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{{Infobox ET}} | |||
'''39EDF''' is the [[EDF|equal division of the just perfect fifth]] into 39 parts of 17.9988 [[cent|cents]] each, corresponding to 66.6709 [[edo]]. It is nearly identical to every third step of [[200edo]]. | '''39EDF''' is the [[EDF|equal division of the just perfect fifth]] into 39 parts of 17.9988 [[cent|cents]] each, corresponding to 66.6709 [[edo]]. It is nearly identical to every third step of [[200edo]]. | ||
== Harmonics == | |||
{{Harmonics in equal|39|3|2}} | |||
{{Harmonics in equal|39|3|2|start=12|collapsed=1}} | |||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals of 39edf | |||
|- | |- | ||
! | degree | ! | degree | ||
| Line 404: | Line 410: | ||
|} | |} | ||
{{todo|expand}} | |||
Latest revision as of 19:22, 1 August 2025
| ← 38edf | 39edf | 40edf → |
39EDF is the equal division of the just perfect fifth into 39 parts of 17.9988 cents each, corresponding to 66.6709 edo. It is nearly identical to every third step of 200edo.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.92 | +5.92 | -6.15 | +3.51 | -6.15 | -3.04 | -0.23 | -6.15 | -8.57 | +6.42 | -0.23 |
| Relative (%) | +32.9 | +32.9 | -34.2 | +19.5 | -34.2 | -16.9 | -1.3 | -34.2 | -47.6 | +35.6 | -1.3 | |
| Steps (reduced) |
67 (28) |
106 (28) |
133 (16) |
155 (38) |
172 (16) |
187 (31) |
200 (5) |
211 (16) |
221 (26) |
231 (36) |
239 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.19 | +2.88 | -8.57 | +5.69 | +8.73 | -0.23 | -3.84 | -2.65 | +2.88 | -5.66 | +7.38 |
| Relative (%) | +28.8 | +16.0 | -47.6 | +31.6 | +48.5 | -1.3 | -21.3 | -14.7 | +16.0 | -31.4 | +41.0 | |
| Steps (reduced) |
247 (13) |
254 (20) |
260 (26) |
267 (33) |
273 (0) |
278 (5) |
283 (10) |
288 (15) |
293 (20) |
297 (24) |
302 (29) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 17.9988 | 100/99, 99/98, 96/95 | |
| 2 | 35.9977 | 50/49, 49/48 | |
| 3 | 53.9965 | 33/32 | |
| 4 | 71.9954 | (25/24), (24/23) | |
| 5 | 89.9942 | ||
| 6 | 107.9931 | 16/15 | |
| 7 | 125.9919 | ||
| 8 | 143.9908 | 25/23 | |
| 9 | 161.9896 | ||
| 10 | 179.9885 | 10/9 | |
| 11 | 197.9873 | ||
| 12 | 215.9862 | 17/15 | |
| 13 | 233.985 | 8/7 | |
| 14 | 251.9838 | ||
| 15 | 269.9827 | 7/6 | |
| 16 | 287.9815 | 13/11 | |
| 17 | 305.9804 | 68/57 | |
| 18 | 323.9792 | 6/5 | |
| 19 | 341.9781 | 39/32 | |
| 20 | 359.9769 | 16/13 | |
| 21 | 377.9758 | lower pseudo-5/4 | |
| 22 | 395.9746 | upper pseudo-5/4 | |
| 23 | 413.9735 | 33/26 | |
| 24 | 431.9723 | 9/7 | |
| 25 | 449.9712 | ||
| 26 | 467.97 | ||
| 27 | 485.9688 | 45/34 | |
| 28 | 503.9677 | 4/3 | |
| 29 | 521.9665 | 27/20 | |
| 30 | 539.9654 | ||
| 31 | 557.9642 | ||
| 32 | 575.9631 | ||
| 33 | 593.9619 | ||
| 34 | 611.9608 | 64/45 | |
| 35 | 629.9596 | (23/16), (36/25) | |
| 36 | 647.9585 | 16/11 | pseudo-36/25 |
| 37 | 665.9573 | 72/49 | |
| 38 | 683.9562 | 95/64, 49/33, 297/200, 40/27 | |
| 39 | 701.955 | exact 3/2 | just perfect fifth |
| 40 | 720.9388 | 50/33, 297/196, 144/95 | |
| 41 | 737.9527 | 75/49, 49/32 | |
| 42 | 755.9515 | 99/64 | |
| 43 | 773.9504 | 25/16, 36/23 | |
| 44 | 791.9492 | ||
| 45 | 809.9481 | 8/5 | |
| 46 | 827.9469 | ||
| 47 | 845.9458 | 75/46 | |
| 48 | 863.9446 | ||
| 49 | 881.9435 | 5/3 | |
| 50 | 899.9423 | ||
| 51 | 917.9412 | 17/10 | |
| 52 | 935.94 | 12/7 | |
| 53 | 954.9388 | ||
| 54 | 971.9377 | 7/4 | |
| 55 | 989.9365 | 39/22 | |
| 56 | 1007.9354 | 34/19 | |
| 57 | 1025.9342 | 9/5 | |
| 58 | 1043.9331 | 117/64 | |
| 59 | 1061.9319 | 24/13 | |
| 60 | 1079.9308 | lower pseudo-15/8 | |
| 61 | 1097.9296 | upper pseudo-15/8 | |
| 62 | 1115.9285 | 99/52 | |
| 63 | 1134.9273 | 27/14 | |
| 64 | 1151.9261 | ||
| 65 | 1169.925 | 49/25 | |
| 66 | 1187.9238 | 135/68 | |
| 67 | 1205.9227 | 2/1 | |
| 68 | 1223.9215 | 81/40 | |
| 69 | 1241.9204 | ||
| 70 | 1259.9192 | ||
| 71 | 1277.9181 | ||
| 72 | 1295.9169 | ||
| 73 | 1313.9158 | 32/15 | |
| 74 | 1331.9146 | 69/32, 54/25 | |
| 75 | 1349.9135 | 24/11 | pseudo-54/25 |
| 76 | 1367.9123 | 108/49 | |
| 77 | 1385.9112 | 285/128, 49/22, 891/400, 20/9 | |
| 78 | 1403.91 | exact 9/4 | |