28edo: Difference between revisions
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| Line 15: | Line 15: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| style="text-align:center;" | Step # | | rowspan="2" style="text-align:center;" | Step # | ||
| style="text-align:center;" | ET | | colspan="3" style="text-align:center;" | ET | ||
| | | colspan="4" style="text-align:center;" | Just | ||
| style="text-align:center;" | Difference | | style="text-align:center;" | Difference | ||
(ET minus Just) | (ET minus Just) | ||
| colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|Up/down ]][[Ups_and_Downs_Notation|Notation]] | | colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|Up/down]] [[Ups_and_Downs_Notation|Notation]] | ||
|- | |||
|Cents | |||
|pions | |||
|7mus | |||
|Interval | |||
|Cents | |||
|pions | |||
|7mus | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| style="text-align:center;" | 0 | | style="text-align:center;" | 0 | ||
| style="text-align:center;" | 0¢ | | style="text-align:center;" | 0¢ | ||
|0π<sup>¢</sup> | |||
|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 35: | Line 50: | ||
| 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>) | |||
| 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 44: | Line 63: | ||
| 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>) | |||
| 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 53: | Line 76: | ||
| 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>) | |||
| style="text-align:center;" | 14:13 | | style="text-align:center;" | 14:13 | ||
| style="text-align:center;" | 128. | | 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 62: | Line 89: | ||
| 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>) | |||
| 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 71: | Line 102: | ||
| 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>) | |||
| 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 80: | Line 115: | ||
| 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>) | |||
| 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 89: | Line 128: | ||
| 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>) | |||
| 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 98: | Line 141: | ||
| 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>) | |||
| 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 107: | Line 154: | ||
| 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>) | |||
| 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 116: | Line 167: | ||
| 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>) | |||
| 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 125: | Line 180: | ||
| 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>) | |||
| 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 134: | Line 193: | ||
| 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>) | |||
| style="text-align:center;" | 4:3 | | style="text-align:center;" | 4:3 | ||
| style="text-align:center;" | 498. | | style="text-align:center;" | 498.045 | ||
| style="text-align:center;" | 16. | |527.93 | ||
|637.5 (27D.7F<sub>16</sub>) | |||
| style="text-align:center;" | 16.245 | |||
| style="text-align:center;" | 4th | | style="text-align:center;" | 4th | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| Line 143: | Line 206: | ||
| 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>) | |||
| 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 152: | Line 219: | ||
| 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>) | |||
| 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 161: | Line 232: | ||
| 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>) | |||
| 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 170: | Line 245: | ||
| 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>) | |||
| style="text-align:center;" | 3:2 | | style="text-align:center;" | 3:2 | ||
| style="text-align:center;" | 701. | | style="text-align:center;" | 701.955 | ||
| style="text-align:center;" | -16. | |744.07 | ||
|898.5 (382.81<sub>16</sub>) | |||
| style="text-align:center;" | -16.245 | |||
| style="text-align:center;" | 5th | | style="text-align:center;" | 5th | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| Line 179: | Line 258: | ||
| 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>) | |||
| 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 188: | Line 271: | ||
| 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>) | |||
| 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 197: | Line 284: | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
| style="text-align:center;" | 814.29 | | style="text-align:center;" | 814.29 | ||
| style="text-align:center;" | 5 | |863.14 | ||
|1042.29 (412.49<sub>16</sub>) | |||
| 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 206: | Line 297: | ||
| 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>) | |||
| 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 215: | Line 310: | ||
| 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>) | |||
| 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 224: | Line 323: | ||
| 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>) | |||
| 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 233: | Line 336: | ||
| 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>) | |||
| 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 242: | Line 349: | ||
| 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>) | |||
| 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 251: | Line 362: | ||
| 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>) | |||
| 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 260: | Line 375: | ||
| 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>) | |||
| 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 269: | Line 388: | ||
| 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>) | |||
| 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 278: | Line 401: | ||
| 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>) | |||
| 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 | ||
| Line 389: | Line 516: | ||
|- | |- | ||
| style="text-align:center;" | 2187/2048 | | style="text-align:center;" | 2187/2048 | ||
| | | -11 7 > | | |<nowiki> | -11 7 </nowiki>> | ||
| style="text-align:center;" | 113.69 | | style="text-align:center;" | 113.69 | ||
| style="text-align:center;" | Apotome | | style="text-align:center;" | Apotome | ||
| Line 395: | Line 522: | ||
|- | |- | ||
| style="text-align:center;" | 648/625 | | style="text-align:center;" | 648/625 | ||
| | | 3 4 -4 > | | |<nowiki> | 3 4 -4 </nowiki>> | ||
| style="text-align:center;" | 62.57 | | style="text-align:center;" | 62.57 | ||
| style="text-align:center;" | Major Diesis | | style="text-align:center;" | Major Diesis | ||
| Line 401: | Line 528: | ||
|- | |- | ||
| style="text-align:center;" | 16875/16384 | | style="text-align:center;" | 16875/16384 | ||
| | | -14 3 4 > | | |<nowiki> | -14 3 4 </nowiki>> | ||
| style="text-align:center;" | 51.12 | | style="text-align:center;" | 51.12 | ||
| style="text-align:center;" | Negri Comma | | style="text-align:center;" | Negri Comma | ||
| Line 407: | Line 534: | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| | | 17 1 -8 > | | |<nowiki> | 17 1 -8 </nowiki>> | ||
| style="text-align:center;" | 11.45 | | style="text-align:center;" | 11.45 | ||
| style="text-align:center;" | Wuerschmidt Comma | | style="text-align:center;" | Wuerschmidt Comma | ||
| Line 413: | Line 540: | ||
|- | |- | ||
| style="text-align:center;" | 36/35 | | style="text-align:center;" | 36/35 | ||
| | | 2 2 -1 -1 > | | |<nowiki> | 2 2 -1 -1 </nowiki>> | ||
| style="text-align:center;" | 48.77 | | style="text-align:center;" | 48.77 | ||
| style="text-align:center;" | Septimal Quarter Tone | | style="text-align:center;" | Septimal Quarter Tone | ||
| Line 419: | Line 546: | ||
|- | |- | ||
| style="text-align:center;" | 50/49 | | style="text-align:center;" | 50/49 | ||
| | | 1 0 2 -2 > | | |<nowiki> | 1 0 2 -2 </nowiki>> | ||
| style="text-align:center;" | 34.98 | | style="text-align:center;" | 34.98 | ||
| style="text-align:center;" | Tritonic Diesis | | style="text-align:center;" | Tritonic Diesis | ||
| Line 425: | Line 552: | ||
|- | |- | ||
| style="text-align:center;" | 3125/3087 | | style="text-align:center;" | 3125/3087 | ||
| | | 0 -2 5 -3 > | | |<nowiki> | 0 -2 5 -3 </nowiki>> | ||
| style="text-align:center;" | 21.18 | | style="text-align:center;" | 21.18 | ||
| style="text-align:center;" | Gariboh | | style="text-align:center;" | Gariboh | ||
| Line 431: | Line 558: | ||
|- | |- | ||
| style="text-align:center;" | 126/125 | | style="text-align:center;" | 126/125 | ||
| | | 1 2 -3 1 > | | |<nowiki> | 1 2 -3 1 </nowiki>> | ||
| style="text-align:center;" | 13.79 | | style="text-align:center;" | 13.79 | ||
| style="text-align:center;" | Septimal Semicomma | | style="text-align:center;" | Septimal Semicomma | ||
| Line 437: | Line 564: | ||
|- | |- | ||
| style="text-align:center;" | 65625/65536 | | style="text-align:center;" | 65625/65536 | ||
| | | -16 1 5 1 > | | |<nowiki> | -16 1 5 1 </nowiki>> | ||
| style="text-align:center;" | 2.35 | | style="text-align:center;" | 2.35 | ||
| style="text-align:center;" | Horwell | | style="text-align:center;" | Horwell | ||
| Line 443: | Line 570: | ||
|- | |- | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| | | 47 -7 -7 -7 > | | |<nowiki> | 47 -7 -7 -7 </nowiki>> | ||
| style="text-align:center;" | 0.34 | | style="text-align:center;" | 0.34 | ||
| style="text-align:center;" | Akjaysma | | style="text-align:center;" | Akjaysma | ||
| Line 449: | Line 576: | ||
|- | |- | ||
| style="text-align:center;" | 176/175 | | style="text-align:center;" | 176/175 | ||
| | | 4 0 -2 -1 1 > | | |<nowiki> | 4 0 -2 -1 1 </nowiki>> | ||
| style="text-align:center;" | 9.86 | | style="text-align:center;" | 9.86 | ||
| style="text-align:center;" | Valinorsma | | style="text-align:center;" | Valinorsma | ||
| Line 455: | Line 582: | ||
|- | |- | ||
| style="text-align:center;" | 441/440 | | style="text-align:center;" | 441/440 | ||
| | | -3 2 -1 2 -1 > | | |<nowiki> | -3 2 -1 2 -1 </nowiki>> | ||
| style="text-align:center;" | 3.93 | | style="text-align:center;" | 3.93 | ||
| style="text-align:center;" | Werckisma | | style="text-align:center;" | Werckisma | ||
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|- | |- | ||
| style="text-align:center;" | 4000/3993 | | style="text-align:center;" | 4000/3993 | ||
| | | 5 -1 3 0 -3 > | | |<nowiki> | 5 -1 3 0 -3 </nowiki>> | ||
| style="text-align:center;" | 3.03 | | style="text-align:center;" | 3.03 | ||
| style="text-align:center;" | Wizardharry | | style="text-align:center;" | Wizardharry | ||
Revision as of 01:10, 31 March 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 | pions | 7mus | Interval | Cents | pions | 7mus | |||||
| 0 | 0¢ | 0π¢ | 0 | unison | 1 | D | |||||
| 1 | 42.86 | 45.43 | 54.86 (36.DC16) | up-unison | ^1 | D^ | |||||
| 2 | 85.71 | 90.86 | 109.71 (6D.B716) | 21:20 | 84.47 | 89.535 | 108.12 (6C.1E16) | 1.24 | double-up, double-down | ^^1, vv2 | D^^, Evv |
| 3 | 128.57 | 136.29 | 164.57 (A4.9216) | 14:13 | 128.3 | 136 | 164.22 (A4.3816) | 0.27 | down 2nd | v2 | Ev |
| 4 | 171.43 | 181.71 | 219.43 (DB.6E16) | 11:10 | 165 | 174.9 | 211.205 (D3.3516) | 6.43 | 2nd | 2 | E |
| 5 | 214.29 | 227.14 | 274.27 (112.4916) | 17:15 | 216.69 | 229.69 | 277.36 (115.5C16) | -2.40 | up 2nd | ^2 | E^ |
| 6 | 257.14 | 272.57 | 329.14 (149.2516) | 7:6 | 266.87 | 282.88 | 341.595 (155.9816) | -9.73 | double-up 2nd, double-down 3rd | ^^2, vv3 | E^^, Fvv |
| 7 | 300 | 318 | 384 (18016) | 6:5 | 315.64 | 334.58 | 404.02 (194.0516) | -15.64 | down 3rd | v3 | Fv |
| 8 | 342.86 | 363.43 | 438.86 (1B6.DC16) | 11:9 | 347.41 | 368.25 | 444.68 (1BC.AF16) | -4.55 | 3rd | 3 | F |
| 9 | 385.71 | 408.86 | 493.71 (1ED.B716) | 5:4 | 386.31 | 409.49 | 494.48 (1EE.7B16) | -0.60 | up 3rd | ^3 | F^ |
| 10 | 428.57 | 454.29 | 548.57 (224.9216) | 9:7 | 435.08 | 461.19 | 556.91 (22A.E816) | -6.51 | double-up 3rd, double-down 4th | ^^3, vv4 | F^^, Gvv |
| 11 | 471.43 | 499.71 | 603.43 (26B.6E16) | 21:16 | 470.78 | 499.03 | 602.6 (25A.9916) | 0.65 | down 4th | v4 | Gv |
| 12 | 514.29 | 545.14 | 658.29 (292.4916) | 4:3 | 498.045 | 527.93 | 637.5 (27D.7F16) | 16.245 | 4th | 4 | G |
| 13 | 557.14 | 590.57 | 713.14 (2C9.2516) | 11:8 | 551.32 | 584.4 | 705.69 (2C1.B16) | 5.82 | up 4th | ^4 | G^ |
| 14 | 600 | 636 | 768 (30016) | 7:5 | 582.51 | 617.46 | 745.62 (2E9.9E16) | 17.49 | double-up 4th, double-down 5th | ^^4, vv5 | G^^, vvA |
| 15 | 642.86 | 681.43 | 822.86 (336.DC16) | 16:11 | 648.68 | 687.6 | 830.31 (33E.516) | -5.82 | down 5th | v5 | Av |
| 16 | 685.71 | 726.86 | 877.71 (36D.B716) | 3:2 | 701.955 | 744.07 | 898.5 (382.8116) | -16.245 | 5th | 5 | A |
| 17 | 728.57 | 772.29 | 934.57 (3A4.9216) | 32:21 | 729.22 | 772.97 | 933.6 (3A5.6716) | -0.65 | up 5th | ^5 | A^ |
| 18 | 771.43 | 817.71 | 987.43 (3DB.6E16) | 14:9 | 764.92 | 810.81 | 979.09 (3C3.1816) | 6.51 | double-up 5th, double-down 6th | ^^5, vv6 | A^^, Bvv |
| 19 | 814.29 | 863.14 | 1042.29 (412.4916) | 8:5 | 813.68 | 862.51 | 1041.52 (411.8416) | 0.61 | down 6th | v6 | Bv |
| 20 | 857.14 | 908.57 | 1097.14 (449.2416) | 18:11 | 852.59 | 903.75 | 1061.32 (425.5116) | 4.55 | 6th | 6 | B |
| 21 | 900 | 954 | 1152 (48016) | 5:3 | 884.36 | 937.42 | 1131.98 (46B.FB16) | 15.64 | up 6th | ^6 | B^ |
| 22 | 942.86 | 999.43 | 1206.86 (4B6.DC16) | 12:7 | 933.13 | 989.12 | 1194.405 (4AA.6816) | 9.73 | double-up 6th, double-down 7th | ^^6, vv7 | B^^, Cvv |
| 23 | 985.71 | 1044.86 | 1261.71 (4DC.4916) | 30:17 | 983.31 | 1042.31 | 1258.64 (4EA.A416) | 2.40 | down 7th | v7 | Cv |
| 24 | 1028.57 | 1090.29 | 1316.57 (524.9216) | 20:11 | 1035 | 1097.1 | 1324.795 (52C.CB16) | -6.43 | 7th | 7 | C |
| 25 | 1071.42 | 1135.71 | 1371.43 (55A.6E16) | 13:7 | 1071.70 | 1136 | 1371.78 (54B.C816) | -0.27 | up 7th | ^7 | C^ |
| 26 | 1114.29 | 1181.14 | 1426.29 (592.4916) | 40:21 | 1115.53 | 1162.465 | 1427.88 (593.E216) | -1.24 | double-up 7th, double-down 8ve | ^^7, vv8 | C^^, Dvv |
| 27 | 1157.14 | 1226.57 | 1471.14 (5C9.2516) | down 8ve | v8 | Dv | |||||
| 28 | 1200 | 1272 | 1536 (60016) | 2:1 | 1200 | 1272 | 1536 (60016) | 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
Compositions
28 tone Prelude by Kosmorksy