29edf: Difference between revisions
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m Todo harmonics collapsible |
m Removing from Category:Edf using Cat-a-lot |
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{{todo|expand}} | {{todo|expand}} | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 19:00, 1 August 2025
| ← 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 | |