363, 540/539, 676/675
 
Mapping: [<1 0 17 4 11 16|, <0 4 -37 -3 -19 -31|]


POTE generator: ~21/16 = 475.996
POTE generator: ~21/16 = 475.996
Map: [<1 0 17 4 11 16|, <0 4 -37 -3 -19 -31|]


EDOs: 58, 121, 179ef, 300bdef
EDOs: 58, 121, 179ef, 300bdef
Line 113: Line 142:
{{see also| Very high accuracy temperaments #Kwazy }}
{{see also| Very high accuracy temperaments #Kwazy }}


Commas: 10976/10935, 65625/65536
Subgroup: 2.3.5.7
 
Comma list: 10976/10935, 65625/65536
 
Mapping: [<2 1 6 1|, <0 8 -5 17|]


POTE generator: ~192/175 = 162.8061
POTE generator: ~192/175 = 162.8061
Map: [<2 1 6 1|, <0 8 -5 17|]


EDOs: 22, 74d, 96d, 118, 140, 258, 398
EDOs: 22, 74d, 96d, 118, 140, 258, 398
Line 124: Line 155:


== 11-limit ==
== 11-limit ==
Commas: 385/384, 3388/3375, 9801/9800
 
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 3388/3375, 9801/9800
 
Mapping: [<2 1 6 1 8|, <0 8 -5 17 -4|]


POTE generators: ~11/10 = 162.7733
POTE generators: ~11/10 = 162.7733
Map: [<2 1 6 1 8|, <0 8 -5 17 -4|]


EDOs: 22, 74d, 96d, 118, 258e, 376de
EDOs: 22, 74d, 96d, 118, 258e, 376de
Line 134: Line 168:
Badness: 0.0321
Badness: 0.0321


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament]]
[[Category:Temperament collection]]
[[Category:Hemimage]]
[[Category:Hemimage]]
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Hemimage_temperaments"