116edt

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116edt

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Prime factorization	22 × 29
Step size	16.3962¢
Octave	73\116edt (1196.92¢)
Consistency limit	5
Distinct consistency limit	5

116 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 116edt or 116ed3), is a nonoctave tuning system that divides the interval of 3/1 into 116 equal parts of about 16.4 ¢ each. Each step represents a frequency ratio of 3^1/116, or the 116th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	16.396
2	32.792
3	49.188	35/34, 36/35, 37/36
4	65.585	27/26
5	81.981	22/21, 43/41
6	98.377	18/17
7	114.773	31/29, 46/43
8	131.169	27/25, 41/38
9	147.565	37/34
10	163.962	11/10
11	180.358	10/9
12	196.754	37/33
13	213.15	26/23, 43/38
14	229.546	8/7
15	245.942	15/13, 38/33
16	262.339
17	278.735	27/23
18	295.131
19	311.527
20	327.923
21	344.319
22	360.716
23	377.112	41/33, 46/37
24	393.508
25	409.904	19/15
26	426.3	23/18
27	442.696
28	459.093	30/23, 43/33
29	475.489	25/19
30	491.885
31	508.281
32	524.677	23/17
33	541.073	26/19, 41/30
34	557.47
35	573.866	46/33
36	590.262	38/27
37	606.658	27/19
38	623.054	33/23, 43/30
39	639.45
40	655.847	19/13
41	672.243
42	688.639
43	705.035
44	721.431	41/27, 47/31
45	737.827	49/32
46	754.224	17/11
47	770.62	39/25
48	787.016	41/26
49	803.412	35/22
50	819.808
51	836.204	34/21, 47/29
52	852.601	18/11
53	868.997	33/20, 38/23, 43/26
54	885.393	5/3
55	901.789	37/22
56	918.185	17/10
57	934.581	12/7
58	950.978	26/15, 45/26
59	967.374	7/4
60	983.77	30/17
61	1000.166	41/23
62	1016.562	9/5
63	1032.958	20/11
64	1049.354	11/6
65	1065.751	37/20
66	1082.147	43/23
67	1098.543
68	1114.939	40/21
69	1131.335	25/13
70	1147.731	33/17
71	1164.128
72	1180.524
73	1196.92
74	1213.316
75	1229.712
76	1246.108	37/18, 39/19
77	1262.505
78	1278.901	23/11, 44/21
79	1295.297	19/9
80	1311.693
81	1328.089
82	1344.485	37/17
83	1360.882
84	1377.278
85	1393.674	38/17
86	1410.07
87	1426.466	41/18
88	1442.862	23/10
89	1459.259
90	1475.655
91	1492.051	45/19
92	1508.447	43/18
93	1524.843	41/17
94	1541.239
95	1557.636
96	1574.032
97	1590.428
98	1606.824	43/17
99	1623.22	23/9
100	1639.616
101	1656.013	13/5
102	1672.409	21/8
103	1688.805
104	1705.201
105	1721.597	27/10, 46/17
106	1737.993	30/11
107	1754.39
108	1770.786	25/9
109	1787.182
110	1803.578	17/6
111	1819.974
112	1836.37	26/9
113	1852.767	35/12
114	1869.163
115	1885.559
116	1901.955	3/1

Harmonics

Approximation of harmonics in 116edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-3.08	+0.00	-6.16	+1.03	-3.08	-7.61	+7.16	+0.00	-2.05	-3.09	-6.16
	Relative (%)	-18.8	+0.0	-37.6	+6.3	-18.8	-46.4	+43.6	+0.0	-12.5	-18.8	-37.6
Steps (reduced)		73 (73)	116 (0)	146 (30)	170 (54)	189 (73)	205 (89)	220 (104)	232 (0)	243 (11)	253 (21)	262 (30)

Approximation of harmonics in 116edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.83	+5.70	+1.03	+4.08	-2.50	-3.08	+1.69	-5.13	-7.61	-6.17	-1.14
	Relative (%)	+17.3	+34.8	+6.3	+24.9	-15.3	-18.8	+10.3	-31.3	-46.4	-37.6	-7.0
Steps (reduced)		271 (39)	279 (47)	286 (54)	293 (61)	299 (67)	305 (73)	311 (79)	316 (84)	321 (89)	326 (94)	331 (99)