15ed9/4: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | |||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 15 | |||
| num = 9 | |||
| denom = 4 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 15 | |||
| num = 9 | |||
| denom = 4 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
{{stub}} | |||
Latest revision as of 18:46, 1 August 2025
| ← 13ed9/4 | 15ed9/4 | 17ed9/4 → |
15 equal divisions of 9/4 (abbreviated 15ed9/4) is a nonoctave tuning system that divides the interval of 9/4 into 15 equal parts of about 93.6 ¢ each. Each step represents a frequency ratio of (9/4)1/15, or the 15th root of 9/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 93.6 | 18/17, 19/18, 22/21, 23/22 |
| 2 | 187.2 | 19/17, 21/19 |
| 3 | 280.8 | 7/6, 13/11 |
| 4 | 374.4 | 5/4, 21/17 |
| 5 | 468 | 17/13, 22/17 |
| 6 | 561.6 | 7/5, 18/13 |
| 7 | 655.2 | 13/9, 19/13, 22/15 |
| 8 | 748.8 | 17/11, 23/15 |
| 9 | 842.3 | 18/11, 21/13, 23/14 |
| 10 | 935.9 | 12/7, 19/11 |
| 11 | 1029.5 | 11/6 |
| 12 | 1123.1 | 17/9, 21/11, 23/12 |
| 13 | 1216.7 | 2/1 |
| 14 | 1310.3 | 15/7, 19/9 |
| 15 | 1403.9 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +16.7 | -30.1 | +33.4 | +21.5 | -13.4 | +0.6 | -43.4 | +33.4 | +38.2 | -33.2 | +3.4 |
| Relative (%) | +17.9 | -32.1 | +35.7 | +23.0 | -14.3 | +0.6 | -46.4 | +35.7 | +40.8 | -35.5 | +3.6 | |
| Steps (reduced) |
13 (13) |
20 (5) |
26 (11) |
30 (0) |
33 (3) |
36 (6) |
38 (8) |
41 (11) |
43 (13) |
44 (14) |
46 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -41.6 | +17.3 | -8.6 | -26.7 | -38.1 | -43.4 | -43.4 | -38.6 | -29.5 | -16.5 | +0.2 |
| Relative (%) | -44.5 | +18.5 | -9.2 | -28.5 | -40.7 | -46.4 | -46.4 | -41.3 | -31.5 | -17.6 | +0.2 | |
| Steps (reduced) |
47 (2) |
49 (4) |
50 (5) |
51 (6) |
52 (7) |
53 (8) |
54 (9) |
55 (10) |
56 (11) |
57 (12) |
58 (13) | |
|
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