118edt

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118edt

119edt →

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	16.118
2	32.237
3	48.355
4	64.473
5	80.591	22/21, 43/41, 45/43
6	96.71	37/35
7	112.828
8	128.946	14/13
9	145.064	25/23
10	161.183	45/41
11	177.301	41/37
12	193.419	19/17
13	209.537	35/31, 44/39
14	225.656	33/29, 49/43
15	241.774
16	257.892	29/25
17	274.01	41/35
18	290.129
19	306.247	37/31
20	322.365
21	338.484	45/37
22	354.602	27/22, 43/35
23	370.72	31/25
24	386.838
25	402.957	29/23
26	419.075
27	435.193	9/7
28	451.311	35/27
29	467.43
30	483.548	41/31
31	499.666
32	515.784	31/23
33	531.903
34	548.021
35	564.139	18/13
36	580.257
37	596.376
38	612.494	47/33
39	628.612
40	644.731	45/31
41	660.849
42	676.967	37/25
43	693.085
44	709.204
45	725.322	35/23
46	741.44	23/15
47	757.558
48	773.677
49	789.795	30/19
50	805.913	43/27
51	822.031	37/23
52	838.15
53	854.268
54	870.386
55	886.504
56	902.623
57	918.741	17/10
58	934.859
59	950.978
60	967.096
61	983.214	30/17
62	999.332	41/23
63	1015.451
64	1031.569	49/27
65	1047.687
66	1063.805
67	1079.924
68	1096.042
69	1112.16	19/10
70	1128.278
71	1144.397
72	1160.515	43/22, 45/23
73	1176.633
74	1192.751
75	1208.87
76	1224.988
77	1241.106	43/21
78	1257.224	31/15
79	1273.343
80	1289.461
81	1305.579
82	1321.698
83	1337.816	13/6
84	1353.934
85	1370.052
86	1386.171	49/22
87	1402.289
88	1418.407
89	1434.525
90	1450.644
91	1466.762	7/3
92	1482.88
93	1498.998
94	1515.117
95	1531.235	46/19
96	1547.353	22/9
97	1563.471	37/15
98	1579.59
99	1595.708
100	1611.826
101	1627.945
102	1644.063
103	1660.181
104	1676.299	29/11
105	1692.418
106	1708.536
107	1724.654	46/17
108	1740.772	41/15
109	1756.891
110	1773.009	39/14
111	1789.127
112	1805.245
113	1821.364	43/15
114	1837.482
115	1853.6
116	1869.718
117	1885.837
118	1901.955	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)