29edf
Jump to navigation
Jump to search
Prime factorization
29 (prime)
Step size
24.2053¢
Octave
50\29edf (1210.27¢)
Twelfth
79\29edf (1912.22¢)
Consistency limit
2
Distinct consistency limit
2
| ← 28edf | 29edf | 30edf → |
29EDF is the equal division of the just perfect fifth into 29 parts of 24.2053 cents each, corresponding to 49.5758 edo. It is related to the sengagen temperament, which tempers out 3136/3125 and 420175/419904 in the 7-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.3 | +10.3 | -3.7 | -2.7 | -3.7 | -4.3 | +6.6 | -3.7 | +7.6 | +12.0 | +6.6 |
| Relative (%) | +42.4 | +42.4 | -15.2 | -11.2 | -15.2 | -17.7 | +27.3 | -15.2 | +31.3 | +49.6 | +27.3 | |
| Steps (reduced) |
50 (21) |
79 (21) |
99 (12) |
115 (28) |
128 (12) |
139 (23) |
149 (4) |
157 (12) |
165 (20) |
172 (27) |
178 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -10.9 | +6.0 | +7.6 | -7.3 | +8.7 | +6.6 | +9.8 | -6.4 | +6.0 | -1.9 | -6.3 |
| Relative (%) | -45.2 | +24.7 | +31.3 | -30.3 | +36.1 | +27.3 | +40.5 | -26.3 | +24.7 | -8.0 | -25.9 | |
| Steps (reduced) |
183 (9) |
189 (15) |
194 (20) |
198 (24) |
203 (0) |
207 (4) |
211 (8) |
214 (11) |
218 (15) |
221 (18) |
224 (21) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 24.2053 | 72/71 | |
| 2 | 48.4107 | 36/35 | |
| 3 | 72.6160 | 24/23 | |
| 4 | 96.8214 | 37/35, 55/52 | |
| 5 | 121.0267 | 15/14 | |
| 6 | 145.2321 | 25/23, 37/34 | |
| 7 | 169.4374 | 54/49 | |
| 8 | 193.6428 | 19/17 | |
| 9 | 217.8481 | 17/15 | |
| 10 | 242.0534 | 23/20 | |
| 11 | 266.2588 | 7/6 | |
| 12 | 290.4641 | 71/60 | |
| 13 | 314.6695 | 6/5 | |
| 14 | 338.8748 | 45/37 | |
| 15 | 363.0802 | 37/30 | |
| 16 | 387.2855 | 5/4 | |
| 17 | 411.4909 | 90/71 | |
| 18 | 435.6962 | 9/7 | |
| 19 | 459.9016 | 30/23 | |
| 20 | 484.1069 | 45/34 | |
| 21 | 508.3122 | 51/38 | |
| 22 | 532.5176 | 49/36 | |
| 23 | 556.7229 | ||
| 24 | 580.9283 | 7/5 | |
| 25 | 605.1336 | ||
| 26 | 629.3390 | 23/16 | |
| 27 | 653.5443 | 35/24 | |
| 28 | 677.7497 | ||
| 29 | 701.9550 | exact 3/2 | just perfect fifth |
| 30 | 726.16035 | ||
| 31 | 750.3657 | ||
| 32 | 774.5710 | ||
| 33 | 798.7764 | ||
| 34 | 822.9817 | 45/28 | |
| 35 | 847.1871 | ||
| 36 | 871.3924 | 81/49 | |
| 37 | 895.5978 | 57/34 | |
| 38 | 919.8031 | 17/10 | |
| 39 | 944.00845 | ||
| 40 | 968.2138 | 7/4 | |
| 41 | 992.4191 | 16/9 | |
| 42 | 1016.6245 | 9/5 | |
| 43 | 1040.8298 | ||
| 44 | 1065.0352 | ||
| 45 | 1089.2405 | 15/8 | |
| 46 | 1113.4459 | ||
| 47 | 1137.6512 | 56/29 | |
| 48 | 1161.8566 | ||
| 49 | 1186.0619 | (2/1-) | |
| 50 | 1210.2672 | (2/1+) | |
| 51 | 1234.4726 | 49/24 | |
| 52 | 1258.6779 | 29/14 | |
| 53 | 1282.8833 | 21/10 | |
| 54 | 1307.0886 | 17/8 | |
| 55 | 1331.2940 | 41/19 | |
| 56 | 1355.4993 | 35/16 | |
| 57 | 1379.7047 | 20/9 | |
| 58 | 1403.9100 | exact 9/4 | |