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	20.87
2	41.739	42/41, 43/42
3	62.609
4	83.478	43/41
5	104.348
6	125.217	29/27
7	146.087	37/34
8	166.957	43/39
9	187.826	39/35
10	208.696	35/31
11	229.565
12	250.435
13	271.304
14	292.174	45/38
15	313.043
16	333.913
17	354.783	43/35
18	375.652	41/33, 46/37
19	396.522	39/31
20	417.391	14/11
21	438.261
22	459.13	43/33
23	480
24	500.87
25	521.739	23/17
26	542.609
27	563.478	18/13
28	584.348
29	605.217
30	626.087	33/23
31	646.957	45/31
32	667.826
33	688.696
34	709.565
35	730.435	29/19
36	751.304
37	772.174
38	793.043
39	813.913
40	834.783	47/29
41	855.652
42	876.522
43	897.391
44	918.261
45	939.13	31/18
46	960	47/27
47	980.87
48	1001.739	41/23
49	1022.609
50	1043.478	42/23
51	1064.348
52	1085.217	43/23
53	1106.087
54	1126.957
55	1147.826	33/17
56	1168.696
57	1189.565
58	1210.435
59	1231.304
60	1252.174	35/17
61	1273.043
62	1293.913	19/9
63	1314.783
64	1335.652
65	1356.522
66	1377.391	31/14
67	1398.261
68	1419.13
69	1440
70	1460.87
71	1481.739
72	1502.609	31/13
73	1523.478	41/17
74	1544.348
75	1565.217	42/17
76	1586.087	5/2
77	1606.957	43/17
78	1627.826
79	1648.696
80	1669.565
81	1690.435
82	1711.304
83	1732.174
84	1753.043
85	1773.913	39/14
86	1794.783	31/11
87	1815.652
88	1836.522
89	1857.391	38/13
90	1878.261
91	1899.13
92	1920
93	1940.87	43/14, 46/15
94	1961.739
95	1982.609
96	2003.478	35/11
97	2024.348	29/9
98	2045.217
99	2066.087
100	2086.957
101	2107.826
102	2128.696
103	2149.565	45/13
104	2170.435
105	2191.304	39/11
106	2212.174
107	2233.043
108	2253.913
109	2274.783
110	2295.652
111	2316.522
112	2337.391	27/7
113	2358.261	43/11
114	2379.13
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)