25edf: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''25EDF''' is the [[EDF|equal division of the just perfect fifth]] into 25 parts of 28.0782 [[ | '''25EDF''' is the [[EDF|equal division of the just perfect fifth]] into 25 parts of 28.0782 [[cents]] each, corresponding to 42.7378 [[edo]] (similar to every fourth step of [[171edo]]). | ||
It is related to the regular temperament which tempers out 703125/702464 and 5250987/5242880 in the 7-limit, which is supported by [[43edo]], [[128edo]], [[171edo]], [[214edo]], [[299edo]], and [[385edo]]. | |||
Lookalikes: [[43edo]], [[68edt]] | Lookalikes: [[43edo]], [[68edt]] | ||
==Harmonics== | |||
{{Harmonics in equal|25|3|2|intervals=prime}} | |||
{{Harmonics in equal|26|3|2|start=12|collapsed=1|intervals=prime}} | |||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals of 25edf | |||
|- | |- | ||
! | degree | ! | degree | ||
| Line 267: | Line 274: | ||
|} | |} | ||
{{todo|expand}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 06:17, 19 December 2024
| ← 24edf | 25edf | 26edf → |
25EDF is the equal division of the just perfect fifth into 25 parts of 28.0782 cents each, corresponding to 42.7378 edo (similar to every fourth step of 171edo).
It is related to the regular temperament which tempers out 703125/702464 and 5250987/5242880 in the 7-limit, which is supported by 43edo, 128edo, 171edo, 214edo, 299edo, and 385edo.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.4 | +7.4 | -6.6 | +0.6 | +4.3 | -4.2 | +8.7 | +12.7 | -9.2 | +10.7 | +7.5 |
| Relative (%) | +26.2 | +26.2 | -23.4 | +2.0 | +15.2 | -14.9 | +31.1 | +45.3 | -32.7 | +38.1 | +26.9 | |
| Steps (reduced) |
43 (18) |
68 (18) |
99 (24) |
120 (20) |
148 (23) |
158 (8) |
175 (0) |
182 (7) |
193 (18) |
208 (8) |
212 (12) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.3 | -3.5 | -4.9 | +3.1 | +11.1 | -12.6 | +10.7 | +10.2 | -9.2 | -3.3 | -5.0 |
| Relative (%) | +45.4 | -12.9 | -18.3 | +11.4 | +40.9 | -46.8 | +39.5 | +37.9 | -34.0 | -12.1 | -18.6 | |
| Steps (reduced) |
232 (24) |
238 (4) |
241 (7) |
247 (13) |
255 (21) |
261 (1) |
264 (4) |
270 (10) |
273 (13) |
275 (15) |
280 (20) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 28.0782 | 51/50 | |
| 2 | 56.1564 | 26/25 | |
| 3 | 84.2346 | 21/20 | |
| 4 | 112.3128 | 16/15 | |
| 5 | 140.391 | 13/12 | |
| 6 | 168.4692 | ||
| 7 | 196.5474 | 28/25 | |
| 8 | 224.6256 | 8/7 | |
| 9 | 252.7038 | ||
| 10 | 280.782 | 20/17 | |
| 11 | 308.8602 | pseudo-6/5 | |
| 12 | 336.9384 | ||
| 13 | 365.0166 | ||
| 14 | 393.0948 | pseudo-5/4 | |
| 15 | 421.173 | 51/40 | |
| 16 | 449.2512 | ||
| 17 | 477.3294 | ||
| 18 | 505.4076 | 75/56 | pseudo-4/3 |
| 19 | 533.4858 | ||
| 20 | 561.564 | ||
| 21 | 589.6422 | 45/32 | |
| 22 | 617.7204 | 10/7 | |
| 23 | 645.7986 | ||
| 24 | 673.8768 | ||
| 25 | 701.955 | exact 3/2 | just perfect fifth |
| 26 | 730.033 | 153/100 | |
| 27 | 757.1114 | 39/25 | |
| 28 | 786.1896 | 63/40 | |
| 29 | 814.2678 | 8/5 | |
| 30 | 842.346 | 13/8 | |
| 31 | 870.2452 | ||
| 32 | 898.5024 | 42/25 | |
| 33 | 926.5806 | 12/7 | |
| 34 | 954.6588 | ||
| 35 | 982.737 | 30/17 | |
| 36 | 1010.8152 | pseudo-9/5 | |
| 37 | 1038.8934 | ||
| 38 | 1066.9716 | ||
| 39 | 1095.0498 | pseudo-15/8 | |
| 40 | 1123.128 | 153/80 | |
| 41 | 1151.2062 | ||
| 42 | 1179.2844 | ||
| 43 | 1207.3526 | 225/112 | pseudo-2/1 |
| 44 | 1235.4408 | ||
| 45 | 1263.519 | ||
| 46 | 1291.5972 | 135/64 | |
| 47 | 1319.6754 | 15/7 | |
| 48 | 1347.7536 | ||
| 49 | 1375.8318 | ||
| 50 | 1403.91 | exact 9/4 | |