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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | |||
== Intervals == | |||
{| class="wikitable mw-collapsible" | |||
|+ | |||
!Step | |||
!Interval (¢) | |||
!JI approximated | |||
!Simplified ratios | |||
|- | |||
|1 | |||
|218.18 | |||
|34/30, 50/44 | |||
|17/15, 25/22 | |||
|- | |||
|2 | |||
|436.36 | |||
|18/14, 39/30, 44/34 | |||
|9/7, 13/10, 22/17 | |||
|- | |||
|3 | |||
|654.54 | |||
|64/44 | |||
|16/11 | |||
|- | |||
|4 | |||
|872.73 | |||
|30/18 | |||
|5/3 | |||
|- | |||
|5 | |||
|1090.91 | |||
|30/16, 34/18, 64/34 | |||
|15/8, 17/9, 32/17 | |||
|- | |||
|6 | |||
|1309.09 | |||
|30/14, 34/16, 64/30 | |||
|15/7, 17/8, 32/15 | |||
|- | |||
|7 | |||
|1527.27 | |||
|34/14 | |||
|17/7 | |||
|- | |||
|8 | |||
|1745.46 | |||
|11/4, 30/11 | |||
| | |||
|- | |||
|9 | |||
|1963.64 | |||
|44/14, 50/16 | |||
|22/7, 25/8 | |||
|- | |||
|10 | |||
|2181.82 | |||
|14/4, 39/11, 64/18 | |||
|7/2, 32/9 | |||
|- | |||
|11 | |||
|2400.00 | |||
|4/1 | |||
| | |||
|} | |||
The [[subgroup]] interpretation used is 4.11.14.18.30.34.39.50. Other interpretations are possible. | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 11 | |||
| num = 4 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 11 | |||
| num = 4 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
{{stub}} | |||
Latest revision as of 08:27, 22 December 2024
| ← 9ed4 | 11ed4 | 13ed4 → |
11 equal divisions of the 4th harmonic (abbreviated 11ed4) is a nonoctave tuning system that divides the interval of 4/1 into 11 equal parts of about 218 ¢ each. Each step represents a frequency ratio of 41/11, or the 11th root of 4.
Intervals
| Step | Interval (¢) | JI approximated | Simplified ratios |
|---|---|---|---|
| 1 | 218.18 | 34/30, 50/44 | 17/15, 25/22 |
| 2 | 436.36 | 18/14, 39/30, 44/34 | 9/7, 13/10, 22/17 |
| 3 | 654.54 | 64/44 | 16/11 |
| 4 | 872.73 | 30/18 | 5/3 |
| 5 | 1090.91 | 30/16, 34/18, 64/34 | 15/8, 17/9, 32/17 |
| 6 | 1309.09 | 30/14, 34/16, 64/30 | 15/7, 17/8, 32/15 |
| 7 | 1527.27 | 34/14 | 17/7 |
| 8 | 1745.46 | 11/4, 30/11 | |
| 9 | 1963.64 | 44/14, 50/16 | 22/7, 25/8 |
| 10 | 2181.82 | 14/4, 39/11, 64/18 | 7/2, 32/9 |
| 11 | 2400.00 | 4/1 |
The subgroup interpretation used is 4.11.14.18.30.34.39.50. Other interpretations are possible.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +109.1 | +61.7 | +0.0 | +50.0 | -47.4 | -96.1 | +109.1 | -94.8 | -59.0 | -5.9 | +61.7 |
| Relative (%) | +50.0 | +28.3 | +0.0 | +22.9 | -21.7 | -44.0 | +50.0 | -43.5 | -27.1 | -2.7 | +28.3 | |
| Steps (reduced) |
6 (6) |
9 (9) |
11 (0) |
13 (2) |
14 (3) |
15 (4) |
17 (6) |
17 (6) |
18 (7) |
19 (8) |
20 (9) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -76.9 | +13.0 | -106.5 | +0.0 | -105.0 | +14.3 | -79.3 | +50.0 | -34.4 | +103.2 | +26.3 |
| Relative (%) | -35.2 | +6.0 | -48.8 | +0.0 | -48.1 | +6.5 | -36.4 | +22.9 | -15.8 | +47.3 | +12.0 | |
| Steps (reduced) |
20 (9) |
21 (10) |
21 (10) |
22 (0) |
22 (0) |
23 (1) |
23 (1) |
24 (2) |
24 (2) |
25 (3) |
25 (3) | |
|
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