11ed4: Difference between revisions

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{{Infobox ET}}
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== Intervals ==
{{Interval table}}
 
== Harmonics ==
{{Harmonics in equal
| steps = 11
| num = 4
| denom = 1
}}
{{Harmonics in equal
| steps = 11
| num = 4
| denom = 1
| start = 12
| collapsed = 1
}}

Revision as of 02:43, 5 October 2024

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← 9ed4 11ed4 13ed4 →
Prime factorization 11 (prime)
Step size 218.182 ¢ 
Octave 6\11ed4 (1309.09 ¢)
Twelfth 9\11ed4 (1963.64 ¢)
Consistency limit 1
Distinct consistency limit 1

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

Steps Cents Approximate ratios
0 0 1/1
1 218.2 19/17
2 436.4 14/11, 17/13
3 654.5 19/13, 22/15
4 872.7 5/3
5 1090.9 13/7, 21/11
6 1309.1
7 1527.3 17/7, 22/9
8 1745.5 19/7
9 1963.6
10 2181.8
11 2400

Harmonics

Approximation of harmonics in 11ed4
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)
Approximation of harmonics in 11ed4
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)