30edf: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{todo|improve synopsis|text=Make the synopsis longer, add a couple paragraphs about the practical music making properties of the tuning}} | |||
'''30EDF''' is the [[EDF|equal division of the just perfect fifth]] into 30 parts of 23.3985 [[cent|cents]] each, corresponding to 51.2853 [[edo]] (practically identical to every seventh step of [[359edo]]). | '''30EDF''' is the [[EDF|equal division of the just perfect fifth]] into 30 parts of 23.3985 [[cent|cents]] each, corresponding to 51.2853 [[edo]] (practically identical to every seventh step of [[359edo]]). | ||
==Harmonics== | |||
{{Harmonics in equal|30|3|2|intervals=prime}} | |||
{{Harmonics in equal|30|3|2|intervals=prime|start=12|collapsed=1}} | |||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals of 30edf | |||
|- | |- | ||
! | degree | ! | degree | ||
Revision as of 08:37, 18 December 2024
| ← 29edf | 30edf | 31edf → |
30EDF is the equal division of the just perfect fifth into 30 parts of 23.3985 cents each, corresponding to 51.2853 edo (practically identical to every seventh step of 359edo).
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.7 | -6.7 | -1.9 | +0.6 | -9.8 | +5.2 | +8.7 | +3.4 | +0.2 | -3.4 | -1.8 |
| Relative (%) | -28.5 | -28.5 | -8.1 | +2.4 | -41.8 | +22.2 | +37.3 | +14.4 | +0.8 | -14.3 | -7.8 | |
| Steps (reduced) |
51 (21) |
81 (21) |
119 (29) |
144 (24) |
177 (27) |
190 (10) |
210 (0) |
218 (8) |
232 (22) |
249 (9) |
254 (14) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.9 | +5.5 | -6.7 | +3.1 | +5.7 | +7.2 | -3.7 | -2.4 | -9.2 | -10.5 | -6.8 |
| Relative (%) | -16.9 | +23.6 | -28.8 | +13.1 | +24.2 | +30.7 | -16.0 | -10.1 | -39.2 | -44.7 | -29.2 | |
| Steps (reduced) |
267 (27) |
275 (5) |
278 (8) |
285 (15) |
294 (24) |
302 (2) |
304 (4) |
311 (11) |
315 (15) |
317 (17) |
323 (23) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 23.3985 | 76/75 | |
| 2 | 46.797 | 77/75 | |
| 3 | 70.1955 | 25/24 | |
| 4 | 93.594 | 19/18 | |
| 5 | 116.9925 | 15/14 | |
| 6 | 140.391 | 13/12 | |
| 7 | 163.7895 | 11/10 | |
| 8 | 187.188 | 39/35 | |
| 9 | 210.5865 | 35/31 | |
| 10 | 233.985 | 8/7 | |
| 11 | 257.3835 | 29/25 | |
| 12 | 280.782 | 20/17 | |
| 13 | 304.1805 | 31/26 | |
| 14 | 327.579 | 29/24 | |
| 15 | 350.9775 | 60/49, 49/40 | |
| 16 | 374.376 | 36/29 | |
| 17 | 397.7745 | 39/31 | |
| 18 | 421.173 | 51/40 | |
| 19 | 444.5715 | ||
| 20 | 467.97 | 21/16 | |
| 21 | 491.3685 | ||
| 22 | 514.767 | 35/26 | |
| 23 | 538.1655 | 15/11 | |
| 24 | 561.564 | 18/13 | |
| 25 | 584.9625 | 7/5 | |
| 26 | 608.361 | 27/19 | |
| 27 | 631.7595 | 36/25 | |
| 28 | 655.158 | ||
| 29 | 678.5565 | 40/27 | |
| 30 | 701.955 | exact 3/2 | just perfect fifth |
| 31 | 725.3535 | 38/25 | |
| 32 | 748.752 | 77/50 | |
| 33 | 772.1505 | 25/16 | |
| 34 | 795.549 | 19/12 | |
| 35 | 818.9475 | 45/28 | |
| 36 | 842.346 | 13/8 | |
| 37 | 865.7445 | 33/20 | |
| 38 | 889.143 | 117/70 | |
| 39 | 912.8415 | 105/62 | |
| 40 | 935.94 | 12/7 | |
| 41 | 959.3385 | 87/50 | |
| 42 | 982.737 | 30/17 | |
| 43 | 1006.1355 | 93/52 | |
| 44 | 1028.534 | 29/16 | |
| 45 | 1052.9325 | 90/49, 147/80 | |
| 46 | 1076.331 | 48/29 | |
| 47 | 1099.6995 | 117/62 | |
| 48 | 1123.128 | 153/80 | |
| 49 | 1146.5165 | ||
| 50 | 1169.925 | 63/32 | |
| 51 | 1193.3435 | ||
| 52 | 1215.722 | 105/52 | |
| 53 | 1240.1205 | 45/22 | |
| 54 | 1263.519 | 27/13 | |
| 55 | 1286.9175 | 21/10 | |
| 56 | 1310.316 | 81/38 | |
| 57 | 1333.7145 | 54/25 | |
| 58 | 1357.113 | ||
| 59 | 1380.5115 | 20/9 | |
| 60 | 1403.91 | exact 9/4 | |