55ed4

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55ed4

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Prime factorization	5 × 11
Step size	43.6364 ¢
Octave	28\55ed4 (1221.82 ¢)
Twelfth	44\55ed4 (1920 ¢) (→ 4\5ed4)
Consistency limit	1
Distinct consistency limit	1

55 equal divisions of the 4th harmonic (abbreviated 55ed4) is a nonoctave tuning system that divides the interval of 4/1 into 55 equal parts of about 43.6 ¢ each. Each step represents a frequency ratio of 4^1/55, or the 55th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	43.6
2	87.3
3	130.9	14/13
4	174.5	21/19
5	218.2	25/22
6	261.8	29/25
7	305.5	25/21
8	349.1
9	392.7
10	436.4
11	480	25/19, 29/22, 33/25
12	523.6	23/17, 27/20
13	567.3
14	610.9
15	654.5	19/13
16	698.2	3/2
17	741.8
18	785.5	11/7
19	829.1	21/13
20	872.7
21	916.4
22	960	33/19
23	1003.6	25/14
24	1047.3
25	1090.9
26	1134.5	25/13
27	1178.2
28	1221.8
29	1265.5	29/14
30	1309.1
31	1352.7
32	1396.4
33	1440
34	1483.6	33/14
35	1527.3
36	1570.9
37	1614.5	33/13
38	1658.2	13/5
39	1701.8
40	1745.5
41	1789.1	31/11
42	1832.7	26/9
43	1876.4
44	1920
45	1963.6	28/9
46	2007.3
47	2050.9
48	2094.5
49	2138.2
50	2181.8
51	2225.5
52	2269.1
53	2312.7	19/5
54	2356.4
55	2400

Harmonics

Approximation of harmonics in 55ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+21.8	+18.0	+0.0	+6.4	-3.8	-8.8	+21.8	-7.5	-15.4	-5.9	+18.0
	Relative (%)	+50.0	+41.4	+0.0	+14.7	-8.6	-20.2	+50.0	-17.3	-35.3	-13.4	+41.4
Steps (reduced)		28 (28)	44 (44)	55 (0)	64 (9)	71 (16)	77 (22)	83 (28)	87 (32)	91 (36)	95 (40)	99 (44)

Approximation of harmonics in 55ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+10.4	+13.0	-19.2	+0.0	-17.7	+14.3	+7.9	+6.4	+9.2	+16.0	-17.4
	Relative (%)	+23.8	+29.8	-43.9	+0.0	-40.5	+32.7	+18.2	+14.7	+21.1	+36.6	-39.8
Steps (reduced)		102 (47)	105 (50)	107 (52)	110 (0)	112 (2)	115 (5)	117 (7)	119 (9)	121 (11)	123 (13)	124 (14)