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	16.539
2	33.077
3	49.616
4	66.155	27/26
5	82.694	21/20, 43/41
6	99.232	18/17
7	115.771	31/29, 46/43
8	132.31	41/38
9	148.849
10	165.387	11/10
11	181.926	10/9
12	198.465	37/33, 46/41
13	215.004	43/38
14	231.542
15	248.081	15/13
16	264.62
17	281.159	20/17
18	297.697
19	314.236
20	330.775	23/19
21	347.314	11/9
22	363.852	21/17, 37/30
23	380.391
24	396.93	39/31
25	413.468	33/26, 47/37
26	430.007
27	446.546	22/17
28	463.085
29	479.623
30	496.162
31	512.701	35/26, 39/29
32	529.24
33	545.778	37/27
34	562.317
35	578.856
36	595.395
37	611.933	37/26, 47/33
38	628.472
39	645.011	45/31
40	661.55
41	678.088
42	694.627
43	711.166
44	727.705	35/23
45	744.243
46	760.782	45/29
47	777.321	47/30
48	793.859
49	810.398
50	826.937
51	843.476
52	860.014
53	876.553
54	893.092
55	909.631
56	926.169
57	942.708
58	959.247	47/27
59	975.786
60	992.324
61	1008.863
62	1025.402	38/21, 47/26
63	1041.941
64	1058.479	35/19
65	1075.018
66	1091.557
67	1108.096
68	1124.634
69	1141.173	29/15
70	1157.712	41/21
71	1174.25
72	1190.789
73	1207.328
74	1223.867
75	1240.405	43/21
76	1256.944	31/15
77	1273.483
78	1290.022
79	1306.56
80	1323.099	43/20
81	1339.638
82	1356.177	46/21
83	1372.715
84	1389.254	29/13
85	1405.793
86	1422.332
87	1438.87
88	1455.409
89	1471.948
90	1488.487	26/11
91	1505.025	31/13
92	1521.564
93	1538.103	17/7
94	1554.641	27/11
95	1571.18
96	1587.719
97	1604.258
98	1620.796
99	1637.335
100	1653.874	13/5
101	1670.413
102	1686.951
103	1703.49
104	1720.029	27/10
105	1736.568	30/11
106	1753.106
107	1769.645
108	1786.184
109	1802.723	17/6
110	1819.261	20/7
111	1835.8	26/9
112	1852.339
113	1868.878
114	1885.416
115	1901.955	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)