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. | ||
=Commatic | = Commatic = | ||
Commas: 10976/10935, 50421/50000 | Commas: 10976/10935, 50421/50000 | ||
| Line 17: | Line 14: | ||
Badness: 0.0843 | Badness: 0.0843 | ||
==11-limit== | == 11-limit == | ||
Commas: 441/440, 3388/3375, 8019/8000 | Commas: 441/440, 3388/3375, 8019/8000 | ||
| Line 43: | Line 40: | ||
Badness: 0.0575 | Badness: 0.0575 | ||
=Degrees= | = Degrees = | ||
Commas: 10976/10935, 390625/388962 | Commas: 10976/10935, 390625/388962 | ||
| Line 56: | Line 53: | ||
Badness: 0.1065 | Badness: 0.1065 | ||
==11-limit== | == 11-limit == | ||
Commas: 1331/1323, 1375/1372, 2200/2187 | Commas: 1331/1323, 1375/1372, 2200/2187 | ||
| Line 67: | Line 64: | ||
Badness: 0.0468 | Badness: 0.0468 | ||
==13-limit== | == 13-limit == | ||
Commas: 325/324, 352/351, 1001/1000, 1331/1323 | Commas: 325/324, 352/351, 1001/1000, 1331/1323 | ||
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Badness: 0.0327 | Badness: 0.0327 | ||
=Subfourth= | = Subfourth = | ||
Commas: 10976/10935, 65536/64827 | Commas: 10976/10935, 65536/64827 | ||
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Badness: 0.1407 | Badness: 0.1407 | ||
==11-limit== | == 11-limit == | ||
Commas: 540/539, 896/891, 12005/11979 | Commas: 540/539, 896/891, 12005/11979 | ||
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Badness: 0.0453 | Badness: 0.0453 | ||
==13-limit== | == 13-limit == | ||
Commas: 352/351, 364/363, 540/539, 676/675 | Commas: 352/351, 364/363, 540/539, 676/675 | ||
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Badness: 0.0238 | Badness: 0.0238 | ||
= Bisupermajor = | |||
{{see also| Very high accuracy temperaments #Kwazy }} | |||
Commas: 10976/10935, 65625/65536 | |||
POTE generator: ~192/175 = 162.8061 | |||
Map: [<2 1 6 1|, <0 8 -5 17|] | |||
EDOs: 22, 74d, 96d, 118, 140, 258, 398 | |||
Badness: 0.0655 | |||
== 11-limit == | |||
Commas: 385/384, 3388/3375, 9801/9800 | |||
POTE generators: ~11/10 = 162.7733 | |||
Map: [<2 1 6 1 8|, <0 8 -5 17 -4|] | |||
EDOs: 22, 74d, 96d, 118, 258e, 376de | |||
Badness: 0.0321 | |||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 06:34, 3 January 2021
Hemimage temperaments temper out the hemimage comma, [5 -7 -1 3⟩ = 10976/10935.
Commatic
Commas: 10976/10935, 50421/50000
POTE generator: ~81/80 = 20.377
Map: [<2 3 4 5|, <0 5 19 18|]
Wedgie: <<10 38 36 37 29 -23||
EDOs: 58, 118, 294, 412d, 530d
Badness: 0.0843
11-limit
Commas: 441/440, 3388/3375, 8019/8000
POTE generator: ~81/80 = 20.390
Map: [<2 3 4 5 6|, <0 5 19 18 27|]
EDOs: 58, 118, 294, 412d
Badness: 0.0305
Chromat
Commas: 10976/10935, 235298/234375
POTE generator: ~28/27 = 60.528
Map: [<3 4 5 6|, <0 5 13 16|]
Wedgie: <<15 39 48 27 34 2||
EDOs: 60, 99, 258, 357, 456
Badness: 0.0575
Degrees
Commas: 10976/10935, 390625/388962
POTE generator: ~3/2 = 703.015
Map: [<20 0 -17 -39|, <0 1 2 3|]
Wedgie: <<20 40 60 17 39 27||
EDOs: 60, 80, 140, 640b, 780b, 920b
Badness: 0.1065
11-limit
Commas: 1331/1323, 1375/1372, 2200/2187
POTE generator: ~3/2 = 703.231
Map: [<20 0 -17 -39 -26|, <0 1 2 3 3|]
EDOs: 80, 140, 360, 500be, 860bde
Badness: 0.0468
13-limit
Commas: 325/324, 352/351, 1001/1000, 1331/1323
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
Badness: 0.0327
Subfourth
Commas: 10976/10935, 65536/64827
POTE generator: ~21/16 = 475.991
Map: [<1 0 17 4|, <0 4 -37 -3|]
EDOs: 58, 121, 179, 300bd, 479bcd
Badness: 0.1407
11-limit
Commas: 540/539, 896/891, 12005/11979
POTE generator: ~21/16 = 475.995
Map: [<1 0 17 4 11|, <0 4 -37 -3 -19|]
EDOs: 58, 121, 179e, 300bde
Badness: 0.0453
13-limit
Commas: 352/351, 364/363, 540/539, 676/675
POTE generator: ~21/16 = 475.996
Map: [<1 0 17 4 11 16|, <0 4 -37 -3 -19 -31|]
EDOs: 58, 121, 179ef, 300bdef
Badness: 0.0238
Bisupermajor
Commas: 10976/10935, 65625/65536
POTE generator: ~192/175 = 162.8061
Map: [<2 1 6 1|, <0 8 -5 17|]
EDOs: 22, 74d, 96d, 118, 140, 258, 398
Badness: 0.0655
11-limit
Commas: 385/384, 3388/3375, 9801/9800
POTE generators: ~11/10 = 162.7733
Map: [<2 1 6 1 8|, <0 8 -5 17 -4|]
EDOs: 22, 74d, 96d, 118, 258e, 376de
Badness: 0.0321