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	16.4
2	32.8
3	49.2	35/34, 36/35, 37/36
4	65.6	27/26
5	82	22/21, 43/41
6	98.4	18/17
7	114.8	31/29, 46/43
8	131.2	27/25, 41/38
9	147.6	37/34
10	164	11/10
11	180.4	10/9
12	196.8	37/33
13	213.2	26/23, 43/38
14	229.5	8/7
15	245.9	15/13, 38/33
16	262.3
17	278.7	27/23
18	295.1
19	311.5
20	327.9
21	344.3
22	360.7
23	377.1	41/33, 46/37
24	393.5
25	409.9	19/15
26	426.3	23/18
27	442.7
28	459.1	30/23, 43/33
29	475.5	25/19
30	491.9
31	508.3
32	524.7	23/17
33	541.1	26/19, 41/30
34	557.5
35	573.9	46/33
36	590.3	38/27
37	606.7	27/19
38	623.1	33/23, 43/30
39	639.5
40	655.8	19/13
41	672.2
42	688.6
43	705
44	721.4	41/27, 47/31
45	737.8	49/32
46	754.2	17/11
47	770.6	39/25
48	787	41/26
49	803.4	35/22
50	819.8
51	836.2	34/21, 47/29
52	852.6	18/11
53	869	33/20, 38/23, 43/26
54	885.4	5/3
55	901.8	37/22
56	918.2	17/10
57	934.6	12/7
58	951	26/15, 45/26
59	967.4	7/4
60	983.8	30/17
61	1000.2	41/23
62	1016.6	9/5
63	1033	20/11
64	1049.4	11/6
65	1065.8	37/20
66	1082.1	43/23
67	1098.5
68	1114.9	40/21
69	1131.3	25/13
70	1147.7	33/17
71	1164.1
72	1180.5
73	1196.9
74	1213.3
75	1229.7
76	1246.1	37/18, 39/19
77	1262.5
78	1278.9	23/11, 44/21
79	1295.3	19/9
80	1311.7
81	1328.1
82	1344.5	37/17
83	1360.9
84	1377.3
85	1393.7	38/17
86	1410.1
87	1426.5	41/18
88	1442.9	23/10
89	1459.3
90	1475.7
91	1492.1	45/19
92	1508.4	43/18
93	1524.8	41/17
94	1541.2
95	1557.6
96	1574
97	1590.4
98	1606.8	43/17
99	1623.2	23/9
100	1639.6
101	1656	13/5
102	1672.4	21/8
103	1688.8
104	1705.2
105	1721.6	27/10, 46/17
106	1738	30/11
107	1754.4
108	1770.8	25/9
109	1787.2
110	1803.6	17/6
111	1820
112	1836.4	26/9
113	1852.8	35/12
114	1869.2
115	1885.6
116	1902	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)