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	Hekts	Approximate ratios
0	0	0	1/1
1	16.5	11.3
2	33.1	22.6
3	49.6	33.9
4	66.2	45.2	27/26
5	82.7	56.5	21/20, 43/41
6	99.2	67.8	18/17
7	115.8	79.1	31/29, 46/43
8	132.3	90.4	41/38
9	148.8	101.7
10	165.4	113	11/10
11	181.9	124.3	10/9
12	198.5	135.7	37/33, 46/41
13	215	147	43/38
14	231.5	158.3
15	248.1	169.6	15/13
16	264.6	180.9
17	281.2	192.2	20/17
18	297.7	203.5
19	314.2	214.8
20	330.8	226.1	23/19
21	347.3	237.4	11/9
22	363.9	248.7	21/17, 37/30
23	380.4	260
24	396.9	271.3	39/31
25	413.5	282.6	33/26, 47/37
26	430	293.9
27	446.5	305.2	22/17
28	463.1	316.5
29	479.6	327.8
30	496.2	339.1
31	512.7	350.4	35/26, 39/29
32	529.2	361.7
33	545.8	373	37/27
34	562.3	384.3
35	578.9	395.7
36	595.4	407
37	611.9	418.3	37/26, 47/33
38	628.5	429.6
39	645	440.9	45/31
40	661.5	452.2
41	678.1	463.5
42	694.6	474.8
43	711.2	486.1
44	727.7	497.4	35/23
45	744.2	508.7
46	760.8	520	45/29
47	777.3	531.3	47/30
48	793.9	542.6
49	810.4	553.9
50	826.9	565.2
51	843.5	576.5
52	860	587.8
53	876.6	599.1
54	893.1	610.4
55	909.6	621.7
56	926.2	633
57	942.7	644.3
58	959.2	655.7	47/27
59	975.8	667
60	992.3	678.3
61	1008.9	689.6
62	1025.4	700.9	38/21, 47/26
63	1041.9	712.2
64	1058.5	723.5	35/19
65	1075	734.8
66	1091.6	746.1
67	1108.1	757.4
68	1124.6	768.7
69	1141.2	780	29/15
70	1157.7	791.3	41/21
71	1174.3	802.6
72	1190.8	813.9
73	1207.3	825.2
74	1223.9	836.5
75	1240.4	847.8	43/21
76	1256.9	859.1	31/15
77	1273.5	870.4
78	1290	881.7
79	1306.6	893
80	1323.1	904.3	43/20
81	1339.6	915.7
82	1356.2	927	46/21
83	1372.7	938.3
84	1389.3	949.6	29/13
85	1405.8	960.9
86	1422.3	972.2
87	1438.9	983.5
88	1455.4	994.8
89	1471.9	1006.1
90	1488.5	1017.4	26/11
91	1505	1028.7	31/13
92	1521.6	1040
93	1538.1	1051.3	17/7
94	1554.6	1062.6	27/11
95	1571.2	1073.9
96	1587.7	1085.2
97	1604.3	1096.5
98	1620.8	1107.8
99	1637.3	1119.1
100	1653.9	1130.4	13/5
101	1670.4	1141.7
102	1687	1153
103	1703.5	1164.3
104	1720	1175.7	27/10
105	1736.6	1187	30/11
106	1753.1	1198.3
107	1769.6	1209.6
108	1786.2	1220.9
109	1802.7	1232.2	17/6
110	1819.3	1243.5	20/7
111	1835.8	1254.8	26/9
112	1852.3	1266.1
113	1868.9	1277.4
114	1885.4	1288.7
115	1902	1300	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)