28edo: Difference between revisions

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→Table of intervals: Removed pions columns and and 7mus column for just intervals
Line 16: Line 16:
|-
|-
| rowspan="2" style="text-align:center;" | Step #
| rowspan="2" style="text-align:center;" | Step #
| colspan="3" style="text-align:center;" | ET
| colspan="2" style="text-align:center;" | ET
| colspan="4" style="text-align:center;" | Just  
| colspan="2" style="text-align:center;" | Just  
| style="text-align:center;" | Difference
| style="text-align:center;" | Difference


Line 24: Line 24:
|-
|-
|Cents
|Cents
|pions
|7mus
|7mus
|Interval
|Interval
|Cents
|Cents
|pions
|7mus
|
|
|
|
Line 37: Line 34:
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:center;" | 0¢
| style="text-align:center;" | 0¢
|0π<sup>¢</sup>
|0
|0
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|
|
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | unison
| style="text-align:center;" | unison
Line 50: Line 44:
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 42.86
| style="text-align:center;" | 42.86
|45.43
|54.86 (36.DC<sub>16</sub>)
|54.86 (36.DC<sub>16</sub>)
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|
|
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | up-unison
| style="text-align:center;" | up-unison
Line 63: Line 54:
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 85.71
| style="text-align:center;" | 85.71
|90.86
|109.71 (6D.B7<sub>16</sub>)
|109.71 (6D.B7<sub>16</sub>)
| style="text-align:center;" | 21:20
| style="text-align:center;" | 21:20
| style="text-align:center;" | 84.47
| style="text-align:center;" | 84.47
|89.535
|108.12 (6C.1E<sub>16</sub>)
| style="text-align:center;" | 1.24
| style="text-align:center;" | 1.24
| style="text-align:center;" | double-up, double-down
| style="text-align:center;" | double-up, double-down
Line 76: Line 64:
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 128.57
| style="text-align:center;" | 128.57
|136.29
|164.57 (A4.92<sub>16</sub>)
|164.57 (A4.92<sub>16</sub>)
| style="text-align:center;" | 14:13
| style="text-align:center;" | 14:13
| style="text-align:center;" | 128.3
| style="text-align:center;" | 128.3
|136
|164.22 (A4.38<sub>16</sub>)
| style="text-align:center;" | 0.27
| style="text-align:center;" | 0.27
| style="text-align:center;" | down 2nd
| style="text-align:center;" | down 2nd
Line 89: Line 74:
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 171.43
| style="text-align:center;" | 171.43
|181.71
|219.43 (DB.6E<sub>16</sub>)
|219.43 (DB.6E<sub>16</sub>)
| style="text-align:center;" | 11:10
| style="text-align:center;" | 11:10
| style="text-align:center;" | 165
| style="text-align:center;" | 165
|174.9
|211.205 (D3.35<sub>16</sub>)
| style="text-align:center;" | 6.43
| style="text-align:center;" | 6.43
| style="text-align:center;" | 2nd
| style="text-align:center;" | 2nd
Line 102: Line 84:
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | 214.29
| style="text-align:center;" | 214.29
|227.14
|274.27 (112.49<sub>16</sub>)
|274.27 (112.49<sub>16</sub>)
| style="text-align:center;" | 17:15
| style="text-align:center;" | 17:15
| style="text-align:center;" | 216.69
| style="text-align:center;" | 216.69
|229.69
|277.36 (115.5C<sub>16</sub>)
| style="text-align:center;" | -2.40
| style="text-align:center;" | -2.40
| style="text-align:center;" | up 2nd
| style="text-align:center;" | up 2nd
Line 115: Line 94:
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| style="text-align:center;" | 257.14
| style="text-align:center;" | 257.14
|272.57
|329.14 (149.25<sub>16</sub>)
|329.14 (149.25<sub>16</sub>)
| style="text-align:center;" | 7:6
| style="text-align:center;" | 7:6
| style="text-align:center;" | 266.87
| style="text-align:center;" | 266.87
|282.88
|341.595 (155.98<sub>16</sub>)
| style="text-align:center;" | -9.73
| style="text-align:center;" | -9.73
| style="text-align:center;" | double-up 2nd, double-down 3rd
| style="text-align:center;" | double-up 2nd, double-down 3rd
Line 128: Line 104:
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| style="text-align:center;" | 300
| style="text-align:center;" | 300
|318
|384 (180<sub>16</sub>)
|384 (180<sub>16</sub>)
| style="text-align:center;" | 6:5
| style="text-align:center;" | 6:5
| style="text-align:center;" | 315.64
| style="text-align:center;" | 315.64
|334.58
|404.02 (194.05<sub>16</sub>)
| style="text-align:center;" | -15.64
| style="text-align:center;" | -15.64
| style="text-align:center;" | down 3rd
| style="text-align:center;" | down 3rd
Line 141: Line 114:
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| style="text-align:center;" | 342.86
| style="text-align:center;" | 342.86
|363.43
|438.86 (1B6.DC<sub>16</sub>)
|438.86 (1B6.DC<sub>16</sub>)
| style="text-align:center;" | 11:9
| style="text-align:center;" | 11:9
| style="text-align:center;" | 347.41
| style="text-align:center;" | 347.41
|368.25
|444.68 (1BC.AF<sub>16</sub>)
| style="text-align:center;" | -4.55
| style="text-align:center;" | -4.55
| style="text-align:center;" | 3rd
| style="text-align:center;" | 3rd
Line 154: Line 124:
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| style="text-align:center;" | 385.71
| style="text-align:center;" | 385.71
|408.86
|493.71 (1ED.B7<sub>16</sub>)
|493.71 (1ED.B7<sub>16</sub>)
| style="text-align:center;" | 5:4
| style="text-align:center;" | 5:4
| style="text-align:center;" | 386.31
| style="text-align:center;" | 386.31
|409.49
|494.48 (1EE.7B<sub>16</sub>)
| style="text-align:center;" | -0.60
| style="text-align:center;" | -0.60
| style="text-align:center;" | up 3rd
| style="text-align:center;" | up 3rd
Line 167: Line 134:
| style="text-align:center;" | 10
| style="text-align:center;" | 10
| style="text-align:center;" | 428.57
| style="text-align:center;" | 428.57
|454.29
|548.57 (224.92<sub>16</sub>)
|548.57 (224.92<sub>16</sub>)
| style="text-align:center;" | 9:7
| style="text-align:center;" | 9:7
| style="text-align:center;" | 435.08
| style="text-align:center;" | 435.08
|461.19
|556.91 (22A.E8<sub>16</sub>)
| style="text-align:center;" | -6.51
| style="text-align:center;" | -6.51
| style="text-align:center;" | double-up 3rd, double-down 4th
| style="text-align:center;" | double-up 3rd, double-down 4th
Line 180: Line 144:
| style="text-align:center;" | 11
| style="text-align:center;" | 11
| style="text-align:center;" | 471.43
| style="text-align:center;" | 471.43
|499.71
|603.43 (26B.6E<sub>16</sub>)
|603.43 (26B.6E<sub>16</sub>)
| style="text-align:center;" | 21:16
| style="text-align:center;" | 21:16
| style="text-align:center;" | 470.78
| style="text-align:center;" | 470.78
|499.03
|602.6 (25A.99<sub>16</sub>)
| style="text-align:center;" | 0.65
| style="text-align:center;" | 0.65
| style="text-align:center;" | down 4th
| style="text-align:center;" | down 4th
Line 193: Line 154:
| style="text-align:center;" | 12
| style="text-align:center;" | 12
| style="text-align:center;" | 514.29
| style="text-align:center;" | 514.29
|545.14
|658.29 (292.49<sub>16</sub>)
|658.29 (292.49<sub>16</sub>)
| style="text-align:center;" | 4:3
| style="text-align:center;" | 4:3
| style="text-align:center;" | 498.045
| style="text-align:center;" | 498.045
|527.93
|637.5 (27D.7F<sub>16</sub>)
| style="text-align:center;" | 16.245
| style="text-align:center;" | 16.245
| style="text-align:center;" | 4th
| style="text-align:center;" | 4th
Line 206: Line 164:
| style="text-align:center;" | 13
| style="text-align:center;" | 13
| style="text-align:center;" | 557.14
| style="text-align:center;" | 557.14
|590.57
|713.14 (2C9.25<sub>16</sub>)
|713.14 (2C9.25<sub>16</sub>)
| style="text-align:center;" | 11:8
| style="text-align:center;" | 11:8
| style="text-align:center;" | 551.32
| style="text-align:center;" | 551.32
|584.4
|705.69 (2C1.B<sub>16</sub>)
| style="text-align:center;" | 5.82
| style="text-align:center;" | 5.82
| style="text-align:center;" | up 4th
| style="text-align:center;" | up 4th
Line 219: Line 174:
| style="text-align:center;" | 14
| style="text-align:center;" | 14
| style="text-align:center;" | 600
| style="text-align:center;" | 600
|636
|768 (300<sub>16</sub>)
|768 (300<sub>16</sub>)
| style="text-align:center;" | 7:5
| style="text-align:center;" | 7:5
| style="text-align:center;" | 582.51
| style="text-align:center;" | 582.51
|617.46
|745.62 (2E9.9E<sub>16</sub>)
| style="text-align:center;" | 17.49
| style="text-align:center;" | 17.49
| style="text-align:center;" | double-up 4th, double-down 5th
| style="text-align:center;" | double-up 4th, double-down 5th
Line 232: Line 184:
| style="text-align:center;" | 15
| style="text-align:center;" | 15
| style="text-align:center;" | 642.86
| style="text-align:center;" | 642.86
|681.43
|822.86 (336.DC<sub>16</sub>)
|822.86 (336.DC<sub>16</sub>)
| style="text-align:center;" | 16:11
| style="text-align:center;" | 16:11
| style="text-align:center;" | 648.68
| style="text-align:center;" | 648.68
|687.6
|830.31 (33E.5<sub>16</sub>)
| style="text-align:center;" | -5.82
| style="text-align:center;" | -5.82
| style="text-align:center;" | down 5th
| style="text-align:center;" | down 5th
Line 245: Line 194:
| style="text-align:center;" | 16
| style="text-align:center;" | 16
| style="text-align:center;" | 685.71
| style="text-align:center;" | 685.71
|726.86
|877.71 (36D.B7<sub>16</sub>)
|877.71 (36D.B7<sub>16</sub>)
| style="text-align:center;" | 3:2
| style="text-align:center;" | 3:2
| style="text-align:center;" | 701.955
| style="text-align:center;" | 701.955
|744.07
|898.5 (382.81<sub>16</sub>)
| style="text-align:center;" | -16.245
| style="text-align:center;" | -16.245
| style="text-align:center;" | 5th
| style="text-align:center;" | 5th
Line 258: Line 204:
| style="text-align:center;" | 17
| style="text-align:center;" | 17
| style="text-align:center;" | 728.57
| style="text-align:center;" | 728.57
|772.29
|934.57 (3A4.92<sub>16</sub>)
|934.57 (3A4.92<sub>16</sub>)
| style="text-align:center;" | 32:21
| style="text-align:center;" | 32:21
| style="text-align:center;" | 729.22
| style="text-align:center;" | 729.22
|772.97
|933.6 (3A5.67<sub>16</sub>)
| style="text-align:center;" | -0.65
| style="text-align:center;" | -0.65
| style="text-align:center;" | up 5th
| style="text-align:center;" | up 5th
Line 271: Line 214:
| style="text-align:center;" | 18
| style="text-align:center;" | 18
| style="text-align:center;" | 771.43
| style="text-align:center;" | 771.43
|817.71
|987.43 (3DB.6E<sub>16</sub>)
|987.43 (3DB.6E<sub>16</sub>)
| style="text-align:center;" | 14:9
| style="text-align:center;" | 14:9
| style="text-align:center;" | 764.92
| style="text-align:center;" | 764.92
|810.81
|979.09 (3C3.18<sub>16</sub>)
| style="text-align:center;" | 6.51
| style="text-align:center;" | 6.51
| style="text-align:center;" | double-up 5th, double-down 6th
| style="text-align:center;" | double-up 5th, double-down 6th
Line 284: Line 224:
| style="text-align:center;" | 19
| style="text-align:center;" | 19
| style="text-align:center;" | 814.29
| style="text-align:center;" | 814.29
|863.14
|1042.29 (412.49<sub>16</sub>)
|1042.29 (412.49<sub>16</sub>)
| style="text-align:center;" | 8:5
| style="text-align:center;" | 8:5
| style="text-align:center;" | 813.68
| style="text-align:center;" | 813.68
|862.51
|1041.52 (411.84<sub>16</sub>)
| style="text-align:center;" | 0.61
| style="text-align:center;" | 0.61
| style="text-align:center;" | down 6th
| style="text-align:center;" | down 6th
Line 297: Line 234:
| style="text-align:center;" | 20
| style="text-align:center;" | 20
| style="text-align:center;" | 857.14
| style="text-align:center;" | 857.14
|908.57
|1097.14 (449.24<sub>16</sub>)
|1097.14 (449.24<sub>16</sub>)
| style="text-align:center;" | 18:11
| style="text-align:center;" | 18:11
| style="text-align:center;" | 852.59
| style="text-align:center;" | 852.59
|903.75
|1061.32 (425.51<sub>16</sub>)
| style="text-align:center;" | 4.55
| style="text-align:center;" | 4.55
| style="text-align:center;" | 6th
| style="text-align:center;" | 6th
Line 310: Line 244:
| style="text-align:center;" | 21
| style="text-align:center;" | 21
| style="text-align:center;" | 900
| style="text-align:center;" | 900
|954
|1152 (480<sub>16</sub>)
|1152 (480<sub>16</sub>)
| style="text-align:center;" | 5:3
| style="text-align:center;" | 5:3
| style="text-align:center;" | 884.36
| style="text-align:center;" | 884.36
|937.42
|1131.98 (46B.FB<sub>16</sub>)
| style="text-align:center;" | 15.64
| style="text-align:center;" | 15.64
| style="text-align:center;" | up 6th
| style="text-align:center;" | up 6th
Line 323: Line 254:
| style="text-align:center;" | 22
| style="text-align:center;" | 22
| style="text-align:center;" | 942.86
| style="text-align:center;" | 942.86
|999.43
|1206.86 (4B6.DC<sub>16</sub>)
|1206.86 (4B6.DC<sub>16</sub>)
| style="text-align:center;" | 12:7
| style="text-align:center;" | 12:7
| style="text-align:center;" | 933.13
| style="text-align:center;" | 933.13
|989.12
|1194.405 (4AA.68<sub>16</sub>)
| style="text-align:center;" | 9.73
| style="text-align:center;" | 9.73
| style="text-align:center;" | double-up 6th, double-down 7th
| style="text-align:center;" | double-up 6th, double-down 7th
Line 336: Line 264:
| style="text-align:center;" | 23
| style="text-align:center;" | 23
| style="text-align:center;" | 985.71
| style="text-align:center;" | 985.71
|1044.86
|1261.71 (4DC.49<sub>16</sub>)
|1261.71 (4DC.49<sub>16</sub>)
| style="text-align:center;" | 30:17
| style="text-align:center;" | 30:17
| style="text-align:center;" | 983.31
| style="text-align:center;" | 983.31
|1042.31
|1258.64 (4EA.A4<sub>16</sub>)
| style="text-align:center;" | 2.40
| style="text-align:center;" | 2.40
| style="text-align:center;" | down 7th
| style="text-align:center;" | down 7th
Line 349: Line 274:
| style="text-align:center;" | 24
| style="text-align:center;" | 24
| style="text-align:center;" | 1028.57
| style="text-align:center;" | 1028.57
|1090.29
|1316.57 (524.92<sub>16</sub>)
|1316.57 (524.92<sub>16</sub>)
| style="text-align:center;" | 20:11
| style="text-align:center;" | 20:11
| style="text-align:center;" | 1035
| style="text-align:center;" | 1035
|1097.1
|1324.795 (52C.CB<sub>16</sub>)
| style="text-align:center;" | -6.43
| style="text-align:center;" | -6.43
| style="text-align:center;" | 7th
| style="text-align:center;" | 7th
Line 362: Line 284:
| style="text-align:center;" | 25
| style="text-align:center;" | 25
| style="text-align:center;" | 1071.42
| style="text-align:center;" | 1071.42
|1135.71
|1371.43 (55A.6E<sub>16</sub>)
|1371.43 (55A.6E<sub>16</sub>)
| style="text-align:center;" | 13:7
| style="text-align:center;" | 13:7
| style="text-align:center;" | 1071.70
| style="text-align:center;" | 1071.70
|1136
|1371.78 (54B.C8<sub>16</sub>)
| style="text-align:center;" | -0.27
| style="text-align:center;" | -0.27
| style="text-align:center;" | up 7th
| style="text-align:center;" | up 7th
Line 375: Line 294:
| style="text-align:center;" | 26
| style="text-align:center;" | 26
| style="text-align:center;" | 1114.29
| style="text-align:center;" | 1114.29
|1181.14
|1426.29 (592.49<sub>16</sub>)
|1426.29 (592.49<sub>16</sub>)
| style="text-align:center;" | 40:21
| style="text-align:center;" | 40:21
| style="text-align:center;" | 1115.53
| style="text-align:center;" | 1115.53
|1162.465
|1427.88 (593.E2<sub>16</sub>)
| style="text-align:center;" | -1.24
| style="text-align:center;" | -1.24
| style="text-align:center;" | double-up 7th, double-down 8ve
| style="text-align:center;" | double-up 7th, double-down 8ve
Line 388: Line 304:
| style="text-align:center;" | 27
| style="text-align:center;" | 27
| style="text-align:center;" | 1157.14
| style="text-align:center;" | 1157.14
|1226.57
|1471.14 (5C9.25<sub>16</sub>)
|1471.14 (5C9.25<sub>16</sub>)
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|
|
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | down 8ve
| style="text-align:center;" | down 8ve
Line 401: Line 314:
| style="text-align:center;" | 28
| style="text-align:center;" | 28
| style="text-align:center;" | 1200
| style="text-align:center;" | 1200
|1272
|1536 (600<sub>16</sub>)
|1536 (600<sub>16</sub>)
| style="text-align:center;" | 2:1
| style="text-align:center;" | 2:1
| style="text-align:center;" | 1200
| style="text-align:center;" | 1200
|1272
|1536 (600<sub>16</sub>)
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:center;" | 8ve
| style="text-align:center;" | 8ve

Revision as of 14:02, 12 December 2019

Basic properties

28edo, a multiple of both 7edo and 14edo (and of course 2edo and 4edo), has a step size of 42.857 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 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.

Subgroups

28edo can approximate the 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 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 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.

Table of intervals

The following table compares it to potentially useful nearby just intervals.

Step # ET Just Difference

(ET minus Just)

Up/down Notation
Cents 7mus Interval Cents
0 0¢ 0 unison 1 D
1 42.86 54.86 (36.DC16) up-unison ^1 D^
2 85.71 109.71 (6D.B716) 21:20 84.47 1.24 double-up, double-down ^^1, vv2 D^^, Evv
3 128.57 164.57 (A4.9216) 14:13 128.3 0.27 down 2nd v2 Ev
4 171.43 219.43 (DB.6E16) 11:10 165 6.43 2nd 2 E
5 214.29 274.27 (112.4916) 17:15 216.69 -2.40 up 2nd ^2 E^
6 257.14 329.14 (149.2516) 7:6 266.87 -9.73 double-up 2nd, double-down 3rd ^^2, vv3 E^^, Fvv
7 300 384 (18016) 6:5 315.64 -15.64 down 3rd v3 Fv
8 342.86 438.86 (1B6.DC16) 11:9 347.41 -4.55 3rd 3 F
9 385.71 493.71 (1ED.B716) 5:4 386.31 -0.60 up 3rd ^3 F^
10 428.57 548.57 (224.9216) 9:7 435.08 -6.51 double-up 3rd, double-down 4th ^^3, vv4 F^^, Gvv
11 471.43 603.43 (26B.6E16) 21:16 470.78 0.65 down 4th v4 Gv
12 514.29 658.29 (292.4916) 4:3 498.045 16.245 4th 4 G
13 557.14 713.14 (2C9.2516) 11:8 551.32 5.82 up 4th ^4 G^
14 600 768 (30016) 7:5 582.51 17.49 double-up 4th, double-down 5th ^^4, vv5 G^^, vvA
15 642.86 822.86 (336.DC16) 16:11 648.68 -5.82 down 5th v5 Av
16 685.71 877.71 (36D.B716) 3:2 701.955 -16.245 5th 5 A
17 728.57 934.57 (3A4.9216) 32:21 729.22 -0.65 up 5th ^5 A^
18 771.43 987.43 (3DB.6E16) 14:9 764.92 6.51 double-up 5th, double-down 6th ^^5, vv6 A^^, Bvv
19 814.29 1042.29 (412.4916) 8:5 813.68 0.61 down 6th v6 Bv
20 857.14 1097.14 (449.2416) 18:11 852.59 4.55 6th 6 B
21 900 1152 (48016) 5:3 884.36 15.64 up 6th ^6 B^
22 942.86 1206.86 (4B6.DC16) 12:7 933.13 9.73 double-up 6th, double-down 7th ^^6, vv7 B^^, Cvv
23 985.71 1261.71 (4DC.4916) 30:17 983.31 2.40 down 7th v7 Cv
24 1028.57 1316.57 (524.9216) 20:11 1035 -6.43 7th 7 C
25 1071.42 1371.43 (55A.6E16) 13:7 1071.70 -0.27 up 7th ^7 C^
26 1114.29 1426.29 (592.4916) 40:21 1115.53 -1.24 double-up 7th, double-down 8ve ^^7, vv8 C^^, Dvv
27 1157.14 1471.14 (5C9.2516) down 8ve v8 Dv
28 1200 1536 (60016) 2:1 1200 0 8ve 8 D

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.

0-8-16 = C E G = C = C or C perfect

0-7-16 = C Ev G = C(v3) = C down-three

0-9-16 = C E^ G = C(^3) = C up-three

0-8-15 = C E Gv = C(v5) = C down-five

0-9-17 = C E^ G^ = C(^3,^5) = C up-three up-five

0-8-16-24 = C E G B = C7 = C seven

0-8-16-23 = C E G Bv = C(v7) = C down-seven

0-7-16-24 = C Ev G B = C7(v3) = C seven down-three

0-7-16-23 = C Ev G Bv = C.v7 = C dot down seven

For a more complete list, see Ups and Downs Notation - Chord names in other EDOs.

Rank two temperaments

Periods

per octave

Generator Temperaments
1 1\28
1 3\28 Negri
1 5\28 Machine
1 9\28 Worschmidt
1 11\28
1 13\28 Thuja
2 1\28
2 3\28
2 5\28 Antikythera
4 1\28
4 2\28 Demolished
4 3\28
7 1\28 Whitewood
14 1\28

Commas

28 EDO tempers out the following commas. (Note: This assumes the val < 28 44 65 79 97 104 |.)

Comma Monzo Cents Name 1 Name 2
2187/2048 | -11 7 > 113.69 Apotome
648/625 | 3 4 -4 > 62.57 Major Diesis Diminished Comma
16875/16384 | -14 3 4 > 51.12 Negri Comma Double Augmentation Diesis
| 17 1 -8 > 11.45 Wuerschmidt Comma
36/35 | 2 2 -1 -1 > 48.77 Septimal Quarter Tone
50/49 | 1 0 2 -2 > 34.98 Tritonic Diesis Jubilisma
3125/3087 | 0 -2 5 -3 > 21.18 Gariboh
126/125 | 1 2 -3 1 > 13.79 Septimal Semicomma Starling Comma
65625/65536 | -16 1 5 1 > 2.35 Horwell
| 47 -7 -7 -7 > 0.34 Akjaysma 5\7 Octave Comma
176/175 | 4 0 -2 -1 1 > 9.86 Valinorsma
441/440 | -3 2 -1 2 -1 > 3.93 Werckisma
4000/3993 | 5 -1 3 0 -3 > 3.03 Wizardharry

Some scales

machine5

machine6

machine11

Compositions

28 tone Prelude by Kosmorksy

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