16ed7/3
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Prime factorization
24
Step size
91.6794¢
Octave
13\16ed7/3 (1191.83¢)
(semiconvergent)
Twelfth
21\16ed7/3 (1925.27¢)
Consistency limit
4
Distinct consistency limit
2
 |
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| ← 15ed7/3 | 16ed7/3 | 17ed7/3 → |
(semiconvergent)
16 equal divisions of 7/3 (abbreviated 16ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 16 equal parts of about 91.7 ¢ each. Each step represents a frequency ratio of (7/3)1/16, or the 16th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 91.679 | 16/15, 18/17, 19/18, 23/22, 24/23 |
| 2 | 183.359 | 11/10, 19/17, 21/19 |
| 3 | 275.038 | 7/6, 13/11 |
| 4 | 366.718 | 5/4, 16/13, 21/17 |
| 5 | 458.397 | 13/10 |
| 6 | 550.077 | 11/8, 15/11 |
| 7 | 641.756 | 16/11, 23/16 |
| 8 | 733.435 | 20/13, 23/15 |
| 9 | 825.115 | 8/5, 13/8 |
| 10 | 916.794 | 12/7, 22/13 |
| 11 | 1008.474 | |
| 12 | 1100.153 | 15/8, 17/9 |
| 13 | 1191.833 | 2/1 |
| 14 | 1283.512 | 19/9, 23/11 |
| 15 | 1375.191 | 11/5 |
| 16 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.2 | +23.3 | -16.3 | -35.9 | +15.1 | +23.3 | -24.5 | -45.1 | -44.1 | -25.7 | +7.0 |
| Relative (%) | -8.9 | +25.4 | -17.8 | -39.2 | +16.5 | +25.4 | -26.7 | -49.1 | -48.1 | -28.1 | +7.6 | |
| Steps (reduced) |
13 (13) |
21 (5) |
26 (10) |
30 (14) |
34 (2) |
37 (5) |
39 (7) |
41 (9) |
43 (11) |
45 (13) |
47 (15) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -39.9 | +15.1 | -12.6 | -32.7 | +45.7 | +38.5 | +36.5 | +39.4 | -45.1 | -33.9 | -19.2 |
| Relative (%) | -43.5 | +16.5 | -13.8 | -35.6 | +49.9 | +41.9 | +39.9 | +43.0 | -49.1 | -37.0 | -20.9 | |
| Steps (reduced) |
48 (0) |
50 (2) |
51 (3) |
52 (4) |
54 (6) |
55 (7) |
56 (8) |
57 (9) |
57 (9) |
58 (10) |
59 (11) | |
Scale tree
Ed7/3 scales can be approximated in EDOs by subdividing their approximations of 7/3.
| Minor tenth | Period | Notes | |||
|---|---|---|---|---|---|
| 6\5 | 90 | Intense Aeolian-Subpental Dorian mode begins | |||
| 17\14 | 91.071 | ||||
| 11\9 | 91.6 | Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins | |||
| 16\13 | 92.308 | ||||
| 5\4 | 93.75 | Subpental Dorian mode ends, Pental Dorian mode begins | |||
| 24\19 | 94.737 | ||||
| 19\15 | 95 | ||||
| 14\11 | 95.45 | Pental Dorian mode ends, Superpental Dorian mode begins | |||
| 23\18 | 95.83 | ||||