115edt

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115edt

116edt →

Prime factorization	5 × 23
Step size	16.5387¢
Octave	73\115edt (1207.33¢)
Consistency limit	2
Distinct consistency limit	2

115 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 115edt or 115ed3), is a nonoctave tuning system that divides the interval of 3/1 into 115 equal parts of about 16.5 ¢ each. Each step represents a frequency ratio of 3^1/115, or the 115th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.5
2	33.1
3	49.6
4	66.2	27/26
5	82.7	21/20, 43/41
6	99.2	18/17
7	115.8	31/29, 46/43
8	132.3	41/38
9	148.8
10	165.4	11/10
11	181.9	10/9
12	198.5	37/33, 46/41
13	215	43/38
14	231.5
15	248.1	15/13
16	264.6
17	281.2	20/17
18	297.7
19	314.2
20	330.8	23/19
21	347.3	11/9
22	363.9	21/17, 37/30
23	380.4
24	396.9	39/31
25	413.5	33/26, 47/37
26	430
27	446.5	22/17
28	463.1
29	479.6
30	496.2
31	512.7	35/26, 39/29
32	529.2
33	545.8	37/27
34	562.3
35	578.9
36	595.4
37	611.9	37/26, 47/33
38	628.5
39	645	45/31
40	661.5
41	678.1
42	694.6
43	711.2
44	727.7	35/23
45	744.2
46	760.8	45/29
47	777.3	47/30
48	793.9
49	810.4
50	826.9
51	843.5
52	860
53	876.6
54	893.1
55	909.6
56	926.2
57	942.7
58	959.2	47/27
59	975.8
60	992.3
61	1008.9
62	1025.4	38/21, 47/26
63	1041.9
64	1058.5	35/19
65	1075
66	1091.6
67	1108.1
68	1124.6
69	1141.2	29/15
70	1157.7	41/21
71	1174.3
72	1190.8
73	1207.3
74	1223.9
75	1240.4	43/21
76	1256.9	31/15
77	1273.5
78	1290
79	1306.6
80	1323.1	43/20
81	1339.6
82	1356.2	46/21
83	1372.7
84	1389.3	29/13
85	1405.8
86	1422.3
87	1438.9
88	1455.4
89	1471.9
90	1488.5	26/11
91	1505	31/13
92	1521.6
93	1538.1	17/7
94	1554.6	27/11
95	1571.2
96	1587.7
97	1604.3
98	1620.8
99	1637.3
100	1653.9	13/5
101	1670.4
102	1687
103	1703.5
104	1720	27/10
105	1736.6	30/11
106	1753.1
107	1769.6
108	1786.2
109	1802.7	17/6
110	1819.3	20/7
111	1835.8	26/9
112	1852.3
113	1868.9
114	1885.4
115	1902	3/1

Harmonics

Approximation of harmonics in 115edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+7.33	+0.00	-1.88	-7.81	+7.33	+5.08	+5.45	+0.00	-0.48	-0.09	-1.88
	Relative (%)	+44.3	+0.0	-11.4	-47.2	+44.3	+30.7	+32.9	+0.0	-2.9	-0.6	-11.4
Steps (reduced)		73 (73)	115 (0)	145 (30)	168 (53)	188 (73)	204 (89)	218 (103)	230 (0)	241 (11)	251 (21)	260 (30)

Approximation of harmonics in 115edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.15	-4.13	-7.81	-3.77	+7.05	+7.33	-3.58	+6.85	+5.08	+7.23	-3.57
	Relative (%)	-49.3	-25.0	-47.2	-22.8	+42.6	+44.3	-21.7	+41.4	+30.7	+43.7	-21.6
Steps (reduced)		268 (38)	276 (46)	283 (53)	290 (60)	297 (67)	303 (73)	308 (78)	314 (84)	319 (89)	324 (94)	328 (98)