72ed5
Jump to navigation
Jump to search
Prime factorization
23 × 32
Step size
38.6988¢
Octave
31\72ed5 (1199.66¢)
(semiconvergent)
Twelfth
49\72ed5 (1896.24¢)
Consistency limit
12
Distinct consistency limit
8
| ← 71ed5 | 72ed5 | 73ed5 → |
(semiconvergent)
Division of the 5th harmonic into 72 equal parts (72ed5) is related to 31 edo, but with the 5/1 rather than the 2/1 being just. The octave is slightly compressed (about 0.3372 cents) and the step size is about 38.6988 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.3 | -5.7 | -0.7 | +0.0 | -6.1 | -2.0 | -1.0 | -11.4 | -0.3 | -10.5 | -6.4 |
| relative (%) | -1 | -15 | -2 | +0 | -16 | -5 | -3 | -30 | -1 | -27 | -17 | |
| Steps (reduced) |
31 (31) |
49 (49) |
62 (62) |
72 (0) |
80 (8) |
87 (15) |
93 (21) |
98 (26) |
103 (31) |
107 (35) |
111 (39) | |
31edo for comparison:
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.0 | -5.2 | +0.0 | +0.8 | -5.2 | -1.1 | +0.0 | -10.4 | +0.8 | -9.4 | -5.2 |
| relative (%) | +0 | -13 | +0 | +2 | -13 | -3 | +0 | -27 | +2 | -24 | -13 | |
| Steps (reduced) |
31 (0) |
49 (18) |
62 (0) |
72 (10) |
80 (18) |
87 (25) |
93 (0) |
98 (5) |
103 (10) |
107 (14) |
111 (18) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 38.6988 | 46/45, 45/44 | |
| 2 | 77.3976 | 23/22, 68/65, 22/21 | |
| 3 | 116.0964 | 15/14 | pseudo-16/15 |
| 4 | 154.7952 | 35/32, 23/21 | |
| 5 | 193.4940 | 19/17, 85/76 | |
| 6 | 232.1928 | 8/7 | |
| 7 | 270.8916 | 76/65 | pseudo-7/6 |
| 8 | 309.5904 | 55/46 | pseudo-6/5 |
| 9 | 348.2892 | 11/9 | |
| 10 | 386.9880 | 5/4 | |
| 11 | 425.6868 | 23/18 | |
| 12 | 464.3856 | 17/13 | |
| 13 | 503.0844 | pseudo-4/3 | |
| 14 | 541.7832 | 175/128, 26/19 | |
| 15 | 580.4820 | 7/5 | |
| 16 | 619.1808 | 10/7 | |
| 17 | 657.8796 | 19/13 | |
| 18 | 696.5784 | meantone fifth (pseudo-3/2) | |
| 19 | 735.2772 | 55/36, 26/17 | |
| 20 | 773.9760 | 25/16, 36/23 | |
| 21 | 812.6748 | 8/5 | |
| 22 | 851.3736 | 85/52, 18/11 | |
| 23 | 890.0724 | pseudo-5/3 | |
| 24 | 928.7712 | 65/38 | |
| 25 | 967.4700 | 7/4 | |
| 26 | 1006.1688 | 25/14 | |
| 27 | 1044.8676 | 95/52, 64/35 | |
| 28 | 1083.5664 | pseudo-15/8 | |
| 29 | 1122.2652 | 21/11, 65/34, 44/23 | |
| 30 | 1160.9640 | 45/23 | |
| 31 | 1199.6628 | 2/1 | |
| 32 | 1238.3617 | 45/22 | |
| 33 | 1277.0605 | 23/11 | |
| 34 | 1315.7593 | ||
| 35 | 1354.4581 | 35/16 | |
| 36 | 1393.1569 | 38/17, 85/38 | meantone major second plus an octave |
| 37 | 1431.8557 | 16/7 | |
| 38 | 1470.5545 | ||
| 39 | 1509.2533 | 55/23 | |
| 40 | 1547.9521 | 22/9 | |
| 41 | 1586.6509 | 5/2 | |
| 42 | 1625.3497 | 23/9 | |
| 43 | 1664.0485 | 34/13 | |
| 44 | 1702.7473 | pseudo-8/3 | |
| 45 | 1741.4461 | 175/64, 52/19 | |
| 46 | 1780.1449 | 14/5 | |
| 47 | 1818.8437 | 20/7 | |
| 48 | 1857.5425 | 38/13 | |
| 49 | 1896.2413 | pseudo-3/1 | |
| 50 | 1934.9401 | 55/18, 52/17 | |
| 51 | 1973.6389 | 25/8 | |
| 52 | 2012.3377 | 115/36, 16/5 | |
| 53 | 2051.0365 | 85/26, 36/11 | |
| 54 | 2089.7353 | meantone major sixth plus an octave (pseudo-10/3) | |
| 55 | 2128.4341 | 65/19 | |
| 56 | 2167.1329 | 7/2 | |
| 57 | 2205.8317 | 25/7 | |
| 58 | 2244.5305 | 95/26, 128/35 | |
| 59 | 2283.2293 | pseudo-15/4 | |
| 60 | 2321.9281 | 65/17 | |
| 61 | 2360.6269 | 90/23 | |
| 62 | 2399.3257 | 4/1 | |
| 63 | 2438.0245 | 45/11 | |
| 64 | 2476.7233 | 46/11 | |
| 65 | 2515.4221 | ||
| 66 | 2554.1209 | 35/8 | |
| 67 | 2592.8197 | 76/17, 85/19 | |
| 68 | 2631.5185 | 32/7 | |
| 69 | 2670.2173 | 14/3 | |
| 70 | 2708.9161 | 110/23 | |
| 71 | 2747.6149 | 44/9 | |
| 72 | 2786.3137 | exact 5/1 | just major third plus two octaves |