6edt
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Prime factorization
2 × 3
Step size
316.993 ¢
Octave
4\6edt (1267.97 ¢) (→ 2\3edt)
Consistency limit
7
Distinct consistency limit
3
Special properties
| ← 5edt | 6edt | 7edt → |
6 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 6edt or 6ed3), is a nonoctave tuning system that divides the interval of 3/1 into 6 equal parts of about 317 ¢ each. Each step represents a frequency ratio of 31/6, or the 6th root of 3.
Theory
Since 6edt contains one interval of 2edt and two intervals of 3edt, it introduces 2 new notes unseen in previous edts. These new notes happen to approximate 6/5 and 5/2 very well, the former being only 1.351 cents sharp. 6edt is therefore the smallest edt other than 5edt to accurately approximate 5-limit harmony, as well as some elements from the 13-limit inherited from 3edt. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54...
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +68 | +0 | +136 | +67 | +68 | +118 | -113 | +0 | +135 | -30 | +136 | -3 | -131 | +67 | -45 | -150 |
| Relative (%) | +21.4 | +0.0 | +42.9 | +21.0 | +21.4 | +37.3 | -35.7 | +0.0 | +42.5 | -9.6 | +42.9 | -0.8 | -41.3 | +21.0 | -14.2 | -47.3 | |
| Steps (reduced) |
4 (4) |
6 (0) |
8 (2) |
9 (3) |
10 (4) |
11 (5) |
11 (5) |
12 (0) |
13 (1) |
13 (1) |
14 (2) |
14 (2) |
14 (2) |
15 (3) |
15 (3) |
15 (3) | |
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 317 | 216.7 | 6/5, 7/6, 11/9, 13/11 |
| 2 | 634 | 433.3 | 7/5, 10/7, 13/9, 19/13 |
| 3 | 951 | 650 | 7/4, 12/7, 19/11 |
| 4 | 1268 | 866.7 | 15/7, 19/9, 21/10 |
| 5 | 1585 | 1083.3 | 5/2, 18/7 |
| 6 | 1902 | 1300 | 3/1 |