13edf
| ← 12edf | 13edf | 14edf → |
13EDF is the equal division of the just perfect fifth into 13 parts of 53.9965 cents each, corresponding to 22.2236 edo. It is nearly identical to every ninth step of 200edo.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.5 | -2.5 | -19.8 | +17.1 | +19.1 | +19.0 | +8.7 | -18.7 |
| Relative (%) | -6.2 | -6.2 | -47.9 | +41.4 | +46.3 | +45.9 | +21.1 | -45.2 | |
| Steps (reduced) |
29 (12) |
46 (12) |
67 (16) |
82 (14) |
101 (16) |
108 (6) |
119 (0) |
123 (4) | |
| Harmonic | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -19.1 | -7.5 | +0.9 | -16.3 | +12.4 | +12.5 | -17.6 | -19.1 |
| Relative (%) | -46.2 | -18.1 | +2.3 | -39.6 | +30.0 | +30.4 | -42.6 | -46.3 | |
| Steps (reduced) |
131 (12) |
141 (5) |
144 (8) |
151 (15) |
156 (3) |
158 (5) |
161 (8) |
166 (13) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 53.9965 | 33/32 | pseudo-25/24 |
| 2 | 107.9931 | 17/16, 117/110, 16/15 | |
| 3 | 161.9896 | 11/10 | |
| 4 | 215.9862 | 17/15 | |
| 5 | 269.9827 | 7/6 | |
| 6 | 323.9792 | 77/64 | pseudo-6/5 |
| 7 | 377.9758 | 56/45 | pseudo-5/4 |
| 8 | 431.9723 | 9/7 | |
| 9 | 485.9688 | 45/34 | pseudo-4/3 |
| 10 | 539.9654 | 15/11 | |
| 11 | 593.9619 | 55/39, 24/17 | |
| 12 | 647.9585 | 16/11 | |
| 13 | 701.9550 | exact 3/2 | just perfect fifth |
| 14 | 755.9515 | 99/64 | |
| 15 | 809.9481 | 51/32, 8/5 | |
| 16 | 863.9446 | 33/20 | |
| 17 | 917.9412 | 17/10 | |
| 18 | 971.9377 | 7/4 | |
| 19 | 1025.9342 | 29/16 | pseudo-9/5 |
| 20 | 1079.9308 | 28/15 | pseudo-15/8 |
| 21 | 1133.9273 | 52/27, 27/14 | |
| 22 | 1187.9238 | 135/68 | pseudo-octave |
| 23 | 1241.9204 | 45/22 | |
| 24 | 1295.9169 | 19/9, 36/17 | |
| 25 | 1349.9135 | 24/11 | |
| 26 | 1403.9100 | exact 9/4 | pythagorean major ninth |
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