118edt

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118edt

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Prime factorization	2 × 59
Step size	16.1183¢
Octave	74\118edt (1192.75¢) (→37\59edt)
Consistency limit	2
Distinct consistency limit	2

118 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 118edt or 118ed3), is a nonoctave tuning system that divides the interval of 3/1 into 118 equal parts of about 16.1 ¢ each. Each step represents a frequency ratio of 3^1/118, or the 118th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.1
2	32.2
3	48.4
4	64.5
5	80.6	22/21, 43/41, 45/43
6	96.7	37/35
7	112.8
8	128.9	14/13
9	145.1	25/23
10	161.2	45/41
11	177.3	41/37
12	193.4	19/17
13	209.5	35/31, 44/39
14	225.7	33/29, 49/43
15	241.8
16	257.9	29/25
17	274	41/35
18	290.1
19	306.2	37/31
20	322.4
21	338.5	45/37
22	354.6	27/22, 43/35
23	370.7	31/25
24	386.8
25	403	29/23
26	419.1
27	435.2	9/7
28	451.3	35/27
29	467.4
30	483.5	41/31
31	499.7
32	515.8	31/23
33	531.9
34	548
35	564.1	18/13
36	580.3
37	596.4
38	612.5	47/33
39	628.6
40	644.7	45/31
41	660.8
42	677	37/25
43	693.1
44	709.2
45	725.3	35/23
46	741.4	23/15
47	757.6
48	773.7
49	789.8	30/19
50	805.9	43/27
51	822	37/23
52	838.1
53	854.3
54	870.4
55	886.5
56	902.6
57	918.7	17/10
58	934.9
59	951
60	967.1
61	983.2	30/17
62	999.3	41/23
63	1015.5
64	1031.6	49/27
65	1047.7
66	1063.8
67	1079.9
68	1096
69	1112.2	19/10
70	1128.3
71	1144.4
72	1160.5	43/22, 45/23
73	1176.6
74	1192.8
75	1208.9
76	1225
77	1241.1	43/21
78	1257.2	31/15
79	1273.3
80	1289.5
81	1305.6
82	1321.7
83	1337.8	13/6
84	1353.9
85	1370.1
86	1386.2	49/22
87	1402.3
88	1418.4
89	1434.5
90	1450.6
91	1466.8	7/3
92	1482.9
93	1499
94	1515.1
95	1531.2	46/19
96	1547.4	22/9
97	1563.5	37/15
98	1579.6
99	1595.7
100	1611.8
101	1627.9
102	1644.1
103	1660.2
104	1676.3	29/11
105	1692.4
106	1708.5
107	1724.7	46/17
108	1740.8	41/15
109	1756.9
110	1773	39/14
111	1789.1
112	1805.2
113	1821.4	43/15
114	1837.5
115	1853.6
116	1869.7
117	1885.8
118	1902	3/1

Harmonics

Approximation of harmonics in 118edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-7.25	+0.00	+1.62	+2.15	-7.25	-0.11	-5.63	+0.00	-5.10	+7.19	+1.62
	Relative (%)	-45.0	+0.0	+10.1	+13.3	-45.0	-0.7	-34.9	+0.0	-31.7	+44.6	+10.1
Steps (reduced)		74 (74)	118 (0)	149 (31)	173 (55)	192 (74)	209 (91)	223 (105)	236 (0)	247 (11)	258 (22)	267 (31)

Approximation of harmonics in 118edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.01	-7.36	+2.15	+3.24	-5.00	-7.25	-4.14	+3.77	-0.11	-0.05	+3.58
	Relative (%)	-49.7	-45.6	+13.3	+20.1	-31.0	-45.0	-25.7	+23.4	-0.7	-0.3	+22.2
Steps (reduced)		275 (39)	283 (47)	291 (55)	298 (62)	304 (68)	310 (74)	316 (80)	322 (86)	327 (91)	332 (96)	337 (101)