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	Hekts	Approximate ratios
0	0	0	1/1
1	16.4	11.2
2	32.8	22.4
3	49.2	33.6	35/34, 36/35, 37/36
4	65.6	44.8	27/26
5	82	56	22/21, 43/41
6	98.4	67.2	18/17
7	114.8	78.4	31/29, 46/43
8	131.2	89.7	27/25, 41/38
9	147.6	100.9	37/34
10	164	112.1	11/10
11	180.4	123.3	10/9
12	196.8	134.5	37/33
13	213.2	145.7	26/23, 43/38
14	229.5	156.9	8/7
15	245.9	168.1	15/13, 38/33
16	262.3	179.3
17	278.7	190.5	27/23
18	295.1	201.7
19	311.5	212.9
20	327.9	224.1
21	344.3	235.3
22	360.7	246.6
23	377.1	257.8	41/33, 46/37
24	393.5	269
25	409.9	280.2	19/15
26	426.3	291.4	23/18
27	442.7	302.6
28	459.1	313.8	30/23, 43/33
29	475.5	325	25/19
30	491.9	336.2
31	508.3	347.4
32	524.7	358.6	23/17
33	541.1	369.8	26/19, 41/30
34	557.5	381
35	573.9	392.2	46/33
36	590.3	403.4	38/27
37	606.7	414.7	27/19
38	623.1	425.9	33/23, 43/30
39	639.5	437.1
40	655.8	448.3	19/13
41	672.2	459.5
42	688.6	470.7
43	705	481.9
44	721.4	493.1	41/27, 47/31
45	737.8	504.3	49/32
46	754.2	515.5	17/11
47	770.6	526.7	39/25
48	787	537.9	41/26
49	803.4	549.1	35/22
50	819.8	560.3
51	836.2	571.6	34/21, 47/29
52	852.6	582.8	18/11
53	869	594	33/20, 38/23, 43/26
54	885.4	605.2	5/3
55	901.8	616.4	37/22
56	918.2	627.6	17/10
57	934.6	638.8	12/7
58	951	650	26/15, 45/26
59	967.4	661.2	7/4
60	983.8	672.4	30/17
61	1000.2	683.6	41/23
62	1016.6	694.8	9/5
63	1033	706	20/11
64	1049.4	717.2	11/6
65	1065.8	728.4	37/20
66	1082.1	739.7	43/23
67	1098.5	750.9
68	1114.9	762.1	40/21
69	1131.3	773.3	25/13
70	1147.7	784.5	33/17
71	1164.1	795.7
72	1180.5	806.9
73	1196.9	818.1
74	1213.3	829.3
75	1229.7	840.5
76	1246.1	851.7	37/18, 39/19
77	1262.5	862.9
78	1278.9	874.1	23/11, 44/21
79	1295.3	885.3	19/9
80	1311.7	896.6
81	1328.1	907.8
82	1344.5	919	37/17
83	1360.9	930.2
84	1377.3	941.4
85	1393.7	952.6	38/17
86	1410.1	963.8
87	1426.5	975	41/18
88	1442.9	986.2	23/10
89	1459.3	997.4
90	1475.7	1008.6
91	1492.1	1019.8	45/19
92	1508.4	1031	43/18
93	1524.8	1042.2	41/17
94	1541.2	1053.4
95	1557.6	1064.7
96	1574	1075.9
97	1590.4	1087.1
98	1606.8	1098.3	43/17
99	1623.2	1109.5	23/9
100	1639.6	1120.7
101	1656	1131.9	13/5
102	1672.4	1143.1	21/8
103	1688.8	1154.3
104	1705.2	1165.5
105	1721.6	1176.7	27/10, 46/17
106	1738	1187.9	30/11
107	1754.4	1199.1
108	1770.8	1210.3	25/9
109	1787.2	1221.6
110	1803.6	1232.8	17/6
111	1820	1244
112	1836.4	1255.2	26/9
113	1852.8	1266.4	35/12
114	1869.2	1277.6
115	1885.6	1288.8
116	1902	1300	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)