115ed4

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115ed4

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Prime factorization	5 × 23
Step size	20.8696 ¢
Octave	58\115ed4 (1210.43 ¢)
Twelfth	91\115ed4 (1899.13 ¢)
Consistency limit	1
Distinct consistency limit	1

115 equal divisions of the 4th harmonic (abbreviated 115ed4) is a nonoctave tuning system that divides the interval of 4/1 into 115 equal parts of about 20.9 ¢ each. Each step represents a frequency ratio of 4^1/115, or the 115th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	20.9
2	41.7	42/41, 43/42
3	62.6
4	83.5	43/41
5	104.3
6	125.2	29/27
7	146.1	37/34
8	167	43/39
9	187.8	39/35
10	208.7	35/31
11	229.6
12	250.4
13	271.3
14	292.2	45/38
15	313
16	333.9
17	354.8	43/35
18	375.7	41/33, 46/37
19	396.5	39/31
20	417.4	14/11
21	438.3
22	459.1	43/33
23	480
24	500.9
25	521.7	23/17
26	542.6
27	563.5	18/13
28	584.3
29	605.2
30	626.1	33/23
31	647	45/31
32	667.8
33	688.7
34	709.6
35	730.4	29/19
36	751.3
37	772.2
38	793
39	813.9
40	834.8	47/29
41	855.7
42	876.5
43	897.4
44	918.3
45	939.1	31/18
46	960	47/27
47	980.9
48	1001.7	41/23
49	1022.6
50	1043.5	42/23
51	1064.3
52	1085.2	43/23
53	1106.1
54	1127
55	1147.8	33/17
56	1168.7
57	1189.6
58	1210.4
59	1231.3
60	1252.2	35/17
61	1273
62	1293.9	19/9
63	1314.8
64	1335.7
65	1356.5
66	1377.4	31/14
67	1398.3
68	1419.1
69	1440
70	1460.9
71	1481.7
72	1502.6	31/13
73	1523.5	41/17
74	1544.3
75	1565.2	42/17
76	1586.1	5/2
77	1607	43/17
78	1627.8
79	1648.7
80	1669.6
81	1690.4
82	1711.3
83	1732.2
84	1753
85	1773.9	39/14
86	1794.8	31/11
87	1815.7
88	1836.5
89	1857.4	38/13
90	1878.3
91	1899.1
92	1920
93	1940.9	43/14, 46/15
94	1961.7
95	1982.6
96	2003.5	35/11
97	2024.3	29/9
98	2045.2
99	2066.1
100	2087
101	2107.8
102	2128.7
103	2149.6	45/13
104	2170.4
105	2191.3	39/11
106	2212.2
107	2233
108	2253.9
109	2274.8
110	2295.7
111	2316.5
112	2337.4	27/7
113	2358.3	43/11
114	2379.1
115	2400

Harmonics

Approximation of harmonics in 115ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+10.43	-2.82	+0.00	+10.21	+7.61	-8.83	+10.43	-5.65	-0.23	+1.73	-2.82
	Relative (%)	+50.0	-13.5	+0.0	+48.9	+36.5	-42.3	+50.0	-27.1	-1.1	+8.3	-13.5
Steps (reduced)		58 (58)	91 (91)	115 (0)	134 (19)	149 (34)	161 (46)	173 (58)	182 (67)	191 (76)	199 (84)	206 (91)

Approximation of harmonics in 115ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.69	+1.61	+7.38	+0.00	-0.61	+4.79	-5.34	+10.21	+9.22	-8.71	-2.19
	Relative (%)	+22.5	+7.7	+35.4	+0.0	-2.9	+22.9	-25.6	+48.9	+44.2	-41.7	-10.5
Steps (reduced)		213 (98)	219 (104)	225 (110)	230 (0)	235 (5)	240 (10)	244 (14)	249 (19)	253 (23)	256 (26)	260 (30)