26edf: Difference between revisions
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'''26EDF''' is the [[EDF|equal division of the just perfect fifth]] into 26 parts of 26.9983 [[cent|cents]] each, corresponding to 44.4473 [[edo]]. It is nearly identical to every ninth step of [[400edo]]. | '''26EDF''' is the [[EDF|equal division of the just perfect fifth]] into 26 parts of 26.9983 [[cent|cents]] each, corresponding to 44.4473 [[edo]]. It is nearly identical to every ninth step of [[400edo]]. | ||
{{Harmonics in equal|26|3|2|columns= | ==Harmonics== | ||
{{Harmonics in equal|26|3|2|columns=8}} | |||
{{Harmonics in equal|26|3|2|columns=8|start=9|title=(contd.)}} | |||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|- | |- | ||
! | degree | ! | degree | ||
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|} | |} | ||
{{stub}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 06:03, 19 December 2024
| ← 25edf | 26edf | 27edf → |
26EDF is the equal division of the just perfect fifth into 26 parts of 26.9983 cents each, corresponding to 44.4473 edo. It is nearly identical to every ninth step of 400edo.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.1 | -12.1 | +2.8 | -5.5 | +2.8 | +6.0 | -9.2 | +2.8 |
| Relative (%) | -44.7 | -44.7 | +10.5 | -20.3 | +10.5 | +22.1 | -34.2 | +10.5 | |
| Steps (reduced) |
44 (18) |
70 (18) |
89 (11) |
103 (25) |
115 (11) |
125 (21) |
133 (3) |
141 (11) | |
| Harmonic | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +9.4 | +6.4 | -9.2 | -12.8 | -6.1 | +9.4 | +5.7 | +8.7 |
| Relative (%) | +34.9 | +23.8 | -34.2 | -47.5 | -22.7 | +34.9 | +21.1 | +32.3 | |
| Steps (reduced) |
148 (18) |
154 (24) |
159 (3) |
164 (8) |
169 (13) |
174 (18) |
178 (22) |
182 (0) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 26.9983 | 66/65, 65/64, 64/63 | |
| 2 | 53.9965 | 33/32, 98/95 | |
| 3 | 80.9948 | 22/21 | |
| 4 | 107.9931 | 16/15 | |
| 5 | 134.9913 | ||
| 6 | 161.9896 | ||
| 7 | 188.9879 | 135/121 | |
| 8 | 215.9862 | 17/15 | |
| 9 | 242.9844 | ||
| 10 | 269.9827 | 7/6 | |
| 11 | 296.981 | 32/27, 19/16 | |
| 12 | 323.9792 | pseudo-6/5 | |
| 13 | 350.9775 | 60/49, 49/40 | |
| 14 | 377.9758 | pseudo-5/4 | |
| 15 | 404.974 | 24/19 | |
| 16 | 431.9723 | ||
| 17 | 458.9706 | ||
| 18 | 485.9688 | 45/34 | pseudo-4/3 |
| 19 | 512.9671 | 121/90 | |
| 20 | 539.9654 | ||
| 21 | 566.9637 | ||
| 22 | 593.9619 | ||
| 23 | 620.9602 | 63/44 | |
| 24 | 647.9585 | 16/11 | |
| 25 | 674.9567 | ||
| 26 | 701.955 | exact 3/2 | just perfect fifth |
| 27 | 728.9533 | 99/65, 195/128, 21/16 | |
| 28 | 755.9515 | 99/64, 147/95 | |
| 29 | 782.9498 | 11/7 | |
| 30 | 809.9481 | 8/5 | |
| 31 | 836.9463 | ||
| 32 | 863.9446 | ||
| 33 | 890.9429 | 405/242 | pseudo-5/3 |
| 34 | 917.9412 | 17/10 | |
| 35 | 944.9394 | ||
| 36 | 971.9377 | 7/4 | |
| 37 | 998.936 | 16/9, 57/32 | |
| 38 | 1025.9342 | pseudo-9/5 | |
| 39 | 1052.9325 | 90/49, 147/80 | |
| 40 | 1079.9308 | pseudo-15/8 | |
| 41 | 1106.929 | ||
| 42 | 1133.9273 | ||
| 43 | 1160.9256 | ||
| 44 | 1187.9238 | 135/98 | pseudo-2/1 |
| 45 | 1214.9221 | 121/60 | |
| 46 | 1241.9204 | ||
| 47 | 1268.9187 | ||
| 48 | 1295.9169 | ||
| 49 | 1322.9152 | 189/88 | |
| 50 | 1349.9135 | 24/11 | |
| 51 | 1376.9117 | ||
| 52 | 1403.91 | exact 9/4 | |
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