35edf
Jump to navigation
Jump to search
Prime factorization
5 × 7
Step size
20.0559¢
Octave
60\35edf (1203.35¢) (→12\7edf)
Twelfth
95\35edf (1905.31¢) (→19\7edf)
Consistency limit
7
Distinct consistency limit
7
| ← 34edf | 35edf | 36edf → |
Division of the just perfect fifth into 35 equal parts (35EDF) is related to 60edo, but with the 3/2 rather than the 2/1 being just. The octave is stretched by about 3.3514 cents and the step size is about 20.0559 cents (corresponding to 59.8329 edo, practically identical to every sixth step of 359edo).
The patent val has a generally sharp tendency for harmonics up to 18, with the exception for 13. Unlike 60edo, it is only consistent up to the 7-integer-limit, with discrepancy for the 8th harmonic (three octaves).
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.35 | +3.35 | +1.45 | +0.56 | +0.24 | -8.18 | +8.73 | -3.33 | +6.86 | +6.68 | -8.50 |
| Relative (%) | +16.7 | +16.7 | +7.2 | +2.8 | +1.2 | -40.8 | +43.5 | -16.6 | +34.2 | +33.3 | -42.4 | |
| Steps (reduced) |
60 (25) |
95 (25) |
139 (34) |
168 (28) |
207 (32) |
221 (11) |
245 (0) |
254 (9) |
271 (26) |
291 (11) |
296 (16) | |
Intervals
| Degrees of 60edo | Cents value | Approximate ratios in the 2.3.5.13 subgroup | Additional ratios of 7 and 11 (assuming flat values for primes) |
|---|---|---|---|
| 0 | |||
| 1 | 20.0559 | 81/80 | |
| 2 | 40.1117 | ||
| 3 | 60.1676 | 28/27, 27/26 | |
| 4 | 80.2234 | 21/20 | |
| 5 | 100.2793 | ||
| 6 | 120.3351 | 16/15 | |
| 7 | 140.391 | ||
| 8 | 160.4469 | 12/11, 11/10 | |
| 9 | 180.5027 | 10/9 | |
| 10 | 200.5586 | 9/8 | |
| 11 | 220.6144 | ||
| 12 | 240.6703 | 15/13 | 8/7 |
| 13 | 260.7621 | 7/6 | |
| 14 | 280.782 | ||
| 15 | 300.8379 | ||
| 16 | 320.8937 | 6/5 | |
| 17 | 340.9496 | 11/9 | |
| 18 | 361.0054 | 16/13 | |
| 19 | 381.0613 | 5/4 | |
| 20 | 401.1171 | ||
| 21 | 421.173 | 14/11 | |
| 22 | 441.2289 | 9/7 | |
| 23 | 461.2847 | 13/10 | |
| 24 | 481.3406 | ||
| 25 | 501.3964 | 4/3 | |
| 26 | 521.4523 | ||
| 27 | 541.5081 | 11/8, 15/11 | |
| 28 | 561.564 | 18/13 | |
| 29 | 581.6199 | 7/5 | |
| 30 | 601.6757 | ||
| 31 | 621.7315 | 10/7 | |
| 32 | 641.7874 | 13/9 | |
| 33 | 661.8433 | 16/11, 22/15 | |
| 34 | 681.8891 | ||
| 35 | 701.955 | 3/2 | |
| 36 | 722.0109 | ||
| 37 | 742.0667 | 20/13 | |
| 38 | 762.1226 | 14/9 | |
| 39 | 782.1784 | 11/7 | |
| 40 | 802.2343 | ||
| 41 | 822.2901 | 8/5 | |
| 42 | 842.346 | 13/8 | |
| 43 | 862.4019 | 18/11 | |
| 44 | 882.4577 | 5/3 | |
| 45 | 902.5136 | ||
| 46 | 922.5694 | ||
| 47 | 942.6253 | 12/7 | |
| 48 | 962.6811 | 26/15 | 7/4 |
| 49 | 982.737 | ||
| 50 | 1002.7929 | 16/9 | |
| 51 | 1022.8487 | 9/5 | |
| 52 | 1042.9046 | 11/6, 20/11 | |
| 53 | 1062.9604 | ||
| 54 | 1083.0163 | 15/8 | |
| 55 | 1103.0721 | ||
| 56 | 1123.128 | ||
| 57 | 1143.1839 | ||
| 58 | 1163.2397 | ||
| 59 | 1183.2956 | ||
| 60 | 1203.3514 | ||
| 61 | 1223.4073 | 81/40 | |
| 62 | 1243.4631 | ||
| 63 | 1263.519 | 56/27, 27/13 | |
| 64 | 1283.5749 | 21/10 | |
| 65 | 1303.6307 | ||
| 66 | 1323.6866 | 32/15 | |
| 67 | 1343.7424 | ||
| 68 | 1363.7983 | 24/11, 11/5 | |
| 69 | 1383.85415 | 20/9 | |
| 70 | 1403.91 | 9/4 | |