11ed4

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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 4^1/11, 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

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)

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