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__FORCETOC__
== Theory ==
=Theory=
28edo, a multiple of both [[7edo|7edo]] and [[14edo|14edo]] (and of course [[2edo|2edo]] and [[4edo|4edo]]), has a step size of 42.857 [[cent|cent]]s. It shares three intervals with [[12edo|12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out|tempers out]] the [[greater_diesis|greater diesis]] [[648/625|648:625]]. It does not however temper out the [[128/125|128:125]] [[lesser_diesis|lesser diesis]], as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7|9/7]] and its inversion [[14/9|14/9]] are also found in 14edo.


28edo can approximate the [[7-limit|7-limit]] subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to [[Semicomma_family|orwell temperament]] now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the [[augmented_triad|augmented triad]] has a very low complexity, so many of them appear in the [[MOS_scales|MOS scales]] for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.
28edo, a multiple of both [[7edo]] and [[14edo]] (and of course [[2edo]] and [[4edo]]), has a step size of 42.857 [[cent]]s. It shares three intervals with [[12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out|tempers out]] the [[greater diesis]] [[648/625|648:625]]. It does not however temper out the [[128/125|128:125]] [[lesser_diesis|lesser diesis]], as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7]] and its inversion [[14/9]] are also found in 14edo.
 
28edo can approximate the [[7-limit|7-limit]] subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to [[Semicomma_family|orwell temperament]] now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the [[augmented_triad|augmented triad]] has a very low complexity, so many of them appear in the [[MOS scales]] for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.


Another subgroup for which 28edo works quite well is 2.5.11.19.21.27.29.39.
Another subgroup for which 28edo works quite well is 2.5.11.19.21.27.29.39.


=Intervals=
== Intervals ==
The following table compares it to potentially useful nearby [[just_intervals|just intervals]].


{| class="wikitable"
The following table compares it to potentially useful nearby [[just intervals]].
 
{| class="wikitable center-all"
|-
|-
| rowspan="2" style="text-align:center;" | Step #
| rowspan="2" | Step #
| style="text-align:center;" | ET
| style="text-align:center;" | ET
| colspan="2" style="text-align:center;" | Just  
| colspan="2" | Just  
| style="text-align:center;" | Difference
| Difference <br> (ET minus Just)
 
| colspan="3" | [[Ups and Downs Notation]]
(ET minus Just)
| colspan="3" style="text-align:center;" | [[Ups and Downs Notation]]
|-
|-
|Cents
| Cents
|Interval
| Interval
|Cents
| Cents
|
|
|
|
Line 28: Line 27:
|
|
|-
|-
| style="text-align:center;" | 0
| 0
| style="text-align:center;" | 0¢
| 0¢
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | unison
| unison
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | D
| D
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | 42.86
| 42.86
| style="text-align:center;" | 41:40
| 41:40
| style="text-align:center;" | 42.74
| 42.74
| style="text-align:center;" | 0.12
| 0.12
| style="text-align:center;" | up-unison
| up-unison
| style="text-align:center;" | ^1
| ^1
| style="text-align:center;" | ^D
| ^D
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | 85.71
| 85.71
| style="text-align:center;" | 21:20
| 21:20
| style="text-align:center;" | 84.47
| 84.47
| style="text-align:center;" | 1.24
| 1.24
| style="text-align:center;" | double-up 1sn, double-down 2nd
| double-up 1sn, double-down 2nd
| style="text-align:center;" | ^^1, vv2
| ^^1, vv2
| style="text-align:center;" | ^^D, vvE
| ^^D, vvE
|-
|-
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | 128.57
| 128.57
| style="text-align:center;" | 14:13
| 14:13
| style="text-align:center;" | 128.3
| 128.3
| style="text-align:center;" | 0.27
| 0.27
| style="text-align:center;" | down 2nd
| down 2nd
| style="text-align:center;" | v2
| v2
| style="text-align:center;" | vE
| vE
|-
|-
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | 171.43
| 171.43
| style="text-align:center;" | 11:10
| 11:10
| style="text-align:center;" | 165
| 165
| style="text-align:center;" | 6.43
| 6.43
| style="text-align:center;" | 2nd
| 2nd
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | E
| E
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | 214.29
| 214.29
| style="text-align:center;" | 17:15
| 17:15
| style="text-align:center;" | 216.69
| 216.69
| style="text-align:center;" | -2.40
| -2.40
| style="text-align:center;" | up 2nd
| up 2nd
| style="text-align:center;" | ^2
| ^2
| style="text-align:center;" | ^E
| ^E
|-
|-
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | 257.14
| 257.14
| style="text-align:center;" | 7:6
| 7:6
| style="text-align:center;" | 266.87
| 266.87
| style="text-align:center;" | -9.73
| -9.73
| style="text-align:center;" | double-up 2nd, double-down 3rd
| double-up 2nd, double-down 3rd
| style="text-align:center;" | ^^2, vv3
| ^^2, vv3
| style="text-align:center;" | ^^E, vvF
| ^^E, vvF
|-
|-
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | 300
| 300
| style="text-align:center;" | 6:5
| 6:5
| style="text-align:center;" | 315.64
| 315.64
| style="text-align:center;" | -15.64
| -15.64
| style="text-align:center;" | down 3rd
| down 3rd
| style="text-align:center;" | v3
| v3
| style="text-align:center;" | vF
| vF
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | 342.86
| 342.86
| style="text-align:center;" | 11:9
| 11:9
| style="text-align:center;" | 347.41
| 347.41
| style="text-align:center;" | -4.55
| -4.55
| style="text-align:center;" | 3rd
| 3rd
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | F
| F
|-
|-
| style="text-align:center;" | 9
| 9
| style="text-align:center;" | 385.71
| 385.71
| style="text-align:center;" | 5:4
| 5:4
| style="text-align:center;" | 386.31
| 386.31
| style="text-align:center;" | -0.60
| -0.60
| style="text-align:center;" | up 3rd
| up 3rd
| style="text-align:center;" | ^3
| ^3
| style="text-align:center;" | ^F
| ^F
|-
|-
| style="text-align:center;" | 10
| 10
| style="text-align:center;" | 428.57
| 428.57
| style="text-align:center;" | 9:7
| 9:7
| style="text-align:center;" | 435.08
| 435.08
| style="text-align:center;" | -6.51
| -6.51
| style="text-align:center;" | double-up 3rd, double-down 4th
| double-up 3rd, double-down 4th
| style="text-align:center;" | ^^3, vv4
| ^^3, vv4
| style="text-align:center;" | ^^F, vvG
| ^^F, vvG
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:center;" | 471.43
| 471.43
| style="text-align:center;" | 21:16
| 21:16
| style="text-align:center;" | 470.78
| 470.78
| style="text-align:center;" | 0.65
| 0.65
| style="text-align:center;" | down 4th
| down 4th
| style="text-align:center;" | v4
| v4
| style="text-align:center;" | vG
| vG
|-
|-
| style="text-align:center;" | 12
| 12
| style="text-align:center;" | 514.29
| 514.29
| style="text-align:center;" | 4:3
| 4:3
| style="text-align:center;" | 498.045
| 498.045
| style="text-align:center;" | 16.245
| 16.245
| style="text-align:center;" | 4th
| 4th
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | G
| G
|-
|-
| style="text-align:center;" | 13
| 13
| style="text-align:center;" | 557.14
| 557.14
| style="text-align:center;" | 11:8
| 11:8
| style="text-align:center;" | 551.32
| 551.32
| style="text-align:center;" | 5.82
| 5.82
| style="text-align:center;" | up 4th
| up 4th
| style="text-align:center;" | ^4
| ^4
| style="text-align:center;" | ^G
| ^G
|-
|-
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | 600
| 600
| style="text-align:center;" | 7:5
| 7:5
| style="text-align:center;" | 582.51
| 582.51
| style="text-align:center;" | 17.49
| 17.49
| style="text-align:center;" | double-up 4th, double-down 5th
| double-up 4th, double-down 5th
| style="text-align:center;" | ^^4, vv5
| ^^4, vv5
| style="text-align:center;" | ^^G, vvA
| ^^G, vvA
|-
|-
| style="text-align:center;" | 15
| 15
| style="text-align:center;" | 642.86
| 642.86
| style="text-align:center;" | 16:11
| 16:11
| style="text-align:center;" | 648.68
| 648.68
| style="text-align:center;" | -5.82
| -5.82
| style="text-align:center;" | down 5th
| down 5th
| style="text-align:center;" | v5
| v5
| style="text-align:center;" | vA
| vA
|-
|-
| style="text-align:center;" | 16
| 16
| style="text-align:center;" | 685.71
| 685.71
| style="text-align:center;" | 3:2
| 3:2
| style="text-align:center;" | 701.955
| 701.955
| style="text-align:center;" | -16.245
| -16.245
| style="text-align:center;" | 5th
| 5th
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | A
| A
|-
|-
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | 728.57
| 728.57
| style="text-align:center;" | 32:21
| 32:21
| style="text-align:center;" | 729.22
| 729.22
| style="text-align:center;" | -0.65
| -0.65
| style="text-align:center;" | up 5th
| up 5th
| style="text-align:center;" | ^5
| ^5
| style="text-align:center;" | ^A
| ^A
|-
|-
| style="text-align:center;" | 18
| 18
| style="text-align:center;" | 771.43
| 771.43
| style="text-align:center;" | 14:9
| 14:9
| style="text-align:center;" | 764.92
| 764.92
| style="text-align:center;" | 6.51
| 6.51
| style="text-align:center;" | double-up 5th, double-down 6th
| double-up 5th, double-down 6th
| style="text-align:center;" | ^^5, vv6
| ^^5, vv6
| style="text-align:center;" | ^^A, vvB
| ^^A, vvB
|-
|-
| style="text-align:center;" | 19
| 19
| style="text-align:center;" | 814.29
| 814.29
| style="text-align:center;" | 8:5
| 8:5
| style="text-align:center;" | 813.68
| 813.68
| style="text-align:center;" | 0.61
| 0.61
| style="text-align:center;" | down 6th
| down 6th
| style="text-align:center;" | v6
| v6
| style="text-align:center;" | vB
| vB
|-
|-
| style="text-align:center;" | 20
| 20
| style="text-align:center;" | 857.14
| 857.14
| style="text-align:center;" | 18:11
| 18:11
| style="text-align:center;" | 852.59
| 852.59
| style="text-align:center;" | 4.55
| 4.55
| style="text-align:center;" | 6th
| 6th
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | B
| B
|-
|-
| style="text-align:center;" | 21
| 21
| style="text-align:center;" | 900
| 900
| style="text-align:center;" | 5:3
| 5:3
| style="text-align:center;" | 884.36
| 884.36
| style="text-align:center;" | 15.64
| 15.64
| style="text-align:center;" | up 6th
| up 6th
| style="text-align:center;" | ^6
| ^6
| style="text-align:center;" | ^B
| ^B
|-
|-
| style="text-align:center;" | 22
| 22
| style="text-align:center;" | 942.86
| 942.86
| style="text-align:center;" | 12:7
| 12:7
| style="text-align:center;" | 933.13
| 933.13
| style="text-align:center;" | 9.73
| 9.73
| style="text-align:center;" | double-up 6th, double-down 7th
| double-up 6th, double-down 7th
| style="text-align:center;" | ^^6, vv7
| ^^6, vv7
| style="text-align:center;" | ^^B, vvC
| ^^B, vvC
|-
|-
| style="text-align:center;" | 23
| 23
| style="text-align:center;" | 985.71
| 985.71
| style="text-align:center;" | 30:17
| 30:17
| style="text-align:center;" | 983.31
| 983.31
| style="text-align:center;" | 2.40
| 2.40
| style="text-align:center;" | down 7th
| down 7th
| style="text-align:center;" | v7
| v7
| style="text-align:center;" | vC
| vC
|-
|-
| style="text-align:center;" | 24
| 24
| style="text-align:center;" | 1028.57
| 1028.57
| style="text-align:center;" | 20:11
| 20:11
| style="text-align:center;" | 1035
| 1035
| style="text-align:center;" | -6.43
| -6.43
| style="text-align:center;" | 7th
| 7th
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | C
| C
|-
|-
| style="text-align:center;" | 25
| 25
| style="text-align:center;" | 1071.42
| 1071.42
| style="text-align:center;" | 13:7
| 13:7
| style="text-align:center;" | 1071.70
| 1071.70
| style="text-align:center;" | -0.27
| -0.27
| style="text-align:center;" | up 7th
| up 7th
| style="text-align:center;" | ^7
| ^7
| style="text-align:center;" | ^C
| ^C
|-
|-
| style="text-align:center;" | 26
| 26
| style="text-align:center;" | 1114.29
| 1114.29
| style="text-align:center;" | 40:21
| 40:21
| style="text-align:center;" | 1115.53
| 1115.53
| style="text-align:center;" | -1.24
| -1.24
| style="text-align:center;" | double-up 7th, double-down 8ve
| double-up 7th, double-down 8ve
| style="text-align:center;" | ^^7, vv8
| ^^7, vv8
| style="text-align:center;" | ^^C, vvD
| ^^C, vvD
|-
|-
| style="text-align:center;" | 27
| 27
| style="text-align:center;" | 1157.14
| 1157.14
| style="text-align:center;" |80:41
| style="text-align:center;" |80:41
| style="text-align:center;" | 1157.26
| 1157.26
| style="text-align:center;" | -0.12
| -0.12
| style="text-align:center;" | down 8ve
| down 8ve
| style="text-align:center;" | v8
| v8
| style="text-align:center;" | vD
| vD
|-
|-
| style="text-align:center;" | 28
| 28
| style="text-align:center;" | 1200
| 1200
| style="text-align:center;" | 2:1
| 2:1
| style="text-align:center;" | 1200
| 1200
| style="text-align:center;" | 0
| 0
| style="text-align:center;" | 8ve
| 8ve
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | D
| D
|}
|}


=Chord Names=
== Chord Names ==


Ups and downs can be used to name 28edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.
Ups and downs can be used to name 28edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.


0-8-16 = C E G = C = C or C perfect
* 0-8-16 = C E G = C = C or C perfect
 
* 0-7-16 = C vE G = Cv = C down
0-7-16 = C vE G = Cv = C down
* 0-9-16 = C ^E G = C^ = C up
 
* 0-8-15 = C E vG = C(v5) = C down-five
0-9-16 = C ^E G = C^ = C up
* 0-9-17 = C ^E ^G = C^(^5) = C up up-five
 
* 0-8-16-24 = C E G B = C7 = C seven
0-8-15 = C E vG = C(v5) = C down-five
* 0-8-16-23 = C E G vB = C,v7 = C add down-seven
 
* 0-7-16-24 = C vE G B = Cv,7 = C down add seven
0-9-17 = C ^E ^G = C^(^5) = C up up-five
* 0-7-16-23 = C vE G vB = Cv7 = C down-seven
 
0-8-16-24 = C E G B = C7 = C seven
 
0-8-16-23 = C E G vB = C,v7 = C add down-seven
 
0-7-16-24 = C vE G B = Cv,7 = C down add seven


0-7-16-23 = C vE G vB = Cv7 = C down-seven
For a more complete list, see [[Ups and Downs Notation #Chord names in other EDOs]].


For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
== Rank two temperaments ==


=<span style="background-color: #ffffff;">Rank two temperaments</span>=
{| class="wikitable center-1 center-2"
 
{| class="wikitable"
|-
|-
! | Periods
! Periods <br> per octave
 
! Generator
per octave
! Temperaments
! | Generator
! | Temperaments
|-
|-
| | 1
| 1
| | 1\28
| 1\28
| |  
|  
|-
|-
| | 1
| 1
| | 3\28
| 3\28
| | [[Negri|Negri]]
| [[Negri]]
|-
|-
| | 1
| 1
| | 5\28
| 5\28
| | [[Machine|Machine]]
| [[Machine]]
|-
|-
| | 1
| 1
| | 9\28
| 9\28
| | [[Würschmidt_family#Worschmidt|Worschmidt]]
| [[Würschmidt_family#Worschmidt|Worschmidt]]
|-
|-
| | 1
| 1
| | 11\28
| 11\28
| |  
|  
|-
|-
| | 1
| 1
| | 13\28
| 13\28
| | <span style="background-color: #ffffff;">[[Thuja|Thuja]]</span>
| [[Thuja|Thuja]]
|-
|-
| | 2
| 2
| | 1\28
| 1\28
| |  
|  
|-
|-
| | 2
| 2
| | 3\28
| 3\28
| |
|
|-
|-
| | 2
| 2
| | 5\28
| 5\28
| | [[antikythera|Antikythera]]
| [[antikythera|Antikythera]]
|-
|-
| | 4
| 4
| | 1\28
| 1\28
| |
|
|-
|-
| | 4
| 4
| | 2\28
| 2\28
| | [[Diminished#Demolished|Demolished]]
| [[Diminished#Demolished|Demolished]]
|-
|-
| | 4
| 4
| | 3\28
| 3\28
| |
|
|-
|-
| | 7
| 7
| | 1\28
| 1\28
| | [[Apotome_family|Whitewood]]
| [[Apotome_family|Whitewood]]
|-
|-
| | 14
| 14
| | 1\28
| 1\28
| |
|
|}
|}


=Commas=
== Commas ==
 
28 EDO tempers out the following [[Comma|comma]]s. (Note: This assumes the val &lt; 28 44 65 79 97 104 |.)
28 EDO tempers out the following [[Comma|comma]]s. (Note: This assumes the val &lt; 28 44 65 79 97 104 |.)


{| class="wikitable"
{| class="wikitable center-all left-2"
|-
|-
! | [[Ratio]]
! [[Ratio]]
! | [[Monzo]]
! [[Monzo]]
! | [[Cents]]
! [[Cents]]
![[Color notation/Temperament Names|Color Name]]
! [[Color notation/Temperament Names|Color Name]]
! | Name 1
! Name 1
! | Name 2
! Name 2
|-
|-
| style="text-align:center;" | 2187/2048
| 2187/2048
| |<nowiki> | -11 7 </nowiki>&gt;
| <nowiki> | -11 7 </nowiki>&gt;
| style="text-align:center;" | 113.69
| 113.69
| style="text-align:center;" |Lawa
| Lawa
| style="text-align:center;" | Apotome
| Apotome
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 648/625
| 648/625
| |<nowiki> | 3 4 -4 </nowiki>&gt;
| <nowiki> | 3 4 -4 </nowiki>&gt;
| style="text-align:center;" | 62.57
| 62.57
| style="text-align:center;" |Quadgu
| Quadgu
| style="text-align:center;" | Major Diesis
| Major Diesis
| style="text-align:center;" | Diminished Comma
| Diminished Comma
|-
|-
| style="text-align:center;" | 16875/16384
| 16875/16384
| |<nowiki> | -14 3 4 </nowiki>&gt;
| <nowiki> | -14 3 4 </nowiki>&gt;
| style="text-align:center;" | 51.12
| 51.12
| style="text-align:center;" |Laquadyo
| Laquadyo
| style="text-align:center;" | Negri Comma
| Negri Comma
| style="text-align:center;" | Double Augmentation Diesis
| Double Augmentation Diesis
|-
|-
| style="text-align:center;" |  
|  
| |<nowiki> | 17 1 -8 </nowiki>&gt;
| <nowiki> | 17 1 -8 </nowiki>&gt;
| style="text-align:center;" | 11.45
| 11.45
| style="text-align:center;" |Saquadbigu
| Saquadbigu
| style="text-align:center;" | Wuerschmidt Comma
| Wuerschmidt Comma
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 36/35
| [[36/35]]
| |<nowiki> | 2 2 -1 -1 </nowiki>&gt;
| <nowiki> | 2 2 -1 -1 </nowiki>&gt;
| style="text-align:center;" | 48.77
| 48.77
| style="text-align:center;" |Rugu
| Rugu
| style="text-align:center;" | Septimal Quarter Tone
| Septimal Quarter Tone
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 50/49
| [[50/49]]
| |<nowiki> | 1 0 2 -2 </nowiki>&gt;
| <nowiki> | 1 0 2 -2 </nowiki>&gt;
| style="text-align:center;" | 34.98
| 34.98
| style="text-align:center;" |Biruyo
| Biruyo
| style="text-align:center;" | Tritonic Diesis
| Tritonic Diesis
| style="text-align:center;" | Jubilisma
| Jubilisma
|-
|-
| style="text-align:center;" | 3125/3087
| 3125/3087
| |<nowiki> | 0 -2 5 -3 </nowiki>&gt;
| <nowiki> | 0 -2 5 -3 </nowiki>&gt;
| style="text-align:center;" | 21.18
| 21.18
| style="text-align:center;" |Triru-aquinyo
| Triru-aquinyo
| style="text-align:center;" | Gariboh
| Gariboh
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 126/125
| [[126/125]]
| |<nowiki> | 1 2 -3 1 </nowiki>&gt;
| <nowiki> | 1 2 -3 1 </nowiki>&gt;
| style="text-align:center;" | 13.79
| 13.79
| style="text-align:center;" |Zotrigu
| Zotrigu
| style="text-align:center;" | Septimal Semicomma
| Septimal Semicomma
| style="text-align:center;" | Starling Comma
| Starling Comma
|-
|-
| style="text-align:center;" | 65625/65536
| 65625/65536
| |<nowiki> | -16 1 5 1 </nowiki>&gt;
| <nowiki> | -16 1 5 1 </nowiki>&gt;
| style="text-align:center;" | 2.35
| 2.35
| style="text-align:center;" |Lazoquinyo
| Lazoquinyo
| style="text-align:center;" | Horwell
| Horwell
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| |<nowiki> | 47 -7 -7 -7 </nowiki>&gt;
| <nowiki> | 47 -7 -7 -7 </nowiki>&gt;
| style="text-align:center;" | 0.34
| 0.34
| style="text-align:center;" |Trisa-seprugu
| Trisa-seprugu
| style="text-align:center;" | Akjaysma
| Akjaysma
| style="text-align:center;" | 5\7 Octave Comma
| 5\7 Octave Comma
|-
|-
| style="text-align:center;" | 176/175
| 176/175
| |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| <nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| style="text-align:center;" | 9.86
| 9.86
| style="text-align:center;" |Lorugugu
| Lorugugu
| style="text-align:center;" | Valinorsma
| Valinorsma
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 441/440
| 441/440
| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| <nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| style="text-align:center;" | 3.93
| 3.93
| style="text-align:center;" |Luzozogu
| Luzozogu
| style="text-align:center;" | Werckisma
| Werckisma
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 4000/3993
| 4000/3993
| |<nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
| <nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
| style="text-align:center;" | 3.03
| 3.03
| style="text-align:center;" |Triluyo
| Triluyo
| style="text-align:center;" | Wizardharry
| Wizardharry
| style="text-align:center;" |  
|  
|}
|}


=Scales=
== Scales ==
 
28edo is particularly well suited to Whitewood in the same way that 15edo is for Blackwood, as it has one third that is heavily tempered, but in a familiar way shared with 12edo, while the other one is significantly closer to just. This makes the 5ths more out of tune, but in a useful way, as you can stack major and minor thirds indefinitely until they repeat 4 octaves and 14 notes up, producing one of the largest nonrepeating harmonious chords possible in an edo this low. This produces mode of symmetry scales with two different modes and 4 different keys, making it equally easy to establish any chord in the scale as the root and modulate between them.
28edo is particularly well suited to Whitewood in the same way that 15edo is for Blackwood, as it has one third that is heavily tempered, but in a familiar way shared with 12edo, while the other one is significantly closer to just. This makes the 5ths more out of tune, but in a useful way, as you can stack major and minor thirds indefinitely until they repeat 4 octaves and 14 notes up, producing one of the largest nonrepeating harmonious chords possible in an edo this low. This produces mode of symmetry scales with two different modes and 4 different keys, making it equally easy to establish any chord in the scale as the root and modulate between them.


Whitewood Major [14] 13131313131313
* Whitewood Major [14] 13131313131313
* Whitewood Minor [14] 31313131313131
* (Whitewood neutral is also theoretically possible, stacking neutral or subminor & supermajor thirds, but in practice that works out as 22222222222222, or 14edo, so it doesn't count as a 28edo scale)
* [[machine5]]
* [[machine6]]
* [[machine11]]


Whitewood Minor [14] 31313131313131
== Music ==


(Whitewood neutral is also theoretically possible, stacking neutral or subminor & supermajor thirds, but in practice that works out as 22222222222222, or 14edo, so it doesn't count as a 28edo scale)
* [http://www.youtube.com/watch?v=26UpCbrb3mE 28 tone Prelude] by Kosmorksy


[[machine5|machine5]]
[[Category:Theory]]
 
[[Category:28edo]]
[[machine6|machine6]]
[[Category:Edo]]
 
[[Category:Twentuning]]
[[machine11|machine11]]


=Music=
[[Category:Todo:unify precision]]
[http://www.youtube.com/watch?v=26UpCbrb3mE 28 tone Prelude] by Kosmorksy
[[Category:28edo]]
[[Category:edo]]
[[Category:theory]]
[[Category:todo:unify_precision]]
[[Category:twentuning]]
Retrieved from "https://en.xen.wiki/w/28edo"