40ed5
| ← 39ed5 | 40ed5 | 41ed5 → |
40 equal divisions of the 5th harmonic (abbreviated 40ed5) is a nonoctave tuning system that divides the interval of 5/1 into 40 equal parts of about 69.7 ¢ each. Each step represents a frequency ratio of 51/40, or the 40th root of 5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 69.7 | 26/25, 28/27 |
| 2 | 139.3 | 25/23 |
| 3 | 209 | 9/8, 26/23 |
| 4 | 278.6 | 20/17 |
| 5 | 348.3 | |
| 6 | 417.9 | |
| 7 | 487.6 | |
| 8 | 557.3 | |
| 9 | 626.9 | |
| 10 | 696.6 | 3/2 |
| 11 | 766.2 | 14/9 |
| 12 | 835.9 | |
| 13 | 905.6 | 22/13, 27/16 |
| 14 | 975.2 | 7/4 |
| 15 | 1044.9 | |
| 16 | 1114.5 | 19/10 |
| 17 | 1184.2 | |
| 18 | 1253.8 | |
| 19 | 1323.5 | 15/7 |
| 20 | 1393.2 | 29/13 |
| 21 | 1462.8 | 7/3 |
| 22 | 1532.5 | 17/7 |
| 23 | 1602.1 | |
| 24 | 1671.8 | 21/8, 29/11 |
| 25 | 1741.4 | |
| 26 | 1811.1 | 20/7 |
| 27 | 1880.8 | |
| 28 | 1950.4 | |
| 29 | 2020.1 | |
| 30 | 2089.7 | 10/3 |
| 31 | 2159.4 | |
| 32 | 2229.1 | |
| 33 | 2298.7 | |
| 34 | 2368.4 | |
| 35 | 2438 | |
| 36 | 2507.7 | 17/4 |
| 37 | 2577.3 | |
| 38 | 2647 | 23/5 |
| 39 | 2716.7 | |
| 40 | 2786.3 | 5/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.4 | -44.4 | +14.8 | +0.0 | -37.0 | -25.2 | +22.2 | +4.1 | +7.4 | +28.2 | -29.6 |
| Relative (%) | +8.0 | -47.8 | +15.9 | +0.0 | -39.8 | -27.2 | +23.9 | +4.4 | +8.0 | +30.3 | -31.9 | |
| Steps (reduced) |
13 (13) |
20 (20) |
26 (26) |
30 (0) |
33 (3) |
36 (6) |
39 (9) |
41 (11) |
43 (13) |
45 (15) |
46 (16) | |
Music
- escape yourself - Merct (2025)
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |