39edf: Difference between revisions
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{{Infobox ET}} | {{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}} | |||
==Intervals== | ==Intervals== | ||
Revision as of 01:39, 24 June 2023
| ← 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) | |
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 | |